Marine design manual for fiberglass reinforced plastics

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FOR FIBERGLASS oo
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MARINE DESIGN MANUAL

FOR
Fiberglass Reinforced Plastics

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MARINE DESIGN MANUAL

FOR
Fiberglass Reinforced Plastics

Gibbs & Cox, Inc.

Naval Architects and
Marine Engineers

Sponsored by
Owens-Corning Fiberglas Corporation

McGRAW-HILL BOOK COMPANY, INC.

NEW YORK TORONTO LONDON

1960

MARINE DESIGN MANUAL FOR FIBER-
GLASS REINFORCED PLASTICS Copyright ©
1960 by the McGraw-Hill Book Company, Inc.
Printed in the United States of America. All
rights reserved. This book, or parts thereof,
may not be reproduced in any form without
permission of the publishers. Library of Con-
gress Catalog Card Number: 60-7732

ISBN 07-023175-3
1213141516 HDBP 75432

The data and information contained in this Design Manual have
been prepared from the best available sources. However, the value
of the test data depends upon the control of so many variables, and
the application of the data depends so much upon skill and experience
that neither Owens-Corning Fiberglas Corporation nor Gibbs & Cox,
Inc. assume any responsibility, expressed or implied, for results ob-
tained inthe application by others of the data and information contained
in this manual. These quantitative data and examples were prepared
with extreme care for general guidance and are accurate for the spe-
cific conditions and processing which pertained to the collection and
compiling of the data.

Foreword

This Design Manual has been prepared by Gibbs & Cox, Inc. under the sponsorship of the
Owens-Corning Fiberglas Corporation, manufacturers of fiberglass products for the rein-
forced-plastics industry, as a part of a program for the advancement of the industry through
the dissemination of technical information on the materials and processes presently in use.
As a firm of Naval Architects, Gibbs & Cox, Inc. has always been interested innew materials
which appear to have application in the Marine Field. Therefore, it was natural that these
two organizations combined their efforts toinvestigate thoroughly this new structural material.

In the compilation of this manual, it was necessary to acquire additional knowledge about
the physical properties of the basic laminates and to determine the types and details of con-
struction considered the most satisfactory. This effort required the contributions of many
organizations and are acknowledged in the Preface. The results of this testing and study are
presented as a Marine Design Manual for guidance in the development of reinforced-plastic
structures for marine and other applications.

This Manual was prepared by the following members of the Hull Division of Gibbs &
Coxe ince:

Matthew G. Forrest = Vice President - Naval Architecture
Thomas M. Buermann-= - Project Engineer

Ralph Della Rocca = Editor and Contributor

Oswald Lourenso = Contributor

John D. Leigh - Contributor

Malcolm Dick = Contributor

John P. Montgomery ~ Contributor

This Manual was also reviewed in detail by Owens-Corning Fiberglas Corporation,

vii

Preface

The rapid expansion of the application of fiberglass reinforced-plastic laminates as a
structural material in many fields has surpassed the accumulation of the necessary technical
data and design information such as is available for the application of other established
structural materials.

Within the relatively short period since the introduction of fiberglass reinforced-plastic
laminates, a considerable amount of research effort has been expended by government and
industry to determine the potential value and limitations of this new material. However,
most of the effort has been spent in developing data for specific applications. Asa result,
little well controlled data has been made available to organizations, designers and fabrica-
tors. The necessity for a large scale program for evaluating the basic engineering properties
of fiberglass material has long been recognized. The influence of geometry, laminate con-
struction, molding methods and fabrication techniques on these basic properties is ex-
tremely important.

To develop this required engineering data, Owens-Corning Fiberglas Corporation spon-
sored a cooperative program which included the following participating organizations:

Participating Organization Function

Owens-Corning Fiberglas Corporation Sponsor

Gibbs & Cox, Inc. Engineering Development
Bellingham Shipyards Co. Fabricator

Glasspar Co, Fabricator

Lunn Laminates, Inc. Fabricator

Zenith Plastics Company, Division of Fabricator

Minnesota Mining and Manufacturing Company

Cornell Aeronautical Laboratory Qualification Tests
Massachusetts Institute of Technology Testing
National Bureau of Standards Testing

TK

PREFACE

Participating Organization Function

New York Naval Shipyard, Material Laboratory Testing
Picatinny Arsenal, U.S, Army Ordnance Testing

The Budd Company Impact Testing
University of Dayton Research Center Data Processing
Forest Products Laboratory Advisory

Sufficient development of the necessary technical information and data has been completed
to justify the compilation of this Design Manual. This development consisted of the evaluating
of the data from an extensive test program to establish necessary physical properties for
fiberglass mat, woven roving and cloth reinforced laminates molded by the contact molding
method. The use of this dataand suggested methods of analyses are demonstrated in the
design examples, as a guide for designers and fabricators.

Throughout this entire program, complete cooperation was maintained by all participating
organizations as well as other interested organizations providing information and assistance.

Gibbs & Cox, Inc. fully realizing that only partial completion of this tremendous task has
been accomplished, sincerely wishes to thank the Owens-Corning Fiberglas Corporation, the
sponsor, and all the other contributing organizations as well as all the individuals, who worked
on and/or assisted in this program for their excellent cooperation.

In addition to the test program referred to above, considerable information was obtained
from an extensive list of available references. Gibbs & Cox, Inc. wishes to acknowledge

these fine references which were of considerable importance in the development of this manual.

GIBBS & COX, INC.

FOREWORD

PREFACE

ABSTRACTS

CHAPTER 1. INTRODUCTION

The Material
Present Applications
Technical Status
Data Presented
Purpose of Manual

CHAPTER 2. BOAT HULL DESIGN

Types of Construction
Selection of Laminates
Basic Design Considerations
Design Loading

Design Examples

CHAPTER 3. DESIGN DETAILS

Application of Loads
Laminate Connections
Appendage Connections
Outfit Connections
Mechanical Fasteners
Trouble Causing Details

Contents

vii

CONTENTS
CHAPTER 4. MATERIALS AND MOLDING METHODS

Reinforcements

Resins

Fillers and Pigments
Stiffener and Sandwich Cores
Molding Methods

CHAPTER 5. ENGINEERING PROPERTIES OF LAMINATES

Directional Properties

Relationships Between Reinforcements, Molding
Methods and Properties

Test Program To Obtain Properties - Contact Molded

Physical Properties

Mechanical Properties

Supplementary Test Program To Obtain Properties

Factors Affecting Engineering Properties

Properties of Low Density Core Materials

CHAPTER 6, DESIGN OF LAMINATES

Behavior of Laminates
Factor of Safety
Tension

Compression

Flexure

Flat Rectangular Plates
Sandwich Construction

APPENDIXES
Appendix A Test Program Fiberglass Polyester Laminates -
Test Procedures
Appendix B Test Program Fiberglass Polyester Laminaies -

Statistical Analysis of Test Data

INDEX follows Appendix B

>ahl

Abstracts

CHAPTER 1. INTRODUCTION

The use and advantages of fiberglass reinforced plastics as structural materials and
their acceptance by major industries, particularly the marine industry, are discussed and
illustrated. Technical status of basic materials, production and engineering experience and
data is presented. The purpose of the manual as a guide for designers and fabricators
is emphasized.

CHAPTER 2. BOAT HULL DESIGN

Types of construction; single skin unstiffened and stiffened, sandwich, and composite
are discussed, Framing is defined and discussed. Reasons for choice of laminate are ex-
plained. Design considerations are discussed and loads to be assumed for design purposes
are given. Detailed examples of the structural design are given for a rowboat, a day sailer,
a runabout, a cruising sailboat, and a displacement type power cruiser.

CHAPTER 3. DESIGN DETAILS

Importance of good design details is explained. Right and wrong loading directions for
laminates are given. Acceptable joint and connection details are discussed and illustrated
for deck edge to shell, gunwales, shell halves, keel ballast to hull, repair, bulkhead or
frame to shell, cabin trunk to deck, fittings with pulling and pushing loads, appendages and
outfitting. Mechanical fasteners are discussed and values given for spacing and strength.
Trouble causing details including hard spots, stress concentrations, and knife edge crossings
are discussed and illustrated.

CHAPTER 4. MATERIALS AND MOLDING METHODS

The basic types of chopped strand, mat, woven roving and cloth fiberglass reinforce-
ments and their application to boat hull construction are discussed and tabulated. The appli-
cations of polyester and epoxy resins, inhibitors, catalysts and accelerators in fiberglass
laminates are discussed. The use of foam plastics for buoyancy, and wood, foams and
honeycombs for stiffener and sandwich core materials are described,

Fundamental methods of molding used in fiberglass boat construction including contact,

bag, autoclave, matched die and the new sprayed reinforcement technique are described
and illustrated.

Xlii

ABSTRACTS
CHAPTER 5. ENGINEERING PROPERTIES OF LAMINATES

Direction properties of cloth and woven roving reinforcements are briefly discussed.
Relationships between reinforcements, molding methods, physical and mechanical properties
are discussed and tabulated. The basic engineering properties of fiberglass laminates
determined from an extensive and supplementary test programs are presented in tabular
form. Graphs indicating impact, fatigue and creep properties are given. Factors effecting
the engineering properties of laminates are discussed and graphs of the effects of water
immersion and long term loading are given. A summary table for the physical and mechani-
cal properties of low density core materials is presented.

CHAPTER 6. DESIGN OF LAMINATES

The behavior of laminates under load are discussed. Suggested factors of safety for
laminates are given. Methods, formulas and approaches to the design of both isotropic and
orthotropic laminates in tension, compression and flexure are presented. Laminates as flat
rectangular plates under various load conditions are analyzed. Tables of approximate criti-
cal buckling loads, and lateral loads are presented. A brief discussion on methods of analy -
sis for sandwich construction is given. Detail design examples applying the methods of
analysis and design approaches discussed are included as guidance for the designer.

MARINE DESIGN MANUAL

FOR
Fiberglass Reinforced Plastics

T

Introduction

THE MATERIAL

Fiberglass reinforced plastics are at this time competitive high performance structural
materials. The basic fibers are among the strongest structural elements known. Although
it would be inadvisable to consider reinforced plastics as the universally superior structural
material, they are clearly superior in many cases and competitive in others. It may also
be expected that additional research and improved processes will further upgrade the basic
materials and the finished products. New confidence in design, coupled with experience in
dependable commercial production, will permit widespread diversification of economically
sound applications,

Although the strength to weight performance has indicated an advantage over some of the
more familiar materials, there are many other characteristics which have influenced the
increasing use of this material. Desirable compound curvatures can readily be achieved
with this moldable material which can be formed as easily in one shape as another without
the use of expensive forming tools. The ability to construct a one piece structure, elimi-
nating complex load carrying joints, improves the performance and dependability of the
complete structure. Particularly in comparison with wooden structures, fiberglass rein-
forced plastics used in an integral structural design eliminates a wide assortment of fasten-
ings and hardware.

In considering the design of a structure to carry different types of loads, variation in
strength can be easily accomplished in any portion of the structure, with the same basic
materials, by simply changing the cross-section and orienting the high strength fibers in the
direction of stress. Large tension loads can be efficiently supported by using cloth or uni-
directional fibers oriented so as to be aligned with the direction of load. An impact resis-
tant area can be created by increasing laminate thickness locally with reinforcements se-
lected for high impact strength and oriented so as to be equally good in all directions. To
support bending loads, stiffeners can be added to a panel in a conventional manner, or sand-
wich construction may be used. In any economic analysis, this factor must receive con-
siderable attention. The same raw materials of fiberglass and resin in the stock room will
produce an unlimited variety of thicknesses and forms. The equivalent of I beams, angle
stiffeners and extruded sections are all available. No longer are the forms and sections
limited to the availability of certain standard stock items. The rib and plate configuration of
most structures need not be tailored specifically to the dimensions of familiar components.
Modification and correction can be accomplished directly without delay and without major ad-
justment of expensive tooling. With proper design many internal components heretofore re-
quiring individual installation can be easily combined with the primary strength structure in
a single molding operation.

1-2 INTRODUCTION

Like most other materials, fiberglass reinforced plastics are subject to some deteriora-
tion with exposure and weathering. But because of their relative inertness to attack by a
large number of deteriorating causes and their ability to minimize water absorption, they
can successfully withstand most of the elements which accelerate the aging processes in
metals and woods, and will therefore need less maintenance.

PRESENT APPLICATIONS

From the time, about 1940, when the first experimental structures were developed using
fiberglass reinforced plastics, the possibilities of widespread application of this new material
were exciting. In almost every case, even for complex high performance items, the strength
to weight performance is excellent. This desirable characteristic has continued to hold true
with well designed and fabricated structures, Figs. 1-1 to 1-4.

Of all the applications of fiberglass reinforced plastics, the marine applications, where
high structural performance and maximum durability are at a premium, seem to illustrate
more of the positive reasons for selecting this material in preference to others. The prima-
ry and well known marine application is in the hull construction of military, pleasure and
commercial craft. Figs. 1-5 to 1-10 illustrate some boat hull applications. The trend
toward the application of this material, in larger boat hulls, Figs. 1-11 to 1-15 is continuing.
Shipboard applications such as fairwaters, tanks, antenna trunks, telephone booths, parti-
tions, torpedo tubes and crew shelters has further proven the material's suitability to the
marine industry. Other successful marine applications are submarine fairwaters, Fig. 1-16,
buoys and floats, Fig. 1-17.

TECHNICAL STATUS

In common with all new materials it has taken time and experience to amass dependable
data on the qualities and performance of the material in different configurations, The very
characteristics which provides the greatest potential benefit in the use of fiberglass rein-
forced plastics also creates the greatest difficulty. This is due to the fact that the composite
laminate is created in place by combining diverse basic materials under a wide variety of
environmental conditions. Obtaining consistent quality in these materials may not be more
difficult than is the case with older and more familiar materials but it involves a vastly dif-
ferent approach compared with manufacturing practices developed over the years for older
and more familiar materials.

Designers who have become experienced in using particular forms of fiberglass rein-
forced plastics have engineered applications which fulfill all the promise of the early experi-
mental structures. Fabricating shops using processes with which they have become familiar
have successfully met the most exacting standards. Quantity production of small boats and
automobile bodies has demonstrated the ability to compete successfully on engineering and
economic grounds. Airplane and missile applications, Figs. 1-18 and 1-19, leave no doubt
that dependable quality can be achieved in limited production. Many applications illustrate an
ability to utilize the unique qualities which can be fashioned into a reinforced plastic structure.
But there has been a legitimate hesitancy to apply fiberglass reinforced plastics, even in situ-
ations where the apparent qualities would indicate them as ideal. This reluctance has been
based upon a lack of reliable engineering data.

The flexibility in choice of the types of reinforcement and resin poses a problem of uti-
lizing experience with one combination in dealing with a different combination. Not only has
the bulk of engineering experience been limited, but lack of standardized data has made it
difficult to utilize experience in dealing with different forms and processes.

Fig. 1-1. Largest Aircraft Radome, 29! Fig. 1-3. Large House (Courtesy Monsanto

Long, 20' Wide and 7' Deep (Courtesy Zenith Chemical Company)
Plastics Company, Division of Minnesota Mining and
Manufacturing Company)

Fig. 1-2. 45' High Radome for NATO Fig. 1-4. Truck Cab (Courtesy White

Early Warning Defense System (Courtesy Truck Company)
Universal Moulded Products Corporation)

1-3

Fig. 1-5, 26' Navy Motor Whale Boat Fig. 1-8. 15' High Speed Runabout
(Courtesy Lunn Laminates Incorporated) (Courtesy Lake and Sea Boat Company)

Fig. 1-6. 36' Navy Landing Craft Fig. 1-9. 18' Day Cruiser (Courtesy
(Courtesy Lunn Laminates Incorporated) Southwest Manufacturing Company)

—
x = awe y
Se mnt ~ ia es

Fig. 1-7. 24' Lifeboat - Dropped Tested Fig. 1-10. 24' Express Carrier

from a Height of 10' Without Damage to Hull (Courtesy Skagit Plastics Incorporated)
(Courtesy Lane Lifeboat Company)

1-4

Fig. 1-11. 40' Yawl
(Courtesy American Boat Building Co.)

Fig. 1-12. 40' Sloop - BOUNTY II
(Courtesy Coleman Boat and Plastics Company)

Fig. 1-13. 40' Coast Guard Patrol Boat Fig. 1-15. 65' Offshore Crew Boat
(Courtesy W.R. Chance Associates) (Courtesy Plastics Research, Inc.)

Fig. 1-14, 50' Utility Boat (Courtesy Sragit Fig. 1-16. Submarine Fairwater
Plastics Incorporated) (Courtesy Lunn Laminates Incorporated)

Fig. 1-17. Pontoon Camel Float
(Courtesy Skagit Plastics Incorporated)

1-6

INTRODUCTION 1-7

Fig. 1-18. Passenger Aircraft with many
Fiberglass Parts; Wing Tips, Tail Cone,
Seats, Coat Racks, Window Frames,
Bulkheads, etc, (Courtesy Lockheed Aircraft
Corporation)

Fig. 1-19. Thor-Able Rocket - with
many Fiberglass Parts; Nozzles, Pres-
sure Vessels, Satellite Container, etc.
(Courtesy U.S. Atr Force)

DATA PRESENTED

Over a period of several years in atest program sponsored by the Owens-Corning Fiber-
glas Corporation and directed by Gibbs & Cox, Inc. and with the cooperation of many agencies,
a correlated body of data has been accumulated and analyzed to provide the basis for the data
presented in this manual.

It would be a task beyond the scope of the manual to present all of the available data per-
taining to the state of the art at the time it is compiled. In this manual the data are applied
by example to marine design. Furthermore, since the data were obtained on a standardized
basis it is possible for any fabricator to make samples following the same construction and
process techniques as those used in the test program. If these fabricator samples are then
tested in accordance with the standard procedure, a calibration factor can be established re-
lating the fabricator's sample data to the whole body of data. If the fabricator continues to
follow the same pattern of calibration testing when working with new formulations of resin and

1-8 INTRODUCTION

reinforcement, his new data will then be comparable with the older data and any other new
data accumulated by the same standard process regardless of where it originates. In prac-
tice the engineer or fabricator should use the data presented for initial selection of a
material combination and molding process. He can then calibrate each material combination
and molding process to obtain refined design data.

The test program was an extensive one which is described in Chapter 5. Aside from the
obvious physical characteristics which are tabulated, there are other significant factors which
are indicated in appropriate parts of this manual. The designer or manufacturer will be able
to draw other conclusions from having the broad body of comparable data to analyze. One of
the most obvious but most important aspects of the data is the indication of the spread in per-
formance values which occurs with material made by different manufacturers all attempting
to reproduce identical specimens. This spread may be the result of many factors besides
the experience of the man making the laminate. Any designer or manufacturer contemplating
a new product must realize that he may inadvertently produce items of varying quality while
following what appears to be good practice.

In order to assist in the use of the data presented, it has been found desirable to divide
some of the data into high and low ranges. If the manufacturer can satisfy himself by sample
testing that he can reproduce materials of the higher quality, then it will be safe to use the
higher values for that material combination and process. It will be noted that in the test pro-
gram, manufacturers were not consistently high or low quality producers. Each fabricator
produced both high and low quality laminates depending on the reinforcements used. There
was no material which appeared to be easy to produce and no material or process which
seemed to be uniformly difficult. The producers making the test laminates were all selected
as highly qualified and dependable fabricators. Therefore a manufacturer may expect to
find that he is a low quality producer for some material or combination.

It will be apparent that a marine design manual deals with structural loads and forms
similar to those that apply to many other construction fields. While there has been no
attempt to consider artistic effects and surface problems, these considerations can be super-
imposed upon the basic structural factors discussed and illustrated in this manual. One re-
striction of this document is that the reinforcements and processes for which detailed data
are available are those of most interest to the marine industry. Some of the higher per-
formance material combinations and forming processes are not included simply because the
magnitude of the job of accumulating and analyzing the data precluded more than this first
basic approach for a major field of interest. It should be noted that the procedure for making
samples, testing and analyzing data will be suitable for any selected material. The data in-
cluded here will serve as a comparison to indicate trends and the illustrations would be ap-
plicable if new data were fed in as acquired and as appropriate.

It may be expected that one of the most interesting and significant advances will be in the
direction of larger structures for boat applications. For this reason the illustrations in this
manual have included an array of sizes to suggest the factors which influence different design
selections, With judgment these factors may be extrapolated to larger sizes than those in-
cluded herein.

As more dependable data is obtained and as quality control develops either through more
precise forming processes or inspection techniques it will be possible to design much more
closely to the potential performance of these materials. Safety factors are discussed in this
manual for specific applications. Some areas of structural loading are imperfectly under-
stood at the present time. If fatigue, for instance, is a critical condition of loading, the

INTRODUCTION To

calibration process discussed as essential for any new product will have to include enough
typical testing to insure that the design factors for this feature are adequate. However, in
most refined articles where design is very precise there is an appreciation of the need for
proof testing and even sample destructive testing, regardless of the amount of data available
and the experience with the material.

PURPOSE OF MANUAL

The primary purpose of this manual is to provide the designer with technical data and
design approaches as guidance for analyzing fiberglass reinforced plastics structures for boat
hulls and other marine applications,

This manual should also serve to persuade serious designers and builders that fiberglass
reinforced materials follow predictable behavior patterns. The data and illustrations should
assist those who are actually working with these materials to utilize them more efficiently.
The presentation of this information in a positive and logical pattern should give economi-
cally minded manufacturers sufficient confidence to use a new material where the economics
indicate a potential gain.

2

Boat Hull Design

This Chapter is devoted to the structural design of the boat hull. No attempt is made to
consider the many and serious problems involved in determining the proper shape of the
hull, laying out satisfactory arrangements, ensuring adequate stability, providing sufficient
buoyancy in small boats, or estimating power required to obtain a predetermined speed.

Solutions to the above problems, and others are important and complex. When a sub-
stantial investment is involved, either in the building of a large boat or the building of a
number of similar small boats, the use of a competent naval architect is highly recommended.

Structural design is one of the most im-
portant parts of the complex problem of boat
design. Its purpose is to insure that the
structural integrity of the boat is maintained
for almost every conceivable loading to which
it will be subjected in service. This Chapter
should enable anyone familiar with the basic
principles of strength of materials, to solve
most of the small boat structural design
problems. Conservative design is stressed
again and again in this manual for a very
simple reason: structural failure in service
usually involves grave risk to human life.
This fact places great responsibility on those
involved in determining the scantlings of any
boat, large or small.

Fig. 2-1. Fiberglass reinforced plastic life-
boat, loaded with sandbags, being swung
against a pier to test for impact resistance

(Courtesy Lane Lifeboat Co.)

In the case of special design problems,
as illustrated in Fig. 2-1, the services ofa
competent structural consultant are required.

A boat hull is essentially an envelope or shell of predetermined shape. The thickness of
this shell and the size and location of whatever supports are provided must be selected to pre-
vent the boat from breaking up or losing its shape under the action of the various loads placed
on it in service.

Traditionally, especially in wooden frame and plank construction, the sizes or scantlings
of the various components of the boat have been chosen on the basis of years of experience
with successful and unsuccessful designs. This experience has been reduced to tables of

2-2 BOAT HULL DESIGN

standard scantlings for boats of a given size andtype, such as the rules for the construction
of wooden yachts published by Lloyds (3), Herreschoff (4) and Nevins (5). These tables and
similar steel scantling tables are not however, applicable to fiberglass reinforced plastic
boats because of the difference between the basic materials and types of construction. A
frame and plank wooden boat must be made rigid to prevent the many joints from working and
starting leaks. This requirement usually results in scantlings larger than necessary to re-
sist the applied loads on a strength basis. Fig. 2-2 indicates the differences between frame
and plank and fiberglass construction. In steel boats corrosion allowances are necessary
which make up a high percentage of the thickness of the thin hull plates.

MOLDED FIBERGLASS
STIFFENERS BONDED OR
MOLDED IN PLACE

FRAMES SCARF JOINT
THROUGH BOLTED

ONE PIECE PLANK TO SNe: WUTURCAUERED
FIBERGLASS FRAME METAL ie
M
SHELL FASTENERS SaaS
a. FIBERGLASS b. WOOD FRAME AND PLANK

Fig. 2-2. Fiberglass and wood frame and plank hull construction

Since the fiberglass reinforced plastic hull eliminates the many seams and butts charac-
teristic of wooden construction and the corrosion allowance required in steel boats, determi-
nation of the hull scantlings should be based on the strength and other characteristics of
fiberglass laminates and not on simple equivalence to a comparable wood or steel hull.

TYPES OF CONSTRUCTION

Fiberglass boat hulls may be constructed of unstiffened single skin laminates, single
skin laminates stiffened with ribs or frames, sandwich construction of thin face laminates
with a low density core, or some combination of these types. Selection of the type of con-
struction is dependent upon the hull size, appearance, intended service, reinforcement,
fabricator experience, quantity, production facilities, and economic considerations. Some
doubt may exist as to the most suitable type of construction for any specific boat hull. Usually
more than one type of construction is suitable, but only one specific type will result in the
most economical design. In general, a fabricator developing a new small boat for quantity
production will produce a prototype to test the soundness of the hull structure, performance
of the hull form and suitability to mass production. Modifications to improve the original
prototype and reduce production costs, are usually necessary prior to and during quantity
production. This is usually impractical for larger boat hulls unless quantity production is
contemplated. In such a case, careful study, from both structural and economic viewpoints,
will usually indicate the best choice.

Unstiffened Single Skin

The simplest form of a fiberglass boat hull is the single skin without stiffening. This
construction consists of a laminate molded to the desired form, the laminate being several

BOAT HULL DESIGN 2-3

plies of resin impregnated reinforcement. This type of construction is used primarily for
small, open, low speed boats up to about eighteen feet in length. The term '‘'unstiffened"
as used here means that no framing is added and the hull has an interior surface unbroken
by projecting ribs Fig. 2-3a. Many times interior fittings such as thwarts and buoyancy
tanks are used to provide some support for the shell in addition to performing their
primary function.

|

CENTERLINE EEWTERCTNE CENTERLINE
’
{

@. UNSTIFFENED b. FLAT AREAS ARE NOT RECOMMENDED C. MOLDED-IN SPRAY STRIP
FOR UNSTIFFENED SKINS

Fig. 2-3. Unstiffened single skin hull construction

The unstiffened single skin may be used with any of the molding methods discussed in
Chapter 4. In selecting this type of construction it must always be remembered that the
single skin derives considerable strength from the curved shape common to most small boats.
Large flat areas, Fig. 2-3b, should be avoided. In vee-bottomed boats a molded in spray
strip, Fig. 2-3c, may sometimes be used in lieu of stiffeners to provide the necessary
rigidity. For an example of a boat with an unstiffened single skin hull see Fig. 2-4.

Single Skin with Framing

As the size of the boat and the severity of
service increases, or when large flat sur-
faces are required, the unstiffened single skin
becomes too flexible or limber. Solving the
problem by means of large increases in thick-
ness, while theoretically possible, causes
molding difficulties and is also very uneco-
nomical. Therefore, for minimum weight and
cost, framing should be added to the hull.
Framing in this case may be a member which
serves only as a stiffener without any other
purpose or it may be a built-in bunk locker,
or other component already serving an addi-
tional function.

The framing is usually oriented in two
basic directions; longitudinal, that is parallel
with the long axis of the boat, or transverse,
which is perpendicular to the long axis of the
boat, Fig. 2-5. In the case of longitudinal
framing, occasional large transverse frames
may be necessary to support the longitudinal
frames. The designation of the framing sys-
tem is determined by the direction of the Fig. 2-4. Unstiffened

greater number of smaller frames which single skin hull (Courtesy Marscott
Plastic Contpany)

2-4 BOAT HULL DESIGN

@. LONGITUDINAL b. TRANSVERSE

Fig. 2-5. Hull framing

Fig. 2-6. 56' Deborine hull. - Transversely stiffened
Single skin (Courtesy P.D. De Laszlo)

support the shell rather than the larger frames. In addition to this primary framing system,
local stiffening must sometimes be added in way of local loads. This stiffening, where
possible is oriented toresist the applied load most effectively. For an example of a stiffened
single skin hull see Fig. 2-6.

The choice of framing orientation depends largely on a compromise between the interior
arrangement and economical construction of the boat. In wood frame and plank construction,
transverse framing is necessary because the planks run longitudinally and the frames must
be perpendicular to them to provide proper support and fastening, Fig. 2-2b. In fiberglass
construction this is not necessary, and the designer has greater freedom of choice. In the
normal small boat, transverse members are in the form of bulkheads, tanks, and seats which
provide support for the longitudinal framing. In larger boats with cruising accommoda-

BOAT HULL DESIGN 2-5

tions, built-in bunk tops and sides, shelves and so forth can be used as the longitudinal
frames to reduce the number of stiffening members. For these reasons, longitudinal fram-
ing is frequently preferred in fiberglass hulls.

The essential requirements for a frame are that it withstand all the applied loads and
provide sufficient stiffness to maintain the form of the entire structure with a minimum
expenditure of material. The construction of the fiberglass frame may vary with the

size requirement.

For small boats, where the required frame sizes are small, frames are sometimes
made of unidirectional roving built up to form a solid rectangular cross-section; Fig. 2-7.

SHELL LAMINATE

UNIDIRECTIONAL FIBERS

Fig. 2-7. Stiffener for small boats - solid laminate
This type of stiffener has the advantage of simplicity and good bending characteristics.

For larger boats and higher loadings, where greater strength and rigidity is required,
the use of the solid stiffener becomes uneconomical because of the amount of material re-
quired. In most hulls a closed shaped stiffener is used which consists of a solid or hollow
core or form covered with a fiberglass laminate. This, in effect, makes a closed box or
semicircle section when combined with the shell. Typical configurations are shown in
Figs. 2-8 and 2-9. Usually the cores or forms, over which the stiffeners are molded, are
used to give the desired shape and are not considered to contribute to the strength. The
effect of the core material on the rigidity of the stiffeners may be considered if warranted.
The material for the form is chosen for lightweight, workability, and ability to withstand
the handling required in the molding process. Typical form choices are cardboard mailing
tubes for the half-round stiffeners, Fig. 2-8 and balsa wood or unicellular foams for the
hat stiffeners, Fig. 2-9. A detailed discussion of low-density core materials is given in
Chapter 4.

NON- STRUCTURAL
FORM

NON- STRUCTURAL
FORM

FIBERGLASS
STIFFENER

FIBERGLASS
STIFFENER

SHELL
LAMINATE

SHELL
LAMINATE

Fig. 2-8, Half-round stiffener, with Fig. 2-9. Hat stiffener with full
hollow core lightweight core

2-6 BOAT HULL DESIGN

Method of analysis and graphs of section modulus and moment of inertia for half-round
and hat stiffeners are given in Chapter 6.

These stiffener configurations give the designer the opportunity to vary the stiffness and
strength of the section simply by changing the cross-sectional dimensions instead of changing
the thickness of the fiberglass laminate. For maximum strength and rigidity the reinforce-
ment preferred for the stiffener laminate is woven roving, with the thickness approximately
equal to that of the shell laminate. In areas where the interior of the shell is covered with
cloth for appearance, this covering can be carried over the stiffeners.

There are two basic ways to connect the frames to the skin. The preferable method is
to add the stiffeners during the molding of the shell before the shell laminate cures. This
may be done with any of the molding systems. Where matched metal molds are used, the
construction of the male portion of the molds is complicated, since it must be recessed to
allow for the stiffeners. The other method consists of bonding the stiffeners to the cured
shell. This eases the molding problem but makes it more difficult to obtain a good bond,

If this method, called secondary bonding is used, care must be taken to ensure that sufficient
faying, or contact, area is provided so that the horizontal shear stress in the bonded joint is
within allowable limits. A reasonable value for ultimate shear stress at the bond line, using
polyester resins, is 800 to 1000 PSI(6). Greater bond shear stress, 1200 to 1500 PSI, can
be obtained with epoxy resins (6). These values are all for the wet condition.

Sandwich Construction

The most complex type of construction, and the most difficult to fabricate, is the
sandwich. This consists of two fiberglass laminates separated by a core of lightweight
material. The purpose of this construction is to increase the rigidity of the flat panel by
increasing its thickness without the use of a solid laminate. A solid laminate of equivalent
thickness would be very heavy, extremely uneconomical, and would also present some mold-
ing difficulties. In sandwich construction it is usually assumed that the fiberglass skins re-
sist all the bending stresses and deflections, while the core resists the shear stresses and
deflections, withstands local crushing loads and prevents buckling of the laminate skins in
compression. This assumption is discussed in Chapter 6.

Since the strength and rigidity of a sandwich depend on both skins working as a unit at
the required separation, the core material must bond firmly to each skin and be sufficiently
strong to withstand the loads previously mentioned, The core of a sandwich must therefore
be carefully chosen since failure of the core will lead to failure of the entire unit.

As an example of the advantage to be gained from using sandwich construction to increase
the strength and rigidity of a given amount of fiberglass laminate, consider a strip of single
laminate 1 inch wide and 1/4 inch thick. This strip has a moment of inertia, I, of .0013 in#
and a section modulus, Z, of .0104 in’, The same amount of fiberglass divided into two 1/8
inch thick laminates, one on each side of a 1/2 inch thick core, has a moment of inertia, I,
of .026 in4, and a section modulus, Z, of .069 in3. Therefore with the same amount of fiber-
glass the strip is now 20 times as stiff and 6 times as strong. The total weight of the struc-
ture is increased by the weight of the core, which is much less than the additional weight of
fiberglass laminate required to provide equal strength and stiffness. In designing a sand-
wich, the skins must be made thick enough to withstand local impact, abrasions, and handling.

It will be noticed that the effect of the core has not been considered in the preceding
example. The effect of the core on the over-all strength and rigidity of the sandwich varies

BOAT HULL DESIGN 2-1

widely with different physical properties of the core. Some cores, notably wood, have suf-
ficiently high flexural moduli to cause an appreciable effect on the flexural rigidity of the
sandwich. Others have such low shear moduli that the effect of shear deflection must be
taken into account. In designing a sandwich the effect of the core material used must be
investigated to determine whether the core should be considered effective.

Because of the great increase in stiffness and load carrying capacity, sandwich con-
struction is frequently used for relatively large flat panels, particularly where the presence
of stiffeners would be objectionable for arrangements. When the shape is complex, the pre-
formed cores are generally difficult and expensive to shape. This difficulty may be overcome
by using foamed in place resins with appropriate molds or troweled in place filled resins.
Common applications of sandwich construction are for bulkheads, decks and cabin tops on
larger boats.

Many different materials have been tried as cores but the most common being used are
balsa wood, foamed resins, and honeycombs. A detailed discussion of these core materials
is presented in Chapter 4 and physical properties are given in Chapter 5,

Core material for use in shell and weather deck sandwiches must have the ability to
prevent water migration within itself and between the core and the fiberglass facings.

Another highly desirable quality is lightweight. In any boat the application of lightweight
materials is an advantage since they will permit a reduction in the portion of the displace-
ment which must be allotted for the hull structure, This will allow a correspondingly larger
portion of the displacement for useful load in the form of stores, fuel, etc., or increase
speed with the same load. For small boats made of sandwich construction to be competitive
with single skin and frame construction the lightweight core should provide a lower over-all
weight and should also provide positive buoyancy. If the sandwich cannot be made buoyant
its lower unit weight compared to an equivalent thickness of solid fiberglass laminate will at
least reduce the requirement for positive buoyancy.

Balsa wood cores and unicellular foamed plastic cores can provide positive buoyancy.
Honeycombs made of heavy cotton duck and resin impregnated paper are satisfactory but
must be handled with extreme care to insure complete resin impregnation for watertightness
and to obtain a good bond between the core and faces. Improperly constructed honeycomb
laminates in boat hulls have, in the past, caused water migration trouble and their use is not
recommended for primary hull construction unless the fabricator has had considerable suc-
cessful experience with them. Their use should be limited to decks, cabins, flats and bulk-
heads where they will be used to maximum advantage.

Composite Construction

The term ''composite"', as used in the marine industry, refers to a boat or ship whose
framing is made of one material while the shell and decks are of another. The use of this
term began during the transition period when ships were built with iron framing and wood
plank shells and decks. For fiberglass boats, it refers to hulls with shell and decks of
fiberglass laminate and framing of wood or metal. The wood framing is by far the most
commonly used,

Composite construction has been used successfully on a number of boats, There are
basic technical objections to composite construction, which will be discussed, but properly
applied it can produce a successful boat.

2-8 BOAT HULL DESIGN

The basic objection to wood framing on a fiberglass shell is that the materials have dif-
ferent physical properties. Wood swells when wet, rots and requires frequent painting while
fiberglass does not. These differences can cause maintenance difficulties which simply would
not occur if both the framing and shell were entirely of fiberglass laminate construction.

From a structural designer's viewpoint, the major objection to composite construction
is the form of the wood stiffeners used. These are normally of the ''plank on edge" type and
the stiffener itself is very rigid locally. This means that the connection of the stiffener to
the shell must be carefully made to prevent the formation of a hard spot. See Chapter 3 for
a discussion of this problem. Fig. 3-24 indicates the recommended treatment for the attach-
ment of wooden framing to a shell laminate.

It is a temptation to the builder to cover wood framing with a thin layer of fiberglass to
avoid painting and improve the appearance of the boat. This practice is very definitely not
recommended, It does not solve the problem of wood swelling or rotting in the presence of
moisture, It simply hides the problem so that the boat owner's first indication that trouble
exists will be cracking or delamination of the covering laminate, or actual failure of the framing.

The use of metal, usually aluminum, for framing is not common, but it has been used in
some designs. The major problems with this type of construction are obtaining a satisfactory
bond between the metal and the fiberglass, and eliminating hard spots. In addition, difficul-
ties may occur due to the difference in the moduli and in the rates of expansion and contrac-
tion with changing temperature. These differences introduce additional shear stresses in the
connecting bond or fasteners.

SELECTION OF LAMINATES

The choice of type and arrangement of reinforcement for a single skin laminate is based
on a number of factors. These factors include strength, rigidity, impact resistance, re-
sistance to passage of water, cost of material and labor, ease of handling and appearance.
Each of the basic types of reinforcement has its own qualities and these must be utilized in
combination to provide the most effective laminate. These are discussed in detailin Chapter 4,

It is obviously impossible to consider all the possible combinations of reinforcement
which might be used. As an indication of the choices which are made, and the reasons for
them, three laminates will be discussed.

The first laminate, Type A: Consists of 1 ply of 10 ounce cloth on the outboard side,
1 ply of 2 ounce mat and a varying number of plies of 25-27 ounce woven roving.

Considering this laminate in detail: The outside ply of cloth is intended primarily for
appearance and as gel coat reinforcement. It is used because of its relatively smooth sur-
face, which reduces the thickness of the gel coat. This ply also provides good tensile quali-
ties for the exterior of the laminate. Some builders replace this ply of cloth with a ply of
3/4 ounce mat as gel coat reinforcement.

The ply of 2 ounce mat serves three purposes. First, it is highly resistant to the pas-
sage of water and minimizes the absorption of water by the laminate. Water absorption re-
duces the strength of the laminate. Second, mat provides greater thickness per layer than
either woven roving or cloth, and thus increases thickness with a minimum of cost. Third,
the mat prevents the pronounced weave pattern of the woven roving from showing through
the cloth and the gel coat. Note that 2 ounce mat is used here, but that 1-1/2 ounce mat

BOAT HULL DESIGN 2-9

can be used to perform the same functions. The 1-1/2 ounce mat is easier to drape and to
wet out with resin, but is less effective in increasing thickness and masking the weave of
the woven roving.

The plies of woven roving provide the bulk of the laminate thickness, strength, and
impact resistance. The number of plies used depends on the strength required for the
particular laminate. Woven roving is used here because it is cheaper and requires fewer
plies than cloth, and has better impact resistance than mat.

An interior layer of cloth may be added for appearance only, if desired.

The second laminate, Type B, consists of: 1 ply of 10 ounce cloth on the outboard side,
a varying number of plies of mat and 1 ply of woven roving on the inboard side.

Considering the laminate in detail: The outboard ply of cloth performs the same function
as in Type A laminate.

The plies of mat provide the thickness and strength of the laminate. The number of
plies used depends on the strength required.

The interior ply of woven roving is used to provide resistance to impact from objects
such as logs.

An interior ply of 10 ounce cloth may be added if desired.

The third laminate, Type C, is identical to Type B except that two layers of woven roving
are used instead of one. Each component performs the same function as before. The reason
for the additional ply of woven roving will be discussed later.

It is sometimes stated that the material with good tensile properties should be placed on
the inboard face of the hull laminate because this is the ''tension side". In this manual it is
recommended that woven roving be placed on the inboard side, for resistance to impact from
objects, as distinguished from water impact. Fig. 2-10, indicating the deflected shapes of
an unstiffened and stiffened hull laminate under water pressure loading on the outboard sides
of the hulls, shows that the outboard face of a hull laminate can also be in tension. There-
fore, the arrangement of laminate reinforcing components should be made to provide for
tension on the outboard face as well as on the inboard face. The layer of 10 ounce cloth on
the outboard side of the laminates previously discussed performs this function. If required,
this portion of the laminate may be increased for higher strength.

Loading due to impact from an object places a concentrated rather than a distributed
load on the laminate. For the unstiffened hull this change does not change the character of
the deflection curve. For the stiffened hull there is a considerable change since the load acts
on only one panel. This means that the loaded panel approaches the condition of simply sup-
ported edges rather than clamped edges as in the case with the distributed or pressure type
of load. In this case, the inboard side of the hull is in tension, and the woven roving is
placed there to resist this tension stress.

As anaidinchoosinga laminate, Figs. 2-1land2-12havebeenprepared. Fig. 2-llisaplot
of material cost versus section modulus at the inboard face of the three laminates, Type A, BandC.
The figure shows that Type A laminate is relatively expensive but it is widely used on larger hulls

COST — DOLLARS PER SQUARE FOOT

IN THIS AREA -
OUTSIDE IN COMPRESSION
INSIDE IN TENSION

ERLE

SHAPE

/
DEFLECTED SHAPE i /

ORIGINAL

IN THIS AREA -
OUTSIDE !N TENSION
INSIDE IN COMPRESSION

EXAGGERATED a.
PRESSURE LOADING

ON BOTTOM

a. UNSTIFFENED

IN THIS AREA -
OUTSIDE IN COMPRESSION
INSIDE IN TENSION

IN THIS AREA ~

DEFLECTED SHAPE
EXAGGERATED

ORIGINAL SHAPE

OUTSIDE IN TENSION PRESSURE LOADING

INSIDE IN COMPRESSION ON BOTTOM

b. STIFFENED

Fig, 2-10. Tensile and compressive

stresses in a boat shell

| TYPE A LAMINATE .

4 1 CLOTH NI
20 4 MAT

|e
Sa al
=:

= $= TYPE C LAMINATE |

hi eo |
eae |
TYPE B LAMINATE ole
|
1 CLOTH —
a
|__|
a

N MAT Z Z _ |
1 WOVEN ROVING TYPE C LAMINATE
4 CLOTH

| N WOVEN ROVING

a , N MAT =|
= if | | AG
=a Loe: 2 WOVEN ROVING
N MAT See |
bee 2 WOVEN ROVING | . GE TYPE A LAMINATE
| | o 4 CLOTH |
eit 2 | al BI : : 1 MAT

TYPE B LAMINATE

N WOVEN ROVING

1 CLOTH
N MAT
1 WOVEN ROVING

WEIGHT — POUNDS PER SQUARE FOOT

T r

4
| N = VARYING NUMBER OF PLIES

Zanes

N = VARYING NUMBER OF PLIES

| ! i | ie 1
C) 2005 2010 2015 2020 2025 2030 t) 2005 2010 2015 2020 2025 2030
SECTION MODULUS AT THE INBOARD FACE SECTION MODULUS AT THE INBOARD FACE
FOR 1" WIDTH OF LAMINATE — INCHES? FOR 1" WIDTH OF LAMINATE — |NCHES3

NOTE: COST BASED ON PRICES AS OF JUNE 1959,
CURRENT FIGURES SHOULD BE USED FOR ACCURATE ESTIMATESs

Fig. 2-11. Cost versus strength of contact Fig. 2-12.

Weight versus strength of contact

molded fiberglass - polyester laminates molded fiberglass - polyester laminates

BOAT HULL DESIGN Pa bt

where laminate cost is relatively a smaller portion of the total cost than itis for the small boats,
Fig. 2-11 also indicates the reason for the difference between Types B and C. For section
moduli below 0.007in°, Type B laminate with one ply of woven roving is less expensive than
Type C with two. For section moduli above this value, Type C becomes less expensive.

Fig. 2-11 considers material cost based on unit prices for the date indicated and glass
percentages and thicknesses usually obtained by contact molding. The effect of changes in
unit prices or molding method should, of course, be considered. In addition, labor costs
for the different types of material, which vary somewhat with different fabricators, should
be considered,

Fig. 2-12 indicates the relationship of weight per square foot of the three laminates
described above and the section moduli at the inboard face of the laminates. These data
are based on contact molding. The data given in Fig. 2-12 will enable the designer to con-
sider the effect of weight when selecting a laminate,

BASIC DESIGN CONSIDERATIONS

The most difficult technical problem in small boat hull design is the selection of the
loads to apply in determining the scantlings of the hull structure, The actual load on any
given part of a vessel in service is extremely complex; consisting not only of loads applied
by external forces such as water pressure which act directly on the part, but also of loads
transmitted from the parts of the boat adjacent to the section or member under considera-
tion. For example, a bulkhead may be loaded directly by equipment mounted on it, and in-
directly by water pressure loads which are transmitted from the shell to the frames sup-
porting the shell, and from the frames to the bulkhead which supports them. Although any
piece of a boat hull is directly or indirectly connected with all the other pieces, it is not
generally practicable to determine the distribution of the loads transmitted from one part
to another

The small boat designer must, therefore, resort to more or less assumed design
loads, These loads, combined with a choice of the factor of safety which represents, in
part, the designer's best judgment regarding the accuracy of his assumed loading, are
applied to determine the required scantlings.

The assumed design loads depend on the function of the part of the boat under considera-
tion, and on the size, type, and intended use of the boat. Large ships must be designed to
withstand the longitudinal bending stresses imposed on them in waves as shown in Fig. 2-13
in addition to the lateral loads due to water pressure and local loads due to equipment
and cargo.

BUOYANCY OVEF WE!GHT BUOYANCY OVER WE! GHT

= iN DECKy
[ Sy a Ky WATER SURFACE
\ /
= r 7 - vA
TENSION Fs

N BOTTOM t

LOCAL EXCESS OF

WEIGHT OVER BUOYANCY

Fig. 2-13, Forces on ship's huil causing
longitudinal bending stress

2-12 BOAT HULL DESIGN

For small boats this same loading condition exists but the length to beam and depth re-
lationships are such that this is usually not a critical loading condition.

In the following pages, the design loads for several general types of boats are discussed,
with the intention of covering the broad field of current fiberglass boat hulls. It is recognized
that in some instances, statements made regarding the loads which should be used may be
controversial. In all cases, the intention is that the loads described shall produce a safe,
trouble free boat for operation in the service as described, The loads have been chosen so
that the resulting scantlings are generally in accord with good modern practice. However,
it must be recognized that fiberglass laminates are a relatively new material for boat hulls
and that as more and more service experience is accumulated, it may become apparent that
some of the recommended loads are too severe and others perhaps not severe enough. Cer-
tainly the standards recommended are not intended as hard and fast rules, nor are they pre-
sented as the last word. In the final analysis the individual designer must use his own best
judgment in producing a balanced design suitable for the intended service.

DESIGN LOADING

In the design of the various components of a boat's structure, there are two basic criteria
which must be considered; vibration and strength.

Vibration Criterion

Critical vibration is familiar to everyone in one form or another. Any physical object
has a natural frequency of vibration; that is it tends to vibrate at a particular rate. This
rate depends on the geometry of the object, the loads imposed on it, and the material used.
If a varying load is imposed on a structure and the frequency of variation is nearly the same
as the natural frequency of that structure, the phenomenon of critical vibration or resonance
occurs, The amplitude of the critical vibration is high, and the resulting shaking or drum-
ming is unpleasant and may cause structural failure. This structural failure may be due to
fatigue at relatively low stress levels or, in the rare case of extreme vibration, to high
stresses induced by large deflections.

To date, the vibration of fiberglass laminate panels has not received sufficient attention.
The theoretical analysis of orthotropic plate vibration has been investigated (7) but the analysis
is quite complex. A further complication is introduced because the modulus of elasticity
values generally measured are static values. For certain materials significantly different
moduli values are obtained under dynamic conditions such as vibration. Published data (8)
on Douglas fir indicates a 10 per cent increase in the dynamic modulus of elasticity compared
to the static modulus of elasticity. The only available published article on the vibration of
fiberglass laminate (9), which is very limited in scope and cannot be used without substanti-
ating tests, indicates a 50 per cent increase in the dynamic modulus compared to the static
modulus of elasticity.

A characteristic of fiberglass laminates which may help alleviate vibration difficulties
is internal damping. This term refers to the ability of a material to absorb vibration energy
by converting it to heat produced by internal friction, Internal damping has two effects on the
vibratory characteristics of a material. First, it reduces, usually to a small degree, the
natural frequency. Second, and more important, it reduces the amplitude of vibration drasti-
cally at frequencies at or near resonance, The amount of internal damping actually present
in fiberglass laminates has not been measured experimentally, but it may be expected to be
substantial compared to metals.

BOAT HULL DESIGN 2-13

In view of the complexity of the theoretical analysis required and the lack of needed ex-
perimental data, vibration analysis of fiberglass panels is not, at this time, a practical boat
design tool.

At the present time the only practical cure for vibration problems is a trial and error
approach. This essentially consists of building the boat, testing it, and if objectionable
vibration occurs making suitable corrections.

Examples of corrective action which might be taken include: additional plies of laminate;
additional stiffening to reduce panel size; and change the number of blades on the propeller if
the measured frequency of vibration equals the RPM times the number of propeller blades.
Of these three, the addition of extra stiffeners is recommended as the most practicable and
economical,

Strength Criterion

For certain hull components, notably the shell, several different criteria are proposed
depending on the type of boat being considered. Following the general discussion, design
examples are presented to illustrate suggested methods for the structural design of several
types of boats.

Shell and Framing: The basic component of all boats is the shell. Structurally this is
a watertight envelope which must be maintained in its designed shape while resisting the ex-
terior water pressure. The framing, in addition to supporting the shell against this pressure
must also spread the local interior loads from the engine, mast etc., over a large area of
the shell.

In small open boats the shell is usually the only structural member. Small, low
speed boats powered by an outboard motor of 10 horsepower or less, and day sailers are
examples of this type.

The shell of a low speed open boat is generally subjected to low stresses from water
pressure on the bottom, torsion from the sails, and various other over-all loads, The
critical loads on these boats are generally local loads due to handling, grounding, minor
collision with docks, and so forth. Since these loads are similar for most of these low speed
boats, the size of the boat has surprisingly little effect on the laminate used. An exception
is the effect of torsion on open, as opposed to decked, sailboats. In order to prevent ex-
cessive twisting of the hull, the laminate for the larger sizes of open boats is generally in-
creased, The loads described above are not susceptible to detailed analysis, and the best
criteria available are the many successful boats in this category.

Based on current practice, the following laminates are recommended:
For round bottom boats under 12 feet in length - normal low speed pleasure service

1 ply 10 ounce cloth on the outboard side
1 ply 1-1/2 ounce mat
1 ply 14-17 ounce woven roving

For round bottom boats 12 to 18 feet in length - normal low speed pleasure service
1 ply 10 ounce cloth on the outboard side

1 ply 2 ounce mat
1 ply 24-27 ounce woven roving

ies)

-14 BOAT HULL DESIGN

Boats intended for rougher service than would be considered normal, such as frequent
beachings in rocky areas should be strengthened with an additional ply of woven roving. For
large open sailboats of the ''Thistle'' type, 2 plies of 1-1/2 ounce mat may be substituted for
the 2 ounce mat, due to the large torsional loading from the sails and the lack of a deck.

The above scantlings are recommended for "round bottom" boats whose shells have
curvature in the transverse direction and have some form of centerline stiffening in the
bottom, This centerline stiffener or keel is very important as it provides support for the
shell when in the water and also when in storage. This member will usually be in the form
of an external keel and skeg. Another common method of adding stiffness to the boat in the
vicinity of the keel is to lap the middle and/or inner plies of the laminate to form a double
thickness in this area. In the case of a flat bottomed boat, such as a conventional skiff, it
is recommended that a stiffener of parallel strands of roving be added approximately midway
between the centerline and the side. These stiffeners should be 1/2 inch thick and of varying
width from a minimum of 1 inch for a 12 foot boat to 3 inches foran18 foot boat. If desired,
the single stiffener may be replaced by a number of smaller longitudinal stiffeners, spaced
at equal intervals across the hull, whose total width is equal to that of the single stiffener.

Sometimes it is desired to produce a fiberglass version of an existing class of wood
racing sailboats. In this case the determining factor in choosing the scantlings may prove
to be the weight limitations of the class rules, and the laminates recommended here may
prove to be too light. The designer is referred to the tables of physical properties in
Chapter 5 for unit weights of laminates with various types of reinforcement,

The most difficult shell loading to evaluate is that experienced by a relatively high speed
planing power boat travelling in waves. Anyone who has experienced a ride on this type of
boat knows that severe impact loads occur on the bottom due to high accelerations,

Although some investigations have been made, (10,11,12), there is no simple theory
available which predicts the maximum impact pressure on the bottom of a boat at high speed.
This is particularly true in the case of small light boats. Also, very little experimental data
are available on this subject. After consideration of several possible approaches to the
problem of predicting bottom pressures for use in design, an empirical relationship has been
developed which is considered practical and conservative, particularly for small boats.

The development of this equation consists basically of considering the impact pressure
developed when the boat strikes the water. This pressure is given by the formula:

p = 1/2 9 v4 (20)

where p = presSure in pounds per square foot

<¢
iT]

speed in feet per second

mass density of water in slugs per cubic foot, 1.992
for salt water at 50 degrees F

D
"

bo

BOAT HULL DESIGN -15

By considering v, the effective relative velocity of the water perpendicular to the struck
surface of the boat, composed of the vertical and horizontal components of boat velocity and
orbital velocity of the water particle in the wave, and relating these values to the forward
speed and size of the boat the following equation may be derived:

pr = AvV@+BVVL + CL (2. 2)
D
Pr = maximum local impact pressure in pounds per square inch to te
: expected when the boat is driven in waves at the
maximum possible speed
V = the forward speed of the boat in miles per hour
IL = waterline length of the boat in the at-rest position
D = il = 1h.55, a constant including water density

and dimension conversion factors
oe x1 ft*
2x 1h in?

A, Band C are constants expressing the relationships between wave height, wave length,
boat size and conversion from feet per second to miles per hour, These have been evaluated
from the experimental data obtained during tests made on a PT boat (13),

Aee= 20; B = 1.267 C = 16.884

The nomograph presented as Fig, 2-14 provides a ready means for evaluating this
equation. To use this nomograph proceed as follows:

Place a straight edge on the graph so that it passes through the appropriate
speed on scale A, and the appropriate length on scale C,

Mark the point at which the straight edge crosses the line located between
scales A and B.

Compute V x VL.

Rotate the straight edge so that it passes through the previously marked
point on the line between scales A and B and the computed value of Vv x VL

on scale D,
Read the pressure at the point at which the straight edge crosses scale B.
A detailed example is indicated on Fig. 2-14.

The pressure obtained from the procedure given above represents the maximum bottom
impact pressure which will be present over a small area of the bottom, for short periods of

MAXIMUM SPEED IN MILES PER HOUR

re
We ws
-_ WW
w uw
yea
Ms =
_ 2 SO er
wo
w __ STEP &— ty
>) oO
—— es
a <
a
a =x
=
S U)
2 a
a a
=
x0 z
= =
= ad
2 s
«<
< =
es
4
20
EXAMPLE
75° WATERLINE LENGTH PT BOAT
MAX. V = 35 KNOTS = 40.3 MPH
v x Vt = 349
10 MAXIMUM IMPACT PRESSURE
py = 36 PSI

Fig. 2-14. Maximum bottom
for high speed planing boats

80

60

pressure

0 SS

450

250

200

150

v xVo

1.00 1,00
0.8 iS 0.8
0.6 =! 0.6

f 0.4 0.4 m1
0.2 0.2
a6 9 8 Z 6 5 4 x) 2 i ie) =

STATIONS

&. FACTOR Fy VERSUS LONGITUDINAL LOCATION FOR SHELL

Fy Fy
9 10 «=620—:—é«‘ 2? 40 5O 6 70 80 90 100
SPAN AS % OF UNSUPPORTED HALF -BREADTH
b. FACTOR FL VERSUS SPAN FOR TRANSVERSES
1.00
0.8
0.6
FL 0.4 Fe
0.2
9.0

STERN STATIONS BOW

CG. FACTOR FL VERSUS LONGITUDINAL LOCATION FOR LONGI TUDINALS

Fig. 2-15, Pressure distribution factors

w

aliis: BOAT HULL DESIGN

time. This pressure will occur only under the most severe sea conditions, which must be
judged in relation to the size of the boat. The intention here is that severe conditions are
those in which the operator of the boat is subjected to acute discomfort, It is recognized
that this does not represent a normal operating condition, but rather one due to some emer-
gency, such as an approaching storm, when the boat must be driven as hard as the operator
is physically capable of driving it.

The pressure given by the nomograph will not occur, at any one time, over a large area
of the bottom, and there are areas of the bottom, both forward and aft where it will never
occur, The pressure to be used for design purposes will vary with the type of member be-
ing designed and its location in the boat. These pressure variations with location and ex-
tent of area loaded were investigated during the PT boat tests (13), and the results, with
some modifications, are summarized in Fig, 2-15.

For the design of the bottom shell the pressure to be used is the full pressure varied
only for longitudinal location. The formula is:

Ppa Pee ees (2.3)
Ph = design pressure
p.. = pressure due to the normal static head of
H water taken in the at-rest position
ae = impact pressure from the nomograph, Fig. e-1
F. = a factor for the shell impact pressure, depending

+ on location along the length of the hull shown in
the top graph of Fig. 2-15

It can be seen from the figure that one-half of the maximum impact pressure may be
expected at the bow, the maximum may be reached anywhere between the forward one-
quarter point and midships, and that the impact pressure drops off to zero at the stern.
For practical construction, the whole bottom laminate forward of station 6 or 7 may be
designed for the maximum impact pressure, and the laminate aft for the impact pressure
at station 6 or 7. In this manual reference to station numbers is based on the water
line length being divided into ten stations from forward.

For the design of transverse members the variation in pressure depends on the
longitudinal location of the member in the boat, and on the span of the member in the
transverse direction. The formula is:

i) ep. p, * PL x Ba (2. 4)

= design pressure considered acting as a
uniform pressure on the shell area supported
by the transverse

Py = static water pressure as previously defined

Py = pressure from nomograph, Fig. 2-1)

Fy = factor taken from the top graph on Fig. 2-15

F_ = factor taken from the second graph on Fig. 2-15

BOAT HULL DESIGN 2-19

The factor Pp varies with the length of span expressed as a function of the half-breadth
of the boat at the transverse. This means that for a boat with a center keel and transverse
framing spanning the entire half-breadth, the design load is a uniform pressure equal to
0.68 times the maximum pressure at the longitudinal position of the transverse in question,
This reduction is due to the fact that only a portion of the shell area supported by the trans-
verse will be subjected to the maximum pressure at any one time.

For the design of longitudinals the variation in pressure is dependent on the longitudinal
location of the member. The formula is:

PS ie py. BL ke (25)

Pp = design pressure considered acting as a
uniform pressure on the portion of the shell
area Supported by the longitudinal

Py = static water pressure as previously defined

Pr = pressure from the nomograph, Fig. 2-1

F, = factor taken from the top graph on Fig. 2-15
F, = factor taken from the bottom graph on Fig. 2-15

To obtain the design pressure for a longitudinal with a particular span, or distance
between transverse supports, calculate the design pressure pp at the ends of the span and
use the average of these two values as a uniform load on the portion of the shell supported
by the longitudinal.

In designing the components of the bottom structure using the pressures obtained by the
methods just described, a factor of safety of 1.5 on the ultimate wet strength of the materialis
suggested. This low factor of safety is permissible because the pressure used is for an
extreme loading condition.

An alternative criterion which should be checked on ali runabout designs is the deflection
of the bottom. The assigning of an allowable deflection is a difficult problem since it depends
on the reaction of the passengers ina boat. People who are accustomed to wood hulls some-
times regard the flexing of a fiberglass boat as a sign of weakness. The reasons that fiber-
glass hulls may flex more than wood hulls are that the hull thickness is reduced because of
the higher strength of the fiberglass laminate, and that the number of transverses is re-
duced compared to that required for a wood hull to prevent working and leaking at the seams.

From a structural point of view, limited deflection of the shell in a boat hull is not, in
itself, a major problem. However, the passenger reaction previously mentioned can be a
serious one from the standpoint of customer acceptance. For guidance, it is recommended
that the deflection of bottom structure under the maximum bottom pressure be limited to
1/100 of the span.

The side thickness of the planing boat is usually sized on the basis of the required
bottom thickness to provide a balanced hull laminate. From a study of a number of existing
designs which are believed to represent good current practice, the side laminate thickness
may be taken as 75 to 80 per cent of the thickness of the bottom hull laminate with a mini-
mum thickness of 1/8 inch. If a boat is intended to be used in service where frequent

2-20 BOAT HULL DESIGN

dockings are required, such as a club launch, or a passenger ferry, the side laminate
should be increased to the same thickness as the bottom laminate.

Side framing for runabouts may be designed to withstand a pressure equivalent to a head
of water six inches above the deck edge. If several side frames are used, they are usually
made the same size throughout. A factor of safety of 4 is suggested for this loading. Side
framing designed to the above criterion will usually support a lower maximum load than the
shell laminate can support. The reason for this difference is that the side laminate thick-
ness, selected as explained above, is chosen partially to resist effectively local impact
loads due to striking docks, partially to reduce torsional deflection of the hull, and
partially to prevent side panel vibration. The side framing in the forward end of a
boat should be designed as bottom framing especially when a Vee form is used since
it is subject to similar impact loadings.

The next shell design to be considered is for displacement type boats, These boats do
not travel fast enough in a seaway to have the large impact pressures experienced by a high
speed planing boat. The shell is therefore designed for a static water pressure,

In the case of the cruising sailboat, the shell and framing should be designed to with-
stand a head of water corresponding to that experienced when the boat is heeled to the point
where the cockpit starts to flood, Depending on the height of the cockpit coaming this height
will vary from 6 inches to a foot or more above the deck edge. Since this is a normal load-
ing condition a factor of safety of four is suggested. Deflection is not normally a problem
with boats of this type.

The displacement type power boat occupies a position midway between the planing power
boat and the cruising sailboat, as far as the shell load is concerned. The shell design load
for this type of boat cannot be taken from the empirical formulation presented for planing
boats, but should be greater than the static pressure existing on the bottom with the boat at
rest because of the additional loading experienced in a seaway. For these boats a bottom
design pressure equivalent to a water head of 2 feet above the main deck forward of Station 7
and 6 inches above the main deck aft of Station 7 is recommended for the shell and framing.

In designing the framing for displacement boats no reduction factors for location and
span, as are used for planing boats, should be applied. The pressures used here are not
local transient impact pressures, such as those that occur on the planing hull, but are con-
sidered as a uniform load over the entire bottom of the boat. A factor of safety of four is
recommended for use with this design loading. As in cruising sailboats, deflection is not
normally a problem with this type of boat.

As with planing hulls, the side shell is proportioned on the basis of the bottom shell.
For normal service this thickness may be taken as approximately 80 per cent of the bottom
thickness, The side framing is designed to withstand a water head to a height six inches
above the deck edge, as in planing boats,

To assist the designer in making preliminary estimates for the bottom laminate of a
cruising sailboat, Fig. 2-16 has been compiled from existing designs. The Figure indicates
required section modulus and stiffener spacing as a function of the cube root of the displaced
volume. The Figure is for guidance only and in the detail design stage the laminate and the
stiffener spacing must be determined for the particular boat by the detailed design methods.
Fig, 2-16, in conjunction with the unit weights given in Fig. 2-12, will aid the designer in
making preliminary weight calculations.

BOAT HULL DESIGN 2-2

Transom: The vast majority of fiberglass

boats built so far are powered by outboard
motors. Even rowboats and small sailboats
are generally arranged so that a small out-
board motor can be used as a means of pro-
pulsion. The transom must therefore, be de-
signed to support a motor of a size suitable
for the boat. The designer should always re-
member the trend toward ever increasing
power and size in outboard motors, and that
boat owners all too often use motors of higher
power than the designer considers necessary
or even safe. In estimating the horsepower to
be used in designing a transom the designer
should be generous, particularly for a stock
boat which will be widely distributed.

As a guide in selecting the transom thick-
ness and in determining the dimensions of the
area of increased thickness for the motor
clamps, minimum standards have been set up
by the Outboard Boating Club of America(14).
These standards call for a minimum transom

LONGITUDINAL STIFFENER SPACING — INCHES

16 18 20 ae
—-

D = UNDERWATER VOLUME
1N CUBIC FEET

SECTION MODULUS

6 =

STIFFENER SPACING

te

| EXAMPLE

NE D= 4.5

STIFFENER SPACING = 18"
SECTION MODULUS = 0.0095 IN
5 PLIES OF WOVEN ROVING

IN TYPE A LAMINATE REQUIRED

=]

3

20100 20140 20180 20220

REQUIRED SECTION MODULUS TO WOVEN ROVING FACE — INCHES?

oH a — — a
4 5 6 x4 8 9

PLIES OF WOVEN ROVING TYPE A LAMINATE
FACTOR OF SAFETY = 4

Fig. 2-16. Bottom shell laminate
for fiberglass polyester cruising
sailboats based on current designs

thickness of 1-3/8 inches for motors, totaling 40 horsepower and less, and 1-1/2 inches for
motors totaling more than 40 horsepower, The maximum thickness in way of the engine
clamping bracket is 1-3/4 inches for a single motor of 40 horsepower and less, and 2-1/4
inches for a single motor over 40 horsepower. In actual practice the entire transom is
sometimes made the thickness required in way of the engine clamping bracket. Alternatively,
the minimum thickness may be used throughout and steel plates added in way of the clamp-
ing bracket.

The over-all dimensions for the area and the increased thickness are given in Table
2-1 below.

TABLE 2-1

DIMENSIONS OF MOTOR SUPPORT AREA

| thine

Under 12
12-40
Over 40

ie OF MOTOR

1-3/4
1-3/4
2-1/4

recs

MOTOR
CLAMPS

pee el

FORWARD FACE OF TRANSOM

AFT FACE OF TRANSOM
LOOKING AFT LOOKING FORWARD

REINFORCED

AREA —

THICKNESS

INCREASED cross

SECTION

2-22 BOAT HULL DESIGN

For boats with high power, the transom design should be checked to insure that the
minimum dimensions given above are adequate. To aid the designer, Fig. 2-17 has been
prepared. This Figure provides the means of determining the required section modulus
of the transom. It has been prepared based on the following assumptions:

250

aS = Secrion MODULUS _X ALLOWABLE stkess |(2.6) The upper portion of the transom is
== roa | considered to be a simply supported beam
Ee aan ed (S| | L LA loaded with the thrust required to move
| ae nee P| the boat.
r Ispowal if
oe || Sy | ee The thrust used in developing the
me | 0) | Poe ay Figure was determined by taking the ef-
B i eo a ] fective horsepower equal to 1/2 the motor
06 | 13° 9108 horsepower (1).
wee Zs <8 :
eS RAS To use Fig. 2-17, enter the graph at the
ea eel ld total horsepower to be used, read up to the
| 7 worors appropriate line for the speed and number of
30 NPN 7 motors, and read across to the value of the
ie) : 20 40 ! 60 ; 80 100 parameter
- A
MOTOR HORSEPOWER TOTAL (z = fp) /B (2. 6)
Z = SECTION MODULUS IN INCHES?
fp = ALLOWABLE FLEXUAL STRESS IN PSI By using the known values of allowable flexural
ae 7 es oe cee i ie stress, fp, and the beam of the transom B,
the required section modulus, Z, may be ob-
Fig. 2-17. Transom section modulus tained. A factor of safety of 6 is recommended
as a function of speed and power in determining the allowable stress. It should

be noted that a stronger transom is required
to support one 40 horsepower motor than to support two 20 horsepower motors mounted side
by side.

The most common and practicable method of construction for transoms is a sandwich
arrangement with a plywood core and fiberglass facings. In computing the effective section
modulus of the transom, it is recommended that the following assumptions be used:

The effective width of the transom should be taken as the maximum vertical!
dimension of the motor clamping area as given in Table 2-1.

Only the plies of plywood whose grain is horizontal, that is parallel to the span
being considered, should be taken as effective. These will normally be the face

plies, and alternating ''center'' plies within the plywood. This procedure is recom-
mended by Ref. 15.

Where a Seat or motor well is made an integral part of the transom, this should
be included in the section modulus.

For an example of the use of Fig. 2-17, see Design Example 2-3 for the 19 foot runabout.

Resonant vibration does notnormally occur atthetransom. The vibrationfeltthere is aforced
vibration excited by the motor, but the fundamental frequency of the transom is so far from any nor -
mal operating range of the motor that resonance with this frequency is not a problem.

The unsupported transom is used for boats with low power, but this not usually satis-
factory for boats in the high power range. Several methods of support are used, singly or

BOAT HULL DESIGN

nN

-23

>
\\ Dd. INNERBOTTOM FLANGED UP
Un TO SUPPORT TRANSOM,
BOAT SHOWN CUT ALONG
a. UNSUPPORTED TRANSOM CENTERLINE

SN Aw
<N
NN x NS
SN i
SN a \
Dine i ‘
Re
C. VERTICAL BRACKETS TO BE d. HORIZONTAL SHELF SUPPORTING
SUPPORTED BY LONGI TUDINALS, TRANSOM.
NOTE: GUNWALE CARRIED |NBOARD NOTE: GUNWALE CARRIED INBOARD
ON TRANSOM ON TRANSOM

Fig. 2-18. Transom configurations

in combination as illustrated in Fig. 2-18. Normally, in boats intended for higher power, a
narrow side deck or heavy gunwale strip will exist which may be carried around the corner
to reduce the span of the transom. If a permanent inner bottom is provided, this may be
given a radius at the stern, and carried up the transom for support. The use of vertical
brackets, which is common in wood construction, should be avoided in fiberglass construc-
tion unless there are corresponding stiffening members on the bottom. This is because the
toe of a bracket landing on unsupported shell constitutes a definite "hard spot" as discussed
in Chapter 3. One of the most common and most effective means of support for the transom
is the horizontal shelf located as close to the top of the transom as the depth of the mounting
bracket of the motor will permit. This horizontal shelf is usually used as a seat, or as the
bottom of a watertight well. Another method of increasing transom rigidity is to curve the
transom aft, The effect of any normal curvature is comparatively small, and it is felt that
the possible reduction in the transom thickness should not be considered.

Decks: For structural design purposes, decks are divided into two types: weather decks
which may be subject to water loading and interior flats and cabin tops which are subject to
loads from personnel and equipment,

For weather decks, including watertight open cockpits, a uniform load corresponding to
2 feet of water is considered a good design value for most pleasure boats. For work boats
and fishing boats designed to operate at sea, a higher figure should be used. In boats with
small partial decks, as in runabouts and small sailboats, an alternative design loading may
be used, assuming the weight of a man concentrated at the center of the deck. A factor of
safety of four is suggested with either of the above loadings.

2-24 BOAT HULL DESIGN

For interior decks, non-tight cockpits, and cabin tops, the design load depends on the
intended use of the boat. The load for the interior deck of a privately owned vessel may be
taken as 40 pounds per square foot, while the passenger deck for a high speed ferry such as
a service craft for offshore drilling rig should be designed for approximately 60 pounds per
square foot. The above loadings are for the at-rest condition. The increase for accelera-
tions due to pounding in a seaway depends on the requirements of the service, and on the
arrangements. In high speed offshore ferry service, where it may be necessary to main-
tain high speed in rough seas, a''g'' or gravity factor of two should be applied to the above
loads for flats in the forward portion of the vessel; that is the loads given above should

be doubled,

An important design consideration for decks, particularly in walking areas, is deflec-
tion. The allowable deflection, as previously discussed in the section on shell design, is a
subjective matter, An allowable deflection of 1/200th of the span under the design loads
discussed above is recommended,

Decks, particularly interior flats, are usually constructed of plywood or of sandwich
construction with a lightweight core and fiberglass faces. For maximum economy with
fiberglass construction, a single molding including deck, seats, and any other interior
accommodation is recommended where feasible.

In small boats, with single skin construction, the use of contour, i.e. raised areas,
in lieu of stiffeners is very common,

Gunwale: For open or partially decked boats, some form of gunwale must be provided
to strengthen the upper edge of the side. The most severe loading likely to occur ona
gunwale will vary according to the size of the boat. However all gunwales are subject to
impact at docks and from other boats, In a boat small enough to be man-handled, it is
possible that the boat will be rolled over on its gunwale for cleaning or storage. The
gunwale should therefore be able to withstand the weight of the boat concentrated at the
ceater of the longest span between gunwale supports. The factor of safety for this loading
condition may be quite small, say 2 on the ultimate wet strength, since it is not a normal
service load.

For larger boats, the gunwale will be used, in many cases, as a step when boarding
or leaving the craft. The stability of the boat should, of course, be checked for this
condition and if found inadequate, the shape of the gunwale should discourage passengers
from attempting to step onit. In the event that the gunwale is intended for use as a step,
the necessary width, approximately 3 or 4 inches, should provide ample strength for boats
with conventional arrangements. For common gunwale types, see Chapter 3.

Bulkheads: Transverse bulkheads in small pleasure boats are not usually intended to
withstand water pressure, as is the case in larger vessels. In some cases Coast Guard
Regulations (16) require bulkheads to resist water pressure. In the case of small com-
mercial vessels carrying more than six passengers the bulkhead must be able to withstand
a head of water to the top of the bulkhead.

In addition to the possible requirement for withstanding a waterhead, bulkheads are
generally required to support the weight of equipment mounted on them, the loads imposed
by the deck and side framing and any local loads, as from a mast. A factor of safety of 4 on
the ultimate wet strength is recommended.

BOAT HULL DESIGN 2-25

All of the foregoing may sound very difficult, but fortunately it is not usually necessary
to perform a detailed analysis on bulkheads except for special cases where large local loads
are to be supported. Usually unstiffened 1/2 to 3/4 inch thick plywood for cruising boats
and 1/4 to 3/8 inch thick plywood for smaller craft, or lightweight sandwich construction
of equal rigidity may be used, This equivalent rigidity is considered necessary since one
of the most important functions of a transverse bulkhead is to provide sufficient stiffness
to maintain the shape of the hull.

Ballast Attachment: The attachment of localized heavy ballast occurs in some sail-
boats, This ballast, usually in the form of lead or grey cast iron is attached to the bottom
of the hull. The attachment is normally made with bolts cast into the ballast and passing
through the heavy laminate at the bottom of the boat. The design loading used to check
the attachment and the surrounding structure is generally taken as twice the weight of the
ballast to allow for acceleration due to heave and pitch. The effect of buoyancy is ignored
as an added safety factor. Since conservative design of this attachment costs very little
and provides added safety at a vital point, a factor of safety of 4 on the ultimate wet strength
of the materials involved is recommended,

For ready reference a summary, Table 2-2, of the design loadings and factors of
safety recommended in this Chapter has been prepared.

TABLE 2-2 SUMMARY OF DESIGN LOADS AND FACTORS OF SAFETY

Boat Type Shell Framing Decks Transom | Gunwale_ | Bulkhead
Weather and Interior and |
Bottom Side Bottom Side *W.T. Cockpit|**N.T. Cockpit | i
Small Open Use Std Use Std Nominal- | None None 40 psf OBC Std | Weight of |None
Boat Laminate |Laminate | use with FS. =4.0 Table 2-1] Boat on
(Low Power) p 2-13 |p 2-13 flat bottom center of
only long span
| p 2-14 F. S.-=2. 0
High Power Impact 75-80% Impact Water - Waterhead Same as OBC Std |Same as /Nominal Size
Planing Pressure | Bottom Pressure | head 6" 2' of water above Table 2-1 | above and Local
(Figs. 2-14] Thick- (Figs. 2-14] above F, 8. =4.0 and Fig. Load
& 2-15) ness & 2-15) deck 2-17 F, 5, =4.0
BS) =h.5 F.S. =1.5 | edge F. 5S, =6.0
FS. =4.0
ae a t a = — —_s >
Cruising Waterhead |Same as Same as Same as Same as Same as Same as_ | None Same as
Sail to Coaming|Bottom Shell Shell above above Shell above
in heeled
condition
F,S, =4.0
= + + ie a
Cruising Waterhead |Waterhead | Waterhead| Water - Same as
Displacement | 2' above 6'' above same as head above for
Low Power Deck Fwd |Deck Shell same as Same as Same as outboard | None Same as
Sta.7. 6" |F.S, =4.0 |F.S.=4.0 | Shell above above power, above
above Deck F,S. =4.0 same as
Aft Sta. 7 shell for
F, 8, =4. 0 inboard
if

* W.T. denotes watertight.
** N, T. denotes non-tight.

2-26 BOAT HULL DESIGN
DESIGN EXAMPLES

The design loadings and methods explained and illustrated in this Chapter can be used
for guidance by the designer in determining the scantlings of major structural components
and other important details for fiberglass boats. A study of Chapter 3, ''Design Details" is
strongly recommended before beginning a fiberglass boat design, since this material, like
wood and other laminated materials, requires proper structural arrangement of panels and

framing members.

Examples of typical structural calculations are given for five different boat types as
follows: rowboat, open sailboat, high speed runabout, cruising sailboat, and power cruiser.
The calculations are based on the design loads and factors of safety summarized in Table
2-2. The physical properties values used for the various types of fiberglass reinforcement
are the low average values given in Tables 5-6 to 5-14. These values have been selected
for consistency in the design examples and are suggested when test data are not available.
When it is desired to use higher values to save weight, cost and building time, it is neces-
sary that tests be made of the actual production laminate to justify these higher values.

Since the purpose of this manual is to guide the designer in the selection and application
of fiberglass laminates, the calculations are based on simplifying assumptions, both for the
loads applied and the methods of analysis. These simplifications are also justified to some
extent by the uncertainty regarding actual service loads which may occur, particularly for
the boats of the sizes discussed.

The methods of calculation used in these design examples are standard methods of
analysis which are readily available in many standard texts, and are therefore notreferenced.
Those calculations which are different from the standard methods because of the character -
istics of the material, such as section modulus calculations, are similar to the methods de-
veloped and explained in Chapter 6.

Because the design examples are intended to illustrate structural calculations, details
are not indicated except where necessary to provide structural arrangement for analysis.
Selection of a particular detail or method of construction for analysis does not imply that
the detail chosen is the only one which may be used.

In all the design examples, unless otherwise noted, reinforcement weights are:
Cloth - 10 ounces per square yard
Woven Roving - 25-27 ounces per square yard
Mat - 2 ounces per square ft.

DESIGN EXAMPLE 2-1. ROWBOAT

This rowboat is a common type suitable as a tender for a large yacht, or for fishing
and general pleasure and is usually used in protected waters. If used as a work boat or a
utility tender for a large commercial fishing vessel the scantlings should be suitably in-
creased, This design allows for the use of a 5 horsepower outboard motor.

Principal Dimensions - See Fig. 2-19 for details.

Length Over-all: 13 ft. - 0 in.
Beam: 4 ft. - 6 in. maximum

yeoqmoy “61-2 ‘STA

TWIVLIG LYWMHL ONY 3 1VMN9

la

13s —{—

——— ) 7
ve | | ya ma
oe ZZ / 4
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SLVNIWV1 SSV1943814

oan / 4
iS zy
3 y
NOILOSS 3SYSASNVY
TIWL30 WOSNWYL
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3409 GoomAdd \
JLWNIWY1 1173HS a3qanoa
— AB G3WHO4 Days
WIdalLvW NOILV¥L0714—— Pas /
. 311 408d ie

To a an Ss ee ee ee ee
\
/ oP
|
I

\
WIy3aLvW NOILV1014—- vA \

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rd — / /
; LauvMHi—“ LYWMHI~
/

SLYVMHL ONY 2TWMNNO HLIM /

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W930 3404 11vwWS—

WiIYSLYW NOILVLO14

/ = 7
| / \ _/f WOSNVdd.

2-27

2-28 BOAT HULL DESIGN
Summary of Scantlings
Shell Laminate: 1 ply cloth on outboard face, 1 ply mat and 1 ply woven roving.

Transom: 1-3/8 in. thick, as required by OBC Standards (14). Sandwich construction -
1-1/4 in. thick waterproof Douglas fir plywood core, 1 ply cloth and 1 ply mat on aft face;
1 ply mat and 1 ply woven roving on forward face. Mat plies placed next to plywood for
maximum bond and to reduce porosity.

Gunwale, Thwart and Fore Deck: Molded in a single unit of 1 ply cloth and 2 plies mat.
Gunwale to be a channel section with 2 in. flanges and web; similar to Fig. 3-17. Thwart
to be a channel section with a 12 in. web and 3-1/2 in. flanges with an additional ply of mat
on the flanges, Fig. 2-20.

Design

Gunwale: Design Loading - Assume weight of boat as a concentrated load at the center
of the longest span.

Factor of Safety = 2.0
Weight of Boats; estimated = 150 lbs.
Maximum Span = 6.5 ft.

Bending Moment, M = PL. (27am)

150) 6.5: 12
\
Use a premolded U-shaped gunwale, similar to Fig. 3-17, with a 2 in. horizontal

web and 2 in. vertical flanges. The laminate should consist of 1 ply cloth on top and
2 plies mat.

M = 2925 in.-lbs.

By separate calculations, not shown, the critical stress is found to occur at the
inboard flange of the gunwale.

Section Modulus, Z, at the cloth = 0.265 in.?
Stress = Bending Moment eee ee (2. 8)
Section Modulus Z
2925 ae
fi = — wall si
Sa ees
Ultimate Stress, cloth in tension, Fy, = 24,100 psi (Table 5-6)
Ultimate Stress A Fey (2.9)
= 3 Fas. = ae :
Be ee Eanes Calculated Stress ” f+
2), 100

F.S. =
11,033

2.18 Satisfactory

BOAT HULL DESIGN 2-29

Thwarts: Consider as a simply supported beam loaded by two 200 pound men, sitting
at one-third of the span from each end.

Factor of Safety = 1.0
Bending Moment, M = P x 2 (2. 10)
2 x Sh
i = ae ee 3600 in.-lbs.
3

1 PLY CLOTH

meer St

[amen]
7 PLIES = Ae

“3 PLIES MAT

Fig. 2-20. Thwart cross-section

Consider a channel shaped thwart integrally molded with the gunwale as shown in Fig.
2-19. The cross-section and laminate construction shown in Fig, 2-20 gives the following
results: Ultimate tensile stresses from Table 5-6,

Stress in Cloth - tension at bottom edge of flange = 5350 psi
Factor of Safety = 2,100 _ 1.5 Satisfactory

5350
Stress in Mat - tension at bottom edge of flange = 2250 psi
Factor of Safety = = = ).9 Satisfactory

Tensile and compressive stresses are used instead of the flexural stresses given in
Chapter 5 because the flexural stresses are obtained from tests of bending in a plane
perpendicular to the plane of the laminate. No experimental information is available
regarding flexural stresses when the bending is in the plane of the laminate.

DESIGN EXAMPLE 2-2. OPEN SAILBOAT

This sailboat is intended for use as a day sailer and for class racing. It is a sloop
rigged, centerboard boat and similar in size, rig, and general layout to many classes in
widespread use. The transom is to be suitable for a 5 horsepower outboard motor.

Principal Dimensions - See Fig. 2-21 for details.

Length Over-all: 14 ft. - 0 in.
Beam: 5 ft. - 2 in. maximum
Sail Area: VSL son hts

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BOAT HULL DESIGN 2-31
Summary of Scantlings
Shell Laminate: 1 ply cloth on outboard face of laminate, 1 ply mat, and1 ply wovenroving.
Centerboard Trunk: Same laminate as shell.

Centerline Stiffener: 1/2 in. deep x 1-1/2 in. wide, parallel roving stiffener in
lieu of keel forward and aft of centerboard trunk.

Thwart and Gunwale: molded in single unit of 1 ply cloth and 2 plies mat. Gunwale to
be’channel shaped with 2 in. flanges and web. Thwart to be 8 in. wide with 2-1/2 in. verti-
cal legs with additional 2 plies of mat on each leg.

Chain Plate: to be 1-1/8 in. wide x 3/16 in. thick stainless steel, connected to a 5 ply
woven roving fiberglass bracket by three 1/8 in. stainless steel bolts.

Mast Step: to be 12 in. x 12 in. and made of mat.

Mast Partner: to be similar to the thwart except for a local increase in way of the mast,
and to be molded in single unit with thwarts, gunwale and fore deck.

Design

Thwart: Consider supported at side, and on centerline by centerboard trunk; loaded by
a 200 pound man at the center of the unsupported span. Except for the bending moment
equation, the calculation is similar to that for the rowboat, Design Example 2-1, and is
not shown.

Use an 8 in. wide, channel shaped thwart with 2-1/2 in. vertical legs. Use 1 ply ofcloth
and 2 plies of mat on the seat, 1 ply of cloth and 4 plies of mat on the vertical legs.

Gunwale: The gunwale of a boat of this type must be wide enough for the crew to sit on
and is assumed to be 4 inches wide. By comparison with the design example for the rowboat,
this will obviously be strong enough, The construction adopted, shown in Fig, 2-21, is
Similar to that used for the rowboat except that the laminate is doubled under at the inboard
edge. This is to provide a "hiking'' hand grip without a rough edge for the crew members.
Vertical loading due to a person stepping on the gunwale need not be checked, since the boat
is not stable to permit such use.

Transom: Since the use of the 5 horsepower outboard motor is contemplated, the
transom may be designed the same as for the rowboat transom. The motor will be mounted
on a bracket attached to the aft face of the transom

This will result in the following:

OBC Standard thickness = 1-3/8 in., from Table 2-1.

Use 1-1/4 in. plywood core; 1 ply cloth, 1 ply mat on aft face; 1 ply mat, 1 ply woven
roving on forward face,

Rigging Supports: The size of the stays on a sailboat is selected to resist the loads
imposed by the sails to cause an overturning moment equal to the maximum heeling moment

aye BOAT HULL DESIGN

available. For illustrative purposes, it is assumed that this calculation has been made and
the stays chosen are 3/32 in. diameter, 1 x 19 stainless steel wire rope with a breaking
strength of 1200 pounds (17), The chain plates are designed to the yield stress of the ma-
terial and the supporting fiberglass laminate to a factor of safety of 2.

Stay Connection:
Stainless steel chain plate and pin;
Tensile Yield Stress, Fy, = 40,000 psi (Reference 18)

Shear Yield Stress, Fgy = 0.6 x Fyy = 24,000 psi

Consider pin in double shear and load P = 1200 lbs.:;
Required pin area, Ay = = (2. Li)
ox "sy
A, = — 2200 = 0.025 sq. in.

e 2 x 2,000

Use 3/16 in. pin diameter; Area = 0.035 sq. in.
Chain Plate:

Thickness required for bearing of pin;

Bearing Yield Stress, Fpy = 1.6 x 24,000 = 38,00 psi

Bearing load, P = 1200 lbs.

t= = B - (2. 12)
By

te eee el eee ee, Gos en,

38,100 x 0.1875
Use 0.1875 or 3/16 in. thick plate

Chain Plate Fastening to Hull: The chain is passed through the gunwale and fastened
to a transverse bracket, which is connected with bonding angles to the shell. The bracket
is used in lieu of bolting directly through the shell for appearance.

Assume the bracket is made of 5 plies of woven roving, and the bolts are 1/8 in.
diameter stainless steel. Design for the wire to fail without permanent deformation of
the laminate:

Total load, P = 1200 lbs.
Laminate thickness, t = .185 in. (Table 5-2)
Rearing area per bolt = Bolt diameter x Laminate thickness
Ap = Dxt (2 ears)
An = 0.125 x 0.185 = 0.023 sq. in.

BOAT HULL DESIGN 2-39

Allowable Polt Bearing Stress - from Table 3-2 and for no permanent deformation:

Fpqa = .Ol)1 x Laminate ultimate tensile strength
Fpa = -Olil x 32,900 = 21,070 psi - Table 5-6 for Ultimate Tensile Stress
Allowable bearing load per bolt = Bearing area x Allowable bearing stress
Baa 20 oP pa (2. 14)
Pog = 0.023 x 21,070 = 488 lbs.
Required number of bolts ; N =~ (27s)
PBa
Y= i = 2.16 bolts

Use three bolts.

Chain Plate Width:

Total Width = Diameter of pin + gee eS ee
thickness of plate x tensile yield stress
b= Det pn eee
t x Fty (2: 16)
t= in. = 0.1875 in.
16
b = 0.1075 + Bigs eee, 5 Os Ui caret sit

0.1875 x 0,000
Use a 1-1/8 in. wide x 3/16 in. thick plate minimum.

Required Vertical Length of Bracket: Assume load carried in shear by shell to bracket
connection, which is made of two 2 in. x 2 in. fiberglass polyester resin angles. The angles
are made of one ply of 1-1/2 ounce mat against the bracket and shell and two plies of woven
roving. The connection between the angles and the shell and bracket is in secondary bond
with polyester resin.

Ultimate Bond Shear Stress, Fosu = 1000 psi
Factor of safety, F.S. = 2.0
. = lee I eh
Vertical length of bracket, L = ————~——— (Den)
Bond Width x Fasu
yp = —t200xX2> . 0.60 in.
2x 2x 1000

The shear connection is obviously not critical so the bracket is made 8 inches long to
accommodate the length of the chain plate and provide a reasonable taper at the bottom as
described in Chapter 3.

Hull Support for Chain Plate: The slope of the side stay places a horizontal load on
the gunwale causing bending and local compression,

2-34 BOAT HULL DESIGN

The horizontal load is 210 pounds, and the distance between the mast partner and thwart
is about 4 ft. 6 in. Following the same procedure as for the gunwale for the rowboat:

RT (ex

Bending Moment, M= += = 210 xh = 280 in.-lbs. (207)
At ai

Factor of Safety = 2.0

Ultimate Stress of Mat in Tension, Fy,, = 11,000 psi (Table 5-6) *

Allowable Tensile Stress = Ultimate Stress. a = tu (2, 9a)

Factor of Safety ; a F.S
11000 5
Fin = ; = 5500 psi
Required Section Modulus = Bending Moment = , 7 . M (2. 8a)
Allowable Stress ite
as _) F260" & Pa
Z = raya) = 0.515 cele
Section Modulus of Gunwale, Figure 2-21, Z = 1.566 in? Satisfactory

For an explanation of the use of tensile rather than flexural stress,
see Design Example 2-1, gunwale and thwart design.

Finally, a check must be made of the shear loading on the horizontal web of the gunwale.
Consider the horizontal load of 210 pounds to be applied by the bracket to the web.

Ultimate Shear Stress of Woven Roving, F,, = 7500 psi (Table 5-14)
Factor of Safety = ?.0
Allowable Shear Stress, f, = 3750 psi

Area = Thickness of Laminate x depth of gunwale x 2

in

A = 0.113 x h.Ox 2 = 0.90) in.*
Stress, f. = P (2. 18)
a A
210 a ee
f — 232 psi Satisfactory

Mast Support: The mast is subjected to loading from two sources. Loads in the hori-
zontal plane from the sail and boom, and vertical and horizontal loads applied by the stays.
The stay loads are of two types; the forestay being loaded primarily by the jib and the side
stay being loaded by the horizontal load at the top of the mast.

The mast is supported by the mast step at the bottom of the hull which resists the
vertical compression in the mast, and also by the mast partner which is a horizontal
Support reducing transverse bending in the mast. The horizontal load at the mast partner

wo

BOAT HULL DESIGN -35

is relatively small and may be ignored. The vertical load may be approximated by assuming
the forestay and one of the side stays to be at the breaking point.

Taking the vertical components of the 1200 lbs. breaking load, the following vertical
loads are found:

From the side stay, P, = 1180 lbs.
From the forestay, Pr = 1160 lbs.
Total Py, = 23h0 lbs.

Considering the built-up mest step to be of mat laminate:

Base of mast assumed 2 in. x 2 in. Mast base periphery, i, = 8 in.
Compressive Stress, f, = 2340 = 5&5 psi Setisfactory
ee D
Pa
; me Load = Bu
Shear Stress | = = —————______-—_____— > f, = — (2, 19)
thickness of shell x mast base periphery t x Ip
Use Factor of Safety = 2.0

For discussion of Factor of Safety see chain plate support.

Allowable Shear Stress, Fg = 200 = 1950 psi (Table 5-14)
9

92) 7 ‘ te)
C340 = O47 in.?

Required shear area, Ag
950

5

Minimum thickness of bottom of hull:
h7 See eae. a ; ye :
t+ = 20 = .059in. This is less than the shell thickness previously
6 specified and is satisfactory

In order to avoid creation of local hard spots, see Chapter 3, the centerline stiffener
will be widened immediately under the base of the mat mast step. This extra width is
tapered off to the normal width to form a 12 in, wide reinforced area.

The Mast Partner: The mast partner is made of the same scantlings as the thwart,
with a local increase in thickness to about 1/2 in. in way of the mast.

DESIGN EXAMPLE 2-3, 19 FT, RUNABOUT

This runabout is representative of the type of boat which has had the most widespread
application of fiberglass construction. It is intended for pleasure use, including day trips
in relatively open water, and for towing water skiers. The boat is somewhat larger than
the majority of its type, but the design principles illustrated are, of course, applicable
to the smaller sizes.

Principal Dimensions - See Fig. 2-22 for details.

Length, Over-all: 19 ft. - 0 in.

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2-36

BOAT HULL DESIGN aor

Length, Water Line: 18 ft. - 6 in.

Beam: 7 ft. - O in. maximum
Draft, at rest: co} alias
Speed = 38 miles per hour
Power = 2 outboard motors at 50 horsepower each

Summary of Scantlings

Shell Laminate: Bottom forward of Station 7 and side forward of Station 4-1/2; 1 ply
cloth on outboard face of shell, 3 plies 1-1/2 ounce mat and 1 ply woven roving.

Note: For rugged service, where maximum impact strength is required, a higher
strength laminate of 1 ply cloth, 1 ply 2 ounce mat, and 3 plies of woven roving could be
used with a slight change in longitudinal size.

Bottom aft of Station 7 and side aft of Station 4-1/2; 1 ply cloth on outboard face of
shell, 2 plies 1-1/2 ounce mat, and 1 ply woven roving.

Note: Same note as above applies except use 2 plies of woven roving.

Shell Framing: Longitudinals No. 1, 2, 3 and 4 - Size as shown on Fig. 2-22. Forward
of midship transverse, 5 plies of woven roving. Aft of midship transverse, 6 plies of
woven roving.

Longitudinals No. 5 and 6: 2 in, deep x 2 in. wide with 4 plies woven roving.

Deck Laminate: Fore Deck, Side Coaming, Motor Well and Transverse Midship Island:
1 ply cloth on top of deck, 2 plies 1-1/2 ounce mat, and 1 ply woven roving.

Deck Framing: Fore Deck, 1 in. deep x 4 in. wide. 2 plies woven roving.

Cockpit Deck: Sandwich construction, core 1/4 in. thick. 1 ply woven roving top and
bottom; 1 ply cloth on top, optional - for appearance.

Transom: Sandwich construction; 1-1/2 in. Douglas fir waterproof plywood core.
Laminate; after face, 1 ply cloth, outboard, 2 plies 1-1/2 ounce mat; forward face, 1 ply
woven roving, inboard, 1 ply 1-1/2 ounce mat against plywood. Increase thickness at motor
support area as specified by OBC standards, Table 2-1.

Bulkheads: 1/2 in. thick core, 1 ply cloth each side, 1 ply 1-1/2 ounce mat each side
against core.

Deck Connecting Angles: 2 in. x 2 in. angle, 5 plies of woven roving with polyester resin.
Design

Bottom Snell Laminate: The bottom shell design loads are taken from Figs. 2-14 and
2-15. An example of the calculation for maximum design pressure is given, and the com-

putation for the shell laminate are arranged in tabular form for convenience, Table 2-3.

The bottom shell laminate is given for two types of laminates, Type A and Type B.
As explained previously, the Type A laminate is the more expensive, but has higher impact

to

-38 BOAT HULL DESIGN

resistance to floating objects than the Type B. Since the service requirement of this boat is
for normal pleasure use, the Type B laminate as specified above is considered satisfactory.

Typical Design Loads:

Waterline Length, L = 18.5 ft.
Speed, V = 36 miles per hour
Vx L = 163.4

p. = 25.0 psi

Determine Design Pressure At Station 7

Pp = Py 3 Py ae (273)
p. at 8 in. draft = 5 x 64 = 0.3 psi
H aes Ty
Jhere: = = head of water in ft.
64 = weight per cubic ft. of salt water
Uj = sq. in. per sq. ft.
i = 260 from Fig. 2-15
Pp = 003 + 25.0 x 0060 = 15.3 psi

Laminate Design: Table 2-3. The panels of shell laminate formed by the longitudinal
and transverse supports are long and narrow, and the laminate is considered as a 1 inch
wide beam spanning between the longitudinals. Due to the continuity of laminate and the
uniform pressure loading, the beam is considered to have fixed ends. The maximum
moment occurs at the ends of the span, i.e. at the longitudinal, and places the inboard
face of the laminate in compression as indicated in Fig. 2-10b.

A typical deflection calculation is also shown.

pyih
Deflection; d= 2 Shear deflection not considered (2. 20)
36) EI
Assumed allowable d = sEyp = 1.81 x 106 (Table 5-10)
100 * WR

Type A Laminate - Forward Station 5

3 (5.3)

a = 25. yer = 0.06 algal
38 x 1.61 x 10° x .000L6

Allowable d= 222 v= <053sin.
100

Calculated deflection is high, but acceptable because of innerbotton.

BOAT HULL DESIGN

Side Shell Laminate:

TABLE 2-3. BOTTOM SHELL
Location [Max. Clear Bending Moment |Section Modulus Laminate
Dist. Betw. - PD x Lé 7 = FSxXM_1.5M | (Figs. 6-31
Long'ls. L Pp deo) Foo = Fou *) ~~ and 6-32)
(In. ) (psi) _|__(in, -Lb. ) (In. 3) (2822) |
Fwd of | dD, 3 20. 3 59.4 ee 0. 0038 Type A - 3 plies
Station 5 of woven roving or
Zo = 0. 0029 Type B -4 ounces
f mat -use 3
Zn = 0.0043 (|?
a plies of 1-1/2
ounce mat
\At 6 Deed 45.9 Zp = 0. 0029 Type A - 2 plies
Station 7 of woven roving or
Coy eee Type B-3ounces
Zm = 0. 0034 of mat - 2 plies of
1-1/2 ounce mat
At 7 10.3 42.1 Za = 0. 0027 Type A - Same as
Station 8 above or
Zo) = 0.0021
cl Type B- Same as
Ze = Op0082, \lapove
At 8 O00 Ziad Zyp = 0.0018 * Type A -2 plies
Station 9 S, of woven roving or
| Paige EN * Type B - 2 ounces
| bu = Os0021 of mat-1ply2 -
ounce mat
sell a eee a

For practical reasons, carry the laminate required at
Station 7 all the way aft to the transom.

Table 2-4.

23,700 psi for woven roving
= 31,100 psi for cloth
= 20,500 psi for mat

Table 5-9

The side shell laminate is determined on the basis of
the bottom laminate thickness, except in the area forward of Station 4-1/2.

Forward of this

point the chine disappears, the laminate is in an area of high impact and the bottom laminate
is carried to the deck edge.

2-40 BOAT HULL DESIGN

TABLE 2-4. SIDE SHELL

Location Bottom Side Thickness Laminate Actual
Thickness = 0.75 x Bottom Selected Thickness
at this Thickness
Location

(In. ) (In. ) ae (In, )

Forward of This is in the impact area, Same as bottom laminate

Station and is considered as bottom

4-1/2 laminate

Stations Oma 0.134 Type B - 2 0.137

Aq /2to 7 plies 1-1/2

ounce mat
Aft Ome 0.103 Reduction to 0.137
Station 7 1 ply mat
results in in-
sufficient
thickness -
use Type B -
2 plies 1-1/2
Ecohle ounce mat

Framing: Bottom Longitudinals, Table 2-5. The bottom longitudinals are considered
as fixed ended beams, due to continuity. The design load is obtained from Fig. 2-15, and
is considered as a uniform load applied to the width of shell supported; thatisa width equal
to the longitudinal spacing. A typical design pressure calculation is shown and the calcula-
tions for the longitudinals are given in Table 2-5. The maximum moment occurs at the
support point and places the inboard face of the longitudinal in compression. As noted in
the description of the design data sheets giving stiffener properties, Chapter 6, the woven
roving at the inboard compression face is the critical material.

Typical Design Loads: For longitudinals No. 3 and 4 between the bulkhead at Station 3
and the transverse island at Station 5-1/2, Fig. 2-22.

Spe ee ee a

(2. 5)
Pre = 25.0 psi - See bottom shell calculation
i 0.3 psi - See bottom shell calculation

F, and F; are from Fig. 2-15

BOAT HULL DESIGN 2-41

At Bulkhead, Station 3

aa = 1,00
Fy, = 0.38
Py = Oss + 25.0 x 150 2 0,38) = «958 pst

At Transverse

F, = 0.93
a
ee = 0.40
Pp = 0.3 + 25,0 x 0.93 x 0.40 = 9.6 psi
. D Fit Bo)
Average Design Pressure pp = 28+ 9 = 9.7 psi
2
TABLE 2-5. BOTTOM LONGITUDINALS
Longitudinal Location Max, Clear Width of Bending Section Modulus Required Stiffener
Number Distance Shell Moment =_— (Fig. 6-37)
Between Supported oe PpxsL2 7-15 xM Depth] Width | No. of plies
Transverses s Py 12 “15,800 4 at of woven
L (2.21) Top | roving
(In, ) (In. ) (psi) | (In. -Lb. ) (In.3) (2.22) | in.) | In.)
Bulkhead to 51 7.5 9.7 15, 800 1.50 3 1-1/2 5 ee
Transverse
Island
Transverse 91.5 a) 4.9 32,500 3. 09 4 1-1/2 6
Island to
Transom
Similar to
No. 3
Between 31 12 520 8, 700 0. 83 2 2 4%
Bulkheads
Similar to
No. 6

=

* These longitudinals are considered bottom longitudinals in this area because they are subject to impact loading.

** Fig, 6-37 does not have the proper stiffener laminate to shell laminate ratio for these stiffeners, When height
limitations make this necessary, the stiffener laminate should be considered as controlling and a margin allowed
in selecting a stiffener. The section modulus for the proposed stiffener - shell combination should be calculated

separately.
{ Ultimate compressive stress, aie from Table 5-11.

The longitudinal stiffener sizes determined from the bending moments must be checked
for shear. A typical calculation is shown. The remaining stiffeners have been checked
and found satisfactory.

2-42 BOAT HULL DESIGN

ener _ VQ
Maximum shear, f, = a (25273)
For longitudinal number 3 between the bulkhead and the transverse island:

Vos eure = (Gi aoe Sl = eto s (2. 24)
2

Stiffener Properties:

Size: 3 in. deep x 1-1/2 in. wide x 5 plies of
woven roving, from Fig. 6=37

Thickness of 5 plies of woven roving = 0.185 in. (Table 5-2)
Lr 23 0 in. This value is based on woven roving equivalence
and all material inboard of the neutral axis is woven roving.
Therefore no modulus connections are necessary.

= a AES: in.
Aap

Distance to neutral axis y = - = “ =P OO ns (2.25)

Moment of area inboard of neutral axis about neutral axis

AD
i]

1 7R vA
= 1.5 x 0,105 = (2.05 = a ) + 2x 2,06 x 0.185 x the ee basis) shies
Deane OOS = reo Olan.
Maximum shear, f, = 1852 x 1.33 = 1852 psi
s B70 Keel 10
Ultimate Parallel Shear Stress for Woven Roving, ee = 7500 psi (Table 5-14)
Factor of Safety = 1.5
Cc

Allowable Parallel Shear Stress, f, = tes = 5000 psi Satisfactory

Finally the stiffener must be checked to ensure that the allowable deflection is not ex-
ceeded, A typical calculation is shown; the remaining stiffeners have been checked and
found satisfactory.

Deflection, d = = a = at Shear deflection not considered (2. 20a)
oh E
For longitudinal number 3 between the bulkhead and the transverse island:
mn
afl x 7.5 (51) = Ons in,

oot Ale
BOh s2.06 x LO? sc 356
Allowable deflection, d = yay = 0.51 in. Satisfactory

BOAT HULL DESIGN 2-43
Side Longitudinals: The side longitudinals are designed to support a pressure equivalent
to a head of water to 6in. above the deck. The longitudinals are designedas uniformly loaded,

fixed ended beams.

Consider Longitudinal No. 6 between the transverse and the bottom of the motor well.

Stiffener Spacing = 10.5 in.
Load = head of water to 6 in. above the deck at side
Factor of Safety = 3 Foy = 15,800 psi (Table 5-11)
Pressure = Head x Density of Sea Water
1.58 x oh = s
jo) ee = f(s} jeieat
144
Load per inch = .703 x 10.5 = 7.38 opi
2
Bending Moment, M = = (2.21)
2
my = 2238 x (81)° = 034 in.-lbs.
2
Required Section Modulus, z = 2:5: xM (2. 22)
Fou
a fethOgu oe.
Z = 15,500 T.O2 ante

From Fig. 6-37, use 1-1/2 in. widex2-1/2in. deep stiffeners with 5 plies of wovenroving.

Decks: Fore Deck - Laminate: Similar to shell laminate; Framing: 3 equally spaced
deck longitudinals, Loading: Head equivalent to 2ft. of water = 0.89 psi, Factor of
Safety = 4. 0.

Laminate Design: The panel is considered fixed ended due to the continuous load and
continuity of the laminate.

Stiffener spacing = 19 in.
Stiffener width = } in.
Unsupported span of laminate = 15 in.
9 IN? .
Bending moment, MN = Se = 16.7 in.-lbs. (2090)
Required Section Modulus, Z = a (2229)
bu

Ultimate Flexural Stress, Fpy from Table 5-9

g = 420 x 16-7 = 09,0033 in.3 Mat
20,500

WO cer
23700

Bee) Onxeelornt
31, 100

0.0028 in.3 Woven Roving

N
"
il}

0.0021 in.3 Gloth

"

2-44 BOAT HULL DESIGN

From Fig. 6-32, Type B laminate with 2 plies of 1-1/2 ounce mat.

Framing:
Spacing = 19 in.
Length =) 3 in.
Load ver inch = 0.69 x19 = 16.91 lbs. per in.
Bending moment, M = Be = eee = 1354 in.-lbs. (2.21)
Required Section Modulus, Z = a = .3l43 ine? (2, 22)

From Fig. 6-37, use 1 in. x 4 in. stiffener with 2 plies of woven roving.

The deflection of the Fore Deck is not checked since it is not a normal walking area in
a boat this size.

Cockpit Deck:

b
ee ee oe
a Sales a
ai
Yee ee

Fig. 2-23. Cockpit deck sand-
wich cross-section
Design Load = 0 psf = 0.28 vsi
Maximum Span = 8 in.
Construction - Use sandwich construction for lightness and rigidity.
Try a 1/4 inch thick core with one ply of woven roving on each face.

For 1 in. strip bending moment:

yo = BL2 2 0.26 x (8)?
2

1D 7 = 1.49 in.-lbs. (7h)

The dimensions for the cross section indicated in Fig. 2-23 are:

b = lin.
hy = 0.25 Ty.
h = 0.25 + 0.07) = 0.32) in.

BOAT HULL DESIGN 2-45

Assume adequate bond between core and faces and that core is not
effective in flexure, the section moculus is:

b x (h3 = hy3)

Dec uiOny MOdUm Sse =e nee (2. 26)
6h
Sor 3
pe, Boe eet NO ae
Ox Oegeli 1.944
Stress in facings, f, = 1.09 165.6 psi
2 ac 009
Maximum Shear; V = = (2, 24)
Vo = 30,28 x 8) =) 2.2l) lbs.
Shear Stress in Core, f, = 3 x - (2. 27)
3 262k ;
hi == SS =
3 ae OO dae 35 1365) psi.
Required ultimate core shear stress = ite > SASS
= 13.5xh = 5h.0 psi Satisfactory

The 1/4 in. thickness is chosen as the minimum for workability. The core material
may be of any of those discussed in Chapter 4, with preference given to a solid material
which will be able to resist the shear loads and high local impact loads as would be caused
by a person jumping into the boat, or heavy objects being dropped on deck.

If desired for appearance reasons, a ply of 10 ounce cloth may be added to the top of
the deck sandwich. Caution should be exercised to avoid too smooth a surface in walking
areas for safety reasons.

Deflection Check: As explained in Chapter 6, a conservative estimate of the deflection
of a sandwich section is the sum of the bending deflection of the faces alone plus the shear
deflection of the core alone.

py 6PLe
Deflection, d = cess enue (2. 28)
38 Erle DGche
Assume a cellular cellulose acetate (CCA Foam) core
of 6 lbs per cubic ft. density
Shear Modulus, Ge = Peeo x 103 psi (Table 5-17)
Area of Core, Ag = 1x 0.25 = 0.25 in.@
are 0.28 x 6 pb de G28 e108
38 x 2.06 x 100 x .009 x «324 HOx 1.25 x 107 x 0.25
2
= O.COM OeOLG= =O, Oli/ als
Allowable deflection, 4 = 2: = —2. = 0.0 an. Satisfactory

200 200

2-46 BOAT HULL DESIGN

Side Deck and Deck Edge or Gunwale:
Vertical Loading - Assume a 200 lb. man at the center of the longest span -
Factor of Safety = 4.

200 LBS

| A=

ht i
63"

a ” - SECTION A-A

Fig. 2-24. Gunwale - assumed section for vertical loading

Bending Moment, M = - = 200 4 83 = 3150 in.-lbs. (Be)

Consider the same laminate as the Fore Deck.

From a detailed calculation the cloth in tension is critical
and controls the strength of the section,

Ultimate tensile strength Fy, = 2,100 psi. (Table 5-6)

Consider only the vertical flange to be effective:

Section Modulus, Z = E = (2. 29)
Required, Z = 3150 x) = 0,523 in? (2522)
24,100

To find required depth, h, where t is the equivalent thickness
if the laminate were all cloth

pe = $2 = & x 0.523 - 31.) sq. in. (2. 29a)
t 0.100
h = 5,60 in.; use 5-5/8 in. deep coaming; Fig. 2-25

Horizontal Loading: Assume weight of boat concentrated at center of longest span;
island to motor well.

From a detailed calculation the cloth in compression is the critical material. For
an explanation of the use of tensile and compressive stresses, rather than flexural
stresses, see Design Example 2-1; Gunwale and Thwart Design.

Factor of Safety = 2.0

2000 lbs.

i]

Weight of Boat; estimated

Bending Moment, M = = = so x 3 = 31,500 in.-lbs. (51)
Ultimate Compressive Stress, ee = 18900 psi from Table 5-11
; 3 1500 2 :
Required Section Modulus, Z = 3 : ae = 3.33 in? (2.22)

Actual Section Modulus of section shown in Fig. 2-25; from
detailed calculation, Z = 4.65 in.3 Satisfactory

BOAT HULL DESIGN 2-47

| PORTION OF SHELL
} CONSIDERED EFFECTIVE

Fig. 2-25. Gunwale - assumed cross-section for horizontal loading

Transom: As a first trial use the dimensions recommended by the OBC for the over 40
horsepower range, Table 2-1.

Thickness = 1-1/2 in. minimum for entire transom
Reinforcing at motors

Thickness = 2-1/4 in.

Inboard Area - 10-1/8 in. horizontal dimension

- 3-5/8 in. vertical dimension

Outboard Area - 12-1/2 in. horizontal dimension
- 11-1/2 in. vertical dimension

Use a sandwich construction.
Plywood core - 1-1/2 in. thick Douglas fir

Outboard Laminate - 1 ply 10 ounce cloth on aft face
2 plies 1-1/2 ounce mat against plywood

Inboard Laminate - 1 ply woven roving on forward face
1 ply 1-1/2 ounce mat against plywood

Design on a Strength Basis: For 38 miles per hour - 2 motors at 50 horsepower =
100 horsepower.

Section modulus x Allowable stress _ Z x fp

(2. 6)
Transom Beam B
From Fig. 2-17; 2x fp .q 87
B
Beam at transom = 66 in.
Required Z x fh = 87 x 66 = 572 (2262)

The portion of the transom considered effective is: The plywood core - parallel
horizontal grain plies only; 11-1/2 in. wide; the fiberglass covering for the above width, and
the motor well - a strip adjacent to the transom of width equal to 30 times its own thickness.

The allowable stresses based on a factor of safety of 6, for the various materials are
as follows:

2-48 BOAT HULL DESIGN

Plywood
Basic working stress - Douglas fir plywood in bending = 2000 psi
Ultimate stress, Fp, for lone term loading = basic working stress

x factor of safety on which basic working stress is based (19)

Fou = 2000 x 2.25 = 500 psi

Allowable stress, fy = 500 = 750 psi (2. 9a)
Mat in tension at motor well :

Ultimate stress, Fy, = 11,000 psi (Table 5-6)

Allowable stress, f4 = 11,000 = 1030 psu (2. 9a)

Multiplying the section modulus, from detailed calculations not shown, of each material
by its allowable stress:

Mat - tension on motor well bottom:

Zxf = 6.26 x 1830 = 11,)56 which is greater than 572 (2. 6a)

Plywood - compression on aft side:

Zx f, = 10.10 x 750 = 755 which is greater than 572 (2. 6a)

Satisfactory
Bulkheads: The critical loading on the bulkheads in this boat is the shear load in way
of the cutout under the forward deck.

Check for shear at Section A-A, Fig. 2-26.
Use a 1/2 in. core nominal for rigidity.

Consider all shear load carried by laminate, i.e. core is nonstructural.

1723

SECTION A-A

Fig. 2-26. Transverse bulkhead

BOAT HULL DESIGN 2-49

Deck area supported = 28 in. x 30 in. = 80 sq. in.
Deck loading = 0.89 psi

Sicer icsa, 7 = on = 37 lbs. (2. 24)

Assume cloth laminate:

Ultimate shear stress, Fs, = 9000 psi (Table 5-14)
Allowable shear stress, f, = 9000 = 2250 psi (2.9)
P h
Area required = 37h = 0,166 in. (2.93))
2250
Thickness of laminate faces, t = Area
ax hb
7 @.2 Aisles Rovere
2x6

Use 1 ply of cloth, t = .016 in. on each side. (Table 5-1)

Add 1 ply of 1-1/2 oz. mat on each side for added
resistance to local impact and to improve the
core to face bond.

Deck Edge Connecting Angle: This connection is required to carry the same ultimate
shear loading as the deck laminate.

Reinforcement woven roving for high impact resistance.
Deck Laminate: 1 ply cloth, 2 plies 2 ounce mat and 1 ply woven roving.

Ultimate shear strength per running in.:

Fley = AciFse1 + Amsm * AwrF swr (2. 30)
Where A = area
F'.., = ultimate shear strength, lbs. per in. (Table 5-14)
cl,m,wr = subscripts referring to cloth, mat, and
woven roving respectively
Go 52 x 106
Pso = Powe X —— = Foy ¥ ———S =F, x 1,16 (2.31)
Gyr Sx 10° a
Gr ho x 106
F hy See a BR eee eee SOs 09) (Ou Sih)
sm ane ae swr “Sx 100 swr
G = shear modulus, psi (Table 5-14)

Ultimate shear strength, F'g, = (1 x .016) 7500 x 1.16 +

(1 x .116) 7500'x 89 + (1 & 5037) 7500 = 139 + 775 + 278
= 1192 lbs. per in.

2-50 BOAT HULL DESIGN

Required thickness of angle, t = Flsy Sine = ;
Re = EOg 7 woo Mims (2.32)
Use 5 plies of woven roving, t = .185 (Table 5-2)

Width of angle legs should be sufficient to transmit this same
shear load, i.e., 1192 lbs. per in.

Ultimate shear stress, secondary bond, Fy, = 600 psi
ee Ft
Width of leg, b=_ Su = 1192 . 40 )9 3;
, eee 5 9 in. (2. 32a)

Use 2 in. x 2 in. for ease in handling.

DESIGN EXAMPLE 2-4. CRUISING SAILBOAT

This cruising sailboat represents a very popular size and type, providing reasonably
comfortable accommodations for four to six people. It is intended for cruising in unprotected
waters and for ocean racing with similar boats.

Principal Dimensions - See Fig. 2-27 for details.

Length,Over-all: 33 ft. - 0 in.
Length,Water Line: 23 ft. - 2 in.

Beam: 9 ft. - 10 in. maximum
Dratt; 4ity — 0 in;,
Rig: Sloop

Auxiliary Power: 6 horsepower engine

Summary of Scantlings

Shell Basic Laminate: 1 ply cloth on outside of hull, 1 ply 2 ounce mat and 4 plies
woven roving.

Bottom shell forward of Station 7 below longitudinal No. 2 similar to basic laminate
except use 5 plies woven roving.

Bottom shell aft of Station 7, from 12 in. below longitudinal No. 1 to keel: similar to
basic laminate except use 6 plies woven roving.

Framing: All stiffeners are hat type.

Depth Width Plies of
lel, In. Woven Roving

Longitudinal No. 1 Bow to Second Bulkhead 3 3 4
Second Bulkhead to Stern 4 3 4

Longitudinal No. 2 Forward of Bulkhead 5 5 4 4
Aft of Bulkhead 5 4 + 6

Longitudinal No. 3 5 3 5
Longitudinal No. 4 5 3 5

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2-51

2-52 BOAT HULL DESIGN

Decks: Sandwich construction; 2 plies cloth on top face, 1 ply 1-1/2 ounce mat, non-
structural core of variable thickness, 1 ply 1-1/2 ounce mat and 1 ply woven roving.

Location Core Thickness
Main Deck - Forward Seine
Main Deck - Cabin Sides 3/8 in.
Main Deck Aft of Cockpit 1-1/4 in,
Cabin Top - Lower Level ain
Cabin Top - Upper Level iain:
Cockpit 1 in,
Interior Decks ain

Built-in Bunks and Lockers in Forward Compartment: 4 plies woven roving.

Bulkheads: 3/4 in. core with 1 ply cloth and 1 ply 1-1/2 ounce mat each side; 4
additional plies of cloth each side locally under mast.

Design

Shell Laminate: The laminate chosen is that referred to as Type A in this manual and
consists of: 1 ply cloth on the outboard face, 1 ply mat, and a varying number of plies of
woven roving.

The laminate selection is based on the excellent laminate impact resistance to floating
objects as previously explained.

The design head of water is taken to 12 in. above the deck edge measured from the
center of the panel, Table 2-2.

Since the panels involved are all relatively long and narrow, the bending moment and
section modulus used are in each case taken for alin. wide strip. This strip is considered
to act as a uniformly loaded, fixed ended beam of span equal to the distance between longitudinals.

Because of the number of areas which must be checked, a tabular arrangement is used
for the calculations; Table 2-6.

Shell Longitudinals: The shell longitudinals are designed as fixed ended beams to with-
stand the same design load as the shell they support. Hat section stiffeners are chosen
because of their greater efficiency due to the high section moduli required. The calcula-
tions have been arranged in tabular form for convenience, Table 2-7. The stiffeners shown
have been checked for shear and are adequate. For a typical shear calculation see Design
Example 2-3.

Decks: All decks are to be of sandwich construction for rigidity. Type B sandwich is
used; Fig. 6-53b. Each deck is checked for stress in the various elements, and for deflec-
tion. The core thickness required is determined for each criterion and the maximum
required is used.

Forward Portion of Main Deck: The largest panel is between bulkhead No. 1 and the
forward end of the cabin trunk.

Panel Dimensions: length = 5 ft.-6 in.; width = 2 ft. -9 in.

2

TABLE 2-6. SHELL LAMINATES
Location Max. Clear | Head to Bending Moment | Section Modulus Type A Laminate
Distance 12: in. Pe cree ae! Required Plies
Between Above pL2 . bu of Woven
Long'ls Deck hx 6) M= me 21) _ uM (2.22)) Roving
10 h Th Fou * (Fig. 6-31)
(In. ) (ft. ) psi (In. -Lbs. ) Req'd. Z in.3
Between
Deck Edge and 18 220 0. 89 24.03 Zur = 9. 0061 es
Long'l No. 1 Gel 0. 0046
Zm = 0. 0071
Long'l No. 1 and 15 3.58 1,59 29,81 2wr 0. 0075 4
Long'l No. 2 Ze1 = 0, 0057
Fwd of Sta. 7 Zn = 0. 0087
Same - Aft of 23 3.67 1,63 71.86 dur 0, 0122 6
Sta. 7 Zo, = 0. 0093
Zm = 0. 0142
Long'l No. 2 and 14 5.0 2,22 36,26 Zwr = 0. 0092 5
Long'l No. 3 Zo, = 9.0070
Fwd Sta. 7 ln = 0. 0108
Same - Aft 19 5.5 2,44 73.40 Zur = 0. 0124 6
Sta. 7 Ze1 = 0.0095
: Zn = 0.0143
Long'l No. 3 and 14 5,92 2, 63 42.96 Zyr = 0.0109 5
Long'l No. 4 Zel = 0. 0083
2m = 0, 0126
Long'l No. 4 - 13 6.25 2.78 392.05 yr = 0. 0099 5
and Keel at cl = 0, 0075
| Centerline Zm = 0, 0114

* F.

= 23,700 psi for woven roving

bu '
= 31,100 psi for cloth
= 20,500 psi for mat
TABLE 2-7. SHELL LONGITUDINALS
Long'l| Location Length Width of Head to Required Stiffener
No. Shell 12 In, (Fig. 6-37)
Supported | Above ae hxs X_ 64 | a _ pL? 2-4% Depth x No. of Plies
Deck Wh 12 15,800 Width Woven
L s h p (2.21) (2, 22) Roving
(In. ) (In. ) (Ft. -In.) (No.-In.) | (In. -Lbs.) (in. 3) (In. )
1 Bhd 1 to 2 80 14-1/2 2-1 13, 41 1,152 1.81 3x3 4
1 Bhd 4 to 5 81 18 2-6 19.98 10,924 enthil 4x3 4
1 Bhd 5 to 7 ee, 22 2-6 24,42 12, 066 3.05 4x3 4
2 Bhd 4 to 5 81 18 4-3 33,97 18,573 4.70 5x4 4
2 Bhd 5 to 7 ck 21 4-3 39. 69 19,610 4,97 4x4 6
3 Bhd 4 to 5 81 15 5-3 34,95 TOP 1109 4.84 5x3 5
4 Bhd 4 to 5 81 15 5-9 38. 40 20,995 5.32 5x3 5

Shell above Longitudinal No. 1 has 4 plies of woven roving.

Shei! Forward of Station 7:

Between Longitudinals Nos. 1 and 2 has 4 plies of woven roving,
Below Longitudinal No. 2 has 5 plies of woven roving.

Shell Aft of Station 7, Below Longitudinal No, 1, has 6 plies of woven roving,

2-93

2-54

BOAT HULL DESIGN

Design Load: p = 2 ft. of water = 0. 89 psi

Flexure:

Considering a 1 in. strip as a fixed ended beam.

pl? _ 0.89 x 33¢

= 8 e j - e
1D 1D O.7 in.-lbs

Bending Moment, M =

Ultimate Stresses, a from Tables 5-6 and 5-11

Cloth; top face in tension Z = L_x 80.7 - 0.013) in.
2ly100
1/, in. deep core required. (Fig. 6-53b)
Woven Roving; bottom face in compression Z = 4 x 80.7 = 0,0232-4an.2
13,900
3/8 in. deep core required. (Fig. 6-53b)
Mat; top face in tension Z = pasee sa 0.029) in.?
11,000
1/ in. deep core required. (Fig. 6-53b)

Shear Stress:

Maximum Shear Load, V = &
0,89 x 33
oe 5 = 1.7 lbs. per in.

Assuming the core carries all the shear load.
3 OV

A

Shear stress, f,

2
Ree wel
2

Ix 078 29. psi

Allowable Shear Stress, f ae Ultimate Shear Stress
6 Factor of Safety

tr = 28

sa ~ 7 = 46.3 psi Satisfactory (Table 5-17)

(2.

(2.

(2.

(2.

~21)

22)

22)

.22)

24)

. 27)

9a)

This shear stress calculation is approximate and over estimates the shear stress in

the core. A more accurate stress value may be obtained by the methods explained in
Chapter 6,
Deflection:
Allowable Deflection, d ee ee 0.165 in
2 200 200 ° .

Maximum Deflection, d =

38h Epig ~ 8 GeA

. 28)

BOAT HULL DESIGN 2-55

Try a 3/l in. thick core of cellular cellulose acetate; 7 lbs. per cu.ft. density.

Eplp = 2.06 x 10° x 0.0172 = 0,036 x 10° (I from Fig. 6-53b)
GeAg = 2.0 x 103 x1% 0.75 = 1500 (G from Table 5-17)
0.89 x 334 0.89 x 332

Maximum Deflection, d = a ee
38) x 0.036 x 10 8 x 1500
= 0.076 in. + 0.081 = 0.157 in.

Therefore deflection is the controlling criterion and a 3/l) in. deep
core is required.

By similar calculations the remainder of the decks may be checked. The results of
these calculations are given below in tabular form, Table 2-8.

TABLE 2-8. DECKS

Req'd. Core
Critical Ult. Shear
Edge Design
Location Panel Size | Condition Criterion

Upper Level Deflection
Lower Level : Deflection

Forward 2'-9'k5'-6§" 0. Deflection 3/4"
Cabin Side | 18" Span : Deflection 3/8"

Aft of 4' x 51-3" ; Deflection Tea /44
Cockpit

Simply : Deflection
Supported

Bill xe blah Simply : Deflection
Supported

we
xk

The deflection of this deck is slightly in excess of the allowable,
but is considered acceptable since this is not a normal walking space.

** Ultimate Shear Stress of 7 lb. per ft3 density CCA = 185 psi (Table 5-17).

Built-in Bunks: Design Loading - 40 1b. per ft2 (0.28 psi) on horizontal surface.

Design Criteria: Horizontal surface to be checked as a plate in bending. Vertical
surface to be checked for column loading.

Factor of Safety = 4. 0 in bending; 2. 0 on buckling stress in compression.

2-56 BOAT HULL DESIGN
Laminate: Use a solid woven roving laminate.

Horizontal Surface:

Load = 0,28 psi
Span = 22 in, (panel length to width ratio is greater than 3 -
design as a 1 in. wide beam simply supported at
the ends)
2
Bending Moment, M = —- (2533)
0 2
0.28 7(22
Oe = 16,95 in.-lbs.
Required Section Modulus, Z = x 16.95 _ 0.0029 in.3
23,700 ez?)
Ultimate flexural strength woven roving, Fpy = 23,700 psi (Table 5-9)

Deflection is neglected, since the bunk will be covered by a mattress.

Section Modulus; Z = = (2, 29)
Cees 6 x .002 ;

te = AS= = aan a = 017) in.@ (2, 29a)
t= 1Os0'32> an.

Use plies of woven roving, t = 0.147 in. (Table 5-2)

Vertical Surface:
Load per inch on loaded edge P = aa = Ohh (2. 24)
= 73.00) lbs.

Length of Loaded Edge = 60 ine = A

Length of Unloaded Edge (taken at Station 2) = 2hin. = B

Load per inch for critical buckling = 8.8 lbs. by interpolation in

Table 6-8 for simply supnorted edges

ALL ble © i = 8.8 i i

owable Compressive Load = —s== 1.4 lbs. per in. Satisfactory (2.9)

Bulkheads
Standard Construction - 5/8 in. Mahogany Plywood
Sandwich Construction with fiberglass laninate facings:
Design Criterion - Equivalent Rigidity (ETI)

Moment of Inertia, I plywood - parallel piss only
Ip = .0t) ane4 for'1 in. strip. (15>)

BOAT HULL DESIGN 2-57

Modulus of Elasticity, E mahogany = 1.6 x 10° psi
Rigidity (EI) sandwich = Rigidity (EI) plywood
from Fig.6-53a for a Type A sandwich
Modulus of Elasticity, E sandwich = 1.95 x 10°

EK plywood

eo ee on : . . E plywood _
equired Moment of Inertia, I sandwich Escandwich * I plywood (2. 34)

Required I = .0115 ind

Sandwich Section 3/) in. core, 1 ply cloth and 1 ply
1-1/2 oz. mat on each face.

Check longitudinal bulkhead for local load from mast.
Assumed vertical mast load = 15,000 lbs. - at breaking strength of stays.

Assume 9 in. width of bulkhead must withstand load.

A factor of safety of 2 is used since the load is based on the
breaking strength of the stays.

Consider load on laminate only; core not effective.

Area of cloth = 2x .016x9 = .288 in.@
Area of mat = 2x .O42x9 = .756 in.2@
; = Ec (mat)
Cloth area equivalent to mat area area mat x ies (cloth) (2. 35)
6
Cloth area = .756 x 22% Se = 4286 in.? (Table 5-12)
Total equivalent area = .288 + .286 = .57) in.?
; _ 15,000 _
Compressive Stress, f, = sarees = 26,132 psi (2. 18)

Cloth Ultimate Compressive Stress F,,, = 15,900 psi (Table 5-11)

This is obviously not satisfactory, and cloth reinforcement should be added
locally. To determine the required reinforcement:

_ 18,900
Allowable Stress fg = os = 9,50 psi (2. 9a)
: 15,000 Pee
Required Area = E = LG Seif satialc
q 9,050 (2/01)
Required Additional Area = 1.537 - .57h = 1.013
Required additional thickness each side, t = — 056 in.

From Table 5-2 - 4 plies of 10 ounce cloth; t = . 064 in.
Add 4 plies of cloth to each side of the bulkhead in way of the mast.

2-958 BOAT HULL DESIGN

Check bond so that the faces will not break away from the core.

Critical stress for face buckling f,,

Sh ee
Gey) Erace * Egore * Pore (See Chapter 6) (2.36)
eee 1.95 x 106 x 1.0 x 10x 2x10
(For 8 lb. per cubic ft. CCA)
= 17000 psi. Satisfactory

Buckling of the panel itself in way of the mast is not a problem due to the close prox-
imity of transverse bulkhead No. 3.

Fittings: The chain plate calculation is similar to that for the open sailing boat
(Design Example 2-2).

Typical cleat attachment: Consider a jib sheet cleat intended to handle a 1/4 in. diame-
ter manila line. The cleat is a standard item and is provided with holes for 2 fasteners.

Design the fasteners for the breaking strength of the 1/4 in. diameter manila line =
550 lbs. (17).

Consider two loading directions, a horizontal pull and a vertical pull (see Fig. 2-28).

VERTICAL PULL

HOR! ZONTAL PULL

—}

To
1-172"
Fig. 2-28. Loading of cleat

Axial Load on Fastener = From vertical pull = 220 = 275 lbs.

From horizontal pull - to resist overturning

moment = 550 lbs.
Transverse Load on Fastener = assuming equal distribution = — = 275 lbs.
Factor of Safety = 2.0

Use a threaded fastener of the self-tapping, thread cutting type with a mat insert in
place of the nonstructural core of the deck. The fastener should not go all the way through
the deck.

BOAT HULL DESIGN Zeoe)

Thickness of deck - 3/8 in. core = ASS)
- 2 plies cloth = ,032 in. (Table 5-2)
- 2 plies 1-1/2 oz. mat = .08) in.
- 1 ply woven roving = .037 in.
2520 in.

For 550 x 2 = 1100 1b. axial load
From Table 3-l: Try No. 10 - 32 self-tapping thread cutting fastener.
Required penetration:

h/16 in. gives 00 1b. minimum holding force

; SOO- Z
Bach additional 1/16 in. cives eee = 263 lbs.
Required additional sixteenths ee = 2,66 - say 3
Total Required Penetration = oe + = =) fy/flley anak

For 275 x 2 = 550 lb. lateral load

From Table 3-4 a No. 10-32 self-tapping thread cutting screw is satisfactory at
3/16 in. penetration.

The controlling penetration is 7/16 in. which is satisfactory.

DESIGN EXAMPLE 2-5. CABIN CRUISER
This cruising power boat represents a type commonly used for pleasure cruising with

accommodations for four to six people. It is of the displacement type, with a cruising
speed of about 12 knots.

Principal Dimensions - See Fig. 2-29 for details.

Length, Over-all: 29 ft. - 3 in.
Length,Water Line: 27 ft. - 5 in.
Beam: 9 ft. - 2 in.

Draft; ~2 ft. — 4 in:

Speed: 15 miles per hour
Engine: 135 horsepower

Summary of Scantlings

Shell Including Transom - Basic Laminate: 1 ply cloth on outside of hull, 1 ply 2 ounce
mat, 2 plies woven roving.

Bottom shell from the bow to Station 7 below Longitudinal No. 3: similar to basic
laminate except 4 plies of woven roving.

Side shell from the bow to Station 7 above Longitudinal No. 3: similar to basic
laminate except 3 plies of woven roving.

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2-60

BOAT HULL DESIGN

a=61

The number and arrangement of stiffeners used aft of Station 7 results in a very thin

laminate.

A better balanced laminate-stiffener combination could be achieved by dropping

one stiffener and respacing the others, using a Type A laminate with 3 plies of woven roving

as the basic laminate.

Framing: All stiffeners are hat type.

Longitudinal No. 1

Longitudinal No. 2
Longitudinal No. 3
Longitudinal No. 4

Longitudinal No. 5
Longitudinal No. 6

Bulkhead 2 to 4

Bulkhead 5 to Transom
Bulkhead 2 to 3

Bulkhead 3 to Transom *
Bow to Bulkhead 2
Bulkhead 3 to Transom
Bow to Bulkhead 3
Bulkhead 2 to Bulkhead 4
Bow to Bulkhead 2

* Carried up transom to deck.

Depth Width Plies of
In. In, Woven Roving

To suit 2 5

Engine

and

Cabin

Floor
3 3 2
4 4 8
4 & 4
5 4 4
4 2 4
5 4 3
+ 4 3
4 = 3

Decks: Sandwich construction - 2 plies cloth on top face, 1 ply 1-1/2 ounce mat, non-
structural core - variable thickness, 1 ply 1-1/2 ounce mat, 1 ply woven roving.

Location

Main Deck

Cabin Top - Lower Level
Cabin Top - Upper Level
Cockpit

Interior Decks

Core Thickness

IPP) shan,
1-1/4 in.
{21/4 4in.

5/8 in.

1/4 in,

Built-in Bunks and Lockers Forward: 4 plies woven roving.

Bulkheads:

Design

Shell Laminate:
consists of:
woven roving.

3/4 in. core with 1 ply cloth and 1 ply 1-1/2 ounce of mat on each face.

The laminate chosen is that referred to as Type A in this manual and
1 ply cloth on the outboard face, 1 ply mat and a varying number of plies of

The laminate selection is based on the excellent impact resistance of this type of laminate.

The design head of water is taken to 24 in. above the deck edge forward of Station 7; and
to 6 in. above deck edge aft of Station 7, Table 2-2.

2-62 BOAT HULL DESIGN

Since the panels involved are all relatively long and narrow, the bending moment and
section modulus used are in each case taken for a one in. wide strip. This strip is con-
sidered to act as a uniformly loaded, fixed ended beam of span equal to the distance

between longitudinals.

The calculations have been arranged in tabular form for convenience, Table 2-9.

TABLE 2-9. SHELL LAMINATE

Location Max. Clear | Head to 24" Bending Moment | Section Modulus | Type A Laminate
Distance Abv. Dk. g = MoS) XM Req'd Plies
Between Fwd. Sta. 7 5 Pou (2.22)! of Woven
Longi- 6" Abyv. Dk. 6h) oy = PLO LM Roving
=h =
tudinals Aft Sta. 7 ce * Tha a ee) = (Fig. 6-31)
bu
L h
(In. ) (Ft. ) p = psi M =in.-lbs. |Req'd Z ¥ - in.3
Deck Edge & Long'l #6 10 2.9 ite lat 9,25 Ze] = - 0012
Forward Station 7
Deck Edge & Long'l #5 14,5 260, 1,24 ales Zu = . 0037
Forward Station 7
Deck Edge & Long'l #4 20 1,3 0.58 19, 33 2m = - 0033
Aft Station 7
Long'l #6 & Long'l #5 10 3.4 1.51 12,58 Zgr = + 0021
Forward Station 7
Long'l #5 & Long'l #4 11-3/4 4.3 191 22. 00 Zr = . 0037
Forward Station 7
Long'l #4 & Long'l #3
Forward Station 7 9 5.3 2.36 15,93 Zywr = . 0027
Aft Station 7 12 3.0 1.33 15.96 Zyr = + 0027
Long'l #3 & Long'l #2 A
Forward Station 7 12 6.4 2.84 34.08 Zwr = .0058
Aft Station 7 10 hel) sb ath} 14, 42 Zwr = . 0024
Long'l #2 & Long'l #1
Forward Station 7 10 6.9 3.07 25.58 Cares ae 0043
Aft Station 7 10 4,2 1.87 15.58 Zyr = . 0026
Long'l #1 & Centerline c
Forward Station 7 8 6.2 2.76 14,72 Zwr = . 0025
Ih

Aft Station 7 10 4.3 Von 15.92 Zur =~. 0027
* Due to space limitations only the critical Z is shown.

“* Forward of Station 7 use 4 plies of woven roving, as required between
Long'ls. #2 and #3, for consistency and ease of construction,

** Between Stations 9 and 10 inboard of Long'l. #2, a local increase to
4 plies of woven roving is recommended because of the pressure
from the propeller.

Shell Longitudinals: The shell longitudinals are designed as fixed ended beams to with-
stand the same design load as the shell they support. The calculations have been arranged
in tabular form for convenience, Table 2-10. Hat section stiffeners have been used throughout.

The stiffener sections indicated have been checked for shear and found satisfactory. For
a typical shear stress calculation see Design Example 2-3.

BOAT HULL DESIGN

2-63

TABLE 2-10. SHELL LONGITUDINALS
Long'l | Location Length Width of Head to 24" Required Stiffener |
No. Shell Abv. Dk, (Fig. 6-37)
Supported Fwd Sta. 7 6h : pLe _ uM Depth x No. of
6" Abv. Dk. -~hxsx7p 12 15,800 Width Plies
Aft Sta. 7 of
1s, s h (2,21) (2. 22) Wover
| (In. ) (In.) (Ft.) p - Lbs. -In, | In.-Lbs in. 3 (In. ) Roving
SS
1 Bhd #5 to 52 10 4.3 nS Pe a 4,306 1,09 3x3 2
Transom
2 Bhd #3 to #4 57 15 5.8 38.67 10,470 2.65 4x3 4
3 Bhd #1 to #2 78 15 5.8 38.67 19, 606 4,96 5x4 4
3 Bhd #3 to #4 57 15 5.2 34.66 9,384 2.38 a 2 4
4 Bhd #1 to #2 78 13 4.8 27.73 14, 069 3.56 5x4 3
5 Bhd #2 to #3 tak 14 3.4 21,15 10, 450 2.65 4x4 3
6 Bhd #1 to #2 78 13 2.9 16.76 8,497 2.15 4x3 3
eee Cee 1 zai [EES

Shell below Longitudinal No. 4 Forward of Station 7 has 4 plies of woven roving.

Shell Forward of Station 7 from Longitudinal No. 4 to deck edge has 3 plies of

woven roving.

Shell elsewhere has 2 plies of woven roving.

Shell Longitudinal No. 2 - Supporting Cabin Flooring: Bulkhead No. 2 to Bulkhead No. 3.

6h,

1, = We slicing! Se MN aig at = Sige stan je) So) 2c ale pet
’ ’ Wh

pL? _

cry

Required, Z

AS an approximation, assume half-round

TSS q PAO) sb ekhc Hotei

WM = 3,99 in.3

15, 800

stiffener with D = h; Z = 3.99 in.23
2

From Pig. 6=39 © = 6 in., h = 3 in.,
8 plies woven roving

Minimum leg ) in.

Assume difference between Z of half-round and Z of angle is provided by support

of the angle by the cabin deck.

(Qe2 1)

(2522)
veo

Fig. 2-30.

31.47 lbs.-in.

Longitudinal No. 2

2-64 BOAT HULL DESIGN
Longitudinal No. 1 - Engine Support

Engine Weight: 850 lbs.

Thrust: 1615 lbs. at 15 knots assuming EHP = 1/2 SHP

Engine Mounting: 4 bolting pads on engine

Engine Support: 4 steel angle clips bolted to fiberglass hat stiffeners

=

—< Lo

STEEL ANGLE
CONNECTING CLIP

SECTION A-A

ENGINE BEARER SIMILAR TO FIG. 3-31

Fig. 2-31. Engine foundation
Assume engine weight is doubled by acceleration forces -

Factor of Safety = 6 (Chosen because of the long term nature of the
loading and the vibration).

Using standard methods of vector analysis, assuming the weight and thrust forces
equally distributed among the four connections and including the force required to resist
the moment introduced by the fact that the line of action of the thrust does not pass through
the bolts the maximum load per attachment P = 700 lbs.

Assume only two bolts per attachment.
Load per bolt Py = 350 lbs.
Using a bolt and spacer combination with a 1/2 in. outside diameter D, determine

the required thickness of woven roving, to give an acceptable bearing stress, considering
all the load taken by one web of the longitudinal.

Ultimate tensile strength, Fy, = 30,100 psi (Table 5-6)
Factor = .91) (Table 3-2)

Bearing stress at failure, Fp, = .91) x 30,100 = 27,500 psi

Allowable bearing stress, fp, = — = )583 psi (2. 9a)

BOAT HULL DESIGN 2-65

1
b
The reauired thickness, t = ———— (ye 12)
Dx f,
3a
=
t= ZAP OO Fes = O53) in.
0.5 x 583
Use 5 plies of woven roving, t = .1@5 in, (Table 5-2)

Use a stiffener width of 2 in. for ease in molding. This stiffener is carried forward
to support the cabin floor.

Decks: All decks are to be of sandwich construction for rigidity. Type B sand-
wich is used Fig. 6-53b. Each deck is checked for stress in the various elements,
and for deflection.

The required core thickness for each criterion, stress or deflection, is determined
and the thickest core is used.

Cabin Top - Lower Level:

Design Load; p = 2 ft. of water = 0. 89 psi
Dimensions: Length = 6 ft. - 5in., width = 7 ft. - 0 in.
Edge Connection: Fixed

Flexure: Consider a 1 in. strip as a fixed ended beam.

2 2
Bending moment, M = — - So =) “LAW ata Silesis (221)

w io
Required section modulus = Z = eke (2.22)

Ultimate stresses, Fu, from Tables 5-6 and 5-11

h x al WAe _ 3
3 i i Lo ee OF in.
Cloth; top face in tension, 31,100 0.028 in
1/2 in. deep core required (Fig. 6-53b)
h elven (ele :
Woven roving; bottom face in compression, Z = ee 0.09 in.
7/8 in. deep core required (Fig. 6-53b)
Leces lee (ale :
Mat; top face in tension, Z = “1,00 = 0,062 in.?
1/2 in. deep core required (Fig. 6-53b)*

* By extrapolation.

2-66 BOAT HULL DESIGN

Shear Stress:

px (2. 24)
2

0.89 x 48 = 21.4 lbs. per in.
a

Shear load, V

Assuming the core material carries all the shear load, the
maximum Shear stress for a rectangular block is for a 1-1/4 in. core:

oe Oy
fs" 37 (2. 27)
eee ae
dee we eae
Allowable shear stress, fsa = Ee ieee Deena (Table 5-17) (2. 9a)

Factor of Safety

185.0 _ 6.3 psi Satisfactory

See Design Example 2-4 for notes regarding this shear calculation.

By similar calculations the remainder of the decks may be checked. The results of
these calculations are given below in tabular form, Table 2-11.

Deflection:
Q
jtreyable demisctiony disse =o. S40 eam
200 +200

Assume a cellular cellulose acetate core weighing 7.0 lbs. per cubic ft.
Go = 2.0 x 103 psi (Table 5-17)
Ultimate shear strength = 185 psi

Try a 1-1/),; in. core

hy 2
Maximum ‘deflections d <2 4 Pe (2. 28)
38) Eel up e
2
: 0.89 x Leh , 0.89 x 8

B30lr sare 106 106 x O16 8 x 2000 x 1 x 1.25 (Fig. 6-53b)*

OBO ine + OF103

0.233 in. Satisfactory

* By extrapolation.

BOAT HULL DESIGN

TABLE 2-11. DECKS
Critical
Edge Load | Design
Location Panel Size | Connection psi Criterion
Deck Fwd Sree Fixed 0.89 | Deflection
of Cabin Edges
Trunk Out-
board of
Hatch
Between 12" (Treat Simply 0.89 | Deflection
Coaming & | as beam) Supported
Cabin Side
Aft of
Bhd i#2
Cabin Upper 81"' x 80" Fixed 0.28 | Deflection
Top Level Edges
Cockpit - 98'"' x 49"' Fixed 0.28 | Deflection
Edges
Interior | Main 15'' (Treat | Fixed 0.28 | Deflection
Cabin as beam) Ends
L zaliens aes

Built-in Bunks:
Use 4 plies wove

Bulkheads:

Req'd
Core
Thick -
ness

Req'd Ult.
Core Shear
Stress

psi

oe

By/8l)

Wserl/2

Nem fake

5/8"

vis"

Use 1/4"

See similar calculation for Cruising Sailboat, Design Example 2-4.

n roving.

Use 3/4 in. core with 1 ply cloth and 1 ply 1-1/2 ounce mat each face.

Fittings:
Example 2-4.

See similar calculation for Cruising Sailboat, Design Example 2-4.

Similar to cleat attachment calculation for Cruising Sailboat, Design

(1)

(2)

(3)

(5)
(6)

(7)

(8)

(9)

(10)

(11)

BOAT HULL DESIGN

REFERENCES
Murray, A. B., ''The Hydrodynamics of Planing Hulls",
Transactions of Society of Naval Architects and Marine
Engineers, 1950

Culwick, E. F. and Savitsky, D., ‘Design and Development
of an Outboard Runabout Boat’. 13th Annual Technical and
Management Conference, Reinforced Plastics Division, The
Society of the Plastics Industry, Inc.

"Rules for the Construction and Classification of Wood Yachts",
Lloyd's Register of Shipping, London, 1929

Herreschoff, N.G., ‘Rules for the Construction, The Scantlings,
and the Other Proportions of Wooden Yachts", 1927

Nevins, H. B., ''Proposed Scantling Rules for Wooden Yachts", 1938

Yustein, S.E., ‘Report of Specification Development on
Adhesives for Glass-Reinforced Plastics’, Progress Report
No. 5, Laboratory Project 5616-1, Material Laboratory,
New York Naval Shipyard, 26 April 1956

Huffington, N. J. Jr., and Hoppmann, W.H. II 'Blast Loading
of Orthotropic Plates'', Operations Research Office, Johns
Hopkins University (Armed Forces Technical Information
Agency No. AD28929)

Bell, E.R., Peck, E.C., and Krueger, N.T., ‘Modulus of
Elasticity of Wood Determined by Dynamic Methods'' Forest
Products Laboratory Report No. 1977, April 1954

Kellam, B., ''Evaluation of Reinforced Plastic Pipe', 11th
Annual Technical and Management Conference, Society of
the Plastics Industry, Inc., February 1956

Markey, M.F. and Carpini, T.D., 'Rough-Water Impact-Load
Investigation of a Chine-Immersed V-Bottom Model having a

Dead-Rise Angle of 10 Degrees'', National Advisory Committee
for Aeronautics Technical Note 4123, Washington, October 1957

Mayo, Wilbur L., ''An Analysis and Modification of Theory
for Impact of Seaplanes on Water'', National Advisory Committee

for Aeronautics Technical Note No. 1008, Washington, December 1945

G2)

(13)

(14)

(al)

(16)

Ca)

(18)

(alts)

BOAT HULL DESIGN
REFERENCES

Edge, Philip M. Jr., ‘Impact-Loads Investigation of Chine -
Immersed Model having a Circular-Arc Transverse Shape |,
National Advisory Committee for Aeronautics Technical
Note 4103, Washington, September 1957

Jasper, Norman H., ‘Dynamic Loading of a Motor Torpedo
Boat (YP110) During High Speed Operation in Rough Water’,
David Taylor Model Basin Report C-175, Washington,
September 1949

Outboard Boating Club of America ''OBC Standards Manual", 1959

Douglas Fir Plywood Association, 'Technical Data on Plywood ',
October 1950

‘Rules and Regulations for Small Passenger Vessels |
United States Coast Guard No. CG-323, June 1, 1958

‘Wire Rope Engineering Handbook”, American Steel and
Wire Company, 1946

Labberton and Marks, ''Marine Engineer's Handbook '
McGraw-Hill Book Company, New York, 1945

Bureau of Ships, Navy Department, ''Wood: A Manual for its
Use in Wooden Vessels’, July 1945

—

ae

Pry

Os
i)
i
:
7
4
?
=

3

Design Details

The use of good details in fiberglass construction is of vital importance in producing a
successful design. It is the purpose of this Chapter to indicate recommended methods of
construction, and to provide guidance for avoiding trouble causing details. Because of the
variety of details possible, the number covered has been held to a minimum and the details
chosen illustrate principles which are applicable regardless of the exact means by which
they are applied. This approach should guide the designer in solving particular problems
and developing successful details, even though the exact situation is not covered here.

APPLICATION OF LOADS

In any structural design work an understanding of the basic properties of the material
used is essential. The basic property of fiberglass laminates which must be clearly
understood is the difference between its tensile strength perpendicular to the plies of the
laminate and its tensile strength parallel to these plies. The tensile strength perpendicu-
lar to the plies is very much less than that parallel to the plies. For this reason there are
right and wrong directions of loading, which are illustrated in Fig. 3-1. The variation in
strength with direction of reinforcement, which is characteristic of cloth and woven roving
reinforced laminates and which is discussed in Chapter 6, has nothing whatever to do with
the ''wrong" loading direction mentioned here. Those directions are all "right" directions
since the loading is parallel to the laminate.

The reason for this right and wrong direction is simple. As explained in Chapter 5,
the properties of fiberglass reinforced laminates are due to the two basic components,
fiberglass and resin. Of these, the fiberglass provides the strength and the plastic or

OIRECTION OF LOAD

Ves

WA

hf
OF LOAD <€ i

a
:

yee
| | ie OF REINFORCEMENT

“a PLIES OF REINFORCEMENT ! | | |
DIRECTION OF LOAD

@. RIGHT — LOAD PARALLEL TO PLIES b. WRONG — LOAD PERPENDICULAR TO PLIES

Fig. 3-1. Right and Wrong Directions of Loading with
Respect to Laminate Reinforcement

Bie DESIGN DETAILS

resin provides the means of holding the fiberglass in place. Loading a laminate in the
wrong direction places the toad on the resin, and the glass reinforcement cannot act.
Therefore, when a load is applied in the wrong direction, as with cleats secured to a deck,
mechanical fasteners completely through the laminate should be used, The only exception
to this rule may be in the case of very light loads.

Assuming the loads are applied in the right direction or parallel to the plies, the next
consideration is the orientation of the reinforcement to suit the loading. This is particu-
larly important with cloth and woven roving reinforcements. The designer should be
familiar with the strong and weak directions, and make every attempt to place the laminate
reinforcement with the strong or warp direction in line with the direction of the principle
stress. This principle applies both to the lay up of the over-all laminate and to local
increases in thickness in way of local loading.

LAMINATE CONNECTIONS

One of the major advantages of fiberglass construction is that, in many cases, the
basic material may be used to form the connection between two parts, in a manner
analogous to welding in steel construction. The basic requirement for all joints is that
the laminate be loaded in a direction that will not tend to delaminate it; that is, pull it
apart.

In secondary bonded joints, i.e. joints using an adhesive to connect cured laminates,
subjected to shear tending to slide one laminate past the other, it is recommended that a
layer of resin impregnated fiberglass mat reinforcement be placed between the joining
surfaces since it acts as the adhesive carrier and as a reinforcement. Fiberglass mat is
preferred since it retains the adhesive and its random distribution of glass fibers provides
reinforcement in the joint opposing the shear force.

Deck to Shell

One of the most common connections which must be made is the deck to the shell.
There are many possible means of making this connection and the final selection of a
detail must be based on satisfying a number of requirements. These requirements will
sometimes conflict and some compromise must be decided upon. The following basic
principles will guide in the design of a good joint:

A joint should develop maximum efficiency or the full strength of the weaker

of the two pieces being joined. This is the most important criterion of a pro-
posed design; the one which overrides all other considerations. The exterior
reinforcement shown in a number of the following figures will create a condi-
tion where good exterior appearance will be difficult to obtain. If, however,

sufficient strength cannot be obtained without this exterior reinforcement, the
effect on appearance must be accepted or the joint design modified if possible.

A joint must be easily made by the fabricators. Quality control in fiberglass
construction is all important, and a joint that the workman can do well will
often be stronger than a joint which appears stronger on paper but cannot be
easily made and inspected,

DESIGN DETAILS 3-3

A joint should be compatible with the molding method used, the speed of con-
struction desired, and the size and type of boat being built. A joint which has
adequate strength and can easily be made with minimum mold accuracy for
small boats, may not be suitable for use with larger boats with higher strength
requirements. These larger boats are not rapidly produced, and therefore
justify the extra cost of using one of the more complex joints requiring more
accurate molds. The parts to be joined should never be forced into place,
since this introduces stresses not contemplated in the design and may drasti-
cally reduce the strength of the structure.

Normal loads on the deck and shell produce either shear loading, or tension
loading on the outside of the hull at the joint. It is the tension on the outside
of the hull which makes exterior reinforcement so effective when compared

to interior reinforcement. With interior reinforcement only, this type of
loading tends to peel the pre-molded laminate away from the bonding rein-
forcement as shown in Fig. 3-2. For this reason, this connection must be
very carefully made. It is recommended that the bond lap be at least 2 inches
in small boats, and be adequately increased for larger hulls with thicker
laminates,

When joints are used which leave an edge of a laminate that is not tapered
or butted to an adjacent piece, this edge should be sealed with resin to prevent

water absorption and delamination.

DECK LOADING Z
P RE—MOL DED ———“—»
DECK LAMINATE“
/

WOOD COAMI NG
os

BONDED LAMINATES

ve : 42223 =
aie Hl “TEND TO PEEL APART 73 = :
a \ vill | =i 1
DEFLECTED /h Z 1S Pe,
SHAPE Ih S SHAPED WOOD CLAMP ibee
/ pil = WITH THROUGH BOLTS “
f
// WH FIBERGLASS JOINT REINE A rveworoeo
L] \ ‘ FORCEMENT COVERING HEADS SHELL LAMINATE
| SIDE SHELL OF BOLTS ws
| LOADING f
Fig. 3-2. Deck Edge Fig. 3-3. Deck Edge Connection -
Connection - Normal Deck Shaped Wood Gunwale Clamp

and Shell Loading Produces
Tension at the Joint

Figs. 3-3 through 3-12 indicate several deck to shell connections.

Fig. 3-3 indicates the use of a shaped wood gunwale clamp. This was common practice
in past years, and was adapted from wood boat construction, but the current trend is to
the all fiberglass boat. Several reasons for this have been given in the discussion of com-
posite construction, Chapter 2.

3-4 DESIGN DETAILS

Fig. 3-4 indicates a connection with a vee or scarf joint in the deck. Fig. 3-5 indi-
cates the same basic connection with a vee or scarf joint in the shell rather than the deck,
but incorporates a molded in deck edge coaming. Usually, joint selection depends on the
molding procedure. The joint shown in Fig. 3-4 may be used when the shell is molded in
two halves, while that in Fig. 3-5 may be used when the shell is molded in one piece.
Although this is not recommended, the joints in Figs. 3-4 and 3-5 may be made without
the additional exterior fiberglass reinforcement. If this is done, the vee joint is pre-
ferred since a better bond will be obtained. In any case, the total joint reinforcing
laminate should be at least equal in strength to the weaker of the laminates joined,

S aea a

PRE-MOL DEOL __
DECK LAMINATE Se

COAMING MOLDED

- re wea aay . PRE-MOL DED ——-—+ IN DECK

A y DECK LAMINATE ,

a WOOD COAMING 5
/ y
/ IF DESIRED

r LLY
heey /
VEE OR SCARF FIBERGLASS JOINT VEE OR SCARF

REINFORCEMENT JOINT

JOINT
FIBERGLASS JOINT
PRE=MOLDED REINFORCEMENT PRE-MOLDED
SHELL LAMINATE \H SHELL LAMINATE
|
Fig. 3-4. Deck Edge Connection - Fig. 3-5. Deck Edge Connection -
Wood Coaming and Joint in Deck Molded in Deck Edge Coaming with

Joint in Shell

Fig. 3-6 indicates a shell to deck connection commonly used in small boats, It has
the advantage of minimizing requirements for dimensional accuracy and provides an easy
means of attaching a rubbing strip. The through bolts in this joint may be eliminated by
clamping the deck and shell edges together until the ply of resin impregnated mat in the

joint is cured. The edges are then ground
SRE MGRRED fe Te SNAP IN PLACE flush and, if necessary, interior reinforce-

ioe ain ment placed, and finally the snap-on rubbing
strip is added. This strip may be of metal

DECK LAMINATE

or plastic.
4 PLY MAT IN JOINT aN =% ; } ; Me
FIBERGLASS JoINtT——— ei > THROUGH BOLTS Fig. 3-7 indicates the use of a lap joint
Otis ahaa! See combining bonding with through fastening.
SHELL LAMINATE The hull and deck molds may be easily made
(be 7 so that the faying or connecting surfaces of
(PY the joint are vertical. The small strip shown
RET ERNE TESHe EUG TIGRrecwAcinia may be added to provide a ready positioning
ENOS TO TAKE SNAP ON STRIP means.

Fig. 3-6. Deck Edge Connection -
Small Boat Type with Snap in Place
Rubbing Strip

Fig. 3-8 illustrates a connection utilizing
a prefoamed resin or a troweled in place
filled resin, described in Chapter 4. This
type of joint maintains the rigidity and strength of the sandwich construction deck right to the
deck edge. In making this joint, the shell and deck laminates are joined in a manner similar
to that shown in Fig. 3-4. A filled resin is then troweled in place, or a prefoamed resin is
shaped and set in place and the second reinforcing laminate is added. The advantage of this
joint is its high rigidity and strength without the addition of exterior layers of reinforcement

DESIGN DETAILS 3-5

which disturb the molded-in gel coat finish. Fig. 3-9 indicates the same basic joint with a
molded-in coaming and the joint in the shell, rather than the deck. As previously mentioned,
choice of joint location depends on molding procedure.

PRE-MOLDED DECK
P RE—MOL DED ie Sp RONECH SS ——
a ae 4 %
DECK LAMINATE ; \ ‘“ fo b

——/— RUBBING STRIP —WOOD COAMING

1 PLY OF MAT IN
LAP JOINT

er - | ——VEE OR SCARF
Ze Hh ig = \\ JOINT
Ea JU |/ | [LAK |:
msROUSH BOLTS yx POSITIONING STRIP ———— Fee 9 Sa eft inks Sef, MI
P RE-MOL DED IF DESIRED Se cs
SHELL LAMINATE oF
FIBERGLASS JOINT
. 5 REINFORCEMENT
Fig. 3-7. Deck Edge Connection -
Combining Bonding and Mechanical TROWELED OR PRE-FOAMED
Fastening RESIN CORE PREOMOLOES
‘SHELL LAMINATE
Figs, 3-10, 3-11 and 3-12 indicate three Fig. 3-8. Deck Edge Connection -
connections which have been successfully used, Sandwich Deck with Wood Coaming

and which have the advantage of simplicity of and Joint in Deck
construction,

Fig. 3-13 indicates a method of connecting a sandwich construction interior deck, such
as a cockpit deck or cabin sole, to the shell. Notice that the connection is a temporary one,
so that the deck may be removed for inspection and cleaning of the bilges.

Gunwale

Gunwale connections on small open boats vary considerably with molding method and
designer's preference. Four common methods are shown in Figs, 3-14 through 3-17.

Fig. 3-14 indicates a common detail for gunwale and shell as one continuous piece.
The edge of the laminate is dressed after removal from the mold. Depending on the
molding method used, the gunwale may be flanged inboard or outboard. This is considered
the simplest and best of the details shown, when flanged outboard.

Fig. 3-15 indicates, in effect, a conventional wood construction applied to a fiberglass
hull. It is chosen partly on an appearance basis and partly because the wood rubbing strip
may be easily replaced. This construction will, however, increase maintenance problems
on what should be a relatively maintenance free boat.

Fig. 3-16 indicates two types of aluminum extrusions bolted to the shell to serve as a
gunwale. The cross-sectional shape of the aluminum may, of course, vary widely.

Fig. 3-17 indicates an all fiberglass construction suitable for a shell molded in one
piece. The gunwale piece is molded separately and bonded or bolted to the completed hull.

Shell at Keel

In some instances the main hull laminate is made in two parts and is then joined to-
gether. This connection is of such importance that some designers use a combination of
mechanical fastening and resin bonding. Special care must be taken when using through
bolting in the shell below the waterline, since this is a possible source of annoying leakage.

PRE-MOLDED
SANDWICH CONSTRUCTION

COAMING MOLDED

IN DECK

PRE-MOLDED eee

a DECK LAMINATE

rs

VEE OR SCARF
JOINT

OPTIONAL EXTERIOR
FIBERGLASS JOINT
REINFORCEMENT

THROUGH BOLTS
OR BONDED CONNECTION

a—______ PRE=MOL DED

SHELL LAMINATE

FIBERGLASS eas 4

REINFORCEMENT

Fig. 3-9. Deck Edge Connection - Fig. 3-10. Deck Edge Connection -
Sandwich Deck with Molded-in Simple Molded-in Coaming with
Coaming and Joint in Shell Mechanical Fastenings

PRE—MOLDED
DECK LAMINATE

J
PRE-MoLDED
7

DECK LAMINATE
SNAP IN PLACE RUBBING
STRIP ON OVERHANG

FIBERGLASS JOINT F1BERGLASS soint——! PRE-MOL DED
REINFORCEMENT Seren paley ain REINFORCEMENT 4 SHELL LAMINATE
J SHELL LAMINATE i
e
Fig. 3-11. Deck Edge Connection - Fig. 3-12. Deck Edge Connection -
Simple Butt Joint Modified Butt Joint with Overhang

for Snap in Place Rubbing Strip

Vi {

FIBERGLASS SHELF ——,
\

THREADED ~
FASTENER SIDE SHELL
: “SSEAL EDGE OF LAMINATE
SANDWICH CONSTRUCTION. BS SHELL WITH RESIN

INTERIOR DECK LAMINATE

Fig. 3-14, Integrally Molded
Gunwale

SANDWICH CORE CUT CLEAR AND

/
FACE LAMINATES BROUGHT TOGETHER SEAL EDGE OF LAMINATE

WITH RESIN
EXTRA PLIES OF REINFORCEMENT

TO RECEIVE THREADED FASTENER

TV a wood CLAMP & Vis

SS RUBBING STRIP

—SIDE SHELL

Fig. 3-13. Deck Edge Connection - THROUGH BOLTS
Interior Deck to Shell

Fig. 3-15. Wood Gunwale

—SEAL EDGE OF LAMINATE
WITH RESIN

Va

/

ALUMI NUM
EXTRUSION

RUBBING STRIP Fig. 3-16. Aluminum
Gunwales

ALUM! NUM
EXTRUSION

THROUGH BOLTS
THROUGH BOLTS SIDE SHELL
SIDE SHELL

DESIGN

SEPARATELY MOLDED——~
GUNWALE

1 LAYER OF ee

IN JOINT —

SIDE SHELL

Fig. 3-17. Separately Molded
Fiberglass Gunwale

Fig. 3-18 indicates a detail suitable for boats such as lifeboats,

DETAILS 3-7
+—~ PRE-MOLDED
\ SHELL HALVES
FIBERGLASS JOINT \
RE| NFORCEMENT. i
FS —_ Nes eee \ ee ——— Ff
JS wy \ /
v5 ra _ 7 Wy
Lf eae Si
Z tae ae if
J Ly . oe
SS
_=H TROWELED IN PLACE
THROUGH BOLTS OR— | FILUEDSRESTN
RIVETS
——1 PLY MAT REINFORCEMENT
IN JOINT
Fig. 3-18. Connection of Shell Halves -

Centerline Skeg

cruising power boats

and small open boats where a small keel is desirable for directional stability. The joint

reinforcement as shown, also prevents leakage.

If a flat bottom is desired, the joining

flanges may be turned inboard and the joint reinforcement placed outside.

Figs, 3-19, 3-20 and 3-21 indicate
various means of forming a similar connec-
tion for a sailboat. Note that where heavy
ballast is required in these boats, it is set
in wet mat reinforcement during or after
joining the shell halves. The ply of mat
covered by a layer of cloth indicated out-
board at the joint in Figs, 3-20 and 3-21, is
intended to keep water out of these secondary
bonded joints which are susceptible to de-
lamination under water pressure. The joint
at the base of the centerboard trunk shown in
Fig. 3-20a is used when the shell is molded
in one piece and the centerboard trunk added
later. The alternate construction shown in
Fig. 3-20b is used when the centerboard
trunk is premolded and set in the wet lami-
nate during the molding of the shell. The

lower flange of the trunk is covered by the inner layers of the shell laminate.

PRE-MOLDED

CENTER BOARD TRUNK
DW)

FIBERGLASS JOINT
RE! NFORCEMENT

4 PLY LIGHT MAT____4—_
AND 1. PLY CLOTH

@.TRUNK AND SHELL MOLDEO SEPARATELY

Fig. 3-20.

Connection of Shell

— PRE-MOLDED SHELL
HALVES

FIBERGLASS JOINT
REINFORCEMENT

—LEAD OR CAST IRON BALLAST
SET IN RESIN IMPREGNATED
MAT REINFORCEMENT

FIBERGLASS JOINT ne
REINFORCEMENT
| NBOARD AND OUTBOARD

Fig. 3-19, Connection of Shell Halves -
Cruising Sailboat with Ballast

The use of a

PRE—MOL DED
CENTERBOARD TRUNK

db. PRE-MOLDED TRUNK SET IN SHELL
LAMINATE DURING MOLDING

and Centerboard Trunk

3-8 DESIGN DETAILS

mold extending slightly up into the centerboard trunk provides a means of locating the trunk
and a smooth mold face surface which will minimize the secondary bond leakage problem
mentioned above.

P RE—MOL DED Ve
FIBERGLASS JOINT SHELL HALVES Y
REINFORCEMENT.
; : bs BASIC SHELLY
) Pe cf. LAMINATE Ya \ y
P / y \ / fs
j y 4 /
y

a 4 PLY LIGHT MAT AND
VEE JOINT 1) PLY CLOTH
LOCAL FIBERGLASS

Fig. 3-21. Connection of Shell Pkt a
Halves - For Small Boats Only LARGE WASHER

Keel Ballast to Hull ADLTSL ORS TAI

BALLAST
Fig. 3-22 indicates a common means of

attaching outside ballast to the hull. The

large washer shown is essential to prevent Fig. 3-22, Ballast to Hull

the securing nut from crushing the laminate. Connection

The local reinforcement is necessary to

prevent the washer from shearing through the laminate, and to provide bearing for the bolt

to enable it to resist sidewards thrust.

Repair Joint

Fig. 3-23 shows a type of connection commonly used in repair work and which may be
used anywhere a butt joint requires surface appearance combined with strength. The joint
reinforcement should be equivalent to the basic laminate for continuity of strength.

BACKING PLATES
TO BE REMOVED

/CELLOPHANE OR OTHER
Ye SEPARATING FILM

OPTIONAL BACKING PLATE

SAND OR GRIND TO
8 TO 1 SLOPE
MINIMUM

SAND OR GRIND TO
8 TO 1 SLOPE
MINIMUM

PRE—MOL DED PRE-MOL DED

MOLDED IN

PRE-MOLDED MOLDED IN PLACE \_p RE-MOL DED LAMINATE TO BE REMOVED PLACE JOINT LAMINATE
LAMINATE JOINT REINFORCEMENT LAMINATE RE| NFORCEMENT
@. PREFERRED CONSTRUCTION b. ACCEPTABLE ALTERNATE

Fig. 3-23. Butt Joints
Bulkhead or Frame to Deck or Shell

Fig. 3-24 shows one of the most common connections, particularly in larger boats
having accommodations, This basically is a connection between the shell or deck and any
member perpendicular to it. This connection performs the dual function of making the joint
and reinforcing the shell at a rigid support. The fillet pieces indicated are to ease the
hard spot caused by the connected member. A detailed discussion of hard spots is given
later in this Chapter. The fillets also prevent resin richness in the corner. The fillets
may be made of balsa, foamed plastic or a filled resin troweled in place and allowed to
set before the joint reinforcement is added.

DESIGN DETAILS 3-9

|

> BULKHEAD OR FRAME

THESE DIMENS!ONS SHOULD \ Fig. 3-24, Connection - Bulkheads and

BE MINIMUM CONSISTENT .
WITH STRENGTH REQUIREMENT, Framing to Shell or Deck
2! MINIMUM RECOMMENDED.

FIBERGLASS ANGLES
TO FORM CONNECTION

jJEXTRA PLIES OF FIBERGLASS MAT
TO REINFORCE SHELL — OPTIONAL

z= = Where incompressible bulkheads and
a= — frames, such as, plywood or hard woods

SHELL OR DECK FILLET CORES — USE CONTINUOUS are connected to thin shell or deck lami-

LAMINATE STRIP WITH NCOVERESS LBCE nates, the length of the fiberglass con-

BULKHEAD OR FRAME

necting angles should be determined by
test to insure that unfairness in the hull or deck will not occur. Shrinkage during cure of
the connecting angles tends to pull the bulkhead or frame through the laminate, causing a
slight bump. Experience has shown that this is particularly noticeable when incompressible
frame cores are completely encased in the laminate. This effect can be minimized by
replacing the separate low density fillet cores with a continuous strip inserted between the
framing member and the shell.

Cabin Trunk to Deck

In wooden construction, the joint between the cabin trunk and the deck causes consider-
able difficulty. In many fiberglass boats the problem is avoided completely by molding the
cabin trunk and the deck in one unit and eliminating this connection entirely. A typical
example of this construction is shown in Fig, 3-25, If this desired one piece construction
is not possible, the connection shown in Figs, 3-26 or 3-27 may be used, The joint between
the cabin trunk and the decks is an important one from a strength viewpoint, and reinforcing

of both sides as shown is considered essential.
PRE-MOLDED CABIN,

,

CABIN Top [4 (a ee
LY

iets A |
A i | } PRE—MOLDED DECK
CABIN SIDE Sy 7-— DECK Va lan we i
Sy VY fy
Jf \ eid
ve
CONTINUOUS LAMINATE / FIBERGLASS JOINT
Fig. 3-25, Cabin and Deck i
Molded as a Single Unit Fig. 3-26. Cabin to Deck Connection -
Pre-molded Cabin and Deck - Single
, Skin Construction
re )\ |
Ie J\\
Vi 4 | }

7 a\ {
| gob 7
PRE-MOLDED CABIN 1|| Vt — Need
i Se o LL J : ©
? \ Vays 5 wv Fig. 3-27.

Bee his Cabin to Deck Connection -
LASS JOINT / / y i .
REINFORCEMENT pret ol “IL Pre-molded Cabin and Deck - Sandwich
1 PLY OF MAT IN JOINT mMPLZZZZ ZL. xy : Construction
= PRE-MOLDED DECK

3-10 DESIGN DETAILS

FITTING CONNECTIONS

All boats have various attachments and fittings which do not affect the over-all strength
of the hull, but are vital for operation. This includes engine mountings, chain plates, bitts,
chocks, cleats, etc. Certain fittings can put severe local loads on the hull, and these loads
must be carefully considered in designing the necessary reinforcement. Loads induced by
fittings generally push down on the boat, such as engines and masts; or pull away from the
boat, such as rigging attachments and cleats. Horizontal thrusts in one or more directions
may also be induced simultaneously.

Pushing Loads

The design of engine mounts, mast steps and similar items is basically a problem of
providing adequate strength directly under the load to prevent local failure, and spreading
the load over a sufficient supporting area. Supports should, wherever possible, be tied
into the main structure of the boat, such as, transverse and longitudinal frames, bulk-
heads, etc.

Engine Mounts: A number of typical mountings for inboard engines are shown in Figs.
3-28 through 3-33. In each case the longitudinal supports are carried a substantial dis-
tance away from the engine, sometimes stopping at a transverse frame or bulkhead, and
sometimes tapering down to a normal longitudinal frame. The engine bearers themselves
may be of steel or fiberglass angles as shown in Figs, 3-31, 3-32 and 3-33, The loading
from the engine is always considered as being supported by the fiberglass laminate, with-
out assistance by the stiffener core, if any. It is recommended that a thin layer of neoprene
or some similar material be placed between the steel engine bolting supports and the fiber-
glass laminate bearers as a means of insulation. Transverse frames are added where
necessary to help distribute the engine thrust and weight to the shell, and to reduce shell
panel sizes compared to the normal size in the area to avoid excessive vibrations.

The mounting of outboard engines has been covered in Chapter 2 under transom design
since this mounting constitutes a major structural portion of the whole craft.

Mast Steps: Masts exert major concentrated loads on the boat. Masts may be divided,
for purposes of design, into those which step on the deck and those which step on the keel.
In wooden construction the keel is a major structural member and can receive the mast,

NORMAL LONGITUDINAL TO EXTEND
FORWARD AND AFT TO TRANSVERSE
SUPPORTS ——— a

GRADUALLY INCREASE LONGI—
TUDINAL TO DEPTH REQUIRED” —
BY ENGINE

ENGINE ———

peinces ie Fig. 3-28. Engine Mount for Inboard
Runabout - Suitable for Low Horse-

power Installations Only

TRANSVERSE WEBS

AS NEEDED
~

o>
a rruren INE

FOR TRANSVERSE SECTIONS IN WAY OF ENGINE BEARER, SEE FIG.
3-31 TO 3-33.

~— BULKHEAD STIFFENERS
\\ TO SPREAD ENGINE

\

\. BEARER LOAD

TRANSVERSES AS NECESSARY

}--——ENGINE COMPARTMENT
BULKHEAD

FORWARD BULKHEAD
OF ENGINE COM-

ae
LONGI TUDINALS IF bbe

USED SHOULD LINE
UP WITH ENGINE
BEARERS

ENGINE BEARERS

A

PLAN VIEW

PARTMENT
TO STIFFEN HULL AND
DISTRIBUTE ENGINE
CCAD ENGINE
ae
ee

ENGINE BEARERS

~-—— CENTERLINE SECTION A-A

FOR TRANSVERSE SECTIONS IN WAY OF ENGINE BEARER
SEECP Gs, S=31" TO: (3934,

Fig. 3-29, Engine Mount for High Powered Inboard Runabouts and Larger Boats.
Note Bulkheads and Additional Stiffening for Greater Strength and Rigidity.

TRANSVERSE MS

BULKHEAD

PLAN VIEW

ENGINE COMPARTMENT
BULKHEAD STIFFENED
IN WAY OF ENGINE BEARER,
BS

ENGINE BEARER —/
EXTENDED AFT TO

TRA RSE F
TRANSVERSE NSVERS LOoRS

FOR RIGIDITY
SECTION A-A

FOR TRANSVERSE SECTIONS IN WAY OF ENGINE
BEARERS SEE FIG. 3-31 TO 3-33

Fig. 3-30, Engine Mount for Cruising Sailboat - Longitudinal or Transverse
Stiffening of Shell Outboard may be required to prevent excessive vibration

ENGINE HOLO—DOWN

aa ee |

ssl

——-—-

~— ENGI NE

COATING OR STRIP

| NSULATOR
STEEL ANGLE | : (
THROUGH BOLTING —— ees!
WITH METAL SPACERS
SHELL
3 ae

—————

\

FIBERGLASS STIFFENER WITH
NON-STRUCTURAL CORE

Fig. 3-31, Engine Bearer - Steel Angle
Bolted to Hat Stiffener

ENGINE HOLO—DOWN
BOLTS

FIBERGLASS ANGLE
PRE-MOLDED WITH
TRANSVERSE WEBS
AND CHOCKS

= — =" ENGINE COATING OR STRIP
Z
! | a INSULATOR
|
( ' | STEEL CLIP IN WAY OF
=

ENGINE HOLD—DOWN BOLTS

\FIBERGLASS STIFFENER WITH
NON-STRUCTURAL CORE

Fig. 3-32. Engine Bearer - Steel
Clip Bolted to Hat Stiffener

COATING OR STRIP
| NSULATOR

tee

ees

FIBERGLASS
CONNECTING ANGLES

Fig. 3-33, Engine Bearer - Pre-molded
Fiberglass Angle Bonded to Shell

3-11

DESIGN

/MAST

_ MAST STEP

TRANSVERSE MEMBER
BELOW

7

Le
CABIN See re

fo

CENTERLINE

Fig. 3-34.

DETAILS

FIBERGLASS OR WOOD
STEP

1 PLY OF MAT
UNDER STEP TO
PREVENT NE
SEEPAGE

FULL LAMINATE IN
WAY OF STEP TO
PROVIDE CRUSHING
STRENGTH

SANDWICH CONSTRUCTION
CABIN TOP WITH LOW
DENSITY CORE

MECHANICAL FASTENERS TO
\ RESIST SIDE THRUST COVERED
— WITH FIBERGLASS CONNECTING

ANGLES
BULKHEAD OR

TRANSVERSE WEB

Cabin Top Mast Step - Fiberglass or Wood

but in fiberglass construction this heavy member is not necessary and a substantial step or

hull reinforcement must be added,
arrangement,

deck, The support under the cabin top must,
most satisfactory solution is to locate the mast directly over a bulkhead.
then a heavy transverse beam with adequate end supports must be provided,

done,

Since definite advantages are gained in accommodation
many fiberglass cruising sailboats have the mast stepped on the cabin top or

however, be very carefully determined. The
If this cannot be
Figs.

3-34 through 3-37 illustrate recommended details of mast steps.

ALUMINUM MAST
1 LAYER OF MAT UNDER

STEP TO PREVENT SEEPAGE

THROUGH BOLTS

4

CLL Um:

FULL LAMINATE IN WAY
OF STEP TO PROVIDE
CRUSHING STRENGTH

COVER FASTENER HEADS
WITH FIBERGLASS CON—
NECTING ANGLES

“UL KHEAD OR
TRANSVERSE WEB

Fig, 3-35, Alternate Cabin Top Mast
Step - Aluminum

Pulling Loads

The principles involved in developing foundations to resist pulling loads are,
similar to those discussed for the pushing loads,
The direction in which the load will be applied is

respects,
a large area to avoid high local stress.
very important,

accurately established. In other cases,

always do so,
which are physically possible,

CAST ALUMINUM OR
yas MAST STEP

SANDWICH CONSTRUC—

TION CABIN TOP
WITH NORMAL CORE

In some cases, particularly standing rigging connections,
such as,
to assume that the loading direction will always be the sensible or obvious one.
that lines should run from the cleat to the chock and from there over the side,
The foundation should therefore be designed on the basis of line directions
rather than those which are considered customary. The

aa

SANDWICH CONSTRUCTION
CABIN TOP WITH LOW

/
CABIN TOP RECESSED —_[ ~~ ry.
TO FORM STEP fe

FULL LAMINATE IN We
WAY OF STEP TO
PROVIDE CRUSHING
STRENGTH

— BULKHEAD OR
TRANSVERSE WEB

Fig. 3-36, Alternate Cabin Top Mast
Step with Recess

in some
The load must be spread over

this can be very

it is dangerous
Granted

they may not

mooring cleats and so on,

amount of load to be applied to a foundation of this type may be considered on one of two

bases.
and the foundation designed to withstand this

Either the normal line pull is arrived at by some service or operational criterion

load with a substantial factor of safety, or the

breaking strength of the line is applied and the foundation is designed to withstand this load

with a small factor of safety.

without causing permanent deformation of the supporting hull structure.

The basic requirement is that the loading line should break

Considering this,

the use of the breaking strength of the line is preferred and is the most commonly used

design criterion,

DESIGN DETAILS 3-13

/MAST

BUILT-UP
F!BERGLASS MAST STEP = =

ADDITIONAL LOCAL FIBERGLASS
REINFORCEMENT TO DISTRIBUTE
LOAD
Fig. 3-37, Mast Step at Bottom of Boat
Note Taper of Fiberglass Mast Step to
Reduce Hard Spot

Figs. 3-38 through 3-41 indicate a number of different attachments. Note that,
wherever possible, the fittings should be located near a structural strong point in the boat
such as, a frame, bulkhead or the deck edge, These locations simplify the design of a
satisfactory foundation and avoid interferences with the arrangement of the boat.

The detail design of bolted and threaded fastener connections is discussed later in this
Chapter, Where attachments become a permanent part of the structure, the bolt heads and
nuts may be sealed with resin or covered with a ply of reinforcement,

LOAD

_-DECK EDGE

FLAT BAR y VA LON ||

CHAIN PLATE

y CHAIN PLATE

>
—DECK EDGE
A

OPTIONAL ADDITIONAL PLATES
WHERE INCREASED BOLTING !S
REQUIRED

ANGLE
CHAIN
PLATE

FIBERGLASS
BRACKET AND
BONDING ANGLES

~LOCAL REINFORCING
AT TOES

b. INTERIOR SIDE CHAIN PLATE. CHAIN PLATES MAY BE CONNECTED
TO A TRANSVERSE BULKHEAD, OR THE BOTTOM OF THE BRACKET MAY
BE CONNECTED TO A LONGITUDINAL FRAME, 80TH ARE IMPROVED
CONSTRUCTIONS, CONSTRUCTION SHOWN |S CONSIDERED THE MIN—
IMUM ACCEPTABLE. A SIMILAR DETAIL 1S USED ON THE TRANSOM
FOR BACK STAY CHAIN PLATES.

a, SIMPLE EXTERIOR SIDE STAY CHAIN PLATE. SIMILAR
DETAIL 1S USED AT THE BOW FOR FORE STAY CHAIN PLATES

Fig. 3-38, Chain Plate Attachments

Z0ECK EDGE
PZ WINGS CUT OFF BELOW
DECK AND WEB EXTENDED

THROUGH DECK

DECK EDGE

THROUGH BOLTS —
COUNTERSINK AND COVER
OUTBOARD SIDE

LOCAL REINFORCEMENT
ADDED TO REDUCE
BEARING STRESS

THROUGH BOLTS —
COUNTERSINK AND COVER
LOCAL REINFORCEMENT ADDED “ OUTSOARD S|DE

TO REDUCE BEARING STRESS

Fig. 3-39, Chain Plate Attachments - Fig. 3-40. Chain Plate Attachment -
Simple Interior Side Stay Chain Plate Wing Channel Side Stay Plate

3-14 DESIGN DETAILS

7—— THROUGH BOLTS |
CHOCK |
WITH LARGE WASHERS I|

SEE DETAIL A

JACK STAFF BASE
SEE DETAIL Ic

DECK EDGE FITTING —
CHOCK OR CLEAT

—NORMAL LAMINATE CLEAT

“ \ LOCAL REINFORCEMENT FOR SEE DETAIL B

INCREASED DECK STRENGTH TRANSVERSE BULKHEAD
) ‘BRACKETS TO BE USED AS NEEDED
FOR HEAVY DUTY FITTINGS WINDSHIELO FASTENERS

SEE DETAIL C
DETAIL A

THROUGH BOLTS WITH MOORING CLEAT

LARGE WASHERS —

DECK LAMINATE

ann
—— S=
SF ae ee SELF TAPPING OR TAPPED MISCELLANEOUS FITTINGS —
FASTENERS. THROUGH BOLTS = WINDSHIELD, JACK STAFF BASE, ETC
a
REINFORCEMENT WITH WASHERS MAY ALSO BE
SHAPE MAY BE USED TO USED DEPENDING ON LOAD >= =a
PROVIDE: REQUIRED STRENGTH S~ LocAL REINFORCEMENT IF REQUIRED

DETAIL B DETAIL C

Fig. 3-41. Attachment of Fittings

APPENDAGE CONNECTIONS

Rudder

The attachment of the rudder to the hull is one of the most important connections which
must be made, and an extremely conservative design is recommended. Consequences of
failure are so serious that the additional cost and weight for an excessively strong joint is
more than justified. The loading on the rudder may be determined by standard formulas
contained in the usual naval architectural texts, In the case of rudder configurations using
gudgeons and pintles, which are often standard pieces, it is recommended that the attach-
ment to the hull be designed so that the pintle will fail before permanent damage is done to
the hull. Figs. 3-42 and 3-43 indicate standard methods for these connections,

Shaft

One of the most frequent causes of annoying leakage and excessive noise in small boats
is the passing of the propeller shaft through the shell. The problems associated with this
connection usually arise from poor workmanship, rather than structural inadequacy. The
designer can help insure proper workmanship, however, by providing a design for the
shaft support and connection to the hull which is simple and easy to install.

The shaft passes through the hull in the conventional manner in a standard type bearing.
Normally, the shell laminate is completed, the hole for the bearing drilled out and the
bearing bonded in place with an adhesive. Some epoxy resins, because of their greater
strength and higher resistance to water penetration, are recommended, but polyester
resins have been successfully used. If required, local reinforcement can be added to
build up the laminate for proper seating of the bearing flange.

OUTFIT CONNECTIONS

On any small boat there are many small miscellaneous items which primarily con-
tribute to the usefulness or appearance of the craft. These items include windshields,
windows, flagstaff fittings, rubber treads, floor boards, etc. The common fastener for

the area to which it is attached,

DESIGN DETAILS 3-15

attaching these items is the self-tapping screw. The only requirement for most of these
fittings is that the laminate be thick enough to retain the screw. In the case of windows,
the fastenings should be designed so that the window will withstand the same loadings as

This is particularly important where shell ports are used,

Pao Neen RUDDER
Z / STUFFING BOX AND BEARING

LOCAL REINFORCEMENT

FOR BOLTING
THROUGH BOLTS es

LOCAL REINFORCEMENT STRAP RIVETED
TO RUDDER
===

ANNULAR METAL RING ai
FOR WASHER ACTION

BASIC HULL
uf A

LAMINATE THROUGH BOLTS AND -

WASHERS ON GUDGEON

a. SPADE RUDDER — ORDINARY SKEG RUDDER SIMILAR %. SMALL SAILBOAT — GUDGEON AND PINTLE

Fig. 3-42, Rudder Connections

STUFFING TUBE — INSTALLATION

SIMILAR TO SPADE RUDDER SKEG

= (a Si ad : = a LAMINATE
x ¥ ¢ a Ze
ee \ ZARY | LOCAL REINFORCEMENT
E - —~ OGEON ———
SHELL } =) ste) \ | OR FILL SKEG IN SMALL
Y | BOAT WITH MIXTURE OF

CHOPPED FIBERS AND
= SSS RESIN

/
RUDDER —+/
ies - THROUGH BOLTS SECTION A-A
Fig, 3-43, Rudder Attachment for
Large Cruising Sailboat

MECHANICAL FASTENERS

In designing connections utilizing mechanical fasteners, it is necessary to provide

adequate strength to prevent failure of the fastener or the laminate retaining the fasteners
Through bolts and threaded fasteners, sometimes used with a bonding adhesive, are the

most commonly used with reinforced plastics.

The selection of the type of fastener to be

used depends on the load, laminate strength and thickness, location in the boat hull

desired appearance of the finished hull

» and ease of disassembly when necessary.

Bolted Connections

strength of the bolt is attained,
of the laminate

between the bolt hole and the edge of the laminate.

For bolted connections, several types of laminate failures may occur before the full

These failures are tearing from the bolt hole to the edge
, tearing the laminate along the line of the bolt holes and shearing a plug

Laminate failures may be avoided by

using the proper spacing of bolts, both with respect to each other and with respect to the

edge and side of the laminate.

The dimensions used are defined in Fig, 3-44.

3-16 DESIGN DETAILS

DIRECTION OF LOAD

¥.

ee
10E DISTANCE
ra gi ee gan | Fig. 3-44, Edge and Side

fo O Vi Distances and Spacing for

, O Wf Bolt Type Fasteners
SPACING—“ // O Up
= DD) SKE

yy r am
‘ Wz /A-EDGE DISTANCE
——s

The required distances, in terms of the bolt diameter, are given in Table 3-1.

TABLE 3-1 - MINIMUM EDGE AND SIDE DISTANCES AND BOLT SPACING

Type of Reinforcement Edge Distance Side Distance Spacing

Woven Roving & Cloth 2.5 diameters 2.5 diameters 3 diameters

Mat 2.0 diameters 2.0 diameters 3 diameters

If the above distances are used, failure of the connection will occur by local laminate
crushing under the bolt or shearing of the bolt (1).

Table 3-2 gives crushing strengths in way of bolts as a function of ultimate tensile
strength of the laminate for woven roving, cloth and mat reinforcement. To determine the
maximum bearing stress at the bolt which the laminate will withstand without permanent
deformation, or without complete breakdown, multiply the ultimate tensile strength of the
laminate by the number given in the ''No Permanent Deformation" or ''Maximum Load"
column respectively in Table 3-2, If several types of reinforcement are used in the
laminate, the bearing stress value should be determined by appropriate tests. In the
absence of specific test information, the bearing stress value may be determined for each
type of reinforcement, and the lowest of these values applied to the whole laminate. This
method of calculation will give conservative values, The values given have been extracted
from test data for laminates 1/4 inch thick with 1/4 inch bolts. Thinner laminates especial-
ly in ranges below 1/8 inch, or larger bolt diameter to thickness ratios, will tend to reduce
these values, The use of a bolt diameter to thickness ratio of 2 reduces these values by
about 65 per cent for the proportional limit and 70 per cent for the maximum load. The
information given here is based on test results reported in References (2) and (3),

TABLE 3-2 - LAMINATE BEARING STRENGTH

Laminate Bolt No Permanent Maximum
Type of Laminate | Thickness | Dia. Deformation Load

Woven Roving or iff

Cloth

Mat 1/4"

* Bolt bearing stress divided by laminate ultimate tensile strength,

DESIGN DETAILS 3-17

Threaded Fasteners

Whenever threaded type fasteners are KEE Fig. 3-45, Right
used in fiberglass laminates, the fastener oa wae <p and Wrong Direction
should always be perpendicular to the plies LEE for Threaded Type
of reinforcement. Edge fastening should —— Fasteners

J. ___ wron
never be used, since this tends to delaminate Ue a
the fiberglass laminate and has very little strength. Fig. 3-45 indicates the right and
wrong directions for fasteners,

The strength of threaded fasteners in fiberglass laminates depends on a number of
factors including the type of laminate, type of fastener, depth of penetration, diameter of
fastener, size of pilot hole, and direction of loading. Tests (1) have been made on two
basic directions of loading: axial, which tends to pull the fastener directly out of the
laminate; and transverse, which pulls sideways on the fastener, Fig. 3-46 clarifies
these loading directions,

DEPTH OF 7 —
a PENETRATION DEPTH OF
= PENETRATION

b. TRANSVERSE LOAD
a. AXIAL LOAD

Fig. 3-46, Threaded Fastener Loading Directions

Also indicated in Fig. 3-46 is the ''depth of penetration'' as defined for both blind and
through holes,

When used in fiberglass laminates, threaded fasteners should have edge and side dis-
tances equal to 2-1/2 times the fastener diameter, and a spacing of 3 times the fastener
diameter, Distances are measured as indicated for bolted joints, Fig, 3-44.

Tables 3-3 and 3-4 give ultimate strengths for axial and transverse loading for three
types of threaded fasteners, Table 3-3 gives strengths for fasteners in 10 ounce cloth-
polyester resin laminates having the following range of physical properties:

Tensile Strength 30, 000 to 45,000 PSI
Edge Compressive Strength 18, 000 to 27,000 PSI
Shear Strength (Perpendicular) 14,000 to 17,000 PSI

Table 3-4 gives strengths for fasteners in mat-polyester resin laminates having the
following physical properties:

Tensile Strength 6, 000 to 25,000 PSI
Edge Compressive Strength 10, 000 to 22,000 PSI
Shear Strength (Perpendicular) 10, 000 to 13,000 PSI

Table 3-4 should also be used for woven roving laminates,

3-18 DESIGN DETAILS

For laminates reinforced with various types of reinforcement, the table giving the
lowest strength should be used, These tables give fastener type, size, recommended
minimum penetration; below this amount strengths are erratic and unreliable; strengths
for this minimum penetration, and maximum strength and penetration. Straight line
interpolation may be used between these values, Penetrations greater than the given
maximum do not increase the strength.

Fasteners given are standard steel machine screws, and self-tapping screws of two
types, thread forming and thread cutting, Drilling and tapping of holes for machine screws
should be in accordance with normal practice. The drilling of pilot holes for the self-
tapping screws was investigated and it was found that, in general, the smallest hole which
permits the screw to be driven without excessive difficulty gives the best results. The use
of either larger or smaller holes results in decreased strengths,

The use of the tables is illustrated by Design Example 3-1, It must be noted that the
strength values given are for load at failure and a reasonable factor of safety must there-
fore be applied as shown in the example.

DESIGN EXAMPLE 3-1 - USE OF TABLES FOR DETERMINING
THREADED FASTENERS

A pad eye is to be fastened to a 1/2 inch thick mat laminate, and the pad eye
holds a line with a breaking strength of 1500 pounds applied normal to the laminate,
The pad eye is held to the laminate by 4 fasteners, which cannot penetrate the
laminate, The problem is to determine the type and size of fastener to use,

If equal load distribution is assumed, each fastener must support 1/4 of the
load, or 375 pounds, When the breaking strength of the load applying part is
used a relatively small factor of safety may be used; assume 2 for this problem,
The choice of factor of safety is discussed in Chapter 6, Each fastener must
therefore be designed to support an ultimate load of 2 x 375 or 750 pounds,

As a first trial, take a number 4-40 thread cutting self-tapping screw, at
a 3/8 inch maximum penetration from Table 3-4,

Axial holding force for minimum 2/16 inch penetration = 80 pounds

Axial holding force for maximum 7/16 inch penetration = 900 pounds

u

Axial holding force for 3/8 inch = 6/16 inch penetration
80 + 4/5 (900 - 80) = 736 pounds

Since 736 pounds is less than the 750 pound ultimate load, this fastener is
not satisfactory.

By repetition of the above calculation for different fasteners, the 6-32 self-
tapping, thread cutting screw is found to be satisfactory. If the maximum allowable
depth of penetration is increased to 7/16 inch the 4-40 fastener will be satisfactory.

Attachments to sandwich construction, decks or bulkheads, require special treatment,
since lightweight core materials cannot retain threaded fasteners and may be crushed when

Fastener

Size Thds.

DESIGN DETAILS

TABLE 3-3 - HOLDING FORCES OF FASTENERS IN 10 OUNCE
CLOTH - POLYESTER LAMINATES (1)

Axial Holding Force

Minimum
Depth of
Penetration
16th in.

Maximum
Depth of
Penetration
16th in.

500

700

1000

1500

2700

4000

4850

6800

7720

9000

11600

24000

1000

1300

2800

3200

4200

MACHINE SCREW

Transverse Holding Force

Vinimum

Depth of
Penetration
16th in.

SELF TAPPING - THREAD CUTTING SCREW

2

3

3

4 1000

6 2000

Laminate Mechanical Properties

Tensile Strength
Edge Compressive Strength
Shear Strength (Perpendicular)

Depth of
Penetration
16th in.

30000 to 45000 PSI
18000 to 27000 PSI
14000 to 17000 PSI

3-20 DESIGN DETAILS

TABLE 3-4 - HOLDING FORCES OF FASTENERS IN
MAT - POLYESTER LAMINATES (1)

aaa Axial Holding Force Lateral Holding Force

Paar ee 7 Minimum Maximum Minimum Maximum

Depth of Depth of Depth of Depth of
Fastener Penetration Horce Penetration Penetration Force Penetration
Size Thds. 16th in. lb 16th in. 16th in, lb 16th in,

MACHINE SCREW

450

600

1150
1500
2300
3600
5000
6500
8300
10000
12000
13500
SELF TAPPING - THREAD CUTTING SCREW

7 900 2

1100

2300 580

2500 720

4100 1600

SELF TAPPING - THREAD FORMING SCREW

Laminate Mechanical Properties

Tensile Strength 6000 to 25000 PSI
Edge Compressive Strength 10000 to 22000 PSI
Shear Strength (Perpendicular) 10000 to 13000 PSI

DESIGN DETAILS 3-21

nuts on bolts are pulled up too tightly. For these fasteners, an insert or build-up of solid
fiberglass laminate should be used to replace the lightweight core material. Fig. 3-47
indicates this insert construction. Plywood, hard wood, filled resin, and metal inserts
have been used, but are not recommended,

An alternate method for the attachment of fittings is the use of a through bolt witha
special sleeve, This construction is shown in Fig, 3-48. The sleeve is used to increase
the bearing area, and to provide a spacer so that the sandwich core cannot be crushed by
indiscriminate tightening of the nut. Local reinforcement of the skins to increase bearing
area may be necessary,

The attachment of heavily loaded fittings to sandwich construction can be accomplished
by the use of through bolting, combined with solid fiberglass inserts or build-up between
the skins. The solid fiberglass insert or build-up should be made as large as required to
distribute the load over a greater area of the sandwich panels,

UPPER SKIN
OF SANDWICH =
» MOLDED—IN OR PRE—MOLDED -
VA \ FIBERGLASS INSERT IN ( Whered
WAY OF THREADED FASTENER : Prete
| CZZZZZZP Ps ZZLL A
a 7 ) : SANDWICH SKINS
se Noche ASR Es Mal” ) LOCALLY REINFORCED
a CORERUTeR Te Zz as | | Gq A ae ee FOR |NCREASED BEARING
| aoe [ = STRENGTH 1F NECESSARY
| _ META
“a—LOWER SKIN OF FLUNG Se MN a aatie SLEEVE
SANDW1 CH | :
L
Fig. 3-47, Fiberglass Insert for Threaded Fig. 3-48. Through Bolting in
or Bolted Fastener in Sandwich Construction Sandwich Construction

TROUBLE CAUSING DETAILS

This Chapter has endeavored to show recommended construction details. The
importance of good design details cannot be over-emphasized, since many of the difficulties
experienced with fiberglass boats in the past can be traced directly to the use of improper
details. Improper details can be easily corrected before construction but are very diffi-
cult to correct after the boat is built. No list of "things not to do'' can cover all the
possibilities, but a discussion of the principal classifications of trouble causing details
should enable the designer to avoid major difficulty.

HARD SPOT

ape te STIFFENER
Oe /, b. DEFLECTED SHAPE OF FLEXIBLE PANEL UNDER

UNIFORMLY DISTRIBUTED TRANSVERSE LOAD

®. DEFLECTED SHAPE OF FLEXIBLE PANEL UNDER WITH RIGIO STIFFENER. NOTE ABRUPT CHANGE
UNIFORMLY DISTRIBUTED TRANSVERSE LOAD (N DEFLECTED SHAPE AT END OF STIFFENER
NO STIFFENING — NO HARD SPOT WHICH CAUSES HIGH STRESS CONCENTRATION

Fig. 3-49. Hard Spot Due to Abrupt Ending of Stiffener on Shell

3-22 DESIGN DETAILS
Hard Spots

Probably the major single trouble-maker in fiberglass construction is the so-called
"hard spot.'' A hard spot is any isolated rigid point of support in a shell panel, and is
caused when the shell panel attempts to flex under load but is prevented from doing so
locally by a rigid support. This in turn causes an abrupt change in the deflected shape with
very high local stresses, Fig, 3-49. These stresses can cause damage to the laminate and,
in extreme cases, actual cracking of the shell will result. Examples of hard spots include
abrupt endings of stiffeners in the middle of a shell panel and abrupt endings of partial
bulkheads. The best cure for hard spots is to avoid them by continuing the offending member
to another point of support, as extending a longitudinal to the next transverse member, Figs.
3-50 and 3-51. Analternate, of considerably less merit, is to taper the end of the member
and to provide additional layers of reinforcement locally under the hard spot to reinforce
the shell. This should be done at the junction of the shell with bulkheads and interior decks
to prevent the formation of a hard line as indicated in Fig. 3-24, Location of bunks, seats,
etc,, against the shell should also be avoided to prevent hard spots, unless each connection
is treated to minimize the abrupt change in panel deflection by local reinforcement,

/SHEce LOCAL RE!NFORCEMENT TRANSVERSE FLOOR

OR BULKHEAD
\
\
Fig. 3-90, Hard Spot -

/ Longitudinal Endings

HARD SPOT

\
\RIGID MEMBER

@. NOT ACCEPTABLE b. BETTER BUT TO BE AVOIDED c. BEST
FULL DEPTH LONGI TUDO! NAL LONGITUDINAL TAPERED TO LONGITUDINAL ENDS AT
ENDING IN UNSUPPORTED REDUCE RIGIDITY. LAMINATE STRUCTURAL TRANSVERSE
PANEL REINFORCED LOCALLY AT HARD MEMBER
SPOT
CABIN SOLE, DECK,
Yr rae LONGITUDINAL

HARD SPOT,

. i Jf We A
ame A e ; Z

i va
PARTIAL FLOOR OR Nas f iw
TRANSVERSE BULKHEAD VNU j FLOOR OR TRANSVERSE
R SS, y BULKHEAD CARRIED TO
eee g NEXT DECK. ACCESS

a. NOT ACCEPTABLE pb. ACCEPTABLE

Fig. 3-51. Hard Spot - Partial Floor or Transverse Bulkhead

A final type of hard spot is one which is not at first obvious, but which could easily
cause failure in a high speed runabout. The condition, shown in Fig. 3-52a, occurs in
double bottom construction, which is relatively very stiff and intended to reduce bottom
deflection, The inner skin, usually a built-in flat, ends at the outer shell on the bottom
of the hull instead of being carried over to the side shell. This, in effect, means that the

DESIGN DETAILS 3-23

stiff doubled portion of the bottom of the hull will deflect as a unit, and modify the deflec-
tion curve which would exist if the hull were single skin throughout, The junction of the
two sections then becomes a hard spot liable to failure. The solution to the problem is to
run the inner bottom to the side as shown in Fig, 3-52b, even at the cost of introducing a
slight slope to the outboard portion of the inner skin.

e—— CENTERLINE La
f+— CENTERLINE
DEFLECTION CURVE INNER BOTTOM ft )

UNDER BOTTOM LOAD va We
INNER BOTTOM ie EDGE OF INNER BOTTOM
y ray / ae NO Ne 3S — CARRIED OUTBOARD TO
K> ee ae NEARLY VERTICAL SIDE
/ LEN TT oak spor ue To SHELL AND LANDED ON
ABRUPT CHANGE IN STIFFENER OR REINFORCED
RIGIDITY AREA TO EASE TRANSITION

b. IMPROVED
a. POOR

Fig. 3-52. Double Bottom Arrangement
Stress Concentrations

A major problem in all structural design is stress concentration, The usual design
formulas give stresses based on the assumption that the member being considered is of
uniform, or at worst gradually changing shape. When an abrupt change in shape occurs,
such as a hole, sharp bend, or a lap joint in a tension member, stresses much higher than
simple standard calculations indicate can occur, As explained in Chapter 5, this is
particularly important in fiberglass design because of the material's lack of ductility.

The nature of a reinforced laminate is such that discontinuities causing stress concen-
trations are often introduced by the laminating process. For instance, a change in the
number of plies of reinforcement, small laps between adjacent pieces of reinforcement,
thick and thin spots in mat, voids and resin rich or poor areas are all examples of discon-
tinuities in the material which should be avoided or compensated for. In the case of the
change in the number of plies, the over-all thickness of the laminate determines the degree
of severity of the discontinuity. A change from 8 to 9 plies is obviously less serious than
a change from 8 to 4 plies. Abrupt changes in the number of plies such as 8 to 4 will
create a high stress concentration which can be easily avoided by gradually reducing the
plies with a generous distance between endings.

There exists a considerable amount of theoretical and experimental data and experience
on stress concentrations in elastic, isotropic materials, to assist designers in determining
their effect and to establish design rules, Unfortunately, similar technical information does
not exist for fiberglass laminates. Some experimental work (4) has been done with laminates
reinforced with 181 glass cloth only, and the number of samples tested for each configura-
tion was limited. Therefore the effects of differences in reinforcements as well as varia-
tions in fabrication could not be evaluated. These effects must be considered when lami-
nates reinforced with different types of reinforcement are used.

The major causes of stress concentrations in any material are holes, notches, and
abrupt changes in the geometric property, Such as, area or section modulus, which con-
trols the stress in the cross section being considered, If holes must be cut, they should
be kept as small as possible in relation to the size of the member. If a transition must be
made in the depth of a shell longitudinal, it should be made gradually, preferably, at a 4
to 1 slope.

3-24 DESIGN DETAILS

Re-entrant corners, generally called notches, should be avoided whenever possible, and
if they must exist should have a generous radius, Fig. 3-53 indicates a re-entrant corner,
— GOOD-RE-ENTRANT CORNER
IMPROVES WITH INCREASED RADIUS A common source of difficulty in steel
vessels is the high stress concentration at the
THIS 1S NOT A RE-enTRANT COrner of a rectangular or square hole, These
Pe bi esl eae ae corners are always given generous radii to
mG ee reduce this stress concentration, The
ray experimental work with glass cloth laminates
(4) indicates, surprisingly, that for 181 cloth
laminate a round cornered cut has slightly
less strength than a cut of the same over-all
hewmen ae size with square corners. No explanation is
NO RADIUS given for this seeming discrepancy, but it is
presumed to be due to the orthotropic proper-
ties of the laminate. Since the reported
difference between strength for square and
round corners is small for orthotropic materials and since most boat laminates contain
mat, which is essentially an isotropic material that should be much stronger with rounded
corners, it is recommended that square or rectangular cuts in boat structure be provided
with corner radii, as indicated in Fig. 3-54b.

! [

BEST CONSTRUCTION
GRADUAL CHANGE IN SHAPE

fee
J

=
LOAD |
—— ee

Fig. 3-53, Re-entrant Corner due
to Change in Shape

\ ROUNDED CORNER
RELIEVES STRESS CONCENTRATION

SQUARE CORNER
CAUSING HIGH STRESS
CONCENTRATION ———

CUMEUNT RECS CUT IN DECK} /
FOR COCKPIT,

eer r
ACCESS HATCH, / J
ETC ‘

a, NOT ACCEPTABLE b. ACCEPTABLE

Fig. 3-54, Deck Cuts

A common source of stress concentration due to structural discontinuity is the bonded
joint. Table 3-5 obtained from (5) indicates, in broad categories, the stress concentration
present in bonded joints between similar materials under three different types of loading.
The loads indicated are tension (T), compression (C), and bending (M). Joints whose
stress concentrations are listed as major for a particular type of loading should be avoided
for major structural parts loaded in a similar way. When stress concentrations are listed
as moderate, it is recommended that the joint be avoided unless the over-all stress level
is kept low.

Notice the difference between the beveled joints and the unbeveled ones of the same
type. This is an excellent illustration of the benefits of gradual changes in shape as
opposed to abrupt changes.

Knife Edge Crossing

The knife edge crossing, illustrated in Fig, 3-55, is a problem which tends to occur
often, and can be more serious in larger boats. As the figure indicates, the stress level

DESIGN DETAILS 3-25

in the load carrying members which meet at right angles to each other need not be high
for this connection to be a trouble-maker, because the reduction in load carrying area is
so great. The problem is magnified if the intervening member which must transmit the
load is made of fiberglass laminate, because this intervening member is being loaded in
the wrong direction, causing delamination, as was previously explained and indicated in
Fig. 3-1. A bolted connection is used to avoid this delamination, Note how the introduc-
tion of small brackets increases the area of load transfer considerably.

TABLE 3-5 - STRESS CONCENTRATIONS IN BONDED JOINTS

c C — COMPRESSION
oS ————— eo
M M

— FLEXURE

JOINT STRESS CONCENTRATION UNDER
T c M
SCARF MINOR MINOR MAJOR
OFFSET LAP MAJOR MAJOR MAJOR
DOUBLE BUTT LAP MODERATE MINOR MAJOR
E =
i — {
= }
LAP MAJOR MAJOR MAJOR
DOUBLE BEVEL LAP MINOR MINOR MODERATE
———————————
INSET LAP MAJOR MINOR MAJOR
BEVELLED INSET LAP MODERATE MINOR MAJOR

TRANSFER MEMBER

TRANSFER MEMBER ALTERNATE 5 “ ies

POSITION OF
BRACKET

VERTICAL LOAD
e CARRYING MEMBER

HOR! ZONTAL
LOAD CARRYING
=

MEMBER
THROUGH BOLTS

= TO AVOID DELAMI NATION
OF TRANSFER MEMBER

b. ACCEPTABLE — LOAD TRANSFERRED BY BOLTS.
BRACKET MAY BE USED ON ONE SIDE ONLY
AND MAY BE HORIZONTAL OR VERTICAL AS

a. at PTA — SMALL AREA OF LOAD SHOWNe

TRANSFER

Fig. 3-55, Knife Edge Crossing

(1)

(2)

(3)

(4)

(5)

DESIGN DETAILS
REFERENCES

Rufolo, A, ''Research and Development Report on Joining

of Reinforced Plastics with Metal Fasteners", Laboratory

Project 4860-Q-14, Final Report (NSS 034-045, Subtask 40)
Material Laboratory, New York Naval Shipyard, 12 December 1957

Werren, F. 'Bolt Bearing Properties of Glass-Fabric-Base
Plastic Laminate", U.S, Forest Products Laboratory
Report 1824, June 1951

Young, R.L. "Supplement to Bolt Bearing Properties of
Glass-Fabric-Base Plastic Laminates", U.S. Forest
Products Laboratory Report No, 1824-A, October 1955

Strauss, Eric L. ''Effects of Stress Concentration on the
Strength of Reinforced Plastic Laminates", 14th Annual
Technical and Management Conference, Reinforced Plastics
Division, The Society of the Plastics Industry, Inc.,
February 1959

Perry, H.A. ''Adhesive Bonding of Reinforced Plastics"
McGraw-Hill Book Company, Inc., 1959

4

Materials and Molding
Methods

MATERIALS

Fiberglass laminates are essentially a combination of high strength glass fibers bonded
together with relatively low strength resin. The glass fibers are distributed throughout the
laminate and provide the strength to the combination. Although individual glass filaments
can develop tensile strengths between 250, 000 and 400, 000 pounds per square inch, the
mechanical distribution of the filaments in a laminate does not permit the combination to
develop this strength.

Structural laminates usually contain 20 to 60 per cent by weight of fiberglass reinforce-
ment. The strength of a laminate is primarily dependent upon the type and the amount of
fiberglass reinforcement it contains. The amount or per cent of fiberglass reinforcement
that can be placed in a laminate depends upon the molding process and type of reinforcement.

Other important factors affecting the strength of a laminate are the resin, chemical
finish on the fiberglass filaments (1, 2) and the handling of these basic materials.

The selection of the type of reinforcement, resin and molding method should be made to
meet the necessary requirements for a specific application. High unit strengths, compara-
ble to other engineering materials such as wood, aluminim and steel, can be developed.

To obtain high stiffness weight ratio economically, molded-in stiffeners or sandwich
construction are used. Sandwich panels are usually made by bonding fiberglass laminate
facings to various low density core materials such as honeycomb, foam plastics, balsa wood
and lightweight plastic spheres embedded in resin (3, 4).

Due to the rapid development and modifications of basic materials and molding methods,
changes in the cost of materials, and variation of laminate construction will continuously
occur in the future. Since such changes cannot be considered within the scope of this text,
the following discussion is limited to presently available materials and molding methods.

To obtain maximum efficiency and economy, selection of basic materials and molding
methods for specific applications should be in accordance with manufacturers! recommenda -
tions,

REINFORCEMENTS
The glass filament used in boat hull construction is a lime-alumina borosilicate E

glass of low alkali content which has high chemical stability and moisture resistance. It
is commonly known as E glass because of its initial development for electrical applications.

4-2 MATERIALS AND MOLDING METHODS

Usually, fiberglass filaments . 00020 to . 00100 inches in diameter, with most plastic rein-
forcement filaments averaging 0. 00040 inches, are manufactured in parallel bundles known
as strands. The strands usually consist of 204 fine glass filaments drawn together without
twisting. The basic strands of glass filaments are used to make all of the different types of
fiberglass reinforcements (1,5). The types used in boat construction are roving, chopped
strand mat, cut strands, cloth and woven roving. Table 4-1 presents current uses of the
various types of reinforcements in boat hull construction.

Rovings

Rovings consist of straight bundles of con-
tinuous strands resembling a loose untwisted rope,
Fig. 4-1. Rovings are one of the most economical
forms of fiberglass reinforcements for boat con-
struction.

Rovings are used as unidirectional reinforce -
ment, woven into heavy coarse fabrics, chopped
into short lengths for use in preforms and mats; or
sprayed directly on the mold.

Unidirectional Roving: Consists of heavy un-
crimped parallel bundles or rovings in the warp
and a smaller number of thinner bundles in the fill
which may be slightly crimped, Fig. 4-2. Non-
woven individual strands or rovings can also be
laid parallel on the mold in alternate plies, at the
same or predetermined angles, to obtain maximum Fig. 4-1. Fiberglass Roving
efficiency in one or more directions. of Continuous Filament Strands

Woven Roving: Consists of flattened bundles or rovings of fiberglass filaments 1/8 "' to
1/4" wide, woven into a plain square pattern, Fig. 4-3. A number of different weave pat-
terns are available ranging in weight from 14 to 27 ounces per square yard. Woven roving
is not a cloth in the sense that the filaments are spun or twisted. The straight bundles of
filaments are woven as strands. In general, the reinforcement in the warp direction is
slightly greater than in the fill direction.

Fig. 4-2. Woven Roving Fig. 4-3. Woven Roving
Unidirectional Weave Plain Weave

MATERIALS AND MOLDING METHODS

TABLE 4-1 - FIBERGLASS REINFORCEMENTS FOR BOAT HULLS

parallel to each
other in one direc -
tion only.

cally, i.e. longi-
tudinally at keel and
deck to side con-

MOLDING
CONSTRUCTION + THICKNESS WEIGHT [be APPLICATION METHOD
Greater number of As required Additional strength Contact
strands in warp. in one direction. Bag
Unidirectional Strands placed Usually placed lo- Autoclave

Matched Die

fibers deposited
over a preform
screen and bonded
together with resin
binder.

Preforms

ment for hull and
deck. Furnishings
and hull components,
i,e., seats, bunks,
hatch covers, etc.

nections, Stiffeners.
Roving formed in . 025- 14-27 oz/sq. yd. Primary reinforce- Contact
heavy plain weave, . 043" 24-27 oz, most ment for hull and Bag
slightly heavier in popular deck.
the warp direction.
Chopped Fibers
Random chopped -030- 3/4 to 3 oz/sq. ft. | Primary reinforce- Contact
fibers bonded to- .080" 1-1/2 and 2 oz. ment for hull and Bag
Mat gether with resin most popular deck. Reinforce- Autoclave
binder or mechani- ment for bonded Matched Die
cally needled to- joints. Water barrier
gether. in cloth or woven
roving laminates.
High bulk for building
thickness,
Random chopped As required Primary reinforce- Autoclave

Matched Die

Random chopped
fiber mixed with
Chopped Strands |resin. Fillers
added as required
for molding com-

As required

Primary reinforce-
ment for hull and
deck. High bulk for
building thickness
and filling small void

Fibers and resin
deposited simul-
taneously on mold
Contact

Bag

Fiberglass mat

Cloth and Mat needled or mechani-

Fiberglass mat
needled to woven
roving.

Rovings and Mat

References 1,

()

cally stitched to cloth.

He

2 oz/sq.ft. mat
with 10 oz/sq. yd.
cloth most
popular

2 oz/sq. ft. mat
with 24-27 oz/sq.
yd. woven roving
most popular

Primary reinforce-
ment for hull and
deck.

pounds, spaces. Small parts, Matched Die
i.e., deck cleats, arm|
rests, trims, etc.

es
Cloth
Plain square open | 008- 7.5 to 19 oz/sq. Primary reinforce- Contact
Weave weave with slightly . 022" yd. 10 0z, most | ment for hull and Bag

greater number of popular deck. Surface coat

strands in warp reinforcement. Local

direction. areas for additional
strength in two

| directions,
Crowfoot satin weave Additional strength Contact
Unidirectional with greater number in one direction. Bag

of strands in warp. Usually placed lo- Autoclave
cally, i.e. longi- Matched Die
tudinally at keel and
deck to side connec -
tions,

asl ee | ee
Combinations

Contact
Bag

Primary reinforce-
ment for hull and
deck,

Contact
Bag

strength retention.

ce)

6 to 13 inclusive.

All reinforcements to have a silane size or finish for maximum wet

Types of reinforcements presented in this table are currently being

used in the molding methods discussed and are suggested for guidance
only since types of reinforcement and molding methods are subject to

change.

The

MATERIALS AND MOLDING METHODS

physical characteristics of woven roving are not only different from those of mat

but are also different from the properties of woven cloth,

Woven roving reinforcements cost more than mat, but are less expensive than cloth re-
inforcements.

The advantages of woven roving reinforcements are:

The

Spun Roving: Under development, but not included
in the test program, is a new type of reinforcement

Good drapeability and handling characteristics in the contact or hand lay up
molding method.

Provides a thicker build-up per ply of laminate than cloth.
Provides a high glass content per ply when molded by the contact molding method.

Has high directional physical strength and moduli for orientation in highly
stressed areas.

Has extraordinary resistance to impact because of the greater number of
untwisted strands in the individual bundles.

disadvantages of woven roving reinforcements are:

The fine, tightly compacted filaments of glass strands in the woven roving are
difficult to wet out or impregnate with resin. This can lead to insufficient bond
between filaments within the individual bundles of rovings.

The coarse weave of woven roving can entrap air bubbles and form voids which
tend to make the laminate porous and penetrable by water. This effect is especially
noticeable in thinner laminates.

The coarse weave of woven roving can also cause
resin rich areas between the individual bundles
and layers of rovings. Resin rich areas are
subject to brittle cracking, crazing, poor shear
strength and poor interlaminar bond.

The high directional properties of woven roving
are, for some considerations, a disadvantage.
As the main directions of reinforcement in woven
roving are in the warp and fill directions of the
weave, the strengths at angles between these
main directions are reduced as indicated in
Chapters 5 and 6,

designated ''Spun Roving". Essentially this is one con-

tinuous filament strand entangled or looped around upon

itself to give the equivalent weight of a standard parallel Fig. 4-4, Fabric made
strand roving. Fabrics made from this spun roving re- from Spun Roving

semble standard woven roving in appearance except that

MATERIALS AND MOLDING METHODS 4-5

they are somewhat more open in structure, Fig. 4-4. Asaresult, these fabrics are much
easier to wet out. Strengths tend to be more isotropic than either woven roving or fiber-
glass cloths. Interlaminar shear strengths are improved. Limited test data indicates that
these spun roving products are intermediate in their properties between standard chopped
strand mats and woven rovings. Thickness per ply, using the contact or hand lay up mold-
ing method, are greater per unit of weight than woven roving, and are somewhat less than
equivalent weight mat laminates.

Mat, Preforms and Chopped Strands

Mat: Consists of chopped strands of fiberglass, Fig. 4-5 randomly deposited, to form
a sheet orlayer. The layer of chopped strands is usually bonded or held together by a high
solubility resin binder, compatible with molding resins, Fig. 4-6. Another type of mat
does not use a binder, but is made from random strands of glass stitched together into a
layer. During manufacture, needles are driven through the mat causing some of the glass
strands to act as stitching.

Random fiberglass mat reinforcement is more economical than both woven roving and
cloth reinforcements. Mats are available in weights of 3/4 ounce to 3 ounce per square
foot. The 1-1/2 ounce and 2 ounce weights are the most suitable for boat hull construction
since maximum economical build-up can be achieved with required conformity to hull forms
and ease of material handling.

The advantages of mat reinforcement are:

Low cost per square foot and thickness.
Equal physical properties in all directions.

Good interlaminar bond due to interlocking action of fibers.

Can be molded or formed into moderate complex surfaces.

Fig. 4-5. Chopped Strands Fig. 4-6. Mat - Resin Bonded

MATERIALS AND MOLDING METHODS

The disadvantages of mat reinforcement are:

Laminate thickness cannot be controlled accurately in contact molding.

Glass content, because of movement of the individual fibers during molding,
becomes a variable and is somewhat difficult to control in contact molding.

In a polyester laminate, a typical mat fiber surface results because of
polymerization shrinkage during cure of the resin, requiring surface
finishing or a surface gel coat (1).

Contact molded mat laminates have a lower glass content than cloth or
woven roving laminates which results in a lower modulus of elasticity for
equal thicknesses. In order to overcome this deficiency, a thicker section
is required,

In matched die molding uneven distribution of the chopped fibers and varying
density can occur with deep draws and sharp corners.

Preforms: These are generally similar to mat except that they are slightly more ex-

pensive but are more practical for complex and deep draw matched die moldings, With
preforms greater utilization of the reinforcement is obtained and the possibility of tearing,
wrinkling and uneven glass distribution is reduced,

Ae

Fig, 4-7. Preform of 15' boat hull
(Courtesy Molded Fiberglass Boat Company)

Preforms are made by depositing chopped fibers of glass over a screen shaped in the

form of the object to be molded (1, 14). Continuous rovings are cut into loose fibers which
are randomly deposited on the screen by a stream of air drawn throughit. Resin binder,
compatible with the molding resin, is sprayed over the preform and cured to hold it to-
gether, Fig, 4-7. The preform is then removed from the screen and placed in the mold.

Chopped Strands: Some hulls and decks for small boats are presently being fabricated

with chopped strands and resin simultaneously deposited on the mold from a spray gun.

MATERIALS AND MOLDING METHODS 4-7

Small inaccessible voids and areas requiring high bulk in small boats are usually filled
with a pre-mix of chopped strands and resin.

Chopped strands mixed with mineral fillers and resins, form molding compounds
readily adaptable to matched die moldings (1, 15). The resin, carrying the reinforcement,
flows into place during the pressure molding process. These compounds can be used for
molding small parts such as deck cleats, arm rests, trim, etc.

Cloth

Cloths and tapes are woven from twisted and plied strands of glass filaments. A wide
range of weights and weaves are commercially available for special applications, Plain or
square weaves, Satin weaves and unidirectional weaves are among the available types.
Good drape or shaping of some cloth reinforcements is possible but the material must be
tailored to obtain proper location and orientation.

Plain Weave: Represents the simplest and commonest construction in woven cloth and
is made ina number of styles. One cloth widely used in boat construction is a plain weave,
weighing 10 ounces per square yard, and is commonly designated as boat cloth(6), Fig. 4-8.

Satin Weaves: Employ warp threads that pass over or under three or more fill threads
giving high strength and directional properties, Fig. 4-9. Satin weave cloths are used pri-
marily in the aircraft industry for obtaining very high strengths.

CO lll

Fig. 4-8. Fiberglass Boat Cloth Fig. 4-9. Satin Weave, 181 Cloth

4-8 MATERIALS AND MOLDING METHODS

Unidirectional Construction: Consists of a relatively large number of uncrimped and
closely aligned heavy yarns in the warp, and a smaller number of light yarns in the fill,
Fig. 4-10. This construction can be made in any style of weaves.

Fig. 4-10, Unidirectional Cloth

Cloth is presently one of the more expensive types of reinforcement but where con-
sistency of high performance and structural efficiency in terms of strength to weight is
required the cost can be justified.

The advantages of cloth reinforcements are:

Cloth provides an effective surfacing material to cover woven roving and

mat laminates to provide a better appearance and strength. One or several
layers of cloth laid up over a rough surface laminate can improve the appear -
ance of the finished hull.

Cloth covered mat laminates can be fabricated by hand lay up, to work out
excess resin and to obtain higher glass loadings.

Cloth laminates and sections have the most consistent glass content, and
have less deviation in physical properties and laminate thickness than any

of the other types of fiberglass laminates.

Cloth may also be used at high stress areas.

MATERIALS AND MOLDING METHODS 4-9

The disadvantages of cloth reinforcements are:

A resin rich bond may exist between heavier cloth plies which will cause
weakness in interlaminar shear. Asaresult, a cloth laminate under
edgewise compressive loading may fail by delamination,

Many layers of cloth are required for thick sections and, as a consequence,
labor and time are increased.

Combinations

Fiberglass reinforcements are also manufactured in several combined forms. Two
types of combined reinforcement are, mat stitched to cloth and mat stitched to woven roving.

The use of combined reinforcements has a number of advantages in boat hull construc -
tion. Mat stitched to cloth or woven roving improves the interlaminar bond of successive

layers and reduces porosity. Combination reinforcements allow several plies to be laid up
at one time.

Preimpregnated

Preimpregnated reinforcements, commonly called pre-preg materials, are reinforce-
ments preloaded with resins. The resins are essentially the same as those used in normal
operations where the resin is added to the reinforcement during molding (1).

The usual method for preloading is to pull the reinforcement through polyester or other
molding resins and remove the excess resins by scrapper bars or squeeze rollers to control
the glass to resin ratio. After resin impregnation, proper storage at low temperature is
required to prevent the polyester resin from curing.

Depending on the application and cost, pre-pregs can be made by the fabricator or can
be obtained to any desired specification from material suppliers.

The advantages of pre-pregs are:
Greater control of glass-resin ratios can be obtained.
Increased wetting of the glass fibers occurs.
Polyester resins of high viscosity can be used.
Resin wastage is reduced.

The disadvantages of pre-pregs are:
Additional equipment and storage facilities are required.
Storage life is reduced.

Tackiness may cause handling difficulties.

4-10 MATERIALS AND MOLDING METHODS

Sizes, Finishes and Binders

The terms size, finish and binder, due to the nature of their functions have been fre-
quently confused by the end users of fiberglass. A size is a chemical treatment applied dur-
ing manufacture to fiberglass filaments immediately after they are formed by drawing
through the bushing orifices. A finish is a chemical treatment applied to a cloth after it is
woven and cleaned. A binder is a bonding resin used to hold the chopped strands of fiber-
glass together in a mat or preform, during manufacturing, handling and molding.

Sizes and finishes are usually methacrylato chromic chloride types or unsaturated
hydrolysis products of vinyl trichlorosilane (2, 7). These sizes and finishes are commonly
known as ''chrome" and ''silane'' types. Fiberglass filaments, used in the manufacture of
mats, preforms and rovings, are usually sized with chrome or silane at the fiber forming
machine.

The chief function of chrome and silane sizes and finishes is to improve the chemical
bond between the molding resin and the glass filaments in the reinforcements. For the
weaving of glass cloth, a different type of sizing is required to lubricate and hold the strand
of filaments together during the weaving process. This sizing consists of oil, wetting agents
and starch applied to the glass filaments during the forming operation. The lubricating
action of this size assists in the weaving process and reduces the abrasion and the breaking
of the glass filaments. Lubricating size for weaving is chemically non-compatible with the
glass and resin and is detrimental to the bond between them, Therefore fiberglass cloth
intended for high dry and wet strength laminates must be heat-treated or chemically washed
to remove this size, and a chemically compatible finish be applied.

Silane sizes and finishes on fiberglass reinforcements are recommended in preference
to chrome types for boat manufacture since greater laminate wet strength is obtained.
Widely used silane finishes are Garan and A172.

The sizes, finishes and binders discussed are for use with polyester resins only. For
epoxy resins, sizes and finishes should contain an aminosilane type similar to OCF -801
size and an A-1100 finish.

Several different binders are in common use (1). Highly soluble polyester resin binders
are used on mat intended for boat construction by hand lay up.

RESINS

The resins most commonly used in the molding of fiberglass boats are thermosetting
types. Thermosetting resins cannot be remolded once cured to the solid state. Thermo-
setting resins include polyesters, epoxies, phenolics and melamine.

With few exceptions, fiberglass boats are presently being made with polyester resins
because of their cost advantage and versatility. Epoxy resins are being used in some boat
hulls and will probably increase in usage (11).

Due to a wide variation in types of resins available, manufacturers maintain Research
and Technical Service Departments for the assistance of fabricators of reinforced plastics.
A large amount of technical data on resins is available from these sources. To obtain the
highest quality laminates, manufacturer's recommendations for quantities and handling of
resins, catalysts, accelerators and inhibitors should be followed. Deviation from the pre-
scribed recommendations should only be made on the basis of extensive shop experience with
the particular materials employed.

MATERIALS AND MOLDING METHODS 4-11
Polyesters

Polyester resins are formed by the reaction of polybasic acids and glycols, A wide
variation in properties can be obtained by the use of various basic ingredients and propor -

tions (5,7). The per cent elongation of the cured resin at rupture under tensile stress is
used here as the basis for polyester classification.

Rigid Polyesters: These have higher physical strength properties than the more elastic
types. Because of their flexural stiffness, rigid polyesters are used in applications such as
smaller motorboat hulls having minimum framing where resistance to flexing under load is
important. Rigid polyesters are more brittle and have less resistance to impact than the
semi-flexible and flexible types. Cured non-reinforced rigid resins under tensile stress
have an elongation at rupture between 0.5% to 3. 0%.

Semi-Rigid Polyesters: These are compounded by the manufacturer to have greater
resiliency and more resistance to impact and to retain much of the strength properties of
the rigid type. A number of specialty polyesters, compounded for boat manufacture, fall
into this classification. Semi-rigid polyesters are preferred for larger boat hulls exceeding
16 feet in length. In large boats the flexibility of the shell is controlled by spacing of the
shell supports so that advantage may be taken of the improved impact resistance of semi-
rigid polyesters. Semi-rigid, non-reinforced polyesters have an elongation at rupture of
3% to 10%. Polyesters with properties similar to semi-rigid types have been made by blend-
ing mixtures of rigid and flexible types. A blend of 90% rigid and 10% flexible polyesters
has been commonly used in small boat construction. This mixture, which has been repre-
sentative of good practice, is an arbitrary compromise between the strength and stiffness of
the rigid type and the elastic flexible type (6).

Many fabricators prefer the single component, semi-rigid type for use in boat manu-
facture since it does not require mixing of the rigid and flexible components, Manufactured
semi-rigid types have better resistance to aging than mechanical mixtures of rigid and
flexible types.

Flexible Polyesters: These resins have an elongation exceeding 10 per cent at break
and are both flexible and elastic. Due to their flexibility, they cannot be used alone in boat
hull construction, but are often blended with rigid polyesters before molding.

Isophthalic Polyesters: These resins are a recent development of interest which ex-
hibit faster curing time and somewhat better wet and dry properties than conventional
polyesters (16). In general, isophthalic polyesters are better suited to pressure molding.

Self-extinguishing Polyesters: These resins are formulated to increase their resistance
to fire (7,17). They will not support combustion when the flame is removed.

Self-extinguishing polyesters are made from a number of compounds which are either
additives to, or integral parts of the chemical structure of the resin. Included among these
materials are chlorinated paraffins, tetrachloro phthalic anyhride, trichlorethyl phosphate,
chlorendic "HET" acid, chloro maleic acid, organic phosphonates, and chlorinated styrenes
(17). Antimony trioxide added to a polyester in small amounts, 1 to 5 per cent, is effectivein
increasing its fire resistance, particularly when used in connection with a chlorinated
polyester. Some self-extinguishing polyesters have a high viscosity making them somewhat
difficult to handle. Compounds added to increase fire resistance, that are not chemically
bound in the resin, may reduce the physical properties and leech out upon exposure, The
effect of these modifying agents on the strength and other properties of a laminate should be
carefully investigated and calibrated prior to specific application.

4-12 MATERIALS AND MOLDING METHODS

One method of increasing the fire resistance of a laminate is to seal its surface witha
self-extinguishing resin. The interior of the laminate is made with ordinary polyesters but
its outermost plies are laid up with a self-extinguishing type.

Air Cured Polyesters: Some types of polyester resins cure in air with a tacky or sticky
surface. Contact with air inhibits the curing reaction and leaves a sticky layer of uncured
resin on the surface of the laminate. This layer of uncured resin can be an advantage where
successive plies of reinforcement are laid up since it provides an effective bond for addi-
tional plies. The outer surface of a laminate made by the contact molding method should
cure with a dry or tack free surface. Resin manufacturers produce special resins capable
of curing tack free in contact with air (7).

Some of the standard rigid and semi-rigid resins produced for the reinforced plastics
industry are air curing types and entire laminates can be made with them.

Epoxy

Epoxy resins are a more recent development which have found application as laminating
resins, adhesives and coatings. Epoxy resins are syrup-like liquids which resemble
polyesters in that they can be cured or polymerized into hard solids. Epoxy resins are
chemically very different from polyesters, exhibit greater adhesion and have higher physical
properties. Shrinkage during cure is also considerably lower than that of polyesters (18).

The limited use of epoxy resins in boat manufacture can be attributed to their higher
cost and tendency of some of the curing agents used to cause skin irritation on contact.
Recently developed curing agents greatly reduce this irritant effect. Also, improved mold-
ing techniques, where the resin and glass fibers are simultaneously deposited on the mold
without appreciable contact by the operator, is increasing the usage of epoxy resin in boat
manufacture (11,13, 19),

Epoxy resins have a wide usage in fiberglass boat construction for bonding component
parts together and in sealing and caulking. Superior coatings and paints with epoxide com-
ponents have also been developed for marine use.

For the fabrication of structural laminates, epoxy resins can be molded by the same
methods used for polyester resins.

Slightly higher mechanical properties can be obtained for structural laminates molded
with epoxy resins as compared with polyester laminates. This is particularly essential
where weight and thickness criteria are of utmost importance (18),

Catalysts

Catalysts, in the form of pastes or liquids, are added to polyesters to start polymeriza-
tion or the curing reaction (7, 20,21). Approximately 1 to 2 per cent by weight of a catalyst
is used in the resin. Benzoyl peroxide dispersed in dibutyl phthalate, and methyl ethyl
ketone peroxide are several of many organic peroxides used for this purpose. If a batch of
resin is catalyzed, it must be used and not returned to storage. The type and concentration
of catalyst used affects the rate and conditions of a curing reaction.

MATERIALS AND MOLDING METHODS 4-13
Accelerators

Accelerators are usually added to polyester resins to initiate a cure at room tempera-
ture (7,21), These compounds are added to a resin in combination with catalysts to start a
rapid curing reaction without the application of heat. Cobalt naphthenate and dimethyl
aniline are two commonly used accelerators. Accelerators and catalysts will only work to-
gether in certain combinations or pairs,

Resins used for contact molding of boats often contain an accelerator added by the manu-
facturer, and these resins require only the addition of a suitable catalyst to cure at room
temperature. A knowledge of the pot life of a particular resin mix is necessary to provide
adequate time for impregnation of the reinforcement between the completion of resin mixing
and the beginning of resin hardening,

Stabilizers

Stabilizers or inhibitors are compounds added to polyesters by the manufacturer to
prolong storage life (7,21). Since polyesters are active chemicals which will slowly set or
gel over a long period of time, depending on storage conditions, overage polyester should
not be used, If tertiary butyl catechol or hydroquinone is added in small amounts to inhibit
the gelling reaction, the catalyst quantity must be modified.

The effective storage life of a polyester is largely determined by its inhibitor level and
the temperature at which it is stored. High ambient temperatures will result in shorter
storage life.

FILLERS AND PIGMENTS

Fillers and pigments are added to the molding resins to reduce shrinkage, minimize
crazing, lower material costs, impart color or opacity and to improve surface finishes (1).
Addition of excessive amounts of fillers can also increase resin viscosity to a point where it
could be difficult to work with. Laminates containing fillers may be opaque and may not be
readily inspected for internal flaws. Filled resins are often used as surfacing materials for
laminates. Commonly used fillers include diatomaceous earths, calcium carbonate and
aluminum silicate (22).

The addition of approximately 3% of silica dioxide filler by weight to a polyester resin
will make it resemble grease in consistency. When these modified resins are applied to
vertical surfaces, they will not drain or run off. Filled resins of this type are called
thixotropic resins, and are available pre-compounded from various manufacturers (6, 7, 22).

STIFFENER AND SANDWICH CORES

When necessary to economically provide greater strength and rigidity to a hull, deck or
bulkhead, stiffeners or sandwich type construction may be used depending on the degree of
strength and rigidity desired (3,4). In concept, the construction of a core stiffener and a
sandwich panel is identical except that the stiffener is proportioned to have a limited width
of flange and the sandwich panel is proportioned to have continuous facings throughout the
entire panel, The flanges of the stiffener and the facings of the sandwich panel are usually
thin high strength fiberglass laminates and the cores are thicker low density materials.

4-14 MATERIALS AND MOLDING METHODS

Commonly used materials for stiffener and sandwich panel cores in boat hull construc-
tion are wood, foamed plastics, honeycomb, and lightweight plastic spheres embedded in
GeEsing Hip. s—l:

For stiffeners, in addition to the full core materials, cores of hollow rectangular
aluminum tubing and half round paper tubing, cut to fit the hull form, are also being used
(6, 7).

Fig. 4-11. Low Density Core Materials - 1. Balsa Wood,
2. Polyurethane, 3. Honeycomb, 4. Polystyrene

Wood

Various types of wood such as hard woods, plywood and balsa have been used as core
materials, Experience has indicated that solid hard wood cores, encased in the laminate,
have a tendency to swell and thereby crack the laminates covering them, causing water
penetration. Both waterproof plywood and balsa wood cores have proven satisfactory,
balsa wood being used more frequently (23).

Foamed Plastics

Rigid unicellular prefoamed or
foamed in place plastics (5) are pri-
marily used in fiberglass boat con-
struction to provide buoyancy by
filling hollow spaces under boat
seats and other locations, Fig, 4-12.
Unlike cork, kapok and other ma-
terials, foam plastics will not decay
or become water-logged. Pre-
foamed polystyrene and foamed in
place polyurethane plastics are
generally used as buoyancy ma-
terials. Polystyrene foam, unless
properly coated to prevent contact,
will be attacked by resins containing
liquid styrene,

Fig. 4-12. Lifeboat with foam for buoyancy
(Courtesy W. Chance Associates)

MATERIALS AND MOLDING METHODS 4-15

Although relatively expensive, unicellular plastic foams, in addition to providing buoy-
ancy have the following important advantages to warrant their use as core materials:

Lightweight.

Resistance to water, fungi and decay.

Can be foamed in place - polyurethane or expandable polystyrene beads (24, 25),
Are available in prefoamed logs, boards or rods and can be easily cut, shaped
and bonded - cellular cellulose acetate and polystyrene (26,27). Unlike the lower

cost prefoamed polystyrene, cellular cellulose acetate does not dissolve in resins,
Fig, 4-13 illustrates the use of foam plastics as a core material,

Fig. 4-13. Polyurethane foamed in place

cores for main longitudinals of 36' LCVP
test section (Courtesy Budd Company)

EAR NS REE as

Honeycomb

Honeycomb cores of aluminum, fiber-
glass laminates, cotton duck and water-
proof paper are available in various sizes
and weights (27,28). Waterproof paper
honeycomb core sandwich construction,
Fig. 4-14, is the most commonly used
in boats for interior bulkheads, decks,
seats, etc.

Fig. 4-14. Sandwich Panel with
Waterproof Paper Honeycomb Core

4-16 MATERIALS AND MOLDING METHODS

Lightweight Plastic Spiieres Embedded in Resin or Syntactic Foams

Lightweight gas filled phenolic spheres embedded in either polyester or epoxy resin
forms a denser troweled in place type of core material, Fig. 4-15, presently being used in
certain areas of some boat hulls (26).

Polystyrene beads expanded to approximately 1/8'' diameter spheres and embedded in
epoxy resin are a new type of troweled in place core material that is presently being in-
vestigated (25).

The advantage of these troweled in place core materials is apparent due to the sim-
plicity of application, particularly in small restricted areas.

Fig. 4-15. Syntactic foam

being troweled in place (Courtesy Union
Carbide Corporation)

MOLDING METHODS

Nearly every type of molding method developed for reinforced plastics has been used to
make fiberglass boats (1). Many methods are in current use and all have distinct advantages
and disadvantages. The selection of a proper molding method for a particular boat construc -
tion is dependent primarily on the size of the boat, production rate, total number to be pro-
duced, and cost of both molding equipment and molded boat hull. The familiarity of the
molder with a given process and the availability of related tooling and equipment may well
be the most important considerations, The molding process most widely used in boat hull
construction is the contact method (6), This discussion indicates available methods and is
not intended to specify any specific molding process for any particular boat.

MATERIALS AND MOLDING METHODS 4-17
Heat Cure

Fiberglass reinforcement and properly catalyzed resin can be cured to a hard structural
laminate by the application of heat to initiate the reaction (21). Steam or electrically heated
molds are used to develop heat cured laminates with superior physical properties at rapid
production cycles. Open molds can be heated by a bank of infra-red heat lamps or resistance
heaters. Heat cure during molding, or subsequent heat cure, can produce superior laminates.

Room Temperature Cure

Room temperature cure does not require a heated mold. The addition of an accelerator
and catalyst to the resin will cause the necessary reaction which produces sufficient heat to
cure the laminate without the application of external heat (7,21). Room temperature cure is
extremely useful for producing very large lay ups as boat hulls because they allow extended
cure time and are difficult to heat. This slow cure cycle limits the rate of production for
any individual mold.

Contact Molding

The contact molding method, as illustrated in Figs. 4-16 and 4-17, is simply the lay-
ing up of plies of resin impregnated fiberglass reinforcement to the required thickness on an
open female or male mold of the desired hull form and allowing the laminate to cure at room
or elevated temperature (14), After the cure is completed, the boat hull is removed from the
mold and the process is repeated. For extremely large size hulls, the molds may be made
in two halves for ease in lay up and removal of the molded hull. It is easier to lay up the
plies of reinforcement over a male mold although an uneven outer surface results. Addi-
tional finishing operations are usually required to obtain a smooth outer surface and good
appearance. Since a smooth outer surface is desirable in boat hulls, the female mold is
generally preferred.

Fig. 4-16. Molding of hull of sailboat in female
mold. Resin mix being sprayed on reinforcement
(Courtesy American Carbide Corporation)

4-18 MATERIALS AND MOLDING METHODS

Fig. 4-17. Fiberglass hull of a 40' ketch
molded ona male form (Courtesy Jean
Filloux)

Bag Molding

This molding method uses a flexible membrane or bag to apply vacuum or positive
pressure to a laminate during the molding operation.

Vacuum bag molding applies pressure against a laminate by drawing a vacuum under the
bag. This molding operation is limited to a pressure Slightly less than atmospheric, 14,7
PSI. Vacuum bag molding of boat hulls is currently not being used to any appreciable extent
except in the autoclave molding method discussed below. Fig. 4-18 illustrates the flexible
rubber blanket in position covering the lay up in the mold prior to placing the entire mold
assembly into the autoclave. Pressure bag molding, Fig. 4-19, uses compressed air or
steam to force the bag down against the laminate during the molding operation. Pressure
bag molding can ordinarily operate at pressures up to 40 PSI. Bag molding operations can
readily use heated mold surfaces to produce superior laminates under rapid cure cycles (9).

Autoclave Molding

Autoclave molding uses steam to apply a uniform pressure, up to 100 PSI, and heat to
the lay up (14). Usually a vacuum is pulled between a bag and the lay up to remove air and

MATERIALS AND MOLDING METHODS 4-19

excess resin prior to applying positive pressure. Fig. 4-20 illustrates a mold assembly
inside a large autoclave.

The hull size that can be made by this molding method is only limited by the size and
initial cost of the necessary equipment.

Fig. 4-18. Rubber blanket in position Fig. 4-19. Molding of 15' hull by pressure
over fiberglass lay up (Courtesy Universal bag method (Courtesy Winner Manufacturing
Molded Products Corporation) Company)

Matched Die Molding

Matched die molding using both a male
and female die combined as shown in Fig.
4-21, applies both pressure up to 170 PSI
(8) and heat to the laminate. In most
operations, mechanical stops are used to
control the applied pressure and laminate
thickness.

It has been demonstrated that the use of
heated, matched metal dies produces fiber-
glass boats on a rapid molding cycle (8, 12).
At present, matched die molds have been
limited in use to hulls of approximately 17
feet in length due to the high cost of the
initial equipment requiring quantity produc-
tion for amortization.

Fig. 4-20. Mold assembly inside of
autoclave (Courtesy Universal Molded Products

Corporation)

Sprayed Reinforcement and Resin

A recently developed production tool, that has caused interest in the boat industry and
could possibly be used in all molding methods to increase production, is a special spray gun,

4-20 MATERIALS AND MOLDING METHODS

Fig. 4-22, capable of simultaneously depositing chopped strand fiberglass and catalyzed
resin on the mold (11, 13, 19).

In contact molding, fiberglass hulls can be rapidly built up over hull forms by use of
this spray gun. This process is presently being used in the production of some boat hulls,

Fig. 4-23.

Fig. 4-21. Molding of 15' hull by
matched die molding

(Courtesy Molded Fiberglass Boat Company)

Fig. 4-22. Spray gun
(Courtesy Rand Development Company)

Fig. 4-23. Spray gun depositing chopped
fibers and resin on hull mold (Courtesy
Larsen Boat Company)

(2)

(3)

(7)

(8)

(9)

(10)

(it)

(12)

(a3)

MATERIALS AND MOLDING METHODS 4-21
REFERENCES

Sonneborn, R.H., Fiberglas Reinforced Plastics, Reinhold
Publishing Corporation, New York, 1954

Perry, H. A. Adhesive Bonding of Plastics, McGraw-Hill
Book Co., Inc. , New York, 1959

Dietz, A.G,H. - Engineering Laminates - John Wiley & Sons,
Inc., New York, 1949

Engel, H.C. et al - Structural Plastics, McGraw-Hill Book
Go.., Ine., New York, 1st Ed. 1950

Modern Plastics Encyclopedia - Modern Plastics,
975 Madison Ave. , New York 22, N. Y., 1959

Della Rocca, R. - Reinforced Plastics in Boat Hull
Construction - 12th Annual Technical and Management
Conference, Reinforced Plastics Division, Society of
the Plastics Industry, Inc., 1957 Reprint - Plastics
Technology, November 1957 and December 1957

Morgan, P. et al - Glass Reinforced Plastics - lliffe & Sons, Ltd.
London, Philosophical Library, 2nd Edition, 1957

Gray, L. B., Molding Fiberglass Reinforced Plastic Boat Hulls
in Matched Metal Dies, 14th Annual Technical and Management
Conference, Reinforced Plastics Division, The Society of the
Plastics Industry, Inc. , 1959

Culwick, E, F., Pressure Bag Molding of Reinforced Plastic
Boat Hulls, 14th Annual Technical and Management Conference,
Reinforced Plastics Division, The Society of the Plastics
Industry, Inc. , 1957

Moore, L.D., Lahde, P. P., Evaluation of Laminate Construction
for Boats, 13th Annual Technical and Management Conference,
Reinforced Plastics Division, The Society of the Plastics
Industry, Inc., 1957

Limbach, A. P., Madden, J. J., A Commercial Process for
Epoxy Boats, 14th Annual Technical and Management
Conference, Reinforced Plastics Division, The Society of
the Plastics Industry, Inc., 1959

Raffel, B.D. & McDonald, W.C., Matched Die Molding

of a Large Outboard Motor Boat Hull, 11th Annual Technical
and Management Conference, Reinforced Plastics Division,
The Society of the Plastics Industry, Inc., 1956

Sprayup - Exciting Economies for Reinforced Plastics -
Modern Plastics, May 1959, Volume 36, Number 9

MATERIALS AND MOLDING METHODS
REFERENCES

(14) Duffin, D.J., Nerzig, C. - Laminated Plastics, Reinhold
Publishing Corporation, New York, 1958

(15) Erickson, W.O., Ahrberg, W.R., An Introduction to
Polyester Premix Molding, 11th Annual Technical and
Management Conference, The Society of the Plastics
Industry, Inc., 1956

(16) Parker, E, E,, Isophthalic Polyesters Modern Plastics,
June 1959
(17) Parkyn, B., Self Extinguishing Polyesters, British

Plastics, January, 1959

(18) Lee, H., & Neville, K. Epoxy Resins, Their Applications
and Technology, McGraw-Hill Book Co., Inc., New York, 1957

(19) Anderson, D.F., Simultaneous Deposition of Fiberglass
and Resin as a Reinforced Plastics Manufacturing Technique,
13th Annual Technical and Management Conference,
Reinforced Plastics Division, The Society of the Plastics
Industry, Inc., 1958

(20) Rybolt, C.H., The use of Organic Peroxides in the
Reinforced Plastics Industry, 11th Annual Technical
and Management Conference, Reinforced Plastics
Division, The Society of the Plastics Industry, Inc. , 1956

(21) Dean, R. T., Weber, A., Crenshaw, J. B., A Theoretical
Consideration of the Influence of Peroxide Catalysts on
Polyester Copolymerization Reactions, 11th Annual
Technical and Management Conference, Reinforced
Plastics Division, The Society of the Plastics Industry,
Ine. 19516

(22) Lubin, G., Wilcox, G., New Developments in Fillers
for Reinforced Plastics, 12th Annual Technical and
Management Conference, The Society of the Plastics
Industry, Iney.. 19a

(23) Mark, R., Zuckerman, B., Reinforced Plastics as
Protective Coatings for Wood, 13th Annual Technical
and Management Conference, Reinforced Plastics
Division, The Society of the Plastics Industry, Inc., 1958

(24) Dumbrow, B., Polyurethanes, Reinhold Publishing
Corporation, New York, 1957

(25)

(26)

(27)

(28)

MATERIALS AND MOLDING METHODS 4-23
REFERENCES

Guiffria, R-, Microscopic Study of Expandable Poly -
styrene Bead, Prepuff and Foam. Modern Plastics,
June 1959

Brenner, W., Foam Plastics - Manual No. 127,
Materials in Design Engineering, Reinhold Publishing
Co. , New York, 1959

Humke, R.K., Selection Guide for Sandwich Panel
Cores - Product Engineering, January 1958 and
April 1958

Marshall, A., Designers! Guide to Honeycomb -
Sandwich Structures, Machine Design, May 15, 1959

-
:

Be

3

Engineering Properties
of Laminates

Basic engineering properties of reinforced laminates, such as, specific gravity,
strength, moduli, Poisson's ratio, resistance to impact, etc. are primarily dependent upon
the type and direction of the reinforcement, the resin, the molding method and fabrication
technique used (1), These properties can be affected after fabrication by extended exposures
to unfavorable environmental conditions and long term loading.

Production methods with good quality controls can consistently produce high quality
laminates, Thoughtful design with the judicious selection of basic materials and molding
methods can minimize the adverse effects of environment and long term loading.

DIREC TIONAL PROPERTIES

One of the important characteristics of glass cloth and woven roving laminates is the
variation of their physical properties with direction (1). This variation of properties is
analogous to the difference in the physical properties of wood measured with and across the
grain, Materials which exhibit this characteristic are referred to as orthotropic as opposed
to isotropic materials, suchas, steel and aluminum, whose properties are essentially the
same in all directions.

Fiberglass laminates with chopped strands reinforced throughout are isotropic. Fiber-
glass laminates with mat reinforcement throughout are also considered as isotropic when
the laminates are thin and the applied stresses are in the plane of the laminate. This
assumption neglects the difference in properties in the direction perpendicular to the plane
of the laminate. When the laminates are thick and when the applied stresses are not in the
plane of the laminates, these differences must be considered.

Figs, 5-1 and 5-2 illustrate the variation in physical properties of glass fabric lami-
nates with direction, Directions referred to are all in the plane of the laminate. Fig, 5-1
shows the difference in tensile and compressive strengths and moduli for a 10 ounce cloth
polyester laminate with changing direction, Fig. 5-2 gives the same information for a
25-27 ounce woven roving polyester resin laminate, The figures show only one quadrant,
the others being similar, The figures indicate the perpendicular axes of major strength,

0 degrees and 90 degrees, which are aligned respectively with the warp and fill directions
of the fabric, The direction of minimum properties is at 45 degrees.

This orthotropic characteristic of glass cloth and woven roving laminates has great
significance in the orientation of the plies of reinforcement in a laminate and in the stress
analysis of these materials (2). A detailed discussion of a directional stress analysis pro-
blem is given in Chapter 6.

PERCENT OF MAX|MUM

PERCENT OF MAXIMUM

inne. Bale

PERCENT OF MAXIMUM

a, TENSION

PERCENT OF MAXIMUM

aN
_\N

20 40 60 80 100

PERCENT OF MAXIMUM

be COMPRESSION

Directional Properties of Parallel-Laminated 10 Ounce Cloth

and Polyester Resin, Contact Molded - Wet Condition

80

60

PERCENT OF MAXIMUM

@. TENSION

PERCENT OF MAXIMUM

PERCENT OF MAXIMUM

bd. COMPRESSION

Fig. 5-2. Directional Properties of Parallel-Laminated 25-27 Ounce
Woven Roving and Polyester Resin, Contact Molded - Wet Condition

ENGINEERING PROPERTIES OF LAMINATES 5-3

RELATIONSHIPS BETWEEN REINFORCEMENTS,
MOLDING METHODS AND PROPERTIES

There exists definite relationships between reinforcements, molding methods and
engineering properties (1,3,4). In general, increased molding pressure decreases laminate
thickness and increases glass percentage. Strength properties are improved in proportion
to increases inthe glass content, Fig. 5-3,

The different types of fiberglass reinforcements vary widely in thickness and weight
per ply in a finished laminate, when molded by the same method. Differences in shop
practices or molding techniques also produce variations in laminate thickness, weight and
strength properties for any particular type
of reinforcement, This variation due to
shop practices can be materially reduced by
quality control. Fabricators experienced in
working with a specific type of reinforcement,
resin system and molding method can con-
sistently produce high quality laminates,

Table 5-1 presents the relationship
between reinforcements, molding methods,
physical and mechanical properties. The
values given in Table 5-1 are over-all
averages presented for comparison only and
should not be used for design unless verified
by qualification tests. Fabricators should
investigate the effects of the important vari-

STRENGTH PROPERTIES

ables to establish the most efficient and Worale Hats
economical relationship for each specific SANs 16)

application. There are a number of other

minor causes of variability in laminate pro- Fig. 5-3, Strength Properties Im-
perties, suchas, humidity, temperature and prove with Increased Glass Content

improper storage and handling of basic
materials which should be considered in the production of fiberglass laminates,

TEST PROGRAM TO OBTAIN PROPERTIES - CONTACT MOLDED

Purpose

Due to practical limitations of the pressure molding methods, the greatest percentage of
fiberglass boats are presently being produced by the contact molding method. All of the
larger sizes of fiberglass boats are being made by the contact molding method, Unless new
molding methods are developed, the contact molding method is the most suitable for con-
struction of the larger fiberglass boats to be built in the near future. With further improve-
ment of the basic materials and techniques for contact molding, an increase in the construc -
tion of these larger sizes of boat hulls is expected (5).

Since the contact molding method is the most widely used for boat construction, this
extensive test program (6) was conducted to obtain necessary properties data for fiberglass
mat, woven roving and cloth reinforced polyester laminates molded by this method. Also,
since marine applications were of primary consideration, all mechanical properties were
obtained from tests of laminates in the ''wet'' condition or immersed in water at room
temperature for 30 days.

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59-4

ENGINEERING PROPERTIES OF LAMINATES Bin)

This test program was limited to those basic properties considered to be of immediate

need to designers and fabricators. Additional spare panels were fabricated and are being
retained for future testing on fatigue, creep and stress rupture properties.

Materials and Method of Fabrication

To properly evaluate the properties, 236 20 inch x 20 inch test panels were fabricated

by the contact molding method. Tests were made on 6500 specimens cut from these panels,
and the results were Statistically analyzed. The following is a list of reinforcements, resin
system and the molding method used to fabricate these panels.

Mat: Chopped strand mat conforming to Military Specification MIL-M-15617-A,
2 ounces per square foot in weight and having a high solubility polyester binder,

Woven Roving: Style HG 56 or BS 6055 with approximately equal strength in both
directions and weighing approximately 25-27 oz. per yard, or equivalent.

Cloth: Style 1000-150 conforming to Military Specification MIL-Y-1140-C, plain
weave construction weighing 9.66 ounces per square yard, or equivalent. For sim-
plicity this material is designated as 10 ounce cloth.

All of the fiberglass reinforcement had a high wet strength Silane, Garan or 136
type finish,

Cloth and woven roving laminates were parallel laminated; warp direction of all
plies were laid up in the same direction,

A blend of approximately 90 per cent rigid and 10 per cent flexible polyester resins
or a suitable modified polyester resin with equal properties was used. The difficult
task of selecting resin systems, without appearing to be arbitrary, leads to this widely
used formulation compromise which has been representative of good practice. All rigid
resin used conformed to Military Specification MIL-R-7575-A,

The catalyst system used and methods of lay up conformed to the resin manu-
facturer's recommendations,

The laminates represent the result of good shop practice with close adherence to
the resin manufacturer's process specifications for producing boat hulls and other large
structures using the contact or hand lay up method. No special post cure by heat or
other procedure was used to produce improved panels,

Types of Laminates:

Mi = Mat - 2 ounces per square foot

M2 = Woven roving - 25-27 ounces per square yard
M3 = Cloth - 10 ounces per square yard

M4 = Mat with 1 ply of 10 ounce cloth on each face

M5 = Woven roving with 1 ply of 10 ounce cloth on each face

5-6 ENGINEERING PROPERTIES OF LAMINATES

Test Procedures

Property Procedure

ASTM LP-406b
Tensile strength D-638 al(@jilal
Flexural strength ID) TASho) HOSA
Compressive strength D-695 1021, 1
Shear strength perpendicular D-732 1041
Shear strength parallel ce
Tensile modulus D-638 1011
Flexural modulus IDS 7/$)0) HOS eel
Compressive modulus D-695 O21
Specific gravity 5011
Per cent glass by volume LORSVAI Ries lane
Per cent glass by weight USA 473. 2.1, 2

Tensile Poisson's Ratio
Compressive Poisson's Ratio

Mechanical properties specimens were wet-conditioned or immersed in water at room
temperature for 30 days.

developed specifically for this program, see Appendix A.

All of the above properties were tested on specimens cut at 0 degrees, 45 degrees and
90 degrees from the warp direction of the test panel.

Statistical Analysis of Test Data

The test program was developed primarily to study the following four main variables
which were considered of primary importance:

1. Fabricators - effects of variations in good shop practice,
2. Laboratories - effects of variations in testing techniques and equipment,
3. Materials - effects of different types of reinforcement.

4, Laminate thickness - effects of number of reinforcement plies,

To keep the number of test samples to a minimum and still obtain the necessary data
for statistical confidence in the results, a balanced fourth of a full set of (4° factorial
design plus additions was used. One material was added and all thicknesses were
studied for one of the materials.

It was necessary to omit a very small portion of the test data because the pattern
of its scatter showed these points to deviate for different reasons, than those determin-
ing the normal scatter. Because the data for different fabricators frequently clustered
around different averages, it was necessary to establish a high and low range of values,
In order to establish reasonable lower limits, few unrealistic test results were ex-
cluded in the computation of the data.

ENGINEERING PROPERTIES OF LAMINATES 5-7

For each range an average value and a lower limit was established, It can be
stated, with 95 per cent confidence, that not more than 5 per cent of the panels made
under similar conditions will give values below the lower limit.

5. A detail discussion of the statistical procedure is given in Appendix B,

Results of Investigation of Main Variables

1. Fabricators - effects of variations in good shop practice,

This variable has considerable effect on some of the properties. The differences
are consistent in the sense that they are the same for all laminate thicknesses and for
angles from the warp.

2, Laboratories - effects of variations in testing techniques and equipment.

Consistent differences among test laboratories were found in some small areas
of the test data. The measurement error between duplicate coupons was not found
to be controlling for any property. In most cases, the measurement error was
negligible compared to the average random variability of a single fabricator making
similar laminates,

3. Materials - effects of different types of reinforcement.

As expected, the different types of reinforcement and glass percentage show
marked differences in physical and mechanical properties,

For most properties, and particularly for the thicker laminates, little apparent
difference exists between laminates faced with single ply 10 ounce cloth and laminates
of equal construction without facings. For these laminates, with and without cloth
facings, some differences do exist in glass content and tensile strength within both
mat and woven roving reinforcements and in tensile and flexural moduli for mat
reinforcement only.

Laminates of mat reinforcement are generally isotropic or nondirectional for all
properties, Laminates of cloth and woven roving reinforcement are orthotropic or
directional for most strength and modulus properties, but are isotropic for shear
strength properties. Laminates of cloth and woven roving are particularly directional
for tensile strength, values at 45 degrees to the warp being much lower than values at
0 degrees and 90 degrees to the warp.

4, Laminate Thickness - effects of number of reinforcement plies.

The thickness of the test laminates is a minor factor in the data for some of the
reinforcements and properties. There seems to be little consistency in this effect.
It is detected in the moduli values for some of the reinforcements and for the
strength values for other reinforcements. Thickness effect is particularly apparent
in all strengths and moduli for woven roving reinforcement,

5-8 ENGINEERING PROPERTIES OF LAMINATES

The flexural strength data for woven roving showed an important difference with
laminate thickness, Flexural strength data for laminates with other reinforcements,
2 ounce mat and 10 ounce cloth did not vary with thickness. Thickness effect for woven
roving and mat laminates faced with 10 ounce cloth was the same for equivalent lami-
nates without the facings.

The flexural modulus values were affected by laminate thickness for all reinforce-
ments and angles to the warp.

Compressive strength was found to vary with each thickness for all reinforcements
except 10 ounce cloth.

For shear strength perpendicular to warp, 10 ounce cloth and woven roving lami-
nates showed some differences with thickness while mat laminates did not.

For shear strength parallel to warp, laminates with all types of reinforcements
showed small differences with thickness.

Discussion of Tables

The data are presented in a manner considered important, from a statistical viewpoint,
to clearly indicate the effect of different shop practices on the properties of laminates
molded by the contact or hand lay up method. For most properties, the tables contain high
and low values as established by the statistical analysis. An average value and a lower
limit value established at a 95 per cent confidence level is given for each range. It is
important to emphasize that both the high and low range of values were determined from
test panels made by good fabrication practice as individually established by the participating
fabricators. The high range of values in the tables may be taken as high standards for good
fabrication practice and experience with the particular type of reinforcement.

The data in the tables would present a much simpler appearance if single property
values were given for each material. Due to the wide differences in the properties of the
laminates produced by the participating fabricators, the use of a single property value
would not be valid and could lead to serious misunderstanding. If the average property
values of the laminates in the lowest range were reported alone, the tables would give no
indication of what can be accomplished by good shop practice. If the average value from the
high range of properties was used as a single value, designers would be misled into thinking
that all fabricators could produce laminates of equally high quality. If an over-all average
of the high and low test results were reported alone, it would differ considerably from the
true values of any fabricator. Any attempt to rectify this situation by establishing some kind
of a range of variation around an over-all average would introduce more confusion, since
this range does not represent the variability of the material of any one fabricator. Rather,
it would be a mixture of the intrinsic and random variability of the material for any one
fabricator with the systematic differences in level due to systematic differences in
shop practices.

There appears to be no valid substitute then for indicating the variation among fabri-
cators, particularly when this variation is large. Therefore this variation is indicated by
giving two separate average values. One value is for those fabricators who maintained a
definitely higher average level; another value is for those fabricators who produce material
at a lower average level,

ENGINEERING PROPERTIES OF LAMINATES 5-9

Below each average value, a lower limit, LL, is also given. It can be taken as assured
that 95 per cent of the panels from a single fabricator who can maintain the average given,
will have values of the property above this lower limit.

Entry into a table's high or low range should be made on the basis of qualification tests.
Basic testing of samples from several large panels for tensile, flexural and compressive
strengths and moduli, and per cent glass would enable a fabricator to determine his laminate
quality. Application of the tables could be made on the basis of a few such fixed points. A
fabricator producing laminates with high tensile and flexural strengths and moduli would
design from the high range values of the table. Conversely, a fabricator obtaining values
in the low ranges would necessarily design to that range. Fabricators with improved shop
practices and rigid quality control can undoubtedly produce the higher strength lami-
nates consistently.

PHYSICAL PROPERTIES

Thickness and Weight

The importance of laminate thickness and its effect on physical properties has been
previously discussed and should be carefully controlled during the molding process, This
is particularly true for contact molding where variation in thickness can occur more readily
than with pressure molding, Table 5-2 presents the relationship between the number of plies
and laminate thickness, and Table 5-3 presents the relationship between the number of plies
and laminate weight. Since the variation in laminate thickness and weight for all fabricators
was not as Significant as the variation in strength properties, over-all averages were con-
sidered sufficiently reliable. In addition to the average values, the ranges of average
variability in thickness and weight are also given,

Glass Content and Specific Gravity

Glass content is controlled by the type of reinforcement and molding method used to
make the laminate. The specific gravity of a laminate is dependent upon the glass content
and, to a lesser degree, upon the voids that may be present in the laminates, Table 5-4
presents per cent glass by weight and volume, and specific gravity for the laminates evaluated,

Void Content

Fiberglass laminates often have small voids or bubbles which detract from their
strength properties (7). Voids are formed chiefly by entrapment of air during lay up of the
resin and reinforcement and by release of volatile components from the resin during cure.

Laminates made by the contact molding method tend to have a higher void content than
laminates molded under pressure. Sufficient pressure on a laminate during molding can
force out a large portion of the air bubbles. Although voids cannot be eliminated entirely
from laminates made by the contact method, careful fabrication techniques can be used to
keep them at a minimum, Laminates that are essentially void free can be made with light
cloth reinforcement by the contact method.

Air bubbles can be worked out of a lay up to a considerable degree by use of rollers
and other implements. Inclusion of air bubbles in the resin during mixing or stirring
operations should be avoided. Resin cure temperatures should be kept below the point

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TABLE 5-4, FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED
GLASS CONTENT AND SPECIFIC GRAVITY

LAMINATE RANGE % GLASS BY WEIGHT | % GLASS BY VOLUME | SPECIFIC GRAVITY
30,7 ** 17.6 ** 1,45 **
2 Oz. Mat 25.0 13,4 1,38
22.4 12,2 1,40
16.7 8.0 1, 33
Soa7 41.8 179
25-27 Oz. W.R. 48.9 35.3 a 1,69
50.4 32.0 1, 64
43.6 25.5 1.54
47.8 30. 8 1,63
10 Oz. Cloth 45.8 27.6 diol
ee
45.7 29,2 1,56
43.7 26.0 1,44
M4
10 Oz. Cloth 34.4 20,2 1.50
2 Oz. Mat
10 Oz, Cloth 28.7 16.0 1, 43
alk
28.3 16.1 1.41
22.6 plat) 1.34
M5
10 Oz. Cloth HIGH 63.0 41.8 1.79
25-27 Oz. W.R. (1)
10 Oz, Cloth 56, 2 35.3 1.69
LOW 50. 4 32.0 1. 64
(3)
43.6 25.5 1.54
* Number of Fabricators L.L. = Lower Limit

** Values the same for all thicknesses

ENGINEERING PROPERTIES OF LAMINATES

where volatiles would form gas bubbles. Careful placement of the plies i
eliminate wrinkles which can result in large voids between the plies.

na lay up will

The following method (8) can be used to calculate the per cent voids in a laminate:

Per cent voids = 100 - 100a |24e+f
Ge) wi" ee:

a = specific gravity of the laminate from Table 5-4

b = specific gravity of fiberglass = 2.55

io)
iT]

specific gravity of cured resin = 1.18 to 1.24 as
obtained from manufacturers.

d = resin content, by weight.

oO
iT]

glass content, by weight.

f = filler content

g = specific gravity of filler

Table 5-5 contains average values of per cent voids for the test laminates calculated by

this method.

M1

M2

M3

M4

M5

Since fillers were not included in the test laminates, filler content and
corresponding specific gravity were omitted.

10 Oz. Cloth

- 20-21 Oz. Woven Roving —- 10 Oz. Cloth «* Die

2 Oz. mat faced on each side with a single layer

of 10 Oz

- cloth.

Woven roving faced on each side with a single layer

of 10 Oz

5 elltejiay,

TABLE 5-5. FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED
VOID CONTENT
Average Per Cent Voids

Laminate in Laminate Volume

- 2 Oz. Mat Doll

- 25-27 Oz. Woven Roving 1,82

- 10 Oz. Cloth dee e2

= 10: Oz, Cloth - 2.Oz, Mat = 10 Oz. Cloth * PAS idk

5-14 ENGINEERING PROPERTIES OF LAMINATES
MECHANICAL PROPERTIES
Tensile, Flexure, Compression and Shear

Tables 5-6 to 5-14 present tensile, flexural, compressive and shear strengths with
corresponding moduli for the laminates tested. Also included are values for Poisson's
ratio for tension and compression. An over-all average value is given for perpendicular
shear modulus since there was insufficient data to determine any level of variability for
this property.

The effects of the different types of reinforcements on these properties have been pre-
viously discussed in the section; Results of Investigation of Main Variables.

Impact Strength

Non-laminated plastics and similar homogeneous materials are often tested for impact
strength by an Izod test in which a small notched or unnotched sample about 1/2 inch x 1/2
inch square is clamped as a vertical cantilever beam and struck by a swinging pendulum.
The test is run on a series of samples under standard conditions and the impact necessary
to break the test sample is determined.

The Izod impact test is less applicable to laminate materials than to homogeneous
materials except when used as a rough screening method. The Izod impact method gives
the energy absorbed at failure and not a partial failure as usually occurs in laminated
materials (1).

Large areas of fiberglass laminates when struck perpendicular to the direction of lami-
nation tend to distribute the impact force due to the arrangement of the reinforcement and
due to their relatively low moduli. Therefore, under impact they deflect readily and are
capable of absorbing heavy blows. Failure of a laminate under heavy impact involves
complex shearing and delamination effects.

To determine the relative impact resistance of laminates with various reinforcements,
a test simulating actual service conditions as nearly as possible was developed. This test
consists of dropping a cylindrical impacter through a smooth steel tube to strike the simply
supported test panels. The impact testing machine consists of a 4 inch inside diameter,
seamless steel tube, 20 feet long, mounted vertically with a cylindrical impact striker having
a hemispherical head 3 inches in diameter, Fig. 5-4, The striker could be varied in weight
from 7 to 150 pounds by the addition or subtraction of cylindrical increments. This test
provides a realistic, comparative test of large panels of fiberglass laminates for resistance
to impact or heavy blows.

Laminated fiberglass panels fail under impact by delamination, puncturing, tearing and
crushing. These complex effects are difficult to evaluate. Under standardized conditions the
following method is considered a reasonable and practical approach to the problem. After
receiving a single blow from the dropped impacter, the panels are tested for leakage under a
2 foot head of water. For comparison, panels which are damaged to approximately one-half
their thickness and which leak more than 3 but less than 6 gallons per hour under the 2 foot
head of water are judged to be in a critical condition. The impact force necessary to produce
a critical condition of leakage is expressed as the weight of the impacter in pounds multiplied
by the height of drop in feet. A series of panels were tested for each of the types of lami-
nates, M1, M2, M3, M4 and Md previously discussed. Comparative evaluation of the

ENGINEERING PROPERTIES OF LAMINATES 5-15

a. Impacter at Top of 20 Ft. Long Seamless b. Panel Under Test on Supporting Frame
Steel Tube

Fig. 5-4. Impact Test Equipment (Courtesy Budd Compan})

laminates tested was made on the basis of panel thickness and weight versus impact strength
values for the critical condition only, and are given in Figs. 5-5 and 5-6. The order of
relative impact resistance for these laminates was found to be:

M2 and M5 - Woven roving and woven roving faced on each side with cloth.
M3 - Cloth

M1 and Mod - Mat and mat faced on each side with cloth.

The addition of the cloth facings to the woven roving and mat laminates has little effect on
the impact strength.

Figs. 5-5 and 5-6 can only give a relative indication of the effect of impact loading. No
test data is available which gives information on combined stresses due to impact plus other
loadings. Until such time as more data is available the designer will have to rely on exper-

ience and judgment for determining laminate configurations where these combined loads
may occur.

IMPACT VALUES — FOOT POUNDS

1400

|

| |

1200 M1 — 2 OZ. MAT

M3 — 10 OZ. CLOTH
M4 — CLOTH—MAT—CLOTH

M2 — 25-27 OZ. WOVEN ROVING

MS — CLOTH—WOVEN ROV!ING—CLOTH
1s

1000

|

M2

—e

800

600

400

LAMINATE THICKNESS — INCHES

Fig. 5-6, Impact Values of Fiber-
glass Polyester Laminates in the

Critical Condition - Based on

Laminate Weight

1400

1200

1

IMPACT VALUES — FOOT POUNDS

000

Fig. 5-5,

Impact Values of Fiber-

glass Polyester Laminates in the

Critical Condition - Based on

Laminate Thickness

M1
M2
M3
M4
M5

ze

2 OZ. MAT

25-27 OZ. WOVEN ROVING

10 OZ. CLOTH
CLOTH—MAT—CLOTH

CLOTH—WOVEN ROVING—CLOTH

+

a

aan

LAMINATE WEIGHT — LBS. PER SQ. FTe

TABLE 5-6,

TENSILE STRENGTH *

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED

Units in 103 psi

LAMINATE RANGE (2 45° iE 908 |
M1
HIGH AVG, 14.69 15.1% 15,9 *
C1) WEE
2 Oz. Mat | ee os 10, 10,7 aa Nt)
LOW AVG. Le a es) ieee
(3)
m.T.R.= 4.4 | ap 6. Maid: 7.9
pe
ae tl t2 t3 t4 tl t2 t3 t4 tl t2 t3 t4
HIGH AVG, 37.8 40.6 42.8 41.8 74 9.8 LED 11,8 35,8 326 39.0 Bin tl
(1)
25-27 Oz. W.R. L.IL 31.5 34.3 36,5 35.5 6,4 at 9,5 eye da) 29,5. 31.3 32.7 31,5
ree 3 = a a
ai t2 ae} t4 tl t2 t3 t4
LOW AVG. 301 32.9 35.1 34.1 28.1 29:9 31.3 30.1
L. T.R. = 6.3 for 0° & 90° (3) nih
= 2.0 for 45° Telos: 23.8 26,6 28.8 27.8 yaa} 23.6 20.0 23.8
M3 tl t2 t3 t4
SINGLE AVG, 24, 12,0 12,2 14.0 14,2 20.2
RANGE
| 10 Oz, Cloth (4) Dela i ee) 8.4 8.6 10.4 10.6 14,0
Ger. R, = 6.2 for 0° & 90° 19 v4 9
= 3.6 for 45°
ee
M4
10 Oz, Cloth HIGH AVG, is 15.8 15.8
2 Oz. Mat (1)
10 Oz, Cloth Lalas 13. 11.4 11.4
LOW AVG, 13.9 12.2 12.2
(3)
L.T.R, = 4.4 L.L 9.5 fet, (a8
M5
tl t2 to t4 tl t2 t3 t4 tl t2 t3 t4
10 Oz. Cloth HIGH AVG, Babs cs} 39.8 41,3 42.3 lee 9,8 This ee 28.0 34.3 oun OF aitae
25-27 Oz. W.R. (1)
10 Oz. Cloth L.L 25.0 33.5 35.0 36,0 5.4 7.8 925 9.8 21.7 28.0 30.7 31,0
+— +
up! t2 t3 t4 tl t2 t3 t4
LOW AVG, 23.6 32,1 33.6 34.6 20.3 26.6 29.3 29.6
L. T.R. = 6.3 for 0° & 90° (3) 719
='2.0\ for 45° Lp ‘Ie 1.3 25.8 27.3 28.3 i 14.0" 2053: 2320: 23,3
* Short Term Loading, Wet Condition L.L. = Lower Limit
** Number of Fabricators L.T.R. = Lower Tolerance Range
‘| Values same for all thicknesses Nominal Thickness Range tl = 1/8", t2 = 1/4"
t3 = 3/8", t4 = 1/2"

v1 Single Range Only

Balk

TABLE 5-7. FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED
TENSILE MODULUS *

Units in 108 psi

LAMINATE RANGE 0° 45° 90°
we tl t2 t3 t4 tl wie ey (ee tl #2.)
HIG AVG. .90 1.10 1.37 1,40 +90) 1.20 1,37 1,40 90 1.10 1.37
(1) oe sfc
2 Oz. Mat Toe 00! «90 12-17 1.20 nttO. 90 a, 1,20 ATA) .90 nee by
tL t2 ue t4 til t2 t3 ta tl t2 t3
LOW AVG. . 82 +90) 1,01 wow . 82 90 1.01 ow . 82 90 1.08
(3)
ec R= 220 Madu 62 70 oO Fein 62 210 81 al 62 70 81
We ti eps OR) t4 tl t2 t3 t4 wil eA
HIGH AVG. 2.26 2,48 2.57 2.61 1, 02 1,24 12:33 1.37 2.06 2.28 2,37
(1)
25-27 Oz. W.R. 5s 1.76 198 2,07 2.11 52 74 . 83 psi 1.56 EET ES i
ua t2 t3 t4 tl t2 a3} t4 tl t2 t3
LOW AVG, 184" “206 "2505 -2).19 . 60 . 82 mo 90 1.64 1.86 1,95
(1)
ie DR = 5.00 L.L 1,34 1,56 1.65 1,69 10 32 41 45 1.14 1.36 145)
M3
SINGLE AVG. 1,954 1.099 1,807
RANGE
10 Oz. Cloth (4) ls 1, 40 94 1,25
suds:
WF 10 a9
be. Re = 2.00
“a tl #2 8th tl 2 Beth tL 2B
10 Oz, Cloth HIGH AVG. 1.13 1,20 Toil 1, 30 alps} 1.20 Le2ih 1,30 1513 1,20 152i
2 Oz. Mat (1)
10 Oz. Cloth LL, Bahk} 1,00 1, 07 110 SS} 1.00 1507 10 | -93 1,00 L0:0
tl t2 £3 t4 tl 2 0 t3th: tl 28
LOW AVG, 93 oe AS PLO 393 AEM! 114 7 V0 ere} Sel 1,14
(3)
ele 5.20 Ue 73 nth 94 now Bis) «7 94 . 81 73 AH 94
ag diss plies Rise ee OSes ee a
10 Oz. Cloth HIGH AVG. 2.26 2.48 2.57 2061 1, 02 1,24 1.33 alah ¢ 2.06 2.28 2,37
25-27 Oz. W.R. (1)
10 Oz. Cloth L.L. 1,76 1.98 2.07 Zod 92 74 . 83 . 87 1.56 i) 1. 87
iin oe, ee | i ee fia, Ps
LOW AVG. 1, 84 2. 06 2.15 2.19 . 60 . 82 wok ALR) 1, 64 1, 86 1,95
Q)
eel. =),.50 | i ibe 1.34 1.56 1,65 1.69 10 32 41 . 45 1,14 1,36 1,45
* Short Term Loading, Wet Condition L.L. = Lower Limit
*s Number of Fabricators L.T.R. = Lower Tolerance Range
§’ Values same for all thicknesses Nominal Thickness Range tl = 1/8", t2 = 1/4"
13°=73/'80, t4-= 1/20

3% Single Range Only

TABLE 5-8,

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED

TENSILE POISSON'S RATIO *

LAMINATE RANGE o°
M1
SINGLE AVG, . 3249
RANGE
2 Oz. Mat (4) L.L 19

10 Oz, Cloth

10 Oz. Cloth
2 Oz. Mat
10 Oz, Cloth

M5
10 Oz. Cloth

10 Oz, Cloth

45° 90°
3279 . 320
Sate) che)

25-27 Oz. W.R.

SINGLE
RANGE
(4)

14

. 06

65

. 30

lal

. 05

SINGLE
RANGE
(4)

SINGLE
RANGE
(4)

25-27 Oz. W.R.

SINGLE
RANGE
(4)

. 06

. 30

bib

14

- 05

99

PAN

** Number of Fabricators

§ Values same for all thicknesses

§ Single Range Only

Short Term Loading, Wet Condition

L.L. = Lower Limit

Bee.

= Lower Tolerance Factor

TABLE 95-9.

FLEXURAL STRENGTH *

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED

Units in 103 psi

LAMINATE RANGE 0° 45° i 90°
M1
HIGH AVG. 27.69 27.6% 27.67
(1)
2 Oz. Mat Eel 21.0 21.0 21.0

25-27 Oz. W.R.

tl t2 t3 t4 “a” 2 wm
HIGH AVG. 27a “Bilge 8259) 73256 a 27H Slee | S290" 33256
(3) j
Lely 21.8 2553 27.0 26.7 21,8 25.3 27.0 26.7
tl t2 t3 t4 tl +2 t3 t4 tl t2 t3 t4
LOW AVG. 23.7 27,2 28.9 28.6 19.1 20.0 185 19.8 23.7 27.2 28,9 28.6
(1)
pie ies eS) ORY PY ERA aa PE Gs alk) Meee PNIRE) PERC Pay

M3
a1 9 bibit
10 Oz. Cloth
IL
SINGLE AVG chal 24.7 31.1
RANGE
Iu. T. R. = 4,..6 (4) L.L 26.5 20.1 26.5
M4
10 Oz, Cloth HIGH AVG,
2 Oz. Mat (G8)
10 Oz, Cloth Db.
> +
LOW AVG,
(3)
bet. RR. = 6.6 os
M5 t2 t3 +2 t3
10 Oz, Cloth HIGH AVG, 27.07 31,2 32:9 32.6 ; ate 3ie2) “3259
25-27 Oz, W.R, (3) bis
10'Oz;, Cloth Leb, Zoe 20.) 2ieOk s2Geim 210) cas
tl t2 +3 t4 tl t2 t3° ita vale t2 t3
LOW AVG, Qa Bins soe 9ls 28.6: LOST 2080), 8b 1958 Zoe sais
(1)
i, TR; = 5.9 L.L. W758: 24,3 233.0) 2257 13,2 14.1 12.6 13.9 Wee: -2assa aS
Short Term Loading, Wet Condition L.L. = Lower Limit
Number of Fabricators L.T.R,. = Lower Tolerance Range

‘ Values same for all thicknesses

1% Single Range Only

5-20

Nominal Thickness Range tl

t3

u

T/'s', +2
= 3/8", t4=

1/4"
1/2"

TABLE o=10.

FLEXURAL MODULUS *

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED

Units in 108 psi

LAMINATE

RANGE

90°

Ml

25-27 Oz. W.R.

10 Oz, Cloth

10 Oz. Cloth
2 Oz. Mat
10 Oz. Cloth

HIGH

AVG, . 82

t4

ti t2 t3

1,22

1.48

1,12 1,24

Ls 1,30 1,61 1.67 2.25 53 73.76 «1.06 114-5 1247 yn doz. a2.28
|
th t2 t3 t4 tl t2 t3 t4 tal) 3. t4
LOW AVG. 1,60 2,00 2.08 2.16 eid) Waid) s04 97 ipa) “1s76) ders) 1n78
(Q)
L.L. 1.17 1.57 1.65 1.73 a2 Tle iG aoe 1.09" (1533 M1s32. 01435

(1)

HIGH AVG. 1,66 1.39 1.54 1,48 RAR OYE) GR Tas; 1,43 1.43 1,36 1.30
(1)

iy) 136). 1,09 “1.24. 12118 .86 .74 .92 .96 Tis 113) 106 ad 00

tl t2 t3 t4 tl ta t3_ ta tl t2 3 t4

LOW AVG. 124 1526 1508 1,20 .69 .82 1.00 98 1,06 1.14 1.04 1,10

10 Oz, Cloth HIGH AVG. 2.25 2.80 2,56 2.67 iyo2)) 189) 1vos ~i;29 2,08 3.08 2.44 2.42
25-27 Oz. W.R. (1)
10 Oz, Cloth .L, T.60 2.20 1,96 2.07 42 59 48 Bah) 1.48 2.48 1, 84 1, 82
tl t2 t3 t4 tl t2 t3 ta ly ee eh
LOW AVG, 1, 66 2,07 nine Bt Tea WG eo . 86 1.00 1.41 1, 46 1. 65 1, 62
(1)
5.7. R. = .60 ies Le [108 1,47 1,31 1,01 16 Sou 26 0 | 2 86 1,05 1, 02
=. SS
* Short Term Loading, Wet Condition L.L. = Lower Limit
** Number of Fabricators L.T.R. = Lower Tolerance Range
Nominal Thickness Range tl = 1/8", t2 = 1/4"
{3:=-3/8",.%4.=°1/2"

5-21

TABLE 5-11.

i

COMPRESSIVE STRENGTH *

Units in 10° psi

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED

al

LAMINATE RANGE 0° + 45° 90°

Ml tl t2 t3 t4 tl . t3 t4 th ta eh t4
HIGH AVG, 210) 2050 (2268). game TSW) SPX) SPER Ge Se) 21.0 20.0 22.8 24.3
(3) aie xk

2 Oz, Mat [eels 1259 HdOmdtay 16s2 ey able) alee Gh 1269, TiO) 147 ea len2

=|
tl t2 t3 t4 tl toe Est t4 oy 2, 3 t4

LOW AVG. 1599 «1459 727 192 15.9 14.9 17.7 19.2 15.9 14.9 17.7 19.2
(1)

lena Sea Teel ee ONE | ORG) Mani al 7.8 6.8 9.6 111 78 6.8) 9,6) tied

Ma tL = 2 tB th tL = #2 3th tl t2 8th
SINGLE AVG. 13.9 15.8 19.2 19,2 10.6 9.5 11,2 11,8 13.9 15,8 19,2 19.2
RANGE

25-27 Oz. W.R. (4) ii oe 4.3 6.2 9.6 9.6 5.3 42 5.9 46.5 4.3 6.2 96 9.6

I Re ='95.6: for’ 0° & 90° 14 qT 11

= 5.3 for 45°

M3
SINGLE AVG. 21,149 16.149 19.49
RANGE

10 Oz. Cloth (4) leplb 13.0 10. 0 13.0

4

L, T.R. =5.9 bill qT b bit

M4 tl +2. 3 t4 (Be 2 £3 t4 tl t2 3 t4

10 Oz. Cloth HIGH AVG. 21,0 20,0 22.8 24.3 2160) 2080) 2248 (2453 21,0 20.0 22.8 24.3

2 Oz. Mat (3)

10 Oz, Cloth Dp Ae, 1219 1is9) “1457 16:2 12.9 11.9 14.7 16.2 12.9 11.9 14.7 16.2

tl 2 t3 ta tL t2 t3 ta ti 2° 3 t4

LOW AVG, 15.9 14.9 17.7 19.2 15.9 14,9 17.7 19.2 1559 1469 Iva7) dose
(1)

Tuts Re= 18 1 oa tet Chch eRe eabial 7.8 6.8 96 111 7.8 6.8 96 111

We tl t2 t3 t4 tl t2 t3 t4 tl t2 t3 th

10 Oz, Cloth SINGLE AVG. 13.9 15.8 19.2 19.2 10.6 9.5 11.2 11.8 13.9 15,8 19.2 19.2

25-27 Oz. W.R. RANGE

10 Oz. Cloth (4) sR ey 453 16,2. 11956 9 9x6 5.3 42 5.9 6.5 4.3 6.2 9.6 9.6

L. T.R. = 9.6 for 0° & 90° aa an or

= 5.3 for 45°

* Short Term Loading, Wet Condition

** Number of Fabricators

J Values same for all thicknesses

17 Single Range Only

5-22

L.L. = Lower Limit

Nominal Thickness Range tl

t3

= 3/8", t4=

L.T.R. = Lower Tolerance Range

LSU taal

1/2"

TABLE 5-12, FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED
COMPRESSIVE MODULUS *

Units in 108 psi

LAMINATE ie RANGE 0° 45° 90° |
M1
HIGH AVG. 1.35 1 1.357 1,35 7
(1) ork
2 Oz. Mat L.L, .74 .74 .74
LOW AVG. .93 .93 .93
(1)
ee a= 55 Tee .51 Pial 51
— 420 t3 th 8th 2 t3 th
SINGLE AVG. 1.90 2.69 2.75 ROSee te7 23 1.82 2.57 2.63
RANGE
25-27 Oz. W.R. (4) Talay 1,02 1.44 1,48 . 52 . 63 . 66 .98 1.38 1,41
79 9 79
LT, F. = .54
M3
SINGLE AVG. 2.46 1,26 250
RANGE
10 Oz, Cloth (4) Teele 1, 82 .93 1. 86
049 bibl "40
L. T, F, = .74
10 Oz, Cloth
2 Oz. Mat (1)
10 Oz, Cloth

t2 t3
1.90 2.69 2.75

t2 t3 t4
298 eli 1,23

10 Oz. Cloth SINGLE AVG. 1.82 2.57 2.63

25-27 Oz. W.R. RANGE

10 Oz, Cloth (4) L,.b, W02)) Waa” 11248 . 52 . 63 . 66 OOo leo 8 ele
lt
1 19
|
Short Term Loading, Wet Condition L.L. = Lower Limit
** Number of Fabricators L.T.F. = Lower Tolerance Factor
‘| Values same for all thicknesses Nominal Thickness Range t2 = 1/4", t3 = 3/8"

t4 = 1/20

1§ Single Range Only

5-23

TABLE 5-13.

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED
COMPRESSIVE POISSON'S RATIO *

| Values same for all thicknesses

IT Single Range Only

LAMINATE RANGE 0° 45° 90° |
M1
SINGLE AVG. naan 42 1 .42 49
RANGE
2 Oz. Mat (4) ** To Las 22 22 22
4 19 7
Loe Ge ea nd
M2
SINGLE AVG, <25 DATA 20
RANGE INADEQUATE
25-=27 Oz. WoR, (4) by ey OK FOR ANALYSIS 07
4 u 4
ta. Tb. = 530
el
M3
SINGLE AVG. 223 .61 23
RANGE
10 Oz, Cloth (4) Toe Te . 06 alt . 06
||
L, T. F. = .25 for 0° & 90° 14 a4 09
= .60 for 45°
M4
10 Oz, Cloth SINGLE AVG. . 42 42 ~ 42
2 Oz. Mat RANGE
10 Oz. Cloth (4) Tei 22 22 22
Te sDies =aa.02 bill 14 79
M5
10 Oz. Cloth SINGLE AVG. 20) DATA PAs]
25-27 Oz, W.R. RANGE INADEQUATE
10: Oz, ‘Cloth (4) Toya 3.0%, FOR ANALYSIS OF
qT q49 a9
i. LB. = 530
* Short Term Loading, Wet Condition li... = Lower Limit
** Number of Fabricators L.T.F. = Lower Tolerance Factor

TABLE 5-14,

FIBERGLASS POLYESTER LAMINATES - CONTACT MOLDED
SHEAR STRENGTH AND MODULUS *

PERPENDICULAR PARALLEL
LAMINATE RANGE STRENGTH - 103 psi MODULUS - 108 psi_[ RANGE STRENGTH - 103 psi
_|
ie tl 638th
HIGH AVG. 13.19 HIGH AVG. TONom daa | el2ede) aes
(1) 2% 0.40 § (1) *%
2 Oz. Mat Tie Diy 112 Ty 8.5 10.7 10.3 12.3
tl t2 t3 t4
LOW AVG. 9.9 LOW AVG. 8.5 9.8 10.7 11,3
(1) (1)
Ip IH, gh ola) Tease 8.0 ier 6x58 “Teds aOR. MeOls
= Se
M2 tl t2 3 t4
HIGH AVG. 15.1 15.9 16.5 16.3
(2) 0.45 u9
25-27 Oz, W.R. Opa 13.2 14,0 14.6 14.4
a
tl t2 t3 t4 tl. ee 3 t4
LOW AVG. Tino, i9n6 ida! aA3K8 SINGLE AVG. Te5963| slogan Tey
(2) RANGE
(4) Lo 5.5 13 8.4 Ot

10 Oz, Cloth

M4

10 Oz, Cloth
2 Oz. Mat
10 Oz, Cloth

10 Oz, Cloth
25-27 Oz. W.R.

0. 52

LOW
(1)

HIGH
(1)

0, 49

(2)

0.52

SINGLE
RANGE
(4)

HIGH
(1)

tl

10.5

10 Oz, Cloth Lie, here 13.2 14.0 14.6 14,4
ay ta t3_ ta tl t2 t3 t4
LOW AVG. M09 43i6 24.1 13.8 SINGLE AVG, Teo Spool Ones el Led
(2) RANGE
Pt Red ..9 1 ra) 10,0 Fis7) 12.2 21,9 (4) Lila, 5.5 753 8.4 9.1
aoe | L
* Short Term Loading, Wet Condition L.L. = Lower Limit
** Number of Fabricators L.T.R. = Lower Tolerance Range
™ Values same for all thicknesses Nominal Thickness Range tl = 1/8", t2 = 1/4"
t3 = 3/8", t4 = 1/2"

iS Single Range Only

§ Over-all Average

5-25

5-26 ENGINEERING PROPERTIES OF LAMINATES
Fatigue

When certain materials are subject to cyclic or repeated loads, fatigue failure can occur
at stresses below the ultimate static strength. Fatigue failure can be due to the reversal of
a tensile, flexural or torsional stress ina member. Reversal of stress can occur with or
without an initial or ''mean" stress, If a mean stress is present in a system that undergoes
stress reversals, the stress at failure is further reduced. In other words, when a member
is preloaded and then subjected to stress reversals, the fatigue strength of the member is
less than the strength of the same member without preload, Fatigue failures are usually
propagated by cracks in high tensile areas and can be accelerated by initial cracks, flaws,
discontinuities, holes, notches, etc.

Fiberglass laminates are subject to fatigue failures. However, because of the nature
of their composition, it is difficult to pinpoint what type of failure actually predominates,
that is, tensile, shear or delamination.

Figs. 5-7 and 5-8 present SN curves or fatigue strengths as per cent of ultimate
strengths for mat-polyester and 181-136 cloth-polyester laminates in the dry condition,
tested parallel to warp and at 73 degrees F and 50 per cent relative humidity. Similar data
for 10 ounce cloth aad woven roving is presently unavailable. These curves indicated that
both tensile and flexural fatigue strengths of fiberglass polyester laminates tend to level off
at approximately 20 to 30 per cent of their ultimate strengths at 10 million cycles (9-16).
This stress level defines the fatigue limit or the value at which the material can undergo
stress reversals for an indefinite period.

IN THE DRY.
AND TESTE
TO
4

100

60

ULTIMATE TENSILE STRESS

PERCENT OF

1 10 10° 103 104 1095 106 40? 108

CYCLES TO FAILURE

Fig. 5-7. Tensile Fatigue Strength of Fiberglass
Polyester Laminates

ENGINEERING PROPERTIES OF LAMINATES 9-27

LAE TT Hl Po aeaceute
| Bill CONDITION AND TESTE

PARALLEL TO WARP,

gaEe
==

PERCENT OF ULTIMATE FLEXURAL STRESS

CYCLES TO FAILURE

Fig. 5-8. Flexural Fatigue Strength of Fiberglass
Polyester Laminates

Laminates exposed to elevated temperatures and extreme weathering conditions or
immersed in water will have reduced fatigue strengths. In most cases, notched laminates
fail at lower stress levels, for a given number of cycles, than unnotched laminates.

Further investigation is required to ascertain whether the effect of fatigue on the
strengths of mat, 10 ounce cloth and woven roving laminates for boat hull construction will
be of greater or lesser magnitudes due to their lower moduli.

For design purposes, when fatigue strength data for a specific application is not availa-
ble, a low enough stress should be selected to insure that the laminate will withstand the
applied loads for the required number of cycles to be expected in the normal life span of
the structure.

@xreep

Creep or deformation of fiberglass reinforced laminates under constant stress is de-
pendent on time and temperature. Laminates made of different fiberglass reinforcements
and resins will exhibit different creep characteristics (17, 18).

Figs. 5-9 to 5-14 illustrate tensile and flexural creep relationships of mat, woven roving
and cloth polyester laminates at various percentages of the short term ultimate strengths.
These curves are for laminates in the wet condition tested at 73 degrees F in water except for
the tensile tests on the mat laminates which were in the dry condition and taken at 73 degrees
F and 50 per cent relative humidity. Figs. 5-9 to 5-14 indicate that creep increases at high
percentages of ultimate stress and with duration of continuous loading. Cloth laminates have
lower creep characteristics than either mat or woven roving laminates,

STRAIN—I NCHES PER | NCH

STRAIN-INCHES PER INCH

ENGINEERING PROPERTIES OF LAMINATES

LAMINATES IN DRY CONDITION

TESTED AT 73°F AND 50% R.He

VALUES INDICATED ON CURVES
ARE PERCENTAGES OF SHORT
TERM ULTIMATE STRESS.

TESTS NOT COMPLETED TO POINT
OF RUPTURE.

=e

\

ae
= ==

ney

2004
2003 ——SSss— H+ TTT [||
2002 ull

0.001 0.01 0.1 o 10 10° 403 104 10

DURATION OF LOAD — HOURS

Fig. 5-9. Tensile Creep for Continuously Loaded
Mat- Polyester Laminates

BE A
aN |
SAME EM LT

LAMINATES IN WET CONDITION
TESTED AT 73°F IN WATER AND
PARALLEL TO WARP.

VALUES INDICATED ON CURVES
ARE PERCENTAGES OF SHORT
TERM ULTIMATE STRESS.

DURATION OF LOAD — HOURS

Fig. 5-10. Tensile Creep for Continuously Loaded
25-27 Ounce Woven Roving-Polyester Laminates

STRAIN—INCHES PER INCH

STRAIN—INCHES PER INCH

ech ine

011

2909

2008

=e OO

2006

2005

~
PT]

DURATION OF LOAD — HOURS

Fig. 5-11.

ENGINEERING PROPERTIES OF LAMINATES

LAMINATES IN WET CONDITION

TESTED AT 73°F IN WATER AND
PARALLEL TO WARP,

VALUES INDICATED ON CURVES
ARE PERCENTAGES OF SHORT
TERM ULTIMATE STRESS.

Tensile Creep for Continuously Loaded
10 Ounce Cloth-Polyester Laminates

LAMINATES IN WET CONDITION
TESTED AT 73°F IN WATER.

VALUES INDICATED ON CURVES
ARE PERCENTAGES OF SHORT
TERM ULTIMATE STRESS,

DURATION OF LOAD — HOURS

Fig. 5-12.

Flexural Creep for Continuously Loaded
Mat-Polyester Laminates

5-29

STRAIN-INCHES PER INCH

TRAIN-INCHES PER | NCH

ENGINEERING PROPERTIES OF LAMINATES

LAMINATES IN WET CONDITION
TESTED AT 73°F IN WATER AND
PARALLEL TO WARP,

VALUES INDICATED ON CURVES
ARE PERCENTAGES OF SHORT
TERM ULTIMATE STRESS,

2040
2030
2020
e010.
2000
0,001 0,01 0.1 1 10 10° 10° 104 10°
DURATION OF LOAD — HOURS
Fig. 5-13, Flexural Creep for Continuously Loaded
25-27 Ounce Woven Roving-Polyester Laminates
LAMINATES 1N WET CONDITION
TESTED AT 73°F IN WATER
EL TTHA | TI AND PARALLEL TO WARP.
VALUES INDICATED ON CURVES
ARE PERCENTAGES OF SHORT
TERM ULTIMATE STRESS,
203 CY TA UIT EL
D aa
HHH ee aaiilll

°
=
+ ©

H

H

2

DURATION OF LOAD — HOURS

Fig. 5-14, Flexural Creep for Continuously Loaded
10 Ounce Cloth-Polyester Laminates

ENGINEERING PROPERTIES OF LAMINATES 9-31

Since the initial strains and total strains indicated in the Figures are relatively small
for the lower stress percentages at room temperatures, it appears that creep in fiberglass
laminates may be negligible when the load percentages are further reduced to normal design
stress levels of 20 to 30 per cent of ultimate stress. When fiberglass laminates are exposed
to higher temperatures, creep may be of considerable importance.

Further investigation of the creep characteristics of commonly used boat hull laminates
is required for normal design stress levels and slightly higher temperatures.

Rigidity

The flexural rigidity of a material is dependent on the moment of inertia of the section
and the modulus of elasticity of the material. With a constant moment of inertia, the
flexural rigidity increases with increased modulus of elasticity. Although the modulus of
elasticity of fiberglass alone is 10.0 x 106, present fiberglass reinforced plastics can only
attain moduli of elasticity between 0.5 x 106 to 5.0 x 106. The range of values is dependent
on the type of reinforcement, resin and the molding method used. Lack of stiffness when
compared to steel and aluminum can be of considerable importance when maximum rigidity
is required. But low stiffness can be advantageous where flexibility is desired for impact.
Lightweight sandwich construction with fiberglass laminate facings can be utilized where
maximum rigidity is necessary.

SUPPLEMENTARY TEST PROGRAM TO OBTAIN PROPERTIES

Purpose

The types of laminate constructions evaluated by the basic test program do not include
all of the many new types recently developed for boat hull construction. This supplementary
test program was conducted to determine engineering properties of some of these new types
of laminate constructions considered to be the most typical of those employed in the boat
industry. Table 5-15 has been developed from the results of this test program. For ease
of comparison both physical and mechanical properties are included.

The values given in Table 5-15 are intended for guidance only and each fabricator should
conduct the necessary tests to establish similar properties representative of the laminates
made in his plant.

Materials and Method of Fabrication

The materials and method of fabrication used were essentially the same as those used
in the basic program except for the weights of the mats which were 3/4 and 1-1/2 ounces
instead of 2 ounces. The laminates were made by the contact or hand lay up method with a
polyester resin and cured at room temperature. The resin was formulated specifically for
the contact molding of boat hulls and to provide some elasticity in the cured laminate. The
catalyst system used was methyl ethyl ketone peroxide. No special post cure by heat was
used to produce improved panels,

Types of Laminates
M6 = 1 ply 10 ounce cloth, 1 ply 1-1/2 ounce mat, 1 ply 25-27 ounce woven roving.

M7

1 ply 3/4 ounce mat, 1 ply 10 ounce cloth, 1 ply 25-27 ounce woven roving.

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ENGINEERING PROPERTIES OF LAMINATES 9-33
M8 = 1 ply 1-1/2 ounce mat, 2 plies 25-27 ounce woven roving.

M9 = 1 ply 1-1/2 ounce mat, 1 ply 25-27 ounce woven roving, 1 ply 3/4 ounce mat,
1 ply 25-27 ounce woven roving.

M10 = 1 ply 25-27 ounce woven roving, 1 ply 3/4 ounce mat, 1 ply 25-27 ounce woven
roving, 1 ply 3/4 ounce mat, 1 ply 25-27 ounce woven roving.

Test Procedures

The test procedures, conditioning and cutting of specimens were the same as those used
for the basic test program with the following exceptions:

All samples were conditioned for 48 hours at 72 degrees F and 50 per cent relative
humidity before being immersed in distilled water for 30 days. The shear test samples
were not immersed in water.

The shear test samples were tested dry at 72 degrees F and 50 per cent
relative humidity.

Per cent glass by volume and weight are determined by an Owens Corning Fiber-
glas test procedure instead of by the USAF method used in the basic test program.

All flexural test specimens were cut 1 inch wide instead of the 1/2 inch width
specified in LP-406-b, 1031.1.

Evaluation of Test Data

Since the purpose of this supplementary program was to evaluate various types of lami-
nate constructions within a limited time, it was necessary to restrict the scope of this pro-
gram to a minimum number of test panels and specimens which would provide maximum
data. All of the panels were fabricated and tested by a single laboratory. ‘These panels

were made with one polyester resin and only one panel was made for each type of lami-
nate construction.

The effects of differences in fabricators, laboratories and thicknesses could therefore
not be evaluated in this program and only the effect of variations in laminate reinforcements
was obtained,

Simple average values without confidence limits were determined from 5 tests per

property, per specimen, per direction except for moduli values which were taken on
two specimens,

FACTORS AFFECTING ENGINEERING PROPERTIES

In addition to the type of reinforcement and molding method used, shop practice,
environmental conditions and duration of loading are other primary factors affecting the
engineering properties of fiberglass reinforced laminates.

Careless production methods which lack proper handling and storage of basic materials
and adequate quality control will produce laminates with defects that will reduce the engineer-
ing properties of the laminates. All fabricators should investigate their facilities and molding
operations to improve their production methods and quality of their products.

5-34 ENGINEERING PROPERTIES OF LAMINATES

When exposed to unfavorable environmental conditions fiberglass laminates can be ad-
versely affected. To minimize these effects, fiberglass laminates should be properly
selected and adequately protected with a suitable gel coat.

Fiberglass laminates under long term continuous loading will exhibit a reduction in
strength properties. This is a characteristic of the material that must be considered in
design and proper stress levels must be selected to assure satisfactory long term service.

Shop Practice

The physical and mechanical properties of a laminate can be considerably reduced by
fabrication defects such as voids, wrinkles, delamination, washing, resin dryness or
richness, crazing and foreign inclusions (7), Also shrinkage of the resin and temperature
changes that occur during curing cause residual stresses in fiberglass laminates affecting
their mechanical properties. These effects can be minimized with properly controlled
curing cycles.

Voids: The causes and effects of voids in laminates have been previously discussed in
this Chapter. Excessive void content can be eliminated by careful lay up and handling
technique, particularly in contact or hand lay up molding.

Wrinkles: Wrinkles in a laminate are caused by the careless handling of the plies of
reinforcement during the lay up and molding process. A wrinkle between the plies of a
laminate causes a weak area in the interlaminar bond and reduces the mechanical strength
properties of the laminate. A wrinkle in the reinforcement causes a change in direction of
an applied stress which is detrimental to the over-all strength of the laminate.

Delaminations: Lack of proper contact between adjacent plies in a laminate during cure
results in interlaminar separation. The area of separation can be a void space or can be
filled with excess resin. Either of these conditions results in a weak spot in the laminate.
This type of defect does not readily occur in laminates cured under pressure but can result
from careless lay up in the contact method.

Washing: The equal distribution of fiberglass mat, preform or chopped strand reinforce-
ment can be disturbed by the relative movement of matched mold surfaces. This will cause
weak spots in the laminate due to the separation and uneven distribution of the reinforcement.
The effect of washing can be largely eliminated by careful mold design and handling of rein-
forcements during the molding process.

Resin Dryness: Laminates are resin dry when made with insufficient or unequally
distributed resin. Resin dryness results in inadequate bonding of the fiberglass reinforce-
ment causing excessive voids or porosityin the laminate resulting in low wet strength retention.

Resin Richness: Excessive amounts or uneven distribution of resin in a laminate can
cause resin rich areas, These resin rich areas are subject to cracking and reduce the
physical properties in a laminate due to the lack of adequate reinforcement in these areas.

Crazing: Crazing is the formation of tiny cracks through the body of a resin due to rapid
or excessively hot curing conditions. Resin rich areas or heavy unreinforced gel coats of a
laminate are subject to crazing. Gradual deterioration in crazed areas of a laminate can
occur when subjected to weather and moisture. Laminates made with rigid polyester resins
have a greater tendency to craze than laminates made with semi-rigid resins.

ENGINEERING PROPERTIES OF LAMINATES 5-39

Foreign Inclusions in Laminates: Boat hulls are usually large and careless handling
during the lay up can cause the inclusion of scraps of wood, pieces of string, paper, dirt,
etc. These foreign inclusions can cause separation and wrinkles in a laminate and reduce
its mechanical properties.

Good shop practice requires that a molding plant be kept as clean as possible to prevent
contamination of the laminates.

Curing Shrinkage: During the curing process, the thermosetting resins used in rein-
forced plastics shrink in volume dueto molecular crosslinking when passing from the liquid
to the solid state. This reduction in volume or polymerization shrinkage is more marked in
the case of polyester than epoxy resins, The resin forms a bond with the glass during the
curing process. Since the glass does not undergo any appreciable change in volume during
cure, Shrinkage of the resin sets up compressive stresses in the glass and residual tensile
stresses inthe resin, In addition, the interfacial bond between the glass and resin may be
subject to shearing stresses during the curing and bonding processes.

Another type of internal stress occurring during cure is due to thermal shrinkage. The
curing process develops a considerable amount of heat in a laminate due to exothermic
chemical reaction, Resins have a considerably higher coefficient of thermal expansion than
glass. A differential thermal shrinkage between the glass and resin occurs when a laminate
cools after curing. The effect of thermal shrinkage is additive to that of polymerization
shrinkage in causing residual stresses in the glass and resin of the cured laminate.

The residual stresses in the complex structure of a fiberglass laminate can affect
its short term or long term loading strength, fatigue strength and resistance to crazing
and weathering.

Since these stresses and defects result from the curing process, they can be minimized
by selection of optimum curing methods. Excessively rapid cures or exotherms higher
than those required for proper cure should be avoided since they can cause damage to a
laminate during cure. Thick laminate sections are particularly subject to uneven cure and
thermal stresses,

The assistance of resin and catalyst manufacturers should be obtained in order to
determine the optimum curing cycle for a molding process unless the fabricator has
established methods from the results of extensive shop practice.

Environment

Fiberglass reinforced plastics can be adversely affected by unfavorable environmental
conditions. Extended periods of water immersion and exposure to extreme weathering con-
ditions can cause some reduction in strength properties and these effects must be considered
when selecting a laminate for a specific application.

Water Immersion: The immersion of a fiberglass polyester laminate in water fora
considerable length of time will result in some reduction in mechanical properties (18). The
degree of reduction is influenced by the types of finish on the fiberglass and the percentage
of voids in the laminate. High void content laminates have low wet strength retention. As
previously discussed, high void content or porosity can occur in laminates with fiberglass
contents exceeding the average fabrication range.

5-36 ENGINEERING PROPERTIES OF LAMINATES

Figs. 5-15 and 5-16 give the relationships between fiberglass content, per cent voids and
wet strength retention for 10 ounce cloth and 25-27 ounce woven roving with silane finishes.
The graphs in these Figures, developed from limited data (19), indicate that laminates with
fiberglass contents within the average fabrication ranges have wet strength retentions of
approximately 80 to 95 per cent with the exception of compressive strength which has ap-
proximately 50 to 80 per cent retention. Laminates with lower fiberglass contents than the
average fabrication range have higher percentages of wet strength retention even though
they have lower initial strengths.

100 7 T 100 T aI T ian T
FLEXURE —}-

COMPRESS!ION

60 |— —

DAYS IN WATER

60 DAYS IN WATER
o
T
|
Eaaze |
|
|

PERCENT WET STRENGTH RETENTION
PERCENT WET STRENGTH RETENTION

408 = SS si ei walt = 1 sea Ua 40 2
7 30 i t————_++—{ 30 2 30 SS L — 30 2
9 | Fa
ae Pave Fascha = R wee ee a Mee GES a 7 ae varns are
a : ae so! : ELPA PA RANGERS +t wa SS an,
| atl | pod i TT L i
° 10 20 30 40 50 60 70 80 90 100 ° 10 20 3c 40 50 60 70 80 90 100
WEIGHT PERCENT FIBERGLASS WEIGHT PERCENT FIBERGLASS
Fig. 5-15, Fiberglass Polyester Lami- Fig. 5-16. Fiberglass Polyester Lami-
nates - Contact Molded 10 Oz. Cloth nates - Contact Molded 25-27 Oz. Woven
with Silane Finish. Relationships Between Roving with Silane Finish. Relationships
Fiberglass Content, Per Cent Voids and Between Fiberglass Content, Per Cent
Wet Strength Retention Voids and Wet Strength Retention

Equivalent data for fiberglass mat laminates relating fiberglass content, per cent voids
and wet strength retention are presently not available. Limited data indicates that fiberglass
mat laminates with silane finish on the reinforcement and fiberglass content within the
average fabrication range, have wet strength retentions of approximately 80 to 95 per cent
for most of the mechanical properties.

Recent tests on fiberglass polyester laminates immersed in water for one year have
been conducted (18) and the results are given in Table 5-16,

In most instances, laminates subjected to extended periods of continuous water immer-
sion will have reduced percentages of wet strength retention. When properly coated with an
effective paint or the more commonly used pigmented gel coat, fiberglass polyester lami-
nates used in boat hull construction will satisfactorily resist the adverse affects of exposure
to normal environmental conditions.

Weathering: Clear or translucent fiberglass polyester laminates exposed to direct sun-
light and weather over a period of years will tend to yellow and show some reduction in
mechanical properties. Fire-retardant resins containing chlorine in their molecular
structure will deteriorate at a faster rate (20). Ultra-violet rays contained in the sunlight
are considered to be the chief cause of weather deterioration.

ENGINEERING PROPERTIES OF LAMINATES 5-37

TABLE 5-16, FIBERGLASS POLYESTER LAMINATES
PER CENT WET STRENGTH FOR EXTENDED PERIOD OF IMMERSION *

Test
Period Tensile Tensile Flexural Flexural
Laminate Days Strength Modulus Strength Modulus i
1-1/2 Oz, 60 Oia) 19.8 Soeo (SENG)
Mat
365 NA 7% NA NA NA
lO) @z: 60 82.4 97.8 Soao) 94.5
Cloth
365 tytn (0) Hla ons 94,3
2o—2 OZ. 60 89.7 (95 0 (0) 94.7
W.R.
365 80. 4 NA *« 62. 0 (HS
Ref. (18)

Wet strength retention expressed as a percentage of short term
dry strength. Dry strength tests at 73°F and 50% Relative
Humidity. Wet strength tests at 73°F after immersion in water.
All test samples cut parallel to warp direction.

steste

aK Not available.

When exposed to the normal range of weathering temperatures, fiberglass polyester
laminates do not exhibit any appreciable change in mechanical properties, In general,
mechanical properties are adversely affected by increasing temperature (21).

Most laminates, particularly those used in boat hulls, are covered by paints, finishes or
pigmented gel coats for appearances. These coatings protect the laminate by screening out
the ultra violet rays and minimizing moisture absorption. Severe weathering exposure tests
of 3 years duration have proven the efficiency of these and other protective coatings in pre-
venting the deterioration of fiberglass polyester laminates,

While extended weather exposures do cause some limited reduction in the strength pro-
perties of fiberglass polyester laminates, these materials are considered superior to wood
under long term exposure. Wood under long term weather exposure is subject to swelling,
cracking, dry rot, warping and fungus attack. Ferrous and some other metals not pro-
tected by coatings, are also subject to severe deterioration under extended weather exposure.

Chemical Resistance: Fiberglass polyester laminates, when properly cured, are resis-
tant to mosi acids, oils and solvents. They are affected by strong alkalis, acids and chlori-
nated solvents (4,22). At normal outdoor exposure temperatures, fresh and salt water,

gasoline and fuel oils can be stored in fiberglass polyester tanks without any deteriorating
effect on the laminate.

Both fuel and potable water tanks can be constructed as integral parts of a
fiberglass hull structure to utilize the tank sides as stiffening for the shell. This

5-38 ENGINEERING PROPERTIES OF LAMINATES

results in a weight saving and reduced cost. Maintenance costs for special linings and
painting are not required for fiberglass tanks.

Long Term Loading

As is the case with other structural materials, fiberglass reinforced laminates will fail
under long term continuous loading at stresses below the ultimate stress for short term
loading (18). Figs. 5-17, 5-18 and 5-19 give tensile, flexural and shear long term loading
characteristics for mat, woven roving and cloth reinforced polyester laminates in the wet
condition. These graphs show the per cent of short term ultimate stress at which the lami-
nates will fail in a giventime. For example; a 10 ounce cloth polyester laminate, M3, when
continuously loaded at 40 per cent of the short term ultimate tensile stress will sustain this
stress for 10,000 hours, Fig, 5-17.

As indicated by these graphs, mat polyester laminates have higher tensile and flexural
strength retention than both cloth and woven roving laminates under long term contin-
uous loading.

The effect of periodic or non-continuous loading has not been investigated. It is felt
that periodic loading will not be cumulative and therefore will not have the same effect as
continuous loading if the working stress level selected is approximately 20 to 30 per cent of
the ultimate stress.

When selecting fiberglass laminates, designers must carefully consider the loading
time intervals as well as the direction and magnitude of the applied loads. The judicious
selection of working stress levels to allow for extended periods of loading is necessary to
provide an adequate structure.

The nature and time interval of boat hull loads is such that the effect of long term con-
tinuous loading will be negligible in most cases. When extended periods of storage are
contemplated for a boat hull, careful distribution of its weight on the supporting structure is
necessary to minimize the effect of long term loading. Maximum design loads usually occur
only momentarily or for short durations in the life span of a boat. Assuming a straight line
extrapolation of these curves, it is believed that for normal design loads which may be
periodic, the factors of safety suggested in Chapters 2 and 6 for fiberglass construction will
allow working stress levels that will not have a long term loading effect on the laminate or
reduce the maximum useful life expectancy of practically all boats.

PROPERTIES OF LOW DENSITY CORE MATERIALS

As previously discussed in Chapter 4, numerous types of core materials for use in
closed frames and sandwich panels are available. The selection of a core material for boat
hull construction depends on its physical and mechanical properties, its location in the hull
and its specific function. Different core materials can be used satisfactorily in similar
applications with minor variations in performance. In many applications the final selection
is based on ease in handling and costs.

Table 5-17 gives physical and mechanical properties data for the most commonly used
low density core materials (23-29). Additional research and development should result in
improvement of these core materials.

Fig. 5-20 present SN or fatigue shear strengths as percentages of ultimate shear
strengths, for the various commonly used core materials (30).

ULTIMATE TENSILE STRENGTH

PERCENT OF

PERCENT OF ULTIMATE FLEXURAL STRENGTH

ENGINEERING PROPERTIES OF LAMINATES

LAMINATES IN WET “CONDITION.
PARALLEL LAMINATED AND
AT O° T.O WARP.

100

90

80

70

60

50

40

; alll

: Be
C)
0,001 0.01 ).1 1 10

OURATION OF LOAD — HOURS

Fig. 5-17. Tensile Strength Retention of Continuously
Loaded Polyester Fiberglass Laminates

TES IN WET CONDITI

EL LAMINATED AND
AT. 0°

Beae
HES

- SN

. CT TTT

; ETE LTT
: ETT TIT TU
A BEL RA
. ME LAME EAI
TTI LATE ETI UT

DURATION OF LOAD — HOURS

Fig. 5-18. Flexural Strength Retention of Continuously
Loaded Polyester Fiberglass Laminates

5-40

STRENGTH

PERCENT OF ULTIMATE SHEAR

PERCENT OF ULTIMATE SHEAR STRESS

100

ENGINEERING PROPERTIES OF LAMINATES

IN WET CONDITION.
AMINATED AND
0° TO Ww

10

90

80

70

60

50

40

30

20

10

ie)

0.001 0.01 1 1 10 10° 10° 10°
DURATION OF LOAD — HOURS
Fig. 5-19. Shear Strength Retention of Continuously
Loaded Polyester Fiberglass Laminates

80

60

40 ja

20

ie)

CYCLES TO FAILURE

Fig. 5-20. Shear Fatigue Strength of Low Density
Core Materials - Dry Condition

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Ty punog Axodq
“OOST - “008 aseg saaaydg
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¢ ‘9 SuOgqIa ar09 04 suoqqia 9109 0}
jaTTered pue saynqj jatered pue saynqj
3109 0} [aTTe41ed 3109 0} [aTTe1eqg
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a109 0} [aTTeIeg 9109 0} [aTTeIed utsay
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0°Se - 0"9T | o9'T - 002° 0°98 - O*Le (mires papuedxq uUleO
0°22 - 0 ‘OT 0S8° - 00F° 0°0€ - 0°%2% Ting We toh 8 weo,y snoauadouloy auaahyssTog
isd 01 x tsd tsd or x tsd es / A NOILISOdNOO | IVINALVW AYOD
SN INGOW NOISSHUdNOD HLDNGULS AAISSHUANOD SON TNGOW UV4AHS HLONUULS UVAHS ALISNAG

x STVIMUALVW AYOO ALISNAG MOT JO SHILYUAdOUd *LI-S ATAVL

5-41

ENGINEERING PROPERTIES OF LAMINATES
REFERENCES

(1) Sonneborn, R., Fiberglass Reinforced Plastics, Reinhold
Publishing Corporation, New York, 1954

(2) Erickson, E.C.O., C.B. Norris, Tensile Properties of
Glass-Fabric Laminates With Laminations Oriented In
Any Way - Forest Products Laboratory, U.S. Department
of Agricultire, Madison 5, Wisconsin, 19595

(3) Perry, H.A., Adhesive Bonding of Plastics, McGraw-Hill
Book Company, Inc., New York, 1959

(4) Morgan, P., et. al. - Glass Reinforced Plastics - Iliffe &
Sons, Ltd., London, Philosophical Library, 2nd Edition, 1957

(5) Della Rocca R. - Reinforced Plastids in Boat Hull Con-
struction - 12th Annual Technical and Management Conference,
Reinforced Plastics Division, Society of the Plastics Industry,
Inc., 1957 - Reprint - Plastics Technology, November 1957
and December 1957

(6) Park, F., Fourteen Organizations Form Team To Set
Reliability Standards For Fiber - Reinforced Plastics,
Product Engineering, New York, February, 1957

(7) Research and Development in Reinforced Plastics and Honey-
comb Construction, Quarterly Progress Report No. 6 January -
February - March, 1957 - Forest Products Laboratory - U.S,
Department of Agriculture, Madison 5, Wisconsin

(8) Military Specification MIL- P-17549(B) SHIPS Dated
2 October 1956

(9) Fried, N., Fatigue Strength of Reinforced Plastics, 12th
Annual Technical and Management Conference, Reinforced
Plastics Division, The Society of the Plastics Industry,
Inc., 1957

(10) Pusey, B.B., Flexural Fatigue Strengths of Reinforced Thermo-
setting Laminates, 12th Annual Technical and Management
Conference, Reinforced Plastics Division, The Society of the
Plastics Industry, Inc., 1957

(Gia) Boller, K.H., Fatigue Properties of Glass Fiber -
Reinforced Plastic Laminates Subjected To Various
Conditions, 12th Annual Technical and Management
Conference, Reinforced Plastics Division, The Society
of the Plastics Industry, Inc., 1957

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

ENGINEERING PROPERTIES OF LAMINATES 5-43
REFERENCES

Kinney, G. F., Engineering Properties and Applications
of Plastics, John Wiley & Sons, Inc., New York, 1957

Plastics for Aircraft, Part I, Reinforced Plastics
ANC-17, June 1955

Fatigue Tests of Glass Fabric Base Laminates Subjected
to Axial Loading, Report 1823, Forest Products Laboratory,
U.S. Department of Agriculture, Madison 5, Wisconsin

Engel, H.C., Hemming, ©. B., Merriman, H.R. ,
Structural Plastics, McGraw-Hill Book Company, Inc., 1950

Hooper, R.C., Molding Finish Interactions in Fatigue of
Glass-Reinforced Polyester Resins, 11th Annual Technical
and Management Conference, Reinforced Plastics Division,
Society of the Plastics Industry, Inc., 1956

Boller, K.H., Effect of Long Term Loading on Glass Fiber
Reinforced Plastic Laminates - 11th Annual Reinforced
Plastics Division, Society of the Plastics Industry, Inc., 1956

Effect of Long Term Loading on Glass Reinforced Plastic
Laminates, Forest Products Laboratory, Report 2039,
Revised to September, 1958

Research and Development in Reinforced Plastics and
Honeycomb Construction, Quarterly Progress Report No. 7,
April, May, June 1957, Forest Products Laboratory, U.S.
Department of Agriculture, Madison, Wisconsin

Lampman,J.R., Damon, G.F., Protective Coatings for
Electronic Laminates, 14th Annual Technical and Manage-
ment Conference, Reinforced Plastics Division, Society
of Plastics Industry, Inc.; 1959

Pusey, B.B., Effect of Time, Temperature and Environ-
ment on the Mechanical Properties of Glass Reinforced
Thermosetting Plastics, 11th Annual Technical and
Management Conference, Reinforced Plastics Division,
Society of Plastics Industry, Inc., 1956

Barker, J. P., Walsh, T. J., The Use of Reinforced
Polyester Resins in Plant Maintenance, 14th Annual
Technical and Management Conference, Reinforced
Plastics Division, Society of the Plastics Industry,
Inez 959

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

ENGINEERING PROPERTIES OF LAMINATES
REFERENCES

Mark, R., Balsa Cores for Reinforced Plastics Structures,
Modern Plastics - 1956

Giuffria, R., Microscopic Study of Expandable Polystyrene
Bead, Prepuff and Foam - Modern Plastics, June 1959

Modern Plastics Encyclopedia - Modern Plastics, New York,
1959, Foamed Plastics Chart, Pages 549-595

Wiepping, C.A., Doyle, D.P., Strength and Related
Properties of Balsa Wood, Forest Products Laboratory,
Report 1511, June 1944

Dunbrow, Bernard, Polyurethanes, Reinhold Publishing
Corp., New York, 1957

Humke, R.K., Selection Guide for Sandwich Panel Cores,
Product Engineering, January 20, 1958

Newberg, R.F., Graham, D.L., Reinforced Low Density
Moldings, 14th Annual Technical and Management Conference -
Reinforced Plastics Division, Society of the Plastics Industry,
Iheies 5 Ie ye,

Werren, F., Shear Fatigue Properties of Various Sandwich
Construction, Forest Products Laboratory, Report 1837,
July 1952

6

Design of Laminates

The efficient and economical utilization of construction materials and the selection of
the appropriate material for specific applications can only be accomplished by knowledge of
the behavior of available materials and associated design theories. This Chapter presents
fundamental structural principles and theories as guidance for designing with fiberglass re-
inforced plastics. The utilization of these materials does not require any new principles of
design but certain principles assume greater importance and require more extended con-
sideration when designing for fiberglass reinforced plastics. Changes in the design pro-
cedures and theories presented will probably occur with increased design experience and
when complete technical data as to the behavior of these materials becomes available.

Some of the design data developed, particularly tables and graphs associated with
compressive strengths, plates, stiffener and plate combinations and sandwich construction,
although considered theoretically sound, have not been completely verified by detail labora -
tory tests, but have proven satisfactory in some limited applications. Therefore careful
interpretation of these data should be made.

Factors affecting the strength of fiberglass reinforced plastics as discussed in Chapter 5
are not considered in the design procedures presented here since they are not functions of
the basic design principles and theories. These factors however should not be ignored and
proper allowances should be provided when necessary. They should be separately considered
for each application and adequately allowed for in the selection of the factors of safety.

The physical properties values for the various types of reinforcements used in the
design examples are values given in Tables 5-6 to 5-14. These values have been selected
at random to demonstrate the suggested methods of analyses. The higher values in the
tables should only be used when justified with necessary strength tests of the actual produc -
tion laminate to be used.

BEHAVIOR OF LAMINATES

Fiberglass laminates are composed mainly of two materials, fiberglass reinforcement
and resin. A laminate is similar to reinforced concrete with the exception that the fibers
are distributed throughout the entire laminate and occupy a greater volume than does the
steel in reinforced concrete. In the fiberglass laminate the glass and resin are assumed to
act as a unit for all combinations of stresses, whereas in reinforced concrete the steel acts
principally to resist tension while the concrete resists compression. This implies that for
any loading condition, both the resin and the fiberglass reinforcement are firmly bonded
together and undergo equal deformations.

6-2 DESIGN OF LAMINATES

In the elastic design of steel, the assumption is made that the material is never stressed
beyond the proportional limit. Within this range, the material obeys Hooke's Law of Pro-
portionality, i.e. the unit stress is directly proportional to the unit strain. Fiberglass
laminates are complex structurally and do not always behave according to Hooke's Law, but
in the majority of cases this assumption can be made without appreciable error in the results.

Therefore in the design procedures and theories for laminates or structures composed
of fiberglass and resin combinations, the following basic assumptions are considered valid:

The fiberglass and resin act as a single unit and have equal strains under
all loading conditions.

The material is considered elastic andobeys Hooke's Law. This assumes
that the stress is directly proportional to the strain and that the material
will return to its original shape when the load is removed,

Most fiberglass reinforced laminates, because of their layered construction, are not
homogeneous. Laminates are built up of a number of layers of the same or different type
of reinforcement and each layer may have different physical properties in different direc-
tions, The physical properties and structural behavior of a laminate are primarily depen-
dent upon the type and orientation of the reinforcement, the resin and the molding method
used to fabricate the laminate.

Since many types of reinforcements and resins are available, there can be many satis-
factory types of fiberglass laminates. Further variations in laminates are due to fillers,
glass and resin content and laminate thickness. These variable factors can be controlled in
some cases by the designer or fabricator,

The factors under control of the designer include the choice of fiberglass reinforce-
ments, resins, dimensions, form and molding method. This gives the designer considerable
latitude in designing boat hulls or other structures. In addition, there are a number of
factors that cannot be controlled to any extent by the designer.

The factors beyond the control of the designer include variability of resins and other
materials from one lot to another and variations in workmanship and technique. The degree
of variability due to these factors may be established by testing methods and allowed for by
the designer. The development of quality control methods by resin manufacturers and the
use of better fabrication techniques are gradually reducing the effect of these variables.

The strength of fiberglass reinforced plastics is basically dependent upon the adhesion
and the greater frictional resistance between the resin and glass fiber (1). The greater the
adhesion and frictional resistance the greater the strength. The maximum theoretical
strength that can be developed occurs when the adhesion strength plus the frictional resistance
between the resin and glass fiber equals the cohesion strength of the resin. To assist in
developing this maximum strength, sizes and finishes are applied to the glass fibers which
react chemically with the glass when applied, and later react with the resin during molding.
The frictional resistance is developed by the shrinkage of the resin during curing.

Stress-Strain Relationship

The mechanical behavior of a material under load can generally be predicted from ob-
servations of its stress-strain curve (2,3). The stress-strain curve is obtained by gradually

DESIGN OF LAMINATES 6-3

loading a test specimen to rupture, usually in tension, measuring the strain at various stress
levels and plotting the results. The two most important characteristics obtained from the
tensile test are strength and ductility. Speed of testing, preloading, form and cross-section
shape will considerably affect the properties of a material.

Figs. 6-1, 6-2 and 6-3 are typical stress-strain curves for metals, wood and fiber-
glass laminates, The curves have several points of inflection and each point is indicative of
a specific change in the behavior of the material. From these points of inflection, properties
such as proportional limit, yield point, initial and secondary moduli of elasticity and point
of rupture or ultimate stress can be determined,

Fig. 6-1 indicates the variation in the stress-strain behavior for some commonly used
structural metals, The first part of the curves in Figs. 6-la, 6-1b and 6-1c are substan-
tially a straight line to point P, the proportional limit. This indicates a constant ratio
between the stress and strain, and within this range the material behaves elastically con-
forming to Hooke's Law of Proportionality. The numerical value of the ratio is the modulus
of elasticity, E, and is determined by dividing the unit stress by the unit strain.

U

n= ft (6.1) caer
=a riers STRESS ULTIMATE TENSILE STRESS ~
P
Where E = Modulus of Elasticity - psi im
a
; ; ' \ PROPORTIONAL LIMIT
f, = Unit stress - psi 4
= a. MATERIAL HAVING A DEFINITE
€ = Unit strain - inches per in. ” YIELD POINT (SUCH AS SOME STEELS)
Oo ,002 STRAIN — INCHES PER | NCH
Beyond the proportional limit, the ratio u
of the stress to strain, designated as the mer eane +S
- : ULTIMATE NSILE S
tangent modulus, varies with the slope of the -
* . Fi oO p {
stress-strain curve and is usually different ‘ YIELD STRESS
Db. MATERIALS NOT HAVING A
at each stress value. 3 PROPORTIONAL LIMIT DEFINITE YIELD POINT (SUCH AS
e ALUMINUM ALLOYS, MAGNES| UM,
. . id
The curve in Fig. 6-lc shows two RUE
° . . ° oO .002
separate proportional limits and moduli of Se re eee a
7 1 * 4 i+4 j NITIAL MODULUS LINE
elasticity; initial and secondary. This curve Ce eee oe CUS NENE Wash
indicates the behavior of clad aluminum alloys : ; eS) MATE ZENS ILE Stress >
where the initial modulus holds up to the ry Fae
. : . . 1P YIELD STRESS
proportional limit of the relatively soft aie
: 1
covering and the secondary modulus holds up ig
to the proportional limit of the stronger 2 ©. CLAD ALUMINUM ALLOYS
core material. Omre0 Oe STRAIN — |NCHES PER INCH
REFERENCE 4
Beyond the proportional limit, the strain
increases at a faster rate with increased Fig. 6-1. Typical Tensile Stress-
stress, and slightly above this limit the Strain Curves for Metals

material begins to retain a permanent set

upon removal of the stress. For some steels, a sharp break in the curve occurs at a stress
considerably below the ultimate tensile stress, Fig. 6-la., At this stress, referred to as
the yield point on the curve, the material breaks down rapidly and a sudden large increase
in deformation occurs with little or no increase in stress. Nonferrous metals and some
steels do not have this sharp break or yield point but yield gradually after passing the pro-
portional limit, Figs. 6-1b and 6-I1c.

6-4 DESIGN OF LAMINATES

Based on practical limitations of permissible deformation in a structure, an arbitrary
strain of 0.2 per cent has been established for most metals and the corresponding stress at
this strain is referred to as the yield stress. This yield stress, point Y on the curves, is
taken at the intersection of the stress-strain curve with a line drawn parallel to the straight
or elastic portion of the curve, OP, through 0.002 strain at zero stress. For metals,
factors of safety are usually based on this yield stress.

The ultimate tensile stress indicated as point U on the curves in Figs. 6-la, 6-1b and
6-lc, is simply the stress at the maximum load based on the original cross-sectional area,
It is interesting to note that most metals including steel and aluminum have yield strengths
considerably lower than their ultimate strengths and have comparatively large deformations
between their proportional limits and ultimate strengths.

The stress-strain curves for plywood, Fig. 6-2a and wood, Fig. 6-2b, similar to the
nonferrous metals curve, Fig. 6-1b, do not have yield points but yield gradually after
passing the proportional limit. The deformations between the proportional limits and the
ultimate strengths, particularly for plywood, are less than for the metals. If a 0.2 per cent
offset line is drawn in Figs. 6-2a and 6-2b to obtain a corresponding yield strength similar
to the metals, Fig. 6-1, it will intersect the curve well above the proportional limit and in
some cases above the ultimate strength. Therefore, only the proportional limit and ulti-
mate strengths are considered when designing with wood.

STRESS — PSI
STRESS — PSI

O 0,002 O 0,002
STRAIN — INCHES PER INCH STRAIN — INCHES PER INCH

@. PLYWOOD — PARALLEL TO FACE GRAIN b. SOLID WOOD — PARALLEL To GRAIN

REFERENCE 5 REFERENCE 6

Hig. 6-2. Typical Tensile Stress-
Strain Curves for Wood

The stress-strain curves for fiberglass laminates are generally similar to most
structural materials since they exhibit a linear portion followed by a nonlinear portion,
Fig. 6-3a, Like some of the metals and like wood no yield point exists. It is important
to emphasize that for loading in the direction of warp, the deviation of the upper nonlinear
portion of the curve from the lower linear portion is usually small at the point of failure.
This limited deviation of the curve indicates that the strain deformations are quite small and
the material has low ductility. This low ductility of fiberglass laminates does not allow for
stress relief around stress concentration raisers such as notches, holes, reduction in area
and sharp angles as the more ductile materials do. Allowance for this low ductility should
be made by increased factors of safety for such points.

In some instances stress-strain curves for fiberglass laminates indicate two separate
proportional limits and moduli of elasticity, Fig. 6-3b. This behavior is predominant for

DESIGN OF LAMINATES 6-5

iz INITIAL MODULUS LINE
/ ~—PRELOAD MODULUS LINE

—_— MODULUS LINE
/ uU

ji

if

/ P2

/fP—PRELOAD POINT

STRESS — PSI
STRESS — PSI

/
REFERENCE 7 ae ane

oO ,002 oO .002
STRAIN — INCHES PER INCH STRAIN — INCHES PER INCH

a. SINGLE PROPORTIONAL LIMIT b. DUAL PROPORTIONAL LIMITS

Fig. 6-3. Typical Tensile Stress-Strain Curves
for Fiberglass Reinforced Laminates

tension, less noticeable for flexure and practically nonexistent for compression, Parallel
laminates made with unidirectional reinforcement do not appear to indicate this dual
characteristic when stress is applied parallel to the warp.

Preloading above the initial proportional limit modifies the lower straight line portion
of the curve to the point of preload, P', Fig. 6-3b, and the slope is altered to an inter-
mediate value between the initial and secondary slopes of the preload curve. As the pre-
loading is increased to the second proportional limit the initial straight line portion of the
curve disappears and a new single straight line portion is obtained to the secondary propor-
tional limit. Repeated preloading to the same stress level appears to cause no addi-
tional change.

This dual proportional limit characteristic, similar to the clad aluminum alloy pre-
viously discussed, is believed to be due to the difference in the individual strengths of the
combined materials. The initial break in the curve probably occurs at failure of the resin
and the entire load is transferred to the fiberglass reinforcement. The effect of preloading
beyond the initial break may then simply be the behavior of the fiberglass reinforcement
with additional failure or cracking of the resin as the stress level is increased,

If a 0.2 per cent offset line is drawn to obtain an apparent yield stress for fiberglass
laminates, Figs. 6-3a and 6-3b, it will intersect the curve well above the proportional limit
and for most laminates will be very close to or beyond the ultimate stress. It is obvious
that establishing a yield stress at 0.2 per cent strain offset as a basis for design safety
factors is quite impractical and should not be done. Therefore it is recommended that
factors of safety be based on the ultimate stress of the laminate.

Directional Characteristics

Homogeneous materials such as steel and aluminum can be assumed as isotropic and
as having the same physical characteristics at any angle or direction. This is not true for
all fiberglass laminates; the exception being mat reinforced laminates which are considered
homogeneous as discussed in Chapter 5, Fiberglass cloth and woven roving when used as
reinforcement in laminates generally produce orthotropic materials. These laminates will
have different ultimate strengths at various angles to the warp direction and must be analyzed

6-6 DESIGN OF LAMINATES

accordingly. Fig. 6-4 illustrates the difference in the distribution of ultimate tensile
strengths for isotropic and orthotropic materials. Values given in Fig. 6-4b are assumed
and will vary with different materials.

100% 100%
100%
S 58% =
100% = Ef 84h
a |SOTROPIC — EQUAL b. ORTHOTROPIC — DIFFERENT
STRENGTHS IN ALL DIRECTIONS STRENGTHS AT VARIOUS ANGLES

Fig. 6-4. Distribution of Tensile Strength for
Isotropic and Orthotropic Materials

For an example of the orthotropic characteristics of fiberglass laminates, Fig. 6-5
illustrates the directional properties of a 10 ounce cloth laminate with the warp fibers placed
in the vertical or 0 degree direction.

If a load P in tension is applied in the direction of the longitudinal L or 0 degree axis,
the laminate exhibits an ultimate tensile strength or tensile strength at rupture that is equal
to an average value of 24,100 psi, Table 5-6. This is the strongest value that the 10 ounce
cloth laminate will exhibit since it is in the
warp direction or the direction with the
maximum number of fibers. A tensile load
applied in the 45 degree direction will cause
the laminate to rupture when the tensile stress
reaches a value of approximately 14, 000 psi.
ee This will be the weakest value for this lami-
nate. At 90 degrees, or the transverse direc-
tion, the laminate will fail when a tensile
T (90°) load, placed in this direction causes a tensile
Eoaoorrs! stress of 20, 200 psi.

L(0°)

i)
24100 PSI

It is apparent from observation of Fig.
6-5 that in order to properly design an ortho-
tropic laminate the strength of the laminate
must be known in all directions and its be-
havior under load must be thoroughly under-

stood,
Fig. 6-5. Orthotropic Characteristics Before a thorough stress analysis can be
of a 10 Ounce Fiberglass Cloth Polyester performed it becomes necessary to have the
Laminate values of the physical constants for all angles

(8-12). The general procedure for the deter-

DESIGN OF LAMINATES 6-7

mination of these constants is to test the laminate at 0 degrees, 45 degrees and 90 degrees to
the warp. The two basic values at 0 degrees and 90 degrees can be used to compute, by
means of mathematical identities, the values at the intermediate angles, The test value at
45 degrees can be used to verify the calculated value. Once the basic values at 0 degrees
and 90 degrees are obtained, graphs can be developed which will give at a glance, the value
of any constant for a specific angle.

The following graphs, Figs. 6-7 to 6-12, which are typical of those that can be esta-
blished, are based upon Fig. 6-6 and the following equations:

= DIRECTION OF WARP
= DIRECTION OF FILL

'~

Fig. 6-6. Orthotropic Laminate

The modulus of elasticity, E,], due to a stress applied in the l-l
direction at an angle @ with the warp direction is obtained from:

E E E
b= costa + sinka + - Se ar} sin?2a (6.2)
By Bp Sai ut

Poisson's Ratio is obtained fron:

Ey i ( 1B L 2
e =—|, == (lb 2s Teac gage Sanco, (6.3)
12. Ey, LT )} LT Ep Grp
The shear strain is obtained from:

it

Yor 1S (6. 4)
oT

where:

ees al 2}
m, = sin 2alo,. 4) Se, eS COS. (1 + 20 eles) (6.5)
LY En 2 Ee Ep

DESIGN OF LAMINATES

The shear stress causes the following strains in the 1-1 and 2-2
directions respectively:

AR
eye ype
Er
4
doo = Moree
: Er,
where:
= _ -
ma = Sin 2a|o ols ol _ sino 1 + 20 oes
LT Ey” 2 Grp DE ae cee

The shear stress T19 applied in the 1-1 anc 2-2 directions causes a
shear strain:

4B
Gigs = 12 and the shear modulus is obtained from:
G19
Grp | Srp Ey EL, Ef
oe eee (0 + 201 + =) - (1 + 25 += - cos22a
hey: yy G
ie ey, Ep p Opp

(6. 6)

(6.7)

(6. 8)

(6.9)

(6. 10)

Some of the physical constants which are important in structural analysisare as follows:

Flexural Modulus = Ebr, and Eur where Eyy is measured parallel to the warp and

Eyp is measured perpendicular to the warp.

Tensile Modulus = Ey; and Eyp measured as above.
Compressive Modulus = E,; and E,p measured as above.
Flexural Stress = fy, and fp measured as above.
Tensile Stress = f4; and fip measured as above,

Compressive Stress = f,; and f,p measured as above.

Poisson's Ratio = Crm strain in the transverse direction due to a load

in the longitudinal direction, and %p,, strain in the longitudinal direction

due to a load in the transverse direction.

Modulus of Rigidity or Shear Modulus = Gy».

uotiIpuoD JaM - a}yeuTMeT

Ja}Ssakj[Og-}eW JO sjuejsuogd oselq oatssatdwog ‘9-9 ‘SIq

» JTSNV

06 08 OL 0g Os ov O€ 02 0)

vi-S aqevi ISd 301 X Oro
El-G 3a1eviL evo
Zi-S a1avL \Sd g0! X €6°0

UOT]IPUOD 19M - J}eUTWIeT
Iaysakjog-jeWW JO SjuejsuoD oselg attsuay, *)-9 ‘“S1q

p JTSNV

06 08 OL 09 Os OV O€ 02 Ot

vi-G a7evi 1Sd Ol X Ov'°O
8-G ATavL rama)
L-S 31avL ISd gOl X 06°0

000*1

6-9

2.50

my, & mp

1.95 x 10° psy 1.80 x 10° ps} TasLe 5-7
= On, = Oot? TABLE 5-8
Ly ™ 0.52 x 10° psi TABLE 5-14

ie) 10 20 30 40 50 60 70 80 90

ANGLE @

Fig. 6-9. Tensile Elastic Constants of 10 Ounce Cloth-
Polyester Laminate - Wet Condition

2200

2.00
=
1.50
sos
N
S
1.00
a2,0)

m, & m

2.46 x 108 PS! TABLE 5-12
= On = 10.23 TABLE 5-13
0.52 x 10 psi _ TABLE 5-14
0 10 20 30 40 5.0. 60 70 80 90
ANGLE @

Fig. 6-10. Compressive Elastic Constants of 10 Ounce Cloth-
Polyester Laminate - Wet Condition

6-11

E 2.06 x 10° PSI TABLE 5-7
Oi = Oa 0.14 TABLE 5-8
G7 = 0.45 x 108 psi TABLE 5-14
0 10 20 30 40 50 60 70 80 90
ANGLE &@

Fig. 6-11. Tensile Elastic Constants of 25-27 Ounce Woven
Roving Polyester Laminate - Wet Condition

6-12

2.0

2 7h0)

. 60

/|

AnAZEE

E,/E,

0 10 20 30 40 50 60
ANGLE &

Fig. 6-12. Compressive Elastic Constants of 25-27 Ounce Woven

i

TABLE 5-12
TABLE 5-13
TABLE 5-14

|
Phi) 80

Roving Polyester Laminate - Wet Condition

V

90

70)

6-14 DESIGN OF LAMINATES

Fig. 6-7 shows the relation that exists between the various physical constants and the
angle to the warp for a laminate in tension made of mat reinforcement. It is readily esta-
blished that mat reinforcement produces an isotropic laminate, i.e., one that has equal
properties at all angles.

Fig. 6-8 is similar to Fig. 6-7 except that it represents a mat laminate in compression.

Figs. 6-9 to 6-12 show the factors that are to be used in determining the elastic con-
stants £1, Gj2, and °% 9 for 10 ounce cloth and 25-27 ounce woven roving laminates, The
influence of the angle of loading or the angle between direction of stress and the longitudinal
axis, is clearly indicated.

In an orthotropic laminate,shear and direct stress cause shear and direct strains, These
strains, at various angles, can be found by substituting the constants from the curves for
my and m5 in equations 6.4, 6.6 and 6.7.

In all of these graphs the angle 0 degree is the longitudinal direction or the warp direc-
tion of the cloth and woven roving reinforcements.

The following examples demonstrate the procedure to be followed in using these graphs.

DESIGN EXAMPLE 6-1. TENSILE PHYSICAL PROPERTIES OF MAT
AND 10 OUNCE CLOTH LAMINATES AT 30 DEGREES TO WARP

Determine the tensile physical properties at 30 degrees to the warp for the materials

shown in Figs. 6-7 and 6-9.

The graphs show the relationships that exist for such constants as modulus of elasticity
E, modulus of rigidity G, Poisson's ratio o, and shear strain constants my and Moe Constants
my, and m5 apply to orthotropic materials only.

a. Modulus of Elasticity
The value of Ey =E390can be found as follows:
For mat laminate; from Fig. 6-7, By = 1.00 or E, = 1,00 BE = E.

This indicates that £, at a specific angle is equal to E at 0 degrees at all times. This
is always the case for an isotropic material.

For 10 ounce cloth laminate, from Fig. 6-9

Ey

- = 0.634 (Value at 30°)

ie

By = 230° = 0.63) BL

E39° = 0.634 x 1.95 x 106 = 1.236 x 106 psi
Modulus of Rigidity G;

For mat laminates, from Fig. 6-7 the plot indicates that ae 0.444 = a constant.
This again is true for isotropic materials. E

DESIGN OF LAMINATES 6-15

For 10 ounce cloth laminate, from Fig. 6-9 the plot of Gi indicates a varying

Q Grr
Oa be orendee

Qa
We)

value dependent upon the angle. At 30°,

|

Gaye = 1.65 x Grp = 1.650 x 0.520 x 106 = 0.858 x 10° psi

Poisson's Ratio

For mat laminate, from Fig. 6-7 the plot of © is a straight line having a
value of 0.320. This indicates a constant value of o equal to 0.320. Constant
value of o is always true for an isotropic laminate,

For 10 ounce cloth laminate, Fig. 6-9, indicates a variable plot for the value

fs H 1 basta oh i = (0), m
fe) 1, At 30° the value is F550 0.460

Example 6-2 will be used to indicate further procedures in the use of these graphs.

DESIGN EXAMPLE 6-2. COMPRESSIVE AND SHEAR STRAINS IN
10 OUNCE CLOTH LAMINATE LOADED AT 30 DEGREES TO WARP

A laminate made of 10 ounce cloth reinforcement is loaded in compression and shear
at 30 degrees to the warp, Fig. 6-13. Determine the strains parallel and perpendicular
to the direction of load.

15000 LBS

5000 LBS AP7 ma 3 =)
i a SP A
| eg
oe YO Zs - aN
CA i \ 30"
at
ie a
Ea
oo a _<_|— pi rection OF WARP
a oa
ie, a ~~ |{s000 LBs

15000 LBS

Fig. 6-13. Cloth Laminate
Loaded in Compression and
Shear at 30 Degrees to Warp

DESIGN OF LAMINATES

E
a = 0.5753 Ey = Ego = 0.575 x 2.46 x 106 = 1,15 x 108 psi
G
--- = 1.850; Gyo = Gy° = 1.850 x 0.520 x 106 = 0.962 x 10© psi
LT
Baa =. 2360 nro 8
m7 = 0.830
m9 = - 0.830

Strains caused by compressive stress fy = 15000 psi are

Vf

fy

15000 é nie Ma. . ,
€,=2=— = = 0.0106 in. (strain in 1 direction
1 EF Ts x 100 berree

Eo= — O19 €1 = -0.558 x 0.0106 = -0.00592 in. (strain in 2 direction )

Hy

1 15000 roe :
= -m — = -0.330 x = - ,00506 in. (shear strain)
12 : E,. 2.46 x 10°

Strains caused by shear stress Tj = 5000 psi are:

Y¢

Total

Tr:
= 12 .__5000 = 0.00520 in,
12s 3G 0.962 x 100
12
ole s
€7 = -m, =< = -0.830 x 000 = -0,00169 in.
’ Ey, 2.6 x 100
T
Ey = ~My 12 = 0,830 x —2000 = + 0,00169 in.
2 Do )6% 100,
E 2.116 x 10
i
Strains are:

7 +e, = 0.01060 - 0.00169 = + 0089 in.
Eo +€9 «= = 0.00592 + 0.00169 = - 0.002 in.

#°Y55)) => 0.00506 #°0.0052 = (0.01026 In.

DESIGN OF LAMINATES 6-17

The relation between stresses at 0 degrees, 90 degrees, and at any other angle can be
found from the expression (9):

il cos! a sint! a sin2 q cos@ q 6.11
Se a ee ee con
ee 'L Fp ne

In equation 6.11 it is best to determine F,, the shear stress, by assigning values Fy, at O°
Fp at 90°,and Fy at 5°, which can be obtained from test results. This is advisable because
of the difficulty encountered in obtaining good shear test results in the laboratory. Knowing
Fy, the right side of the equation can be completed and the stress at any angle to the warp,
Fj, can be computed. Design Example 6-3 illustrates the application of this equation.

DESIGN EXAMPLE 6-3. TENSILE STRESS AT 30 DEGREES
TO WARP FOR WOVEN ROVING LAMINATE

The following high range ultimate tensile values are given for a woven roving laminate.
See Table 5-6.

Po at O° = 11,800 psi
F, at 15° = 11,800 psi
Fp at 90° = 37,800 psi

Find the ultimate tensile strength Fo at 30° to the warp,

ys
7
s

S
tS
_

41800 PSI

S
Y
a \
"
=
we
\ ]
\ x | DIRECTION OF WARP
\ 30 |
A |
° ||
2 \ |
bi \ |
F \
= 37800PSI { \
uy eed . NY

Fig. 6-14. Woven Roving Laminate
in Tension at 30 Degrees to Warp

Rearranging equation 6-11 to solve for Fg and using )|5° values

pin! ie 1 1 _ cosh a _ sink o (6. lla)
ue sin? a cos? a | Fy@ Pye Fre

sine 5° = 0.4998 sin 5° = 0.2h98

cos2 5° = 0.4998 cost 5° = 0.2498

DESIGN OF LAMINATES

(6. lla)

te es Gee 1-298 _ 0.298
Fee 0.1998 x 0.4998 | 11800° 18002 378002
F, = 5960 psi
Stress at 802; Fo
sin? 30° = 0.25 sin4 30° = 0.0625
cos* 30° = 0.750 cosl 30° = 0.563
1. 0.563) , 0.0625 | 0.25 x 0.750
Fe :1800° 378002 59602
F, = 13,300 psi

FACTOR OF SAFETY

Before actual design problems can be considered it is important to discuss factor of
safety. Factor of safety is defined as the ratio of the ultimate strength of the material to
the allowable working stress.

In many fields the allowable working stresses or design stresses are specified by codes or

Ultimate Strength

ES
Allowable Working Stress

recognized authorities. When allowable stresses are not specified, the factor of safety
must be carefully chosen based upon the following considerations:

ie

Accuracy of the estimated load on the structure. A precise load value allows
for a lower factor of safety.

Precision of analysis and stress determination. Where analysis for stresses
are accurate and precise a lower factor of safety can be used. Inexact or
approximate analysis requires a higher factor of safety.

The probable homogeneity and consistency of behavior of the material. Since
stress patterns are a function of the homogeneous character of the material
this variable must be taken into account in establishing the factor of safety.
Metals are considered homogeneous and consistent in behavior while fiberglass
laminates, even those made under controlled experimental conditions, show
some inconsistency in the physical properties.

Deterioration due to environmental conditions.

Nature of Loading. Certain types of loads have greater effect than others.
The effect on the ultimate strength of the material produced by different types

DESIGN OF LAMINATES 6-19
of loading should be known so that the most appropriate factor of safety can be
established. The following factors of safety for various load conditions should be
considered for fiberglass structures:

a. Static short term loads FS = 2 minimum

b. Static long term loads FS = 4 minimum on reduced values
from tests

c. Variable or changing loads FS = 4 minimum
d. Repeated loads FS = 6 minimum
e. Fatigue or load reversal FS = 6 minimum
f. Impact loads - repeated FS = 10 minimum

6. Service requirement. Where failure of a material can cause personal injury
or extensive damage to expensive equipment, a high factor of safety should
be used.

Safety factors are dependent on many variables which only the design engineer can
analyze. Every problem presents its own peculiarities and requirements and therefore the
judgment and experience of the designer plays a most important part. The final selection
of a factor of safety, unless established by a specific code or authority, becomes the re-
sponsibility of the designer.

TENSION
Members subjected to axial pulling loads are under tensile stress. The magnitude of
stress is directly proportional to the load and the resisting area. In isotropic materials the
tensile stress distribution is assumed to be uniform throughout the entire cross-sectional
area, This assumption is not valid for composite orthotropic materials.

Isotropic Laminates

When a member, such as shown in Fig. 6-15, is subjected to an axial tensile load, the
stress relationship in its cross-section is indicated by means of the following formulas:

Fig. 6-15, Isotropic Tension Member I

6-20 DESIGN OF LAMINATES

P= Axfy, (6.12)
EP igl
or fy = = (Griz)
A
Or A = Je (6 .12b)
fy
Where P = total tensile load = pounds
A = cross-sectional area - square inches
f, = tensile stress - psi

DESIGN EXAMPLE 6-4. MAT LAMINATE UNDER TENSILE LOAD

The fiberglass laminate shown in Fig. 6-15 is made of 2 ounce mat and is to support a
load P, in tension of 10,000 lbs. The maximum thickness, t of the laminate is to be 1/8 in.
Find the width ''a'' for a required factor of safety of 2 on the ultimate stress.

The required area is found by using equation 6. 12b.

<2 Pe 105000
a i

Referring to Table 5-6 the ultimate strength in tension is 11,000 psi. Higher values of
ultimate strength may be used when verified by qualifying tests. Applying a factor of safety
of 2 to this ultimate value gives the allowable design stress:

f, . 11000 _ 5s£00 psi

al
Therefore A =axz=
B 5500
from which a = 1.5) in., say 1-5/8 in. wide

DESIGN EXAMPLE 6-5. ULTIMATE TENSILE STRENGTH OF MAT LAMINATE
What is the ultimate load carrying capacity of a 2 ounce mat laminate, 1/2 in. thick
and 4 in. wide?

.
Nia

Ee

ees eee -P

Fig. 6-16. Mat Laminate Under Tensile Load

DESIGN OF LAMINATES 6-21

From Table 5-6 the value for the ultimate strength of a 2 ounce mat laminate is given
as 11,000 psi. Referring to Fig. 6-16 and using equation 6.12.

P= Axf, = 4 xix 11,000 = 22,000 lbs.

Examples 6-4 and 6-5 outline the procedure for analyzing simple tension members of
isotropic materials. In using equations 6.12 to 6.12b it is recommended that the value of
the tensile ultimate stress be a test determined value.

Orthotropic Laminates

The following design examples illustrate the method of analysis for orthotropic lami-
nates. All plies are parallel laminated; the direction of warp is the same for all plies.

DESIGN EXAMPLE 6-6. WOVEN ROVING LAMINATE
UNDER TENSILE LOAD AT 30 DEGREES TO WARP

A woven roving laminate, with the fibers oriented as shown in Fig. 6-17 is to support
a load of 15,000 lbs. What is the required width for a 1/4 in. thick laminate with a factor
of safety of 2 on the ultimate strength? Laminate not restrained.

eo 15000 LBS
3051

DIRECTION OF WARP

1/4"

15000 LBS
Fig. 6-17. Woven Roving Laminate
Under Tensile Load

Since the warp is oriented at an angle of 30 degrees to the applied load, the ultimate
tensile strength of the woven roving, at 30 degrees, is required. This value was computed
in example 6-3 and was found to be 13, 300 psi.

The allowable design stress, for a factor of safety of 2, is then sat = 6650 psi.

Using equation 6-12b, A = Po
ay

all 15000

A F=ax=- = =——

4 6650

or @ = 9.0 in.

6-22 DESIGN OF LAMINATES

DESIGN EXAMPLE 6-7. CLOTH LAMINATE UNDER
LONG TERM TENSILE LOAD PARALLEL TO WARP

A 10 ounce cloth laminate, 8 in. wide, is to support a load of 10,000 lbs. for a period
of 1,000 hours. If the load is applied parallel to the warp what should the thickness of the
laminate be? Use a factor of safety of 4 on the ultimate.

8" t

10000 LBS 10000 LBS

Fig. 6-18. Cloth Laminate Under
Tensile Load

The ultimate tensile stress of a 10 ounce cloth laminate at 0 degrees, from Table 5-6,
is given as 24,100 psi. Higher values of ultimate strength may be used when verified by
qualifying tests. The reduction factor due to long term loading, from Fig. 5-17, for a wet
laminate, is 49 per cent. The ultimate design tensile stress is then:

Fy, = 24,100 x 0.49 = 11,809 psi.

The allowable design stress based on a factor of safety of 4 is:

f, = 11809. 2952 psi
n
Using equation 6.12b, A = = 5
t

Area = 6 xt = =

4 = P_ ~ 10000 espa ine say, Oiny
B x 2952 16

Composite Orthotropic Laminates
Fig. 6-19 shows a composite laminate made of two laminae of differing physical properties,

When several laminae are combined to form a composite section as shown in Fig. 6-19,
the basic formula 6.12b relating stress, load and area, f = . must be modified.

A member subjected to a tensile load P will stretch a given amount. The amount that a
laminate will stretch or elongate can be expressed as:

DESIGN OF LAMINATES 6-23

DIRECTION OF WARP ——
FOR ALL PLIES

1/16" ttt 1/16"

1/4"

Fig. 6-19. Composite Laminate Under
Tensile Load

PL
AE

e =

(6. 13)

where total elongation, in.

load, lbs.

length, in.

area, sq. in.

modulus of elasticity in tension, psi

e
P
L
A
E

For two laminae of identical length and area, and subjected to the same load P,
equation 6.13 indicates that the elongation of each lamina will then be proportional to E,
the modulus of elasticity in tension.

DESIGN EXAMPLE 6-8, ELONGATION OF VARIOUS TYPES OF LAMINATES

Find the total elongation, e, for the laminates shown in Fig. 6-20. The laminates are
loaded parallel to the warp direction.

— 2 OZ MAT 10 0Z CLOTH WOVEN ROVING

A=5 SQ INe A= 5 SQ INe A= 5 SQ INe

TE =i am

50000 LBS 50000 LBS

50000 LBS

a b c

Fig. 6-20. Elongation of Various Laminates

6-24 DESIGN OF LAMINATES

Referring to Table 5-7, the following values for tensile moduli are obtained:

(a) Mat Laminate By = 0.90 x 10° psi

(b) 10 Ounce Cloth Laminate iy ES ALES; oe 106 psi
t

(c) Woven Roving By = 2.06 x 10° psi

Substituting the given values in equation 6. 13:

50,000 x 36. :
(a) Mat e = 2 0.90 x 100 = 0,02 in.

(b) 10 Ounce Cloth e = 2000 x 36 = 0.18) in.
Die > 10

_ 50,000 x 36_

(c) Woven Roving e Z
bx 2.00. 10

0.175 in.

Design Example 6-8 illustrates the effect of the tensile modulus on the ability of a
material to stretch or elongate. The mat laminate stretches approximately 2.25 times
as much as the 10 ounce cloth laminate and the woven roving laminate.

In a composite laminate, such as the one shown in Fig. 6-19, the total elongation must
be the same for all the laminae that make up the composite laminate. For this condition
not to be true would imply that the mat lamina would have to shear away from the cloth
lamina. Therefore sufficient shear stress between the laminae must exist. Equation 6. 13
can be rearranged to indicate the strain or the elongation per inch in a laminate:

PL = fl (6. 13a)
a0} ° = —_— «= = 2
Total elongation e iE 5
Unit strain: a eee (6. 13b)
L E

where € = strain; inch per inch and the other terms are as previously defined. Referring
to Fig. 6-19 and using equation 6.13b, the strain in the various laminae are as follows:

fo1

€
a 10 Ounce cloth: 1] = —
(a) aT

(b) Mat: oi

In order for the mat and cloth laminae to be compatible in the same composite laminate,
it follows that the strain in the mat lamina must be the same as the strain in the cloth lamina
or €) = 2 .- The following identity therefore is established:

DESIGN OF LAMINATES 6-25

cl
a ant 6, 14a)
fo tn = Em
EB (6. 14b)
= Ses .
fn fol - Eel

Examination of equations 6.14a and 6.14b reveals that the actual stress values for
either material will be dependent upon the ratio of the moduli or the values of the right hand
portion of the equations. The only restriction that must be placed on equations 6.14a and
6.14b is that the actual stress in any lamina cannot exceed its ultimate stress value. The
ultimate stress is used since no actual proportional limit has been established for these
materials, The stress strain curves are almost straight lines indicating that the ultimate
value can be used without appreciable error, Example 6-9 will serve to illustrate the
recommended procedure,

DESIGN EXAMPLE 6-9. ULTIMATE TENSILE LOAD OF A COMPOSITE LAMINATE

Determine the ultimate tensile load P, per inch of width, that the composite laminate
of Fig. 6-19 can support.

From Table 5-7, the following lower limit values for E are chosen for the individual
laminae:

6
z = 0.70 x 10 psi

i}

E 1.0 x 106 psi
oul

From Table 5-6, the following lower limit values for ultimate tensile strength are chosen:

hy
i]

6600 psi

Foz = 17900 psi

Values for f,; and f,, can now be calculated using equations 6.14a and 6.14b:

_ 1.10 x 106

(a) Pol = 6600 x 0.70 x 100 = 13200 ps1
6

(b) £, = 127900 x QO X10) - goco psi

1.10 x 10

6-26 DESIGN OF LAMINATES

Part (a) above states that if the stress in the mat laminate is assumed as the controlling
stress, then for the ultimate values selected, the maximum stress in the cloth laminate will
never exceed 13,200 psi. Since this value of 13,200 psi is less than the ultimate for the 10
ounce cloth laminate of 17,900 psi, the composite laminate is not overstressedinany lamina.

Part (b) states that if the ultimate stress for cloth, 17,900 psi, is assumed as the con-
trolling stress then the stress indicated in the mat lamina will reach a value of 8, 950 psi.
Since this value exceeds the ultimate value of 6,600 psi given for the mat lamina this clearly
indicates that the mat lamina will be overstressed if the cloth lamina is assumed to govern.
Consequently, this condition of overstress cannot be allowed for a safe design.

The stresses of part (a) are then chosen as the ultimate values for the composite
laminate, namely:

a = 6,600 psi

fo, = 13,200 psi

The ultimate load that the laminate can carry can now be computed by using the basic
equation, P = f,A where f,A is the summation for both mat and cloth laminae as follows:

Poe fate “ta on (6. 15)
i ak
6600 x i + 13,200 x 3

= 3300 lbs. per in. of width

Example 6-9 indicates the need for establishing the correct values of the stress f in the
basic formula P = fA. The value of the stress f to be used is dependent upon the compatibility
condition that all layers of a composite laminate are equally strained and follow the equa-
tion € =

tle

DESIGN EXAMPLE 6-10. ULTIMATE TENSILE LOAD OF A COMPOSITE LAMINATE

The composite laminate of Fig. 6-21 is assumed to be made of several different
materials as follows:

One lamina of 1/8 in. thick woven roving
One lamina of 1/4 in. thick mat
One lamina of 1/16 in. thick cloth

gestae

—}~

| CLOTH
DIRECTION OF WARP___|, | Ce
FOR ALL PLIES |

| | MAT

WOVEN ROVING

1/16"

24"
=
Po
o
=
eal

7

P

Fig. 6-21. Composite Laminate Under Tensile Load

eo

DESIGN OF LAMINATES 6-27
Find: the ultimate load carrying capacity intension of the composite laminate per inch of width.

Using equation 6.13b, the strain in each layer can be found:

Emat - =
om
F

Ecloth = ol
“cL

euR = ‘NIR
WR

Em = &§ol = WR or

= co. .SwR oF

F BE,
=R xy we wR
(a) Ee en Ea EX Bap
F Fur
b F = & x i = Wy x at
(>) cl oul, Ee cl” iim
Fy fel

Cc) Eup Byrn * Pw * ba

Values for Fy are selected from Table 5-6 and values
for Ey, are selected from Table 5-7 as follows:

Mat Cloth vioven Roving
Ft = 6600 psi 17,900 psi 23,800 psi
Be = 0.90 x 10° psi 1.0 x 106 psi 1.3 x 10° psi

Substituting the values for the stress F in the left hand portion of equations (a), (b) and
(c) above, the following relative stresses are obtained:

ee fw
i =0, 6 ms =0, oO ee
(a) 6600 psi 90 x 10 = To = 105 90 x Tal e066
from which fg, = 10,267 psi
fm ad 95827 psi

6-28 DESIGN OF LAMINATES

a f
Gh) ) -rs000 pea = VO ae aio oles
0.90 x 106 TA sil 6 sole
from which f. = 11,507 psi
m
f= (5133. psx
- aR f
Mele PS 800 gmat St) 3) OC ase Spain oe yee
0.90 x 106 Tore toe

from which f,, = 15,985 psi

f 4 = 21,866 psi

Part (a) states that if the mat ultimate stress of 6,600 psi is assumed as the controlling
stress then the ultimate stresses obtained in the cloth and woven roving laminae are 10, 267

psi and 9, 827 psi respectively. Since all values do not exceed the ultimate, part (a) stresses
can be used,

Part (b) states that if the cloth ultimate stress is assumed as the controlling stress then
the ultimate values for the mat and woven roving laminae would be 11,507 psi and 17,133 psi

respectively. Since the mat stress of 11,507 psi exceeds the ultimate of 6, 600 psi this
combination cannot occur without failure.

Part (c) also indicates an ultimate value for mat of 15,985 psi which cannot occur,

Therefore Part (a) is the only condition under which the laminate will be stable without
overstressing an individual lamina. The final stresses to be used are therefore:

2 = 6,600 psi
oot = 10,267 psi
fon = 9,827 psi

The total ultimate load P that the composite laminate can carry is now found as the sum
of the individual carrying capacity of each lamina:

P = fmAm + fe14c1 * fwrAwR (6.15)

Mt

6600 psi x 0.25 + 10,267 psi x 0.0625 + 9,827 x 0.125

1650 + 602 + 1228

3520 lbs. per in. of width

DESIGN OF LAMINATES

In Design Example 6-10 the composite laminate is made of 3 separate materials, mat,
cloth and woven roving. These three materials each have their own value for the modulus
of elasticity, E. The value of E for the composite laminate is not equal to any of the indi-

vidual lamina values but is a function of these values and the individual lamina areas.
equation 6.16 expresses this relationship.

L=n
BXxA= > Ej Ay (6. 16)
ial
where E = composite modulus of elasticity, psi
A = composite area, sq. in.
E; = modulus of elasticity of i-th lamina
A; = area of i-th lamina

1

means summation of all laminae

DESIGN EXAMPLE 6-11. MODULUS OF ELASTICITY OF COMPOSITE LAMINATE

For the laminate in Design Example 6-10 find the modulus of elasticity, E of the
composite laminate.

From Design Example 6-10 the following values are:

Modulus of

Elasticity Area

E, psi sq.in. per in.
Mat Lamina 0.90 x 108 0.25
Cloth Lamina 1.40 x 10® 0. 0625
Woven Roving Lamina 1.34 x 108 0.125

Using equation 6.16

i=zn
EA = > Fuki
1 =
= 0.90 x 100 x 0.25 + 1.40 x 10© x 0.0625 + 1.34 x 10° x 0.125
= 0,225 x 106 + 0.0875 x 106 + 0.1475 x 106
BA = 0.48 x 106 lbs.

Area of composite = (0.25 + 0.0625 + 0.125) x 1 = 0.4375 sq.in. = 7/16 sq.in.

Therefore

BATE Q 6
C= 5 OBE Ae oe 16o pet (6. 16a)

A 0.4375

6-30 DESIGN OF LAMINATES
DESIGN EXAMPLE 6-12. ELONGATION OF COMPOSITE LAMINATE
Find the elongation of the composite laminate described in Design Examples 6-10 and 6-11,

From Design Example 6-10 the total load P is 3520 lbs. Poe in. of width. From Design
Example 6-11, the final modulus of elasticity, E is 1.10 x 10” psi and the area of the com-
posite, A is 0.4375 sq. in. Substituting these values in equation 6,13 the following elonga-

tion results:

P
a SES = 0.176 in.
AE 0.4375 x 1.10 x 10°

e =
Where L = 2) in. from Fig. 6-21

DESIGN EXAMPLE 6-13. ELONGATION OF COMPOSITE LAMINATE AT ANGLE TO WARP

A composite laminate is made up of 2 laminae of 10 ounce cloth reinforcement and one
lamina of mat reinforcement as shown in Fig. 6-22. The following properties of the com-
posite are required:

1. Total ultimate tensile load, per in. of width, that the laminate can carry when the
load is applied at an angle of 15 degrees to the warp direction.

2. Elongation of the composite in the direction of the applied load.

4/2"
P

4

CLOTH 1/16"
__ 2 oz MAT 3/8"
CLOTH 1/16"
Pp

Fig. 6-22. Composite Laminate Under Tensile Load
at an Angle to Warp

DIRECTION OF WARP
FOR ALL PLIES

20"!

Information required for solution of problem:
Tensile strength of mat and cloth laminates at 15 degrees to warp direction.
Moduli of elasticity for mat and cloth laminates at 15 degrees to warp direction.

Properties of Mat Laminate: Since mat laminates are considered to be isotropic in
behavior, the values for F; and E can be chosen from Tables 5-6 and 5-7.

6600 psi

by
"

0.81 x 10° psi

z

DESIGN OF LAMINATES 6-31

Properties of 10 Ounce Cloth Laminate: Cloth laminates are considered to behave as
orthotropic materials therefore the valuesforF and E at 15 degrees must be calculated since
they vary with the angle chosen.

(a) Value of the tensile strength can be found by using the method of Design Example 6-3,
based on equation 6.11 as follows:

al cost a sina sin? a cos? a
Tore 2 To eo ine oe anne (6,11)
PF, Fy Fp Ie

Finding first the value of Fg from the physical properties given for Ose niS?
and 90°, where F, is the value at U5°:

al al oo coslt a sink a
Pee 9 2 (6, 11a)
a sine a@ cos? a 1G) Fre Fre
where sin 5° = 0.70711 cos liS° = 0.70711 sin? @ cos@a@ = 0,21,98
sine 5° = 0.1998 cos2 45° = 0.4998
sind lS° = 0.298 cosh 45° = 0,298
and from Tables 5-6 and 5-7:
FL = 17,900 psi F, = 6400 psi Fp = 14000 psi
By = 1-40 x 10° psi
Therefore
ee 1 if 0.298 0.2498
F2 0,2h98 81002 179002 140002
s
fron which F, = )5),0 psi.
The value at 15 degrees can now be computed; again using equation 6.1lla.
) eel sae) 2
1 cos+ a sint a Sahgl= (oMiolokoies (04
ar a a a aes a a: ae (Get Tal)
Fo Ey Fre ee
where sin 15° = 0.25882 cos 15° = 0.96593
sin? 15° = 0.4699 cos¢ 15° = 0.93302

sint 15° = 0,00kL9 cos 15° = 0.8705

6-32 DESIGN OF LAMINATES

1 _ 0.0625 , 0.8705 , 0.005
G6 eter oar | eee
Fo 540 17900 1,000
from which Fy = 13170 psi = Fy,at 15°

(b) The value of E can be found by referring to Fig. 6-9. From the graph for an
ae
the ratio et 15° is equal to 0.8)5

Then ~15°

=0,845 or Byge = BE, x 0,815 = 1,40 * 105 x 0.8h5

onl

Bye Totes 106 psi

(c) With the required F and E values known at 15 degrees the maximum stress that each
lamina of the composite can withstand is now found by means of equations 6,14aand 6 ,14b:

ies

cl
for = Fm * i, (6 .14a)
oe eg (6, 14b)
Eo)
ee
or f,, = 6600 x 1.103 x10 - 9639 psi
0.61 x 100
Q 6
f= sox, See Os = 9017 pet

1.183 x 10°

If the cloth laminate ultimate tensile stress of 13,170 psi is used as the controlling
stress, the mat laminate would attain a value of 9017 psi. This value exceeds the allowable
ultimate and therefore failure would occur.

The cloth laminate attains a safe stress of 9639 psi since the mat laminate tensile
ultimate controls. Consequently these values are the values to be used, namely:

fo) = 9639 psi

fm = 6600 psi

The total load on the composite laminate is then found by means of equation 6.15;

i)

ae Am x fm + Ae] Xx fey

ia a
i}

9639 x 0.125 + 6600 x 0.375

1205 + 825 = 2030 lbs. per in. of width

DESIGN OF LAMINATES 6-33

The elongation of the laminate is given by equation 6.13, where the factor E is for the
entire laminate and has to be determined according to equation 6. 16;

pA = > ByAg

where A = (0.0625 + 0.375 + 0.0625) x 1 = 0.50 sq.in.

= = Wa iteisieo'e 10° x 0.0525 + 0.81 x 10° x Oca (oe+ LedlGs) x 106 x 0.0625
= 0.4515 x 10° lbs.
aren eek OeS NS RAMOS” 2 6,524 too pad
0.50
and the elongation is calculated from equation 6. 13;
= nly 2030 x 20 0.0899 in.
AE 0.50 x 0.903 x 100

COMPRESSION

The behavior of fiberglass laminates in compression such as columns, struts, etc. is
complex and many tests are required before definite conclusions can be made as to the ap-
propriate method of analysis. Materials that behave isotropically can be analyzed by ana-
lytical methods that have been developed for homogeneous isotropic materials. Glass rein-
forced laminates however may fail by interlaminar shear or at the bond between the glass
fibers and resin. Therefore any compressive design criteria is dependent on the behavior
of the laminate and precautions should be taken in the compression analysis of reinforced
plastic laminates whether they are isotropic or orthotropic.

The data presented here is primarily for laminates that are used individually or as part
of a member in compression. The compression buckling of plates is discussed later in
this Chapter.

Short Members

For laminates whose dimensions are Such that buckling is precluded, the basic relation
of equation 6.12,P = A f, canbe applied. These laminates will usually fail under ultimate
axial compressive loads by crushing or delamination.

DESIGN EXAMPLE 6-14. WOVEN ROVING LAMINATE
IN COMPRESSION WITHOUT BUCKLING

A woven roving reinforced laminate, 1/2 in. thick, is to support a load of 35, 000 lbs.
Find the width of the laminate. The length is such that the laminate will not buckle. Use
a factor of safety of 2 on the ultimate compressive strength. See Fig. 6-23.

6-34 DESIGN OF LAMINATES

beoicad alter

tht MPV IE TT T
p

Fig. 6-23. Woven Roving
Laminate in Compression

From Table 5-11 the ultimate compressive strength, F., selected is 9600 psi.

The allowable design stress, based on a factor of safety of 2, is then:

9600 :
f= ee 800 psi
P 35000 a
7 ee aD oa Sofie e e 6.12
Then A fo 1,800 7029 sqein ( e)
ees
and: SS Sco. 11.58 in.

Column Characteristics of Laminates

When the length of the compression member is such that buckling will occur, the critical
load, P.,, can be calculated with equation 6,12 provided that the ultimate stress,F,is
reduced to allow for the unsupported length of the member (13). Structural members, in
the buckling range, can be divided into two groups, namely:

1. Members in which the compressive stress is less than the proportional limit
of the material or follows Hooke's Law under a critical load P.,.

2. Members in which the compressive stress exceeds the proportional limit of the
material, under a critical load Por.

If the member is in the first group the following equations can be used to determine

the load Per:

yg, SEL (6. 17)
(Gig Le

2
_ TEA (6. 17a)

DESIGN OF LAMINATES 6-35

or F = = (6. 18)

re
and r= ye (6512)
A

critical load - lbs.

where Pop

i) = modulus of elasticity below the proportional
limit - psi

I = moment of inertia - in.

A = area - in.@

16 = radius of gyration - in.

L! = effective length - in.

Me critical stress - psi

The effective length, L', will be the length of the specimen for a pin-ended element, one
half the length for a fix-ended element and twice the length for a free-ended element as
shown in Fig, 6-24,

A/271

Fig. 6-24. Effective Length \ =
of Column ‘
Al =I
iF
a. PIN ENDED b. FIXED ENDED |

6-36 DESIGN OF LAMINATES

a or the slenderness ratio is associated with the ability of a section to resist buckling.
Since the ratio is based on the geometry and length of the element it can be readily
determined by the cross-section of the member. Also by substituting various values of stress
with the appropriate modulus of elasticity, E, in equation 6.18, corresponding values for

- can be obtained.

When the member is in the second group or does not follow Hooke's Law, the critical
buckling load can be determined if the value of E used is the value corresponding to the
particular stress. The buckling formula then becomes:

2
n Eal (6. 20)

IS
cr rte

where the value of Eg is the tangent modulus and is obtained from a stress-strain curve,
Consequently for every Per there exists a value of Eg.

When the stress exceeds the proportional limit, the buckled member no longer obeys
Hooke's Law. The critical stresses are now dependent not only upon the critical load Po;
but also upon the bending of the member. The compressive stresses will increase on the
concave side and decrease on the convex side.

Under this condition two values of the modulus of elasticity are involved. A new tangent
modulus E, for an increased load on the concave side will be necessary while on the convex
side of the material the usual modulus E for the decreased load will be applicable (13).

The critical load, therefore, will now be a function of a new reduced bending rigidity
Eyl. It can be shown that the value of Ey can be determined by the following expression:

ao ee (6.21)

Vi + Vi)

where E, = reduced modulus of elasticity
E = as previously defined

E, = modulus of elasticity above the proportional
limit, or tangent modulus of elasticity

The critical buckling load is then:

m2
Eyl
sae r (6, 22)
(ola )
Tat

Per, I and L' as previously defined,

Figs. 6-25, 6-26 and 6-27 indicate ultimate compressive strength curves for mat, woven
roving and 10 ounce cloth laminates for various slenderness ratios; =+ The curves are for
laminates in the wet condition and tested parallel to the warp. Tables 6-1, 6-2 and 6-3 give
the slenderness ratios at various compressive stresses and for the appropriate moduli of
elasticity obtained from the stress-strain diagrams. Further testing should be conducted to
verify these curves or similar curves for other laminates.

ULTIMATE COMPRESSIVE STRESS, Fop - PSI

18000

16900

16000

14000

12000

:

8000
7500

6000

2000

HORT TERM RUPTURE STRESS

LAMINATES IN WET CONDITION

°
TESTED AT 73 F

OPORTIONAL LIMIT

0) 20 40

a

6

SLENDERNESS RATIO,

trA

0 80

BG

Fig. 6-25. Ultimate Compressive Stress Versus Slenderness Ratio

for Mat-Polyester Laminates - Contact Molded

6-37

a
a
'
we
n
7)
lu
a
m
nn
Ww
>
nn
n
WW
a
a
=
3°
rs)
WwW
=
<
=
=
|
>

20000

18000

17000

16000

14000

13800

12000

10000

6000

4000

2000

SHORT TERM RUPTURE STRESS

a
a
cor

PROPORTIONAL LIMIT

ine

PEE

LAMINATES IN WET CONDITION
TESTED AT 73°F AND PARALLEL
TO WARP

20 40 60 80 100 120
SLENDERNESS RATIO, L/p

Fig. 6-26. Ultimate Compressive Stress Versus Slenderness Ratio for
25-27 Ounce Woven Roving-Polyester Laminates - Contact Molded

6-38

ULTIMATE COMPRESSIVE STRESS, For - PSI

20000

SHORT TERM RUPTURE STRESS

18900

18000

LAMINATES IN WET CONDITION
°

TESTED AT 73 F AND PARALLEL

TO WARP

16000

14000

12000

PROPORTIONAL LIMIT

11400

10000 nano

8000 soca! | imei | ae

6000

2000

0) 140

ce) 20 40 60 80 100 12

SLENDERNESS RATIO, L/,,

Fig. 6-27. Ultimate Compressive Stress Versus Slenderness Ratio
for 10 Ounce Cloth-Polyester Laminates - Contact Molded

6-39

6-40 DESIGN OF LAMINATES

TABLE 6-1. SLENDERNESS RATIOS FOR MAT-POLYESTER LAMINATES
CONTACT MOLDED - WET CONDITION

Tangent Reduced
Modulus of Modulus of | Slenderness | Modulus of Slenderness
Compressive Elasticity Elasticity Ratio for Eg | Elasticity Ratio for Ey
Stress psi x 106 psi x 108 psi x 106
psi E
16,900 (Rupture)
16, 000
15,000
14, 000
13,000
12,000
11,000
10, 000

9,000

8, 000

7,500 (Proportional
Limit)

7,000
6, 000
5, 000
4,000
3, 000
2,000

1,000

DESIGN OF LAMINATES 6-41

TABLE 6-2, SLENDERNESS RATIOS FOR 25-27 OUNCE WOVEN ROVING-
POLYESTER LAMINATES CONTACT MOLDED - WET CONDITION

Tangent
Modulus of Modulus of Slenderness
Compressive Elasticity Elasticity Ratio
Stress psi x 106 psi x 106
psi E ie

17,000 (Rupture) 2.37
16,000 2.40
15,000 2.43
14,000 2.44
13,800 (Proportional Limit) 2,45 2.45
13, 000 2.45
12,000 2.45
11,000 2.45
10, 000 2.495

9,000 2.45

8, 000 2.45

7,000 2.45

6, 000 2.45

5, 000 2.45

4,000 2.45

3,000 2.45

2,000 2.45

1,500 2.45

6-42 DESIGN OF LAMINATES

TABLE 6-3. SLENDERNESS RATIOS FOR 10 OUNCE CLOTH- POLYESTER
LAMINATES CONTACT MOLDED - WET CONDITION

Tangent
Modulus of Modulus of Slenderness
Compressive Elasticity Elasticity Ratio
Stress psi x 106 psi x 106
psi E
18,900 (Rupture)
18, 000
17,000
16,000
15, 000
14,000
13,000

12,000

11,400 (Proportional Limit)

11,000
10, 000
9,000
8, 000
7,000
6, 000
5,000
4,000
3,000
2,000

1,500

DESIGN OF LAMINATES 6-43

J

Table 6-1 gives the values for J; ratios based on E below the proportional limit, Eg
above the proportional limit and Ey the reduced modulus above the proportional limit. A
comparison of these values indicate that for materials that have continuous sloping stress-
strain curves with no abrupt point of inflection, the = values based on Eg and Er are al-
most identical. Therefore, the more complex method of solving for Per based on the reduced
modulus need not be used. For practical purposes the value of Fer based on Eg can be used
without appreciable error, The = values above the proportional limit in Tables 6-2 and

6-3 have been based on Ea.
DESIGN EXAMPLE 6-15. CRITICAL COMPRESSIVE LOAD OF MAT LAMINATE

Compute the critical compressive load, Pcey,for a mat-polyester laminate, 6 in. wide
x 1/2 in. thick and 15 in. long, simply supported at the ends, Fig. 6-28.

P

|

|
‘ : ee

oH 1/2"
Pp

Fig. 6-28. Mat Laminate in Compression

Area = 6 x 0.50 = 3.0 sq.in.

bd
Moment of Inertia, I = oe (6. 23)
1Oux (0.50) 2 Geogse an
x = Yo 7 0 in
3
1 = (0.50) 6° = 9.0 Salil

JV al

6-44

DESIGN OF LAMINATES

Radius of Gyration, r =V # (6. 19)
pen 222 = 1 ane
xx 3.0

sf 050625. © :

yy = S200 = oO.) ine

Maximum = = a = 10)

From Fig. 6-25 Fo, = 850 psi

Por = AFop = 320 x 850 = 2550 lbs.

DESIGN EXAMPLE 6-16. COMPRESSION IN WOVEN ROVING LAMINATE
A simply supported woven roving laminate 36 in. long and 12 in. wide is to support a
compressive load of 7,500 lbs, in the warp direction.
7500 LBS

What must its thickness be for a
factor of safety of 2 on the ultimate compressive stress? See Fig. 6-29.

ro

tat

a6!
+

i J —
|

7500 LBS

Fig. 6-29. Woven Roving Laminate
in Compression

Area = 12x t
12 +3
Imin = I = 1D = +3

DESIGN OF LAMINATES 6-45

OF ee Oe
"xx “SJ ioxt 2xf3 346k

L — 36 x 3.464 . 124.70
T. 1 t
F
P = ~~ x12t = 7500 Ibs.
; ela
Assume t = 1 in.3 then= = “oo = 12.70
From Figure 6-26, For = 1550 psi
1550 ;
Boreas, = 2:0 f= 1380 = 775 psi
P = 775 x 12 x 1.00 = 8600 lbs. Greater than required.
ty Ol
Try 15/16: r 7.9375 133
From Figure 6-26 Foy, = 1350 psi
1320
For a FS of 2; ie = 220 - 675 psi

P = 675 x 12 x .9375 = 759 lbs.

Use a 15/16 in. thick laminate.

Composite laminates made of several laminae of different materials have properties
which are different from the physical properties of any of the individual laminae. These
properties for composite laminates have to be computed before the ultimate compressive
stress can be determined. The properties for a composite laminate can be found by means
of the following equations:

Neutral Axis x = poe (6. 24)
Stiffness Factor BI= ) Ely (6. 25)
Modulus of Elasticity E = > EjAi (6. 26)
Shear Modulus a= > D Gia, (6. 27)

Where kg

xs

DESIGN OF LAMINATES

modulus of elasticity of i+th lamina
about the neutral axis.

moment of inertia of i-th lamina
about the neutral axis.

area of i-th lamina.
modulus of rigidity of i-th lamina.

distance from some reference line to the
center of gravity of the i-th lamina.

DESIGN EXAMPLE 6-17. CRITICAL COMPRESSIVE LOAD OF COMPOSITE LAMINATE

Given the laminate of Fig. 6-30, compute the following constants: x, I, E, r, and the
critical compressive load parallel to the warp for simply supported ends.

Fig. 6-30. Composite Laminate in Compression
Neutral Axis:

A, = Area Cloth = 6x 1/16 = 0.375 in@

Ay = AreaMat = 6x 3/8 = 2,250 in®

Az = AreaW.R, = 6x1/8 = 0.750 in?

Given: E,: Cloth

P

| 0.226!" —s—+

24"

au

9/16"

}e— CLOTH

| | | Si MAT
Be

++ WOVEN ROVING

| he 1/16"

| eae

1/8" ae

2.46 x 10° at 0° or warp direction

He
Eo: Mat = 0.93 x 106 at 0° or warp direction
Ey: WeRe = 2645 x 106 at 0° or warp direction
z yg Ey Agxy (6

. 24)

DESIGN OF LAMINATES 6-47

X1, Xg and x3 from woven roving face.

ie 246x100, 375x0.5313 + 9.93x106x2.250x0.3125 + 2.45x106x0.750x0.0625
2.46x106x0.375 + 0.93x106x2.250 + 2.145x106x0.750

x = 0.226 from face of woven roving.

Solving for E:

aa (6. 26)
E = S)EA,
Cloth Mat W.R.
Ee 2.46 x 106 0.93 x 10° 2.45 x 106
i 1.22 x 10-6 = 26 x 10-4 = 977 x 10-6
A. 0.375 2.250 0.750

EA = 2.46x106x0.375 + 0.93x10x2.250 + 2.1,5x106x0.750
= 2,967 x 10°

2.967 x 10° P
E ee (0) i
3.375 gee lO? psa

Solving for EI

figs Bile (6. 25)

EIxx = 2.46x106( 122x106+0, 375x0, 30532) +0.93x10 (26 x 107° + 2.250 x 0.08652)

+2.45x106(977x15°+0. 750x0. 16382)

178002 lbs-in2
178002 becils
Ween 0.2025 in

0.879x10

Be eee
Nai ete 9 ees aie ee (6.28)

3
= —— [ 0625x2.16x100+. 375x0.9 3x106+,125x2, isa |
12x0.879x10

Sai NE ie.

6-48 DESIGN OF LAMINATES

Solving for the radius of gyration, r

a I (Gzan9)
ee ar
/ 0.2025 .
Yxx = 3.375 = /.060 = 0.245 in,
by

To 2

= — > = 97.96
Hee 0.2h5 ie
W6567 = 2 ;
r = fee = 909) t=" 222 am.
vy 3.375
i 2h 10.81
Tyy 2.22
Critical Load
2
1g aa “ES
( By (6. 17a)
1c
2 6
me x ae x 10 = 3052 lbs.
(97.96)
FLEXURE

As previously stated fiberglass laminates may be homogeneous and isotropic or com-
posite and orthotropic depending on the type of reinforcement used. Mat reinforced lami-
nates are considered to be isotropic with equal strength and elastic properties in every
direction and can be analyzed with the same elastic theories as used for metals. Cloth and
woven roving laminates are considered orthotropic with different strength and elastic pro-
perties in different directions and the method of analysis will depend on the direction of load
in relation to the glass fibers. For laminates reinforced with a single type of reinforcement
and for loading parallel to the direction of the glass fibers, the method of analysis will be
similar to the method used for mat laminates. For composite laminates reinforced with two
or more types of reinforcement and for loading parallel to the direction of the glass fibers,
the same type of analysis as used for any other composite section where the moduli are con-
sidered is applicable. The method of analysis for stiffener and plate construction is the same
as for composite laminates with loading in the direction of the glass fibers. In the develop-
ment of stiffeners molded or bonded to the skin laminate, care must be taken to be sure that
the horizontal shear stress at the plane between the stiffeners and plate does not exceed the
laminate interlaminate or bond stress.

Simple One-Way Plates

The differences in analysis for the homogeneous and composite laminates in simple one-
way bending will be illustrated in the design examples which follow. A discussion on the
bending of plates loaded normal to their surface is presented later in this Chapter. For
guidance, graphs of section moduli and moments of inertia have been prepared for several
composite laminates, Figs. 6-31 to 6-33, commonly used in boat hull construction.

Z -— tncH3

2070

2060

2050

2040

2 030

2020

2010

2 000

TOTAL THICKNESS — | NCHES

1413 2150 2187 2224 2261 +298 2335 2372 2409 2446
——_ — = 2000
=
=e
—
+ fas de = —_ all =
=~
Ne

at meee = f | { /| 2001

r all wall = —
ak 2002

— + -— + 4 4

TYPE A LAMINATE “
ee ae FRU S002 SOL OTH
2003
VARIABLE PLIES OF 25-27 OZ
WOVEN ROVING

<
Oo
=
\
H
-004
2005
2006
-007

1 2 3 4 5 6 it 8 9 10

NUMBER OF PLIES OF WOVEN ROVING

Fig. 6-31. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, Type A Laminate - 1 In. Wide Strip

6-49

ABOUT NEUTRAL AXIS — WOVEN ROVING EQUI VALENCE

1.81 x 10° psi

E=

2060

2050

2040

2030

Z - iNncH3

2020

2010

2000

0143 0173

0203 0233

THICKNESS — INCHES

0263 0293

ees:

0353

0383

0413

0443

0473

|

1"

type B LAMINATE
ey A R.LY, (OF M0 OZ. GLOTH

VARIABLE OUNCES OF MAT

| 1 PLY OF 25-27 OZ WOVEN ROVING

ear

Fig. 6-32.

NUMBER OF OUNCES OF MAT

Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, Type B Laminate - 1 In. Wide Strip

6-50

2000

2001

2002

2003

2004

2005

2 006

I - 1ncH4

ABOUT NEUTRAL AXIS — WOVEN ROVING EQU! VALENCE

E = 1.81 x 108 psi

THICKNESS — INCHES

2150 2180 0210 2240 2270 2300 aoa0: °360 23.910 2420 2450 0480 2510
2000
2060
2001
2050 + +
TYPE C LAMINATE
1 PLY (OF 10 OZ CLOTH
VARIABLE OUNCES OF MAT
2002
2 PLIES OF 25-27 OZ WOVEN ROVING
2040
2003
°
x
°o
= .030
'
N
2004
«020
2005
2010
2006
2000

NUMBER OF OUNCES OF MAT

Fig. 6-33, Fiberglass Polyester Laminates, Section Modulus, Z,
and Moment of Inertia, I, Type C Laminate - 1 In. Wide Strip

6-51

I = )ncw*

ABOUT NEUTRAL AXIS — WOVEN ROVING EQU! VALENCE

4.81% 10° Psi

(SS

6-52 DESIGN OF LAMINATES

In obtaining the deflection of a laterally loaded member, the effect of shear may be
appreciable depending upon the material used and the depth to span ratio. When considering
the shear effect in fiberglass reinforced laminates, the shear modulus, G, is important.
The shear modulus for a composite laminate will vary with the different types of reinforce-
ments used and an assumed value based on any one of the reinforcements may not be correct.
Therefore, when the accuracy of the deflection is important, tests on the particular com-
posite laminate in question should be made.

For a uniformly loaded simply supported beam the total deflection for flexure and shear
deformation is (14):

eee (6. 28)
38h EL BAG

where d = deflection, in.
p = load, lbs. per in.
L = span, in.
E = flexural modulus of elasticity, psi
I = moment of inertia, in,4

A = shear area, in.?

G = shear modulus, psi

The above equation assumes uniform shear distribution across the section and can be
considered approximately correct for sections with thin deep webs where all the shear is
taken by the web, similar to an I-beam.

For rectangular sections where the shear is taken by the entire section and the shear
distribution across the section is non-uniform with a maximum at the neutral axis, equa-
tion 6,28 becomes:

a= sf, Bu P 2 «|B | (6. 28a)

DESIGN EXAMPLE 6-18. BENDING OF A MAT OR ISOTROPIC LAMINATE

The fixed ended beam indicated in Fig. 6-34 is made of mat reinforcement and is 12 in.
long and 2 in. wide. What should the thickness of the laminate be if it is to support a uni-
form load of 10 lbs. per linearin. and have a factor of safety of 4 on the ultimate strength?
Also compute the beam deflection.

DESIGN OF LAMINATES 6-53

igi Wop | |
(ee an ee a eae ie ales

es St Nee

Fig. 6-34. Bending of Mat Laminate

sas

Bending Moment M = on (6, 29)
where M = bending moment, in. lbs.

OG e= Feuns load. lost pers ins.

IL, = span, in.

9
Therefore M = 10 x 122 = 1202 O. nea ss
es

The maximum shear on the section is equal to the end reaction:
y = Bb (6. 30)
2

where V = maximum shear, lbs.

Vo= 10 x 22 60.0 lbs.

For the required factor of 4 on the ultimate strength of the laminate, the ultimate
moment and shear becomes:

Mu iy S% AUAXO) 480 in. lbs.

Vu bh x 60

2h0 lbs.

The following properties of the mat laminates are obtained from the tables in Chapter 5:

6-54 DESIGN OF LAMINATES

Ultimate flexural strength, ie 20500 psi Table 5-9

Flexural modulus of elasticity, E

Ultimate shear strength, perpendicular, F

6

0.86 x 10° psi Table 5-10

- 9900 psi Table 5-1)

By use of the standard beam formula, the required section modulus, Z is obtained:

f, * wy = 3 (6.31)
where fy = bending stress, psi
y = distance from neutral axis to the outermost fiber, in.
I = moment of inertia, in.
Z = section modulus, in.

Rearranging the terms in the formula the required section modulus is:

M
cs (6. 31a)

480 = 0,023) in.3

The section modulus, Z, for the outermost fiber of the beam is obtained from:

Ns (6.32)
aa

stH

where I, the moment of inertia is:

1b =

en
"

ct
if

3
bt
ie (6. 23)

width, in.

thickness, in.

Therefore the required depth or thickness of the laminate is:

D (6, 32a)

=O 1205 sins

DESIGN OF LAMINATES 6-55

The maximum shear stress at the neutral axis is obtained from:

fare eer ge (6.33)
Ib abit
where fs = shear stress, psi
Q = static moment of area above the neutral axis
2
t bt 538)
Q = bxe= x— = in
h 8

t ae ee
2 (6. 33a)
_ See = :

to o= ax 2x 900 ~ 0.018 in.

The thickness required is governed by flexure and is 0.265 in.

The maximum deflection of the fixed ended uniformly loaded beam, including the effect
of shear is obtained from:

a pit oe (6.34)
38)E1 5 8 AG
Shear modulus, G, for mat laminate = 0.0 x 10° psi (Table 5-14)
3} 3
p= BE 2 2002657 2 O31 ink (6.23)
12 ie
in 2
Deflection d = 10 x le + o x 10 x 12
38hx0. 86x100x,09 310 5 8x2x0 «265x0 «hOx10©

0.2026 + 0.0011 = 0.2037 in.

DESIGN EXAMPLE 6-19. BENDING OF A COMPOSITE LAMINATE

Compute the ultimate carrying capacity per in. of width of the simply supported com-
posite laminate when uniformly loaded, Fig. 6-35. Assume the cloth and woven roving plies
to be parallel laminated in the direction of the span.

6-56 DESIGN OF LAMINATES

p LBS PER IN,

| Ce eG eee ee eee Wet sleles ee

= — 4. PLES: 25-27) OZ : — 0.148
ae ee = WOVEN ROVING = ee ee

Fig. 6-35, Bending of Composite Laminate
The engineering properties for the three laminae are different and the analysis for a
composite section must be used, To obtain the necessary properties of the section such as

neutral axis, x, stiffness factor, EI, etc. equations 6.24 to 6.27 can be used.

The section modulus may be obtained from:

Zz = (6.35)
Eyy
where y = distance from the neutral axis to any point, in.
Ey = modulus of elasticity of lamina at that point, lbs./in.
El ) mils stiffness factor of the entire section, lbs .-in.@

And the flexural stress may be obtained from:

5, = M - Mave (6. 36)

Z EI

The maximum flexural stress may not occur at the extreme fiber as for isotropic
materials but may occur at any fiber in the section depending on its distance from the neutral
axis and its modulus of elasticity.

The maximum shear stress may be obtained from:

Boe vou (6.37)
s Elb

where V, EI and b are as previously defined.

Q! = Weighted static moment, > EsAay's of the areas
between the extreme edge and the plane being con-
sidered about the neutral axis of the section.

It is considered advantageous when obtaining the section properties of a composite lami-
nate to transform the areas of the different laminae to equivalent areas of one of the lamina.
This method will be used in this design example.

DESIGN OF LAMINATES 6=57

The necessary physical and mechanical properties for the different laminae are assumed
to be the same as for a laminate of the same reinforcement. The values are obtained from
Chapter 5.

Property Cloth Mat W.R. Table No.
Mhickniess its eit. 1 ply = 0.016 1 ply = 0.060 4 ply = 0.148 oo
Flexural Modulus of 1.96 0.86 lege 5-10

Elasticity, E x 10 psi

Ultimate Flexural 31,100 20, 500 28,200 5-9
Stress Fp, psi

Ultimate Inter- ARs) 1/10) 25400 2, 600 5-1
laminar Shear
Stress, Fyg, psi

Transforming the respective areas of the cloth and mat laminae to equivalent area of a
woven roving lamina, the areas as indicated in Fig. 6-36 are obtained.

1.0829!
—<—<$< —$—_r}
pe 004751"
4
Te ae ae = Ota & t
" A = - pa
0.060 { pie a Teoral T
] | 0.216"
A a N
Nene R oa qoze" Aso 178!
0.0148" ' I oval! an |
ae = 0.102"

Fig. 6-36, Equivalent Laminate

A, = WR. area = 0.148 x 1.0 = 0.118 in®
' a (6.38)
A'y = Mat area = Ay x oy .
where A’ = Equivalent area for woven roving lamina.
Ay = Area of mat lamina
Ey = Flexural modulus of elasticity for woving roving lamina
Ey = Flexural modulus of elasticity for mat lamina
0.060 x 0.86 x 10° 2
A, = = eee = 0,000 x O.751 = 0.0285 in
- Tesi x 10
’ a. a (6. 38a)
A cee Cloth area = A3z xX By .

0.016 + 1.96 x 10°

= 0.016 x 1.0829 = 0.0173 in2
1.81 x 10 = ? Ee

6-58 DESIGN OF LAMINATES

The neutral axis of the transformed area can now be found as follows:

vee

ea

1
x oe ileal (6.39)
Beak
where x = distance to neutral axis, in.
A'; = Equivalent area of i-th lamina, in2
x; = Distance to center of i-th lamina, in.
Taking moments about the bottom face of the woven roving lamina:
_ (0.0173 x 0.216 + 0.0285 x 0.178 + 0.148 x 1 x 0.07))
(0.0173 + 0.0285 + 0.18)
0.0198 : a ; :
x = = = 0.102 in. from bottom face of woven roving lamina
0.1938
Obtaining the neutral axis by using equation 6, 24:
= Se EAALME (6. 24)

> EYAy

6 6 6
= (0.016x1.09 621000 .216+0 .960x0 86x10°x0 »178+0 1,81. 81x10°X9 07M). 9 190 Gn.

(0 016x1.96210640 .0 0x0 .86x10040 . 1,821. 81x106 )

The results are the same. The transformed section method, however, gives the
designer a clearer indication of how the components of the laminate behave.

The equivalent moment of inertia and section modulus of the composite section can now
be obtained,

Moment of inertia:

Tihatte =
Th me yee + oe (6. 40)
where b! = equivalent width for woven roving lamina
3 183
0829x0, «l:751x0.0603 0.118
I! = 2a + 0,0173x0.11)2 + pe ae eae + 0,0285x0.0762 + Cee a 0.18x0,0282

(3700x1079 + 2252x1079) + (8552x1079 + 16l6x107%) + (2701x107? + 1160x1077)

7849 x 107? = 0.00078 inl

DESIGN OF LAMINATES 6-59

Section moduli to various laminae:

ee eh (6.41)
2 Ji Ei
where Z; = section modulus of i-th lamina
E; = modulus of elasticity of i-th lamina
Cloth top fiber:
0.00078 1.81 x 106 tee
L = ——— xX Le = 0.0059 in
al :
: 0.122 1696 x 100
Mat top fiber:
0.90078 6
Wh = 9.90070 x 1.81 x 10° = 0.0155 ine
zm 0.106 0.86 x 106
Woven roving bottom fiber:
( 8 6
Im 0.00078 , 1.81x 10% 9.0076 ind
0.102 1.31 x 10°
The ultimate moments for the ultimate flexural stresses are obtained from:
M = Fp xZ (Ges)
Cloth, Met = 31,100 x 9.0059 = 183 in-lbs.
Mat, MU 20,500 x 0.0155 = 318 in-lbs.

Woven Roving, Myr 28,200 x 0.0076 = 21) in-lbs.

TT

The minimum resisting moment of the laminate is Myjyn = 183 in-lbs.

The ultimate uniform load for the minimum resisting moment and simply supported
laminate:

Blin
i = Le (6 e 42)
where Py = maximum uniform load, lbs. per ine
M, = maximum resisting moment, in-lbs.
L = span length, in.
a = sae = 22.9 lbs. per in.

The ultimate vertical shear that the composite laminate will resist due to the ultimate
horizontal shear at the neutral axis and at the shear planes between the different laminae is
obtained from:

6-60 DESIGN OF LAMINATES

fSel "bls E
pena Pe (6. 43)
i = Q'. 5, Ei

where Q!'. = pat -y'. = equivalent weighted static moment of the
m aaa equivalent areas between the extreme edge and
the plane being considered, about the neutral
axiS.

Woven roving at neutral axis:

2600 x 0.00078 x 1.0 1.81 x 106
Y, = see UNO xe x = 389.9 lbs.
1 1,0 = 0.105 + 0,05 elecoe ree

Shear plane between woven roving and mat laminae:

Woven roving?

_ 2600 x 0.00078 x 1,000 1.81 x 106 _
as WO cr Ona Bis ONO 26 = koe 189eh lbs.
Mats
6
Vo 2780 x 0.00078 x 0.4751 1.81 x 10° _~ 293.4 Ibs,

1.0 x Oolh® x 0.028 * 0.86 x 106

Shear plane between mat and cloth laminae:

Mat:
6
Cloth:
The minimum shear strength of the laminate iss Vmin = 389.9 lbse

The ultimate uniform load for the minimum shear strength and simply supported laminae:

P. = 2Vm (6. 30a)
u ia
P = 2 x 389.9 e 9705 lbse

u 8

The ultimate flexural stress controls and the ultimate carrying capacity per in. of
width of the composite laminate is 22.9 lbs. per in.

In order to eliminate the work required in calculating the flexural strength of a given
composite laminate, the graphs of Figs. 6-31 through 6-33 may be used. Given the bending
moment and the bending stress for a particular laminate various values of section moduli
can be found for the components mat, cloth and woven roving. Entering the graphs with the

DESIGN OF LAMINATES 6-61

various section moduli the required laminate may be obtained. The largest number of plies
would control the construction of the laminate.

The composite laminate problem in Design Example 6-19 will now be done by using the
graphs, to obtain the minimum resisting moment of the laminate.

From the graph in Fig. 6-31 for a Type A laminate:

The equivalent moment of inertia for woven roving:

I! = 0.00079 inl!
and the section moduli ares
Cloth Zo = 0.006 in?
Mat Zu = 0.0156 in’

Woven Roving 4yR = O.0077 in

These values are approximately equal to the values previously calculated and the final
resisting moments should be the same.

Stiffener and Plate Construction

Beams of reinforced fiberglass can be molded in numerous shapes with various combi-
nations of reinforcements and core materials. To list all the possibilities would be a
voluminous task beyond the scope of this manual. For this reason only a few sections have
been chosen as representative.

To expedite the work of the designer the graphs of Figs. 6-37 through 6-40 have
been prepared.

Figs. 6-37 and 6-38 give the section modulus, Z, and moment of inertia, I, for hat
stiffeners made up of woven roving. Fig. 6-37 is for hat stiffeners in conjunction with type
A laminate, where the number of plies of woven roving in the laminate is the same as the
number of plies in the stiffener. Fig. 6-38 is for hat stiffeners in conjunction with type B
laminate, where the number of ounces of mat in the laminate is approximately one and one-
half times the number of plies of woven roving in the stiffener. The exact relationship used
is indicated on each Figure. In all cases the effective width of the plate laminate assumed
acting with the stiffener is taken as twice the width of the top of the stiffener. Similar to
the laminates Figs. 6-31 to 6-33, the section moduli given for the cloth face of the laminate
and the woven roving face of the stiffener are corrected so that stress values may be calcu-
lated without modification for moduli values of the different reinforcements. The moment of
inertia, I, values are based on woven roving equivalence with a tension modulus of elasticity
approximately equal to 2.06 x 106 psi. The tension moduli have been used since it is
questionable which moduli will control. Tests of these hat sections arenecessary to ascertain
the correct moduli. The stiffener laminate faying, or touching flange has been taken as
twice the width of the top of the stiffener to ensure that the horizontal secondary bond shear
stress at the interface is never critical.

PART —& PART ©

9 12
—- ne = aa f)
| =
SS Nos
as Ul
7 - "1
| Sees /
| ‘ /
E /
10 + “ i 5
STIFFENER — 2 WOVEN ROVING o Hf
PLATE — 2 WOVEN ROVING ans °
NEN » “ ip
>
2
5 —— t 9 aE zl \ i
\
|
= | / rf +
| \ ii Z
es 8 a —f 10 7
N \ yi hs
STIFFENER — 4 WOVEN ROVING /
PLATE — 4 WOVEN ROVING
H tj
”
x
Fay
z
4 =
i 15
N
1 5
4 20
to) 1 2 3 4 5 6
nh — INCHES
Part b a
10 °
2 25
9
1
6 5
30
7
t) 1 2 3 ‘4 5 6
STIFFENER — 3 WOVEN ROVING
PLATE — 3 WOVEN ROVING hie NCHES
10
Zwr — TO WOVEN ROVING FACE OF STIFFENER
= — ——— Zc - TO CLOTH FACE OF PLATE
2
j ———~—— I -— AsouT NEUTRAL AXIS — WOVEN ROVING
Si EQUIVALENCE, E = 206 X 10° Psi
15
NUMBER OF PLIES OF 25-27 0Z
WOVEN ROVING IN STIFFENER AND
ne IN PLATE VARIES AS INDICATED.
20 1 1 PLY OF 2 OZ MAT — INNER
ASSUMED EFFECTIVE 4 PLY OF 10 OZ CLOTH — OUTER
WIOTH OF PLATE
25
° 1 2 3 4 s 6
h - INCHES

Fig. 6-37. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Hat Stiffeners
with Type A Laminate. Core Considered Ineffective

6-62

PART d

STIFFENER — 5 WOVEN ROVING

PLATE

— 5 WOVEN ROVING

h - INCHES

Fig. 6-37.

I - incu

PART &
/
15 = =e
/
/
/
14 fm
/
/
13 +}
/
/ /
12 -} i 10
/ /
/ /
11 — L L
/
STIFFENER — 6 WOVEN ROVING ABS / /
PLATE — 6 WOVEN ROVING \ |/
10 +- 4 15
y
y)
ae =
zr \
2 f :
; \
as Noa
ui
6 L | 25
\
5
\
4 | 30
3 3
\
2 35
1
40
1 2 3

INCHES

(Cont'd)

Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Hat Stiffeners
with Type A Laminate.

Core Considered Ineffective

Z = 1ncH3

20

—
Part f SI
‘\
19 —
fe) \ X
6
\ \
ee
. |
\
5 17 + W
16 =
10 15 +
14 =i
m5, 3) a
STIFFENER — i anes ooh STIFFENER — 8 WOVEN ROVING
PLATE a N IG PLATE — 8 WOVEN ROVING
if v2
|
20 ah!
= /
< 2 /
+ =
Go
= ' 40 |
N
1
- /
25 9 f /_\
ii]
"
2
8 / \
30 7 V {
|
6 t
35 5
4 +
40 3 °b
2
Uy), \
= 45 1
1 2 3 4 5 6
h - INCHES
° 1 2 ‘] 4 s c

Fig. 6-37. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Hat Stiffeners
with Type A Laminate. Core Considered Ineffective (Cont'd)

6-64

I - incu

Z — incu?

Z = 1ncH3

PART @

h - INCHES

STIFFENER — 2 PLIES WOVEN ROVING
BoA — 2 OZ MAT

PART b

h - INCHES

STIFFENER — 2 PLIES WOVEN ROVING
PLATE — 3 0Z MAT

Fig. 6-38.

15

15

I - incu4

I — 1ncw4

PART ¢

Z - incu?

fo) it 2 3 4 5 6

h = INCHES

STIFFENER — 3 PLIES WOVEN ROVING
PEATE —- 4 OZ MAT

Zwr -— TO WOVEN ROVING FACE OF STIFFENER

Se ZcL — TO CLOTH FACE OF PLATE

——— el — ABOUT NEUTRAL AXIS — WOVEN ROVING EQUI VALENCE

E = 2.06 x 108 psi

NUMBER OF PLIES OF 25-27 OZ
WOVEN ROVING IN STIFFENER
VARIES AS INDICATED

he 1 PLY OF 25-27 OZ WOVEN ROVING

2b

NUMBER OF OUNCES OF MAT IN
PLATE VARIES AS INDICATED

ASSUMED EFFECTIVE
WIDTH OF PLATE

1 PLY OF 10 OZ CLOTH — OUTER

Fiberglass Polyester Laminates - Section Modulus, Z,

and Moment of Inertia, I, for 25-27 Oz. Woven Roving Hat Stiffeners

with Type B Laminate.

Core Considered Ineffective

6-65

Z -— INcH3

PART @
a
/
7
i
/
/
ze
Mi rs
/
is
pli
Ay /
/ \
/ a e
4 ans
| v7 /
Ly, 7
\
a

ea} 3 4 5
h - INCHES

STIFFENER — 4 PLIES WOVEN ROVING
BUALE — 6 OZ MAT

20

25

I - incw4

10

Z = 1NcH3

PART €&

1 2 3 4 5 6
h - INCHES

STIFFENER — 5 PLIES WOVEN ROVING
PEATE — 8 OZ MAT

Fig. 6-38. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Hat Stiffeners
with Type B Laminate. Core Considered Ineffective (Cont'd)

6-66

10

25

30

Z -— 1ncH3

te

PART €

10
o
Ps
Oo
4
\
N
<
=
[S}
4
epee
\
H
20
25
30
2 3 4 5 6 0 al 2 3 4 5 6
h - INCHES
h - INCHES
STIFFENER — 6 PLIES WOVEN ROVING STIFFENER — 7 PLIES WOVEN ROVING
PLATE — 9 0Z MAT PLATE — 10 OZ MAT

Fig. 6-38. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz, Woven Roving Hat Stiffeners
with Type B Laminate. Core Considered Ineffective (Cont'd)

I - incu

PART h

Z - incH3
I - incw4

25

ie) 1 2 3 4 5 6
ho= INCHES
STIFFENER — 8 PLIES WOVEN ROVING
PLATE — 12 0Z MAT

Fig. 6-38, Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Hat Stiffeners
with Type B Laminate. Core Considered Ineffective (Cont'd)

6-68

Z - 1nev3

Z -— incH3

+

10 2
\
H

15

4 6 8 10 12
NUMBER OF PLIES WOVEN ROVING IN STIFFENER
PLATE — 2 PLIES WOVEN ROVING
Part _b

°

5

10
s
3
i)
nH

15

4 6 8 10 12
NUMBER OF PLIES WOVEN ROVING IN STIFFENER

PLATE — 3 PLIES WOVEN ROVING

Z -— incH3

2 4 6 8 to 12
NUMBER OF PLIES WOVEN ROVING IN STIFFENER

PLATE — 4 PLIES WOVEN ROVING

Zwre — TO WOVEN ROVING FACE OF STIFFENER

eee ee, Ze, — TO CLOTH FACE OF PLATE

— ABOUT NEUTRAL AXIS — WOVEN ROVING EQU! VALENCE
— = 2,06 x 10° Ps!

NUMBER OF PLIES OF 25-27 OZ
| WOVEN ROVING IN STIFFENER AND
\ IN PLATE VARIES AS INDICATED.

j

20
ASSUMED EFFECTIVE as ae PLY OF 2 OZ MAT — INNER

WIDTH OF PLATE 1 PLY OF 10 OZ CLOTH — OUTER

Fig. 6-39. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Half-Round

Stiffeners with Type A Laminate.

6-69

Core Considered Ineffective

10 |

I - incr!

15

PART @

PART a

as
we
= 10
ae o
=
°°
4
1
6 N
= ~
x=
3 4 3
2 2
1 1
N 5 15)
=
ae
aa
4
5}
es
Z 1
SS
1
to)
2 4 6 8 10 a2 2 4 6 8 10 12
NUMBER OF PLIES WOVEN ROVING IN STIFFENER NUMBER OF PLIES WOVEN ROVING IN STIFFENER
PLATE — 5 PLIES WOVEN ROVING PLATE — 6 PLIES WOVEN ROVING
Fig. 6-39.

Fiberglass Polyester Laminates - Section Modulus, Z,

and Moment of Inertia, I, for 25-27 Oz. Woven Roving Half-Round
Stiffeners with Type A Laminate.

Core Considered Ineffective (Cont'd)

Z - incu}

PART f

a — t) 13 )
= - a
—— | Sse
~ Se ee
i iaeee Hi Bice 4 12
— a
Os yo
™ =< hee
3 ; : 5 MW P
oO aa
ae od
4
Z|
BI . 10
iS
SS LS
oA
ra 4 | 10 9 10
7 oe
we °
> od
Z er 2
/ Ps
of
raat a > 8
/ oy.
=
7 a
PA ae
—
fzM ies | 15 7 15
/ Z | = *
y, Bon = - ty
o7 2 S 3
Za - = P-4
a | \ \
a
H N 6 4
20 5 20
4
3
2
|
te)
4 6 8 10 12 | 4 6 8 10 qe
NUMBER OF PLIES WOVEN ROVING IN STIFFENER NUMBER OF PLIES WOVEN ROVING IN STIFFENER
PLATE — 7 PLIES WOVEN ROVING PLATE — 8 PLIES WOVEN ROVING

Fig. 6-39, Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Half-Round
Stiffeners with Type A Laminate. Core Considered Ineffective (Cont'd)

G=t1

Z — incH3

a
I - 1ncw4

Z = tNncH3

10

NUMBER OF PLIES WOVEN ROVING IN STIFFENER

PLATE

10

Ae

2 OZ MAT

NUMBER OF PLIES WOVEN ROVING IN STIFFENER

PLATE — 3 OZ MAT

Zwr — TO WOVEN ROVING FACE OF STIFFENER

Zot — TO CLOTH FACE OF PLATE

—-—— =I

— ABOUT NEUTRAL AXIS — WOVEN ROVING EQUIVALENCE

E = 2,06 x 10° ps}

NUMBER OF PLIES OF 25-27 OZ WOVEN ROVING IN
STIFFENER VARIES AS INDICATED

1 PLY OF 25-27 OZ WOVEN ROVING

NUMBER OF
ASSUMED EFFECTIVE

OUNCES OF MAT IN PLATE
VARIES AS
WIDTH OF PLATE

INDICATED

1 PLY OF 10 OZ CLOTH — OUTER

Fig. 6-40.

Fiberglass Polyester Laminates - Section Modulus, Z,

and Moment of Inertia, I, for 25-27 Oz. Woven Roving Half-Round
Stiffeners with Type B Laminate.

Core Considered Ineffective

= (2

Z = incr?

Z - incr?

| 7 =
Seale -— +> ———-_]
| T- | o0=3 a
7 = | aie alee
ae ———l
; ———~Le , | x
+ >~—
os
x Sih} oa —
6 | a ae Z (a
ae
6 te 4 5
| so 22
= =
5 | 287 o eed
etd s
e | 6 a
5 =
ae =e aa
| =
2 | | a
4 7 7 | os = *
Ee y | ised
= ral Z | oF g
= Cer i be plo
z ] -
< i] | = =
' N = ° Lal
3 H z sm
oan 2 = -
- ess
2 =
bp | =
==
a 4
4 5 =
2 Sea ee °
[-
2 = i cote 15
a. | a
4 0 eels
=
— =a
a+ | o=
1
SS
2 4 6 8 10 12 F
NUMBER OF PLIES WOVEN ROVING IN STIFFENER 2 4 é 8 10 12
PLATE -— 4 OZ MAT NUMBER OF PLIES WOVEN ROVING IN STIFFENER
PLATE - 8 OZ MAT
9 0
8
' b}
6
5 10
7 -
°
= 2 2
- z =
2 1 '
= ee, et
\
H
3 15
2
4

NUMBER OF PLIES WOVEN ROVING IN STIFFENER NUMBER OF PLIES WOVEN ROVING IN STIFFENER

PLATE — 6 OZ MAT PLATE -— 9 OZ MAT

Fig. 6-40. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Half-Round
Stiffeners with Type B Laminate. Core Considered Ineffective (Cont'd)

6-73

Z - 1NcH3

PART g

ie) 9
8
5 7
~
x
(3)
2
~ 6
i}
1
10 5
”
cL
iS)
ra
i}
Lee
15 3
a
1
i)
a 4 6 8 10 We
NUMBER OF PLIES WOVEN ROVING IN STIFFENER NUMBER OF PLIES WOVEN ROVING IN STIFFENER
PLATE — 10 OZ MAT PLATE — 12 OZ MAT

Fig. 6-40. Fiberglass Polyester Laminates - Section Modulus, Z,
and Moment of Inertia, I, for 25-27 Oz. Woven Roving Half-Round
Stiffeners with Type B Laminate. Core Considered Ineffective (Cont'd)

6-74

DESIGN OF LAMINATES 6-75

Figs. 6-39 and 6-40 give the same information for woven roving half-round stiffeners as
is given for hat stiffeners. The Figures provide for varying stiffener core diameter and
varying thickness of shell laminate for a given number of plies of woven roving in the
stiffener laminate. The effective width of the laminate is taken as twice the stiffener dia-
meter. Using "low average’ ultimate stresses, as given in the physical properties tables in
Chapter 5, the critical bending stress will be in the compression face, cloth or woven roving
as the case may be for all stiffener sizes shown in these graphs.

If a type C laminate is used, the section properties will be intermediate between those
given for types A and B laminates.

DESIGN EXAMPLE 6-20. BENDING OF A STIFFENER AND PLATE SECTION

The member whose cross-section is given in Fig. 6-41 has a span of 48 in. and is
simply supported. Compute the ultimate carrying capacity and deflection when uniformly
loaded. Assume all the plies of the various reinforcements to be parallel laminated in the
direction of the span and the core material is ineffective.

L be 4

4 PEVLES ‘25-27 02
WOVEN ROVING

1 PLY 2 OZ MAT

1 PLY 10 0Z CLOTH

| |
a 2b= 8" 4 ASSUME

SECONDARY BOND

Fig. 6-41. Composite Stiffener and Plate Section
The necessary physical and mechanical properties for the different laminae are assumed
to be the same as for a laminate of the same reinforcement. The values are obtained from

Chapter 5.

Property Cloth Mat W.R. Table No.

Thickness, t, in. 1 ply = 0,016 1 ply = 0. 060 4 ply = 0.148 oI

Tensile Modulus of
Elasticity, E, 106 psi 1.95 0.91 2. 06 5-7

Ultimate Compressive
Stress, Fe, psi 18,900 15, 900 15, 800 5-11

The transform area method and equations similar to those used in Design Example 6-19
will be used.

Transforming the respective widths of the cloth and mat laminae to the equivalent width
of a woven roving lamina, the dimensions of the composite section will be as indicated in
Fig. 6-42.

DESIGN

OF LAMINATES

0.148" + [

2,298

qe2ge!!

Equivalent width of cloth lamina:

Equivalent width of mat lamina:

Teogal

Fig. 6-42.

ber

pb!

E
=O.
Del x E

EB.
st

= 8.0 x =

a 8.0 x

Equivalent Stiffener and Plate Section

7.573 in.

SA ine

(6. 38b)

(6. 38b)

Equivalent woven roving laminate moment of inertia and section moduli to the face
furthest from the neutral axis of the cloth, mat and woven roving laminae are obtained from
equations 6.40 and 6.41.

Calculation of properties of section:

Section
Plate

Cloth

Mat

W.R.

W.R. Stiffener

Bottom Flanges
Webs

Top Flange

Dimensions

7.573 x .016
3.534 x .060
8.0 x .148

2x2.0x .148
2x 1.852 x .148
4.296 x .148

0.0010 =
0.0098

0.1776

0.1764 0.0526

OLS Ono 2313

1.4615 3.3585

2.5376
> Atx? = 1.9565

= 2.5663in

0.0537
1.0800

3997

9228
.99565

me PP 1

4

DESIGN OF LAMINATES 6-77

Neutral axis from equation 6.39

205376

= 0.771 in.
3.293
Section moduli to outermost fibers and various laminae in plate, from equation 6.41.

Stiffener; woven roving outermost top fiber:

2.5663 2.06 x 106
ZR ee LN, es

1.603 in
1.601 2.06 x 10°

Plate

Cloth outermost bottom fibers

, 2.5663 , 2006x109 _ 3 oy5 an3
cl 0.771 1.95 x 106

Mat bottom fiber:

2.5663 2.06 x 106 A
et = 76
sewn icon a
Woven roving bottom fiber:
6
2.5663 2406 x 10° _ 3 603 473

mR - 0.695 * 5,06 x 100

Values for the moment of inertia and section moduli to cloth, and woven roving can be
easily obtained from Fig. 6-37 part c. The corresponding values from the curves are:

i = 2,53 int

"NA
Stiffener + Zp = 1.62 ir?

Plate $ 25) = 3.33 in

The ultimate moments for the ultimate compressive stresses are obtained from:
M = FoxZ (6. 31b)
Stiffener
Woven roving: Myp = 15800 x 1.603 = 25,330 in-lbs.
Plate

18900 x 3.515 = 66,))30 in-1lbs.

Q

ao

ct

ey

é
pas)
i}

Mat: ee 15900 x 72695 = 122,350 in-lbs.

"

Woven roving: Mop 15800 x 3.693 = 58,350 in-lbs.

6-78 DESIGN OF LAMINATES

The minimum resisting moment of the section is:

Main = 259330 in-lbs.

The ultimate uniform load for the minimum resisting moment and simply supported beam
from equation 6, 42 is:

8M_s
1 —nin = 8x 25.330 . 88.0 lbs. per in.
be 482

The ultimate vertical shear that the composite section will resist due to the ultimate
horizontal shear at the neutral axis and at the secondary bond at the interface between the
stiffener and plate is obtained from equation 6.43.

For ultimate shear at neutral axis:

Q's = h.296 x 0.148 x 1.527 + 2x 1.53 x 0.18 x oo
= 1,283 in?
Ultimate parallel shear stress for woven rovingy Fs = 9,300 psi
95300 x 2.566 x 0.18 x 2, 206x109 . ge
V A = 10 lbs.
: 1.263 2.06 x 106 :

For ultimate shear of secondary bond at interface of stiffener and plate:

oe = 1.296 x 0.148 x 2.07) + 2 x 1.852 x 0.148 x 1.07 + 2 x 2.000 x 0.18 x 0.07)
= 1.952 in
Ultimate secondary bond shear stress, Fp. = 1,000 psi
1,000 x 2.566 x 2 x 2.000 2.06 x 10°
y= ooo C—O SCé#=:«sCOD“= 20 lbs.
2 1.952 2,06 x 10°

The minimum shear strength of the section is:

Vinin = 539260 lbs.

The ultimate uniform load for the minimum shear and simply supported composite sec-
tion is obtained from equation 6. 30a.

p= 242220 _ 519.0 ips. per in.

u 8

The ultimate flexural stress controls and the ultimate carrying capacity of the composite
section is 88.0 lbs. per in.

The maximum deflection of the simply supported uniformly loaded beam, including the
effect of shear is obtained from equation 6. 28).

DESIGN OF LAMINATES 6-79

Shear modulus for woven roving, Gyp = O.u5 x 106 (Table 5-14)

Deflection, d 2 a = ye - De Oeics Oe See
i 384 2.06 x 10 x 2.566 8x08 x 2.18 x 2x05 x 106
d = 1.1507 + 0.0886 = 1.2393 ine

FLAT RECTANGULAR PLATES

A laminate whose thickness is much smaller than its width and length can be classified
as a plate. The analysis of plate sections is both complex and lengthy because of the many
variables which enter into the configuration of a plate. The problem of plate analysis is
further complicated by the fact that plates can be either orthotropic or isotropic in behavior,
Most of the research to date has been based on isotropic materials, such as steel and alumi-
num. When a laminate behaves isotropically, such as a mat reinforced laminate, the
methods generally used for steel plates can be adopted. When the plate is made of materials
that produce an orthotropic laminate however, different approaches to the problem must
be used,

During World War II, a good deal of use was made of plywood plate sections. Forest
Products Laboratory conducted a series of experiments and performed basic research on
this material to better understand its behavior. This effort led to several publications which
outlined methods that could be used for the analysis of plywood plate sections. Since fiber-
glass reinforced plastic laminates are, in general, orthotropic in behavior, it is possible to
use the approaches and formulas developed for plywood plates. In the final analysis, how-
ever, the results would have to be verified by actual experimentation,

Plates can be subjected to many different combinations of loads, boundary conditions,
aspect ratio, etc. There are however, three basic configurations from which most of the
analysis begin; these are as illustrated in Fig. 6-43:

A. Plates loaded in edgewise compression.

B. Plates loaded in uniform shear.

C. Plates loaded laterally.

D. Plates loaded in any combinations of the above.

P

eat er eee

Fig. 6-43. Loads \
on Flat Plates

c. PLATES LOADED LATERALLY

P
b. PLATES LOADED IN

@. PLATES LOADED IN UNIFORM SHEAR
EDGEWISE COMPRESS! ON

6-80 DESIGN OF LAMINATES

Groups A, B, C and Dcan be further subdivided according to boundary conditions, that
is, free edges, clamped edges, or a combination of free and clamped edges.

The designer, when analyzing plates, is usually interested in the critical buckling load,
bending stress and deflection. Formulas, methods, etc. have been established by which
these variables can be obtained for plywood (5, 13, 15-20).

A. Plates Loaded in Edgewise Compression

Mathematical procedures are available by which the critical buckling load for plates
under various edge conditions can be obtained (13,15), The discussion presented here is for
loads applied parallel to or at 90 degrees to the warp direction, Fig. 6-44.

Fig. 6-44, Flat Plate
in Compression - Load
Parallel to Warp

The following terminology will apply to plate analysis for edgewise compression:

<

a = width of plate; = b
b = length of plate
h = thickness of plate

n = number of half-waves into which the panel buckles

Ep = Young's flexural modulus in a direction parallel to the T-axis
Ey, = Young's flexural modulus in a direction parallel to the L-axis

Gry, = Modulus of rigidity associated with a shearing strain corresponding
to the axes of T and L

Oy, Poisson's ratio associated with a contraction parallel
to the T-axis and a tensile stress parallel to the L-axis
out = Poisson's ratio associated with a contraction parallel

to the L-axis and a tensile stress parallel to the T-axis

DESIGN OF LAMINATES 6-81
Weg! Seay
Z = Coordinate measured perpendicular to the middle plane of the panel
w = Lateral deflection (namely in the Z direction) of points on the
middle plane of the panel
P = Load per in. of edge of panel
Poy = Buckling load per in. of edge of panel
er = Goefficient in buckling formula
For an isotropic material Dy = Do, Fp = Ey, % 7, Srp = 9 and
oa ae 02
Constants:
it 3
iD) e2 h
D =/ ae 2°dz cs (6. 44)
1 gee 12)
Oe)
ee 3
2 Fy 22a, Eph (6. 44a)
Do =f — 2 —————" =
n A 12,
2
A «= Ep orn + 2X Gor, (6. 45)
h
2
K =/ A 2 (6. 46)
a 2Z-dz
2
m K
= (6.47)
DyD5
aL
_ b| Aly (6. 48)
ce a Dy
h h h
P 5 2 9 12, 2 2 (6. 49)
= z-dz = 2°dz = x Zaz .
a ‘ Ep cs cc Sh Ep
2 2 2
h
12 : 24
Eo= x iS Ez Zi (6. 49a)

ne

6-82 DESIGN OF LAMINATES

Case 1. All Edges Simply Supported

The critical buckling load, Per, per in. of width can be determined from the equation:

12 vi diD2 (6. 50)

2 2 2
where are 1D E tr = + a

and the panel will buckle in
one half wave if r< vo
two half waves if V2< r< V6

n half waves if Vn(n - 1)< r<Vn(n + 1) (6. 52)

Case 2. Loaded Edges Simply Supported - Remaining Edges Clamped

The critical load is

12 /D4Do (6.50)

Perce = hea
er cr 7)

WiereaKe lie® a + say + (6. 51a)
2 \\ a l6r 2

The plate will buckle in n half waves when

= Yn(n Save rei Va(n ance (6, 52a)

Case 3. Loaded Edges Clamped - Remaining Edges Simply Supported
When the loaded edges are clamped and the remaining edges simply supported the critical

buckling load, Per, becomes a function of the method in which the surface buckles. Conse-
quently for each mode of buckling, there exists a critical load. The critical load then becomes

Keen 12 YD D5 (6. 50)
Cre ae ‘

where a different value of Koy will exist for each mode of buckling as follows:

ae buckling in one half wave

a
: 1 2 16
ker = 1g E ++ | (6. 51b)

DESIGN OF LAMINATES 6-83

\oie buckling in two half waves

2 yl
Ker eds re + +2 + 10x 6.5l1lc
2G L ae (6% )
(ere buckling in three half waves
2
Kor = a | v2 + 238 + 20% (6, 51d)
120 re
d. buckling in four half waves
22. fe
Kae = tT sat ae ao + Bh. (6. 51le)
20) re

Case 4, All Edges Clamped

When all edges are clamped, the buckling load is again dependent upon the form assumed
by the buckled surface. The basic formula

12,/ D,D
P =e an ete has the following (6.50)

cr cr
a

values for Lore

a. buckling in one half wave
2 2 3
Kor | — x (6. 51f)

b. buckling in two half waves

2

eta Ales)

ea a dors eee bon | (6. 51g)
Ge S80 ne

c. buckling in three nalf waves

2
k,, = [° ib — + 10 (6. 51h)

he h 72

dad. buckling in four half waves

o
4a 2, 1059
kup = as Ea + a + 16 (6. 51i)

iy

In Cases 3 and 4, the least value of P., will be the critical value for the plate.

In order to expedite the work of the designer, Tables 6-4 through 6-15 for mat, woven
roving and cloth laminates have been prepared using an electronic digital computer. In
setting up the above equations for the computer solution the following assumptions were made:

6-84 DESIGN OF LAMINATES

The values of Ej, and ET, modulus of elasticity, in the L and T direction respective-
ly, were assumed to be constant throughout the range of the stress-strain curve.
For the laminates tested this assumption appears valid since the stress-strain
curves are almost straight lines.

Since fiberglass laminates do not exhibit a true proportional limit, the values used
were ultimate values obtained by testing.

The panels were considered loaded along the ''a'' dimension with the warp fibers

running parallel to the ''b"’ dimension.

For the development of Tables 6-4 through 6-15, the following low average values from
the tables in Chapter 5 were used:

Ultimate Flexural Stress (Table 5-9)

2 Oz. Mat 6 yore 2 sae 20,500 psi

25-27 Oz. Woven Roving : Fy; = Fur 28,200 psi
10 Oz. Cloth : Foy = Fprp = 31,100 psi

Flexural Modulus of Elasticity (Table 5-10)

2 Oz. Mat : Ey, = 0.86 x 10° psi- Ep = 0.56 x 10° psi

25-27 Oz. Woven Roving: E, = 1.01x 106 psi Ep = 1.5) x 10° psi

10 Oz. Cloth -) EL = 1.96 x 10° psi Ep = 1.70 x 10° psi
Ultimate Compressive Stress (Table 5-11)
2 Oz. Mat 5 Map = Fon = 19,200 psi
25-27 Oz. Woven Roving : Foy, = Fer = 19,200 psi
10 Oz. Cloth : Foz = Fer = 18,900 psi
Ultimate Shear Stress, Parallel (Table 5-14)
2 Oz. Mat tg eg = 10,100 psi

25-27 Oz. Woven Roving : Fsz, = Fst = 9,500 psi

LO Oz... Cloth 5 Poy = Faq = 10,500 psi

Shear Modulus Poisson's Ratio

(Table 5-14) (Tables 5-8 and 5-13)
2 Oz. Mat G20. Ox 10° psi oO =o. = 0.37

a Poel : LT 7;
/ ; 6. a
25-27 Oz. Woven Roving : Gop = 0.5 x 10> psi on Onn, 0.19
6 :

10 Oz. Cloth : Grp = 0,52) 10 psi opp *opy = 0.20

TABLE 6-4,

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED

a

PHYSICAL CONSTANTS:
E, = Ey = 0.86x10® PSI

Gxy = 0.40x10° PS|
Oxy = yx = 0.37
THICKNESS=H EQUALS 000625 INCHES
H=
MINCHES. “Tnenes “INCHES.
6 8 10 iz 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 24 15 va) 9 8 7 7 me tf 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
8 26 14 re 7 6 Lj 5 4 4 4 4 4 4 4 4 3 J 3 3 3 3 3 3 8
10 25 14 9 6 5. 4 4 3 3 3 3 3 3 r) 2 2 2 2 2 2 rf 2 2 10
12 24 a3 i} 6 5 4 =| 2 rs 2 a ©; 2 2 2 2 2 2 il a a4 12
14 25 14 10 6 4 3 3 2 2 2 2 2 2 2 1 1 1 1 1 7) 1 1 i 14
16 24 14 9 7 5 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 16
18 24 14 9 7 5 3 3 2 2 2 1 1 1 1 T rT 1 1 1 1 1 1 1 18
20 24 14 ) 6 5 4 3 2 2 rd 1 1 1 1 1 1 1 1 1 1 1 1 1 20
22 24 14 9 6 5 4 3 a 2 2 1 1 1 1 1 a 5 ai aE i at 1 fe) 22
24 24 14 9 6 +] 4 a 2 2 3 1 1 Zz x, 1 1 1 1 1 to) te) Le) fe) 24
26 24 14 9 6 4 4 3 2 2 2 1 1 al 2 Z 1 | a ) ) to} ° fe) 26
28 24 14 9 6 4 i} 3 2 2 2 1 1 5 4 1 1 ny ° (a) io) ° ° i) 28
30 24 14 | 6 4 e} a 2 2 4 1 1 1 i 1 1 1 fa) fo fo 0 fo} 0 30
32 24 14 ") 6 5 | 3 2 2 2 1 1 a 1 1 al 1 ° te} ° to} 0 ° 32
34 24 14 c) 6 5 3 3 a 2 2 1 1 1 1 if 7 1 0 oO (a) (a) 0 0 34
36 24 14 9 6 5 e} 3 2 2 2 2. 1 1 1 bt of v to oO 0 [o} fe) fe) 36
38 24 14 9 6 4 x) 3 2 2 2 1 1 vt 1 1 1 O oO ° oO io) Lo) 0 38
40 24 14 b 6 4 3 3 i 2 2 1 rl 1 7: 1 1 to) ° fo) (0) fo) (c) (0) 40
42 24 14 9 6 4 3 3 2 2 2 1 Zz 1 1 1 al 0 t) ° 0 0 0 ° 42
44 24 14 9 6 4 3 3 r] 2 2 1 1 1 1 1 1 fe) 0 ) te) i) to) ° 44
46 24 14 3 6 4 a 3 e 2 1 1 1 pl 1 Zz i} to} 0 0 ie} fe) ° 46
48 24 14 ci 6 5 i} 3 2 2 1 1 1 1 a 1 1 oO ° ° oO ° 0 48
THICKNESS=H EQUALS 001250 INCHES

LENGTH=8 WIOTH=A LENGTH-B

INCHES INCHES INCHES
6 8 10 ples 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 2 78

6 193 117 88 73 65 60 Siti 54 52 51 50 49 49 48 48 47 47 46 46 46 45 45 45 6
8 208 109 ina 56 47 41 38 35 33 32 hl 30 29 vac) 28 28 27 27 26 26 26 26 26 8
10 199 114 70 50 39 ck] 29 26 24 23 22 21 20 20 oho) 19 18 18 i? a a as ‘WA 10
12 193) 7 nics 48 36 29) 25 22 20 18 a7 16 16 15 15 14 pie 13 12 12 12 12 12 12
14 197 110 mir 49 35 28 23 20 17 16 14 13 13! v2 12 ll 10 10 9 9 9 ) c} 14
16 196 109 73 52 36 27 22 18 16 14 13 12 ay 10 10 2 9 8 8 7 ty of, it 16
18 193 110 70 52 38 28 21 18 15 sie 12 11 10 o 9 8 uf 7 6 6 6 6 6 18
20 195 112 70 50 39 28 22 i? 14 a2, ll 10 9 8 8 7 6 6 Ei 5 a a 5 20
22 195 109 70 49 37 30 22 18 14 12 11 t) 8 8 Tf iY 6 5 5 4 4 4 4 22
24 193 109 72 48 36 29 23 18 14 12 10 3) 8 i 7 6 5 B 4 4 4 4 a 24
26 194 109 71 49 36 28 24 19 15 12 10 9 8 Li 6 6 5 4 4 a 3 3 3 26
28 194 110 70 49 35 28 23 19 15 12 10 €) 8 7 6 6 5 4 eS eh 3 a < 28
30 193 109 70 50 36 27 22 19 16 Ne} 10 a 8 7 6 6 4 4 2 E) 3 3 2 30
32 194 109 70 49 36 27 22 18 16 13 11 o 8 Hi 6 5 4 4 3 3 3 2 2 ee
34 194 109 tpt 48 a7 20 22 18 15 13 ll 9 8 7 6 a 4 3 3 3 2 2 2 34
36 193 110 70 48 36 28 21 18 15 13 ll 9 8 7 6 L} 4 3 3 2 a 2 2 36
38 194 109 70 48 36 28 22 Pye 15 13 ll 10 8 7 6 5) 4 3 3 2 2 2 2 38
40 194 109 70 49 36 28 22 17 14 12 11 10 8 7 6 5 4 = e) 2 2 2 2 40
42 193 109 70 49 35 28 22 17 14 12 i 10 9 7 6 5 4 3 3 2 2 2 2 42
4 194 109 70 49 36 27 22 18 14 12 ll 2 8 7 6 6 4 | 2 2 2 2 2 44
46 194 109 70 48 36 27 22 18 14 12 10 c) 8 7 6 4 3 2 2 2 2 1 46
48 193 109 70 48 36 27 22 18 14 12 10 9 8 7 7 6 4 =} 2 2 ie re 1 48

TABLE 6-4. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 001875 INCHES

LENGTH=8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 652 396 296 247 220 203 191 183 TTT 173 169 167 164 163 161 160 157 156 154 154 153 153 152 6
8 703 367 246 189 158 139 127 118 112 107 104 101 99 Sit: 96 94 ae: 90 89 88 87 87 86 8
10 672 384 235 168 223 112 98 89 83 78 74 qk 69 67 65 64 61 60 58 58 St 56 56 10
12 652 396 242 163 122 99 84 74 67 62 58 55 53 51 49 48 45 43 42 41 40 40 40 12
14 667 373 260 167 120 te) nite 66 58 53 49 45 43 41 39 38 23 ete 32 31 cpl 30 30 14
16 660 367 246 176 122 92 ite) 61 53 47 43 40 37 35 33 32 29 27 26 25 24 24 23 16
18 652 ar2 237 176 127 bie) 72 59 50 44 Bo 36 33 31 29 ray 24 23 21 20 20 19 19 18
20 659 378 235 168 133 96 73 59 49 42 ed 33 30 28 26 25 21 19 18 17 Ti 16 16 20
22 657 369 237 164 126 101 afc} 59 49 41 36 32 28 26 24 22 19 a7 16 15) 14 14 13 22
24 652 367 242 163 122 a9) 78 61 49 41 35 31 27 25 22, 21 18 15 14 iis) LZ 12 12 24
26 656 369 239 164 120 95 80 62 50 41 35 30 rat? 24 22 20 16 14 13 12 11 ll 10 26
28 655 373 236 167 120 Ek} 77 65 51 42 os) 30 26 23 21 19 15 13 12 ll 10 9 9 28
30 652 368 235 168 120 92 75 63 LE) 43 35 30 26 23 21 19 15 12 11 10 L} 9 8 30
32 655 367 236 165 122 o2 ue} 61 53 44 36 30 26 23 20 18 14 12 10 Ch 8 8 8 32
34 654 368 238 164 124 92 ie, 60 52 45 aim 31 26 23 20 18 14 gh 10 =) 8 7 Tf 34
36 652 371 237) 163 i22 93 72 59 50 44 38 32 27 23 20 18 14 ll 9 8 7 ze 6 36
38 654 368 235 163 121 94 re) Li} 49 43 38 33 ain: 24 eu: 18 13 ll 9 8 Hs 6 6 38
40 654 367 235 165 120 95 73 59 49 42 37 33 28 24 21 18 13 1l 9 8 7 6 6 40
42 652 368 235) 166 120 93 4 59 49 41 36 32 29 25 21 19 13 10 9 7 6 6 5 42
ised hk el 164 120 92 75 59 49 41 36 32 28 25 22 19 13 10 8 7 6 6 5 44
46 653 367 236 163 121 92 14 60 49 41 35 31 28 25 22 19 13 lo 8 7 6 5 5 46
48 652 367 235 163 122 92 73 61 49 41 35 31 27 25 23 20 146 10 8 a 6 5 5 48

THICKNESS=H EQUALS 002500 INCHES

“INCHES. “INCHES “INCHES.
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 a2) 78
6 1546 938 702 587 521 480 453 434 420 409 401 395 390 385 382 379 373 369 366 364 363 362 361 6
8 1667 870 582 448 ee fs) 330 301 280 266 255 246 240 234 230 227 224 217 213 211 209 207 206 205 8
10 1594 910 556 398 315 265 reek) 211 196 184 ils get 168 163 159 155 152 145 1461 138 136 135 134 133 10
12 1546 938 574 386 290 234 199 176 159 147 137 130 125 120 116 113 107 102 99 97 96 95 94 12
14 1580 8B4 617 395 284 221 182 156 138 125 iS, 108 102 97 93 90 83 719 16 4% 72 71 70 14
16 1566 870 582 417 289 217 174 146 126 112 102 94 87 82 78 75 68 64 61 59 57 56 55 16
18 1546 881 562 417 301 220 172 141 21g) 104 93 85 78 73 69 65 58 53 50 48 47 45 45 18
20 1562 896 556 398 Bis’ 228 174 129 116 100 88 79 ne: 66 62 58 51 46 43 41 39 38 37 20
22 1556 876 561 389 299. 238 178 140 GE oF: 84 73: 67 62 57 Ee) 45 41 37 B5) 34 32 32 22
24 1546 870 574 386 290 234 185 143 116 oF 83 ie} 65 59 54 50 42 37 33 31 30 26 “27 24
26 1555 875 567 389 285 226 189 148 116 97 82 7 63 57 51 47 39 34 30 28 26 25 24 26
28 1553 884 559 395 284 221 182 154 vey ce} 83 71 62 55 50 45 37 31 28 25 24 22 22 28
30 1546 873 556 398 285 218 Lint 150 125 101 84 7 62 55 49 44 35 29 26 23 22 20 19 30
32 1552 870 559 Aag9h 289 217 174 146 126 104 B86 72 62 54 48 43 34 28 24 22 20 19 18 32
34 1550 872 565 388 294 218 172 143 122 108 88 73 63 55 68 43 33 27 23 21 19 17 16 34
36 1546 B78 562 386 290 220 172 141 119 104 91 75 64 55 48 43 32 26 22 20 18 16 is 36
38 1550 872 558 387 287 223 172 139 117 102 90 77 65 56 49 43 32 25 21 19 17 15 146 38
40 1549 870 556 390 285 224 174 139 116 100 88 79 67 57 49 43 32 25 21 18 16 15 13 40
42 1546 871 558 393 284 221 176 139 115 98 86 77 69 58 50 44 32 25 20 17 15 14 13 42
44 1549 876 261 389 284 219 178 140 115 97 84 75 67 60 51 45 32 24 20 17 15 13 12 44
46 15468 871 560 387 266 218 176 142 115 97 83 m4 66 60 52 “5s 32 24 20 16 14 13 12 46
46 1546 870 557 386 289 eat 174 143 116 97 83 TK) 65 59 54 46 32 24 19 16 14 12 ll 48

6-86

TABLE 6-4,

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

2 OZ, MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 003125 INCHES
LENGTH=B WLOTH=A LENGTH=B8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 3019 1831 1371 1146 1017 938 885 B47 820 199 783 771 761 753 746 740 728 720 215 71 708 707 705 6
8 3256 «©1698 1138 875 732 644 587 547 519 498 481 468 458 450 443 437 424 416 411 407 404 402 400 8
10 3112. «1777-1087 778 615 517 455 412 382 359 342 329 318 310 303 297 284 276 270 266 264 261 260 10
12 3019 1831 1121 755 567 458 389 343 310 286 268 254 243 234 227 221 2c8 200 194 190 187 185 184 12
14 3086 1726 1205 rie 555 432 355 305 270 244 225 210 199 190 182 176 162 154 148 144 141 139 137 14
16 3058 1698 1138 814 564 425 340 284 246 219 198 183 iz 161 153 147 134 1246 119 114 r12 109 108 16
18 3019 1720 1098 B14 587 430 335 275 233 203 182 165 152 142 134 127 113 104 98 94 91 89 87 18
20 3050 1751 1087 778 615 444 339 272 226 195 171 154 140 129 121 114 99 90 84 80 7 74 72 20
22 3040 1710 1096 760 585 466 348 274 225 190 165 146 132 121 lll 104 89 79 73 69 66 63 62 22
24 3019 1698 1121 755 567 458 362 280 226 189 162 142 126 114 105 97 81 72 65 61 58 55 53 24
26 3037. 1708 1108 759 557 442 369 289 230 190 161 139 123 110 100 92 16 66 59 55 51 49 47 26
28 3032 1726 1092 rapt 555 432 355 301 237 193 162 139 121 108 97 89 7 61 54 50 46 44 42 28
30 3019 1705 1087 778 Ch) 426 346 293 245 197 164 139 121 107 95 86 68 57 51 46 42 40 38 30
32 3031 1698 1091 764 564 425 340 284 246 203 167 141 121 106 94 85 66 55 48 43 39 37 35 32
34 3028 81704 1103 757 574 426 336 278 239 210 172 144 123 107 94 84 64 53 45 40 37 34 32 34
36 3019 1716 1098 755 567 430 335 275 233 203 177 147125 108 94 84 63 51 43 38 34 32 30 36
38 3027 1702 1090 757 560 436 336 272 229 198 176 151 127 109 95 B4 62 50 42 36 33 30 28 38
40 3026 1698 1087 763 556 438 339 272 226 195 171 154130 111 96 85 62 49 40 35 31 28 26 40
42 3019 1702 1089 767 555 432 343 272 225 192 168 149° 134 114 98 86 62 48 39 34 30 27 25 42
44 3025 1710 1096 760 556 428 348 274 225 190 165 146 = 132 116 100 87 62 48 a9 33 29 26 24 44
46 3024 1701 1094 756 559 425 343 277 225 189 163 144 129 117 102 a9 62 47 38 32 28 re 23 46
48 3019 1698 1089 755 564 425 340 280 226 189 162 142, 126 114 105 90 63 47 38 32 27 24 22 a
THICKNESS=H EQUALS 063750 INCHES
LENGTH=B WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 5217 3164 2370 1980 1758 1620 1528 1464 1417 1381 1354 1332 4315 1301 1289 1279 1258 1245 1236 1229 1224 1221+ 1218 6
8 5625 2935 1966 1513 1265 1113 1015 946 897 860 631 809 791 777 765 755 733 720 711 704 699 695 692 8
10 5378 3071 1878 1345 1062 894 786 713 660 621 592 569 550 535 523 513 491 477 467 461 456 452 449 10
12 5217 3164 1936 1304 979 791 672 592 536 495 464 440 420 405 393 382 360 345 336 329 324 320 317 12
14 5332 2983 2041 1333 958 746 614 527 466 422 389 364 344 328 314 304 281 266 256 249 244 240 237 14
16 5284 2935 1966 1406 974 734 587 491 426 378 343 316 295 278 265 254 230 215 205 198 193 189 186 16
18 5217 2972 «1897 «1406 =-1015 743 580 474 403 352 314 285 263 246 232 220 195 180 170 163 157 153 150 18
20 5271 3025 1878 1345 1062 768 586 470 391 336 296 265 242 226 209 197 171 155 145 138 132 128 125 20
22 5253 2955 1894 1313 1011 804 601 473 388 328 285 253 228 208 193 180 153 137 127 119 114 110 106 22
24 5217 2935 «1936 = 1304 979 791 625 484 391 326 279 245 218 198 181 168 141 124 113 105 100 96 92 24
26 5248 2952 1914 1312 963 763 638 500 398 328 278 241 213 191 173 160 131 113 102 94 89 85 61 26
28 5240 2983 1886 1333 958 746 614 520 409 333 279 240 210 186 168 154 123 106 94 86 80 76 73 28
30 5217 2946 1878 1345 962 736 598 506 424 341 283 241 209 184 165 149 118 99 87 79 73 69 66 30
32 $237 2935 18385 1321 974 734 587 491 426 352 289 244 209 183 163 147 114 95 82 74 68 63 60 32
34 5233 2944 1905 1308 992 736 581 481 412 363 297 248 212 184 162 1465 111 91 78 69 63 Ce) 55 34
36 5217 2965 1897 1304 979 743 580 474 403 352 306 254 215 186 163 145 109 88 1) 66 60 55 52 36
38 5231 2942 1883 1308 967 754 581 471 396 343 304 261 220 188 164 1465 107 86 72 63 56 52 48 38
40 5228 2935 1878 1316 960 756 586 470 391 336 296 265 225 192 166 1466 107 84 70 61 54 49 46 40
42 5217 2941 1882 1326 958 746 592 471 389 331 290 258 231 196 169 148 106 83 68 59 52 47 43 42
44 5227 2955 1894 1313 960 739 601 473 388 328 285 253° 228 201 173 150 107 82 67 57 50 45 41 44
46 5226 2939 1890 1306 966 735 593 478 389 327 282 248 = 223 203 177 153 107 82 66 56 49 43 40 46
48 5217 2935 1881 1304 974 734 587 484 391 326 279 245 218 198 181 156 108 82 65 55 47 42 38 48

6-87

TABLE 6-4. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 004375 INCHES

Nene. “INCHES Nate
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7740 5025 3763-3243. «2792-2573. 2427 «= «2324 «= 22502193. 2149) 2115 2088 = 2066 = 2047 = 20311997 = 1977 19621951 194% = 1939-1934 6
8 7740 4660 3121 2402 2008 1768 1611 1502 14246 1365 1320 1285 1256 1234 1215 1199 1165 1143 1129 1118 1110 11046 1098 8
1o 7740 4877 2982 2135 1686 1420 1248 1132 1048 986 940 903 874 850 831 814 780 758 742 731 724 17 713 10
12 7740 5025 3075 2071 1555 1256 1068 941 851 786 736 698 668 643 623 607 571 548 533 522 514 508 504 12
14 7740 4737 3305 2117 1522 1184 975 837 740 670 618 577 546 520 499 482 446 422 407 396 388 382 377 14
16 7740 4660 3121 2233 1547 1165 932 780 676 601 545 502 469 442 420 403 365 341 325 314 306 300 295 16
18 7740 4720 3013 2233 1612 1180 921 753 639 558 499 453 418 390 368 349 310 286 270 258 250 244 239 18
20 7740 4804 2982 2135 1686 1219 930 746 621 534 470 422 384 355 331 312 272 247 230 218 210 204 199 20
22 7740 4693 3007 2086 1605 1277 955 752 616 521 453 401 362 331 306 286 244 218 201 189 181 174 169 22
24 7740 4660 3075 2071 1555 1256 993 769 621 518 444 389 347 314 288 267 223 196 179 167 158 152 147 24
26 7740 4687 3039 2083 1529 1212 1013 794 632 521 441 382 338 303 276 253 208 180 162 150 141 134 129 26
28 7740 4737 2995 2117 1522 1184 975 826 650 529 443 380 333 296 267 244 196 168 149 136 127 121 115 28
30 7740 4678 2982 2135 1528 1169 949 804 673 542 450 382 331 292 262 237 187 158 139 126 116 110 104 30
32 7740 4660 2994 2098 1547 1165 932 780 676 558 459 387 333 291 259 233 181 150 130 117 108 101 95 32
34 7740 4676 3026 2077 1575 1169 923 764 655 577 471 394 336 292 258 231 176 144 124 110 100 93 88 34
36 7740 4708 3013 2071 1555 1180 921 753 639 558 486 403 342 295 259 230 173 140 119 105 95 87 82 36
38 7740 4671 2990 2077 1536 1197 923 747 628 544 482 414 349 299 261 231 171 136 114 100 90 82 77 38
40 7740 4660 2982 2092 1525 1201 930 746 621 534 470 422 357 305 264 232 169 133 lll 96 86 78 72 40
42 7740 4670 2989 2105 1522 1184 941 747 617 526 460 410 367 312 269 235 169 132 108 93 82 74 69 42
44 7740 4693 3007 2085 1525 1173 955 752 616 521 453 401 362 319 274 239 169 130 106 90 79 71 65 44
46 7740 4668 3002 2075 1533 1167 942 759 617 519 447 394 353 322 280 243 170 130 105 88 77 69 63 46
48 7740 4660 2987 2071 1547 1165 932 769 621 518 444 389 347 314 287 248 172 129 104 87 75 67 61 48
THICKNESS=H_ EQUALS 95000 INCHES
LENGTH=S WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9600 7501 5617 4692 4167 3341 3623 3469 3358 3274 3208 3158 3117 3084 3055 3032 2981 2951 2929 2913 2902 2894 2887 6
8 9600 6956 4659 3586 2997 2639 2405 2242 2125 2038 1970 1918 1875 1842 1813 1790 1739 1706 1685 1669 1656 1648 1639 8
10 9600 7280 4452 3187 2517 2119 1864 1689 1565 1472 1402 1348 1304 1269 12460 1216 1164 1131 1108 1092 1080 1071 1064 10
12 9600 7501 4590 3092 2321 1875 1596 1404 1271 1173 1099 1042 997 960 930 906 852 818 796 779 767 758 752 12
14 9600 7071 4934 3160 2271 1768 145€ 1249 1105 1000 922 862 814 7176 745 720 665 631 607 591 579 570 563 14
16 9600 6956 4659 3334 2309 1739 1392 1165 1009 896 813 749 700 660 628 601 545 509 486 469 457 448 440 16
18 9600 7045 4498 3334 2406 1761 1374 1124 954 833 144 CHAL 624 582 549 521 463 427 403 385 373 364 356 18
20 9600 7171 4452 3187 2517 1820 1388 1113 928 797 Tol 629 574 530 495 466 405 368 343 326 313 304 297 20
22 9600 7005 4489 3113 2395 1907 1426 1122 920 778 676 599 540 CE 457 427 364 325 300 262 269 260 252 22
24 9600 6956 4590 3092 2321 1875 1482 1147 926 773 662 580 518 469 430 398 333 293 267 249 236 226 219 24
26 9600 6997 4536 3110 2283 1809 1513 1185 944 777 659 571 504 452 411 378 310 269 242 2246 210 200 193 26
28 9600 7071 4471 3160 2271 1768 1456 1233 970 790 662 568 497 462 399 364 293 250 223 204 190 180 172 28
30 9600 6983 4452 3187 2281 1746 1416 1200 1004 809 671 570 495 436 391 354 280 235 207 188 174 164 156 30
32 9600 6956 4469 3131 2309 1739 1392 1165 1009 833 685 577 497 435 386 348 270 224 195 175 161 150 142 32
24 9600 6980 4516 3101 2351 1745 1378 1140 977 861 703 588 502 436 385 345 263 215 185 164 150 139 131 34
36 9600 7027 4498 3092 2321 1761 1374 1124 954 833 725 602 510 440 386 344 258 208 177 156 141 130 122 36
38 9600 6973 4463 3100 2292 1787 1378 1116 938 812 720 618 521 447 390 344 255 203 171 149 134 123 114 38
40 9600 6956 4452 3123 2276 1793 1388 1113 928 797 701 629 533 455 395 347 253 199 166 143 128 116 108 40
42 9600 6971 4462 3143 2271 1768 14604 1115 922 786 687 612 548 465 401 351 252 196 162 139 123 111 102 42
44 9600 7005 4489 3113 2276 1751 1426 1122 920 778 676 599 540 477 409 356 253 195 159 135 oO) 107 98 44
46 9600 6967 4480 3097 2289 1742 1407 1133 921 774 668 588 528 480 418 363 254 194 156 132 115 103 94 46
48 9600 6956 4459 3092 2309 1739 1392 1147 926 773 662 580 518 469 429 370 257 193 155 129 112 100 90 48

6-88

TABLE 6-4,

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 005625 INCHES

pecs wince ny
— a 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
Gumnoscomancdo Nysas m Géele Uss3. Gea st59) Ayal s7a2z) (Acee) “45ea™ 4496)" «4428) 0439) 4350 4317 4245 4201) 4170) 4147) 4131 #1214121 S
8 10800 9904 6634 5105 4268 3758 3424 3193 3026 2902 2806 2731 2670 2622 2582 2549 2475 2428 2399 2376 2359 2346 2334 8
10 10800 10366 6339 4538 3584 3018 2653 2405 2228 2096 1997 1919 1857 1607 1766 1731 1657 1610 1577 1554 1538 1525 1515 10
12. "10800 10680 6535 4402 3305 2670 2269 2000 1809 1670 1565 1483 1419 1367. 1325. 1290 -«s«-:1214=0s 11650-1133) 1110-1093. 1079-1070 12
14 10800 10068 7025 4499 32346 2517 2073 1778 1573 1424 1313 1227 1160 1106 1061 1025 948 898 B65 B42 B24 812 801 14
16 10800 9904 6634 4747 3287 2476 1981 1659 1436 1276 1158 1067 996 940 894 856 776 725 691 668 650 637 627 16
18 10800 10031 6404 4747 3426 2508 1956 1601 1359 1187 1060 963 889 829 782 742 659 608 573 549 531 518 508 18
20 10806 10211 6339 4538 3584 2592 1976 1585 1321 1135 998 896 817 754 704 663 577 524 489 464 446 433 422 20
22 10800 9973 6392 4433 3411 2715 2030 1598 1310 1108 962 853 769 703 650 607 518 463 427 402 384 370 359 22
24 10800 9904 6535 4402 3305 2670 2110 1634 1319 1100 943 8260737 667 = 612 567 = 474 418 380 355 336 322 312 24
26 10800 9962 6459 4428 3250 2576 2154 1687 1344 1107 938 813 718 644 586 538 441 383 345 318 300 285 275 26
28 10800 10068 6366 4499 3234 2517 2073 1756 1381 1125 942 809 707 629 568 518 417 356 317 290 271 256 245 28
30 10800 9942 6339 4538 3248 2486 2017 1709 1429 1152 956 812 704 621 556 504 398 335 295 267 248 233 222 30
32 10800 9904 6363 4458 3287 2476 1981 1659 1436 1187 975 822 707 619 550 495 384 319 277 249 229 214 203 32
34 10800 9938 6431 4415 3348 2484 1962-1624 1391 1226 =1001 837 715 621 548 491 374 306 263 234 214 198 187 34
36 10800 10006 6404 4402 3305 2508 1956 1601 1359 1187 =—1032 857 726 627 950 489 367 297 252 222 201 186 174 36
38 10800 9929 6354 4414 3264 2544 1962 1589 1336 1157 1025 880 741 636 555 490 363 289 243 22 191 75 163 38
40 10800 9904 6339 4447 3241 2553 1976 1585 1321 1134 998 896 759 648 562 494 360 284 236 204 162 166 154 40
42 10800 9926 6353 4475 3234 2517 2000 1588 1312 1119 978 872 781 662 571 500 359 280 230 198 175 158 146 42
44 10800 9973 6392 4432 3241 2493 2030 1598 1310 1108 962 853-769 679 583 507 360 277 226 192 169 152 139 44
46 10800 9920 6379 4409 3259 2480 2003 1613 1312 1102 951 838 0751 683 596 517 362 276 223 188 164 146 134 46
48 10800 9904 6348 4402 3287 2476 1981 1634 1319 1100 943 B26 737 667 611 527 365 275 220 184 160 142 129 48
THICKNESS-H EQUALS 006250 INCHES
LENGTH=-B WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 12000 12000 10971 9165 8139 7501 7076 6776 6559 6394 6266 6167 6083 6023 5967 5922 5823 5763 5721 5689 5667 5653 5639 6
8 12000 12000 9101 7003 5854 5155 4697 43480 4151 3980 3849 3746 3663 3597 3542 3497 3396 3331 3291 3259 3235 3218 3202 8
10 12000 12000 8695 6225 4916 4140 3640 3299 3056 2876 2739 2632 2547 2478 2422 2375 2273 2209 2164 2132 2110 2092 2079 10
12 12000 12000 8964 6038 4534 3662 3112 2743 2482 2291 2147 2035 1947 1875 1817 1769 1665 1599 1554 1522 1499 1481 1468 12
14 12000 12000 9636 6171 4436 3453 2843 2439 2158 1954 1801 1683 1591 1517 1456 1406 1300 1232 1186 1155 1131 1113 1099 14
16 12000 12000 9101 6511 4510 3397 2718 2275 1970 1751 1588 1464 1366 1289 1226 1174 1064 995 949 916 892 874 860 16
18 12000 12000 8784 6511 4700 3440 2684 2196 1864 1628 1454 1322 1219 1138 1072 1018 904 833 786 753 729 710 696 18
20 12000 12000 8695 6225 4916 3555 2711 2174 1812 1556 1370 1229 1120 1035 966 910 792 719 670 637 612 594 580 20
22 12000 12000 8768 6080 4678 3724 2784 2192 1797 1520 1320 1179 1054 964 892 833 711 635 586 551 526 507 493 22
24 12000 12000 8964 6038 4534 3662 2894 2241 1809 1510 1294 1134 1011 916 840 778 650 573 522 487 461 442 428 24
26 120C0 12000 8860 6074 4459 3533 2955 2315 1843 1518 1286 1115 984 883 803 739 606 525 473 437 411 392 377 26
28 12000 12000 6733 6171 4436 3453 28463 2409 1895 1543 1293 1109 970 863 779 71 572 488 435 398 371 352 337 28
30 12000 12000 8695 6225 4456 3409 2767 2344 1961 1580 1311 1114 966 852 763 692 546 460 404 367 340 320 304 30
32 12000 12000 8728 6116 4509 3397 2718 2275 1970 1628 1338 1127 970 B49 755 680 527 438 380 342 314 294 278 32
34 12C00 12000 6821 6056 4592 3408 2692 2227 1909 1681 1374 1148 980 852 752 673 513 420 361 321 293 272 256 34
36 12000 12060 8784 6036 4534 3440 2684 2196 1864 1628 1416 1175 996 860 754 671 504 407 346 305 276 255 239 36
38 12000 12000 6716 6054 4477 3490 2691 2179 1832 1587 1407 1207 1017 872 761 673 497 397 333 291 262 240 223 38
40 12000 120C0 8695 6100 4446 3502 2711 2174 1812 1556 1370 1229 1042 889 771 678 494 389 324 280 250 227 211 40
42 12000 12000 8714 6138 4436 3453 2743 2179 1800 1534 1341 1196 1072 908 784 686 493 384 316 271 240 217 200 42
44 12000 12000 8768 6089 4445 3420 2784 2192 1797 1520 1320 1170 1054 931 799 696 494 380 310 264 232 208 191 44
4e 12000 12000 8751 6048 4470 3402 2748 2213 1800 1512 1304 1149 1030 938 817 709 497 378 305 258 225 201 183 46
48 12000 12000 8708 6038 4509 3397 2718 2241 1809 1510 1294 1134 1011 916 638 723 501 377 302 253 219 195 176 4s

6-89

TABLE 6-5, FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ, MAT - LOADED EDGES SIMPLY SUPPORTED -
REMAINING EDGES CLAMPED

P PHYSICAL CONSTANTS:

Ex = Ey = 0.86x10® PSI

Gxy = 0.40x10® PSI
THICKNESS=H EQUALS 000625 INCHES Oxy = Ox = 0.37
ee “INCHES “INCHES,
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 47 25 16 12 10 9 8 7 7 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6
8 43 26 16 1l 8 az 6 5 a 4 4 4 4 4 4 cf 3 3 3 3 ) 3 8
10 45 24 la 1 8 6 5 4 4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 10
12 43 25 16 v2 9 6 5 4 3 3 3 2 2 2 2 2 2 2 2 2 2 2 1 12
14 44 25 16 ll 9 7 5 4 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 14
16 43 24 16 ll 8 7 5 4 3 3 2 2 2 2 2 i 1 1 7 1 Z 1 1 16
18 43 25 16 yt 8 6 5 4 3 3 2 2 2 2 1 1 1 i i 1 1 1 1 18
20 43 24 15 11 8 6 5 4 4 3 2 2 2 2 1 1 1 1 1 1 1 1 1 20
22 43 24 16 il 8 6 5 4 5) 3 2 2 2 2 1 1 1 1 1 1 1 1 1 22
24 43 24 16 11 8 6 5 4 3 3 3 2 2 2 1 1 1 1 1 1 1 () ° 24
26 43 24 15 ll 8 6 5 4 3 3 3 2 2 2 it | 1 1 1 5 0 t) ° 26
28 43 24 le ll 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 0 () t) C) 28
30 43 24 16 ll 8 6 5 4 3 3 2 2 2 2 1 i il 1 1 0) () () 0 30
32 43 24 16 ll 8 6 5 4 3 3 2 2 2 2 2 1 1 1 1 0) to) 0 ° 32
34 43 24 16 11 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 0 Co) 0 ° 34
36 43 24 16 1 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 () 0 ° C) 36
38 43 24 16 11 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 0) Co) 0 0 38
40 43 24 15 vl 8 6 a 4 3 3 2 2 2 2 1 1 1 1 1 Cy) ° C) Co) 40
42 43 24 16 ll 8 6 5 4 3 3 2 2 2 2 rt qi 1 1 1 0 () ° 0 42
44 43 24 16 ll 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 0 0 t) Co) 44
46 43 24 15 ll 8 6 5 4 3 3 2 2 2 2 1 1 x 1 1 to) 0) 0 ° 46
48 43 24 16 ll 8 6 5 4 3 3 2 2 2 2 1 1 1 1 1 0) C) ° 0 48
THICKNESS=H EQUALS 01250 INCHES
LENGTH=B8 WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 376 198 125 94 78 69 63 59 56 54 53 51 50 50 49 48 oh 47 46 46 46 45 45 6
8 344 212 130 86 65 53 46 41 368 35 34 32 31 30 30 29 28 27 27 26 26 26 26 8
10 356 194 135 92 64 49 4u 34 30 27 25 24 23 22 21 20 19 18 18 17 17 17 17 10
12 344 198 125 94 69 49 36 31 27 24 2l 19 18 17 16 16 14 14 13 13 12 12 12 12
14 350 197 125 88 69 53 40 31 26 22 19 17 16 15 14 13 12 ll 10 10 9 9 9 14
16 344 194 130 86 65 53 43 32 26 22 18 16 15 13 12 11 10 9 8 8 8 7 7 16
18 348 198 125 88 63 50 42 25) 27 22 168 16 14 12 ll 10 9 8 7 7 6 6 6 18
20 344 194 124 89 64 49 40 34 29 23 19 16 14 12 ll 10 8 7 6 6 5 5 5 20
22 347 194 126 87 66 49 39 a2 28 24 20 16 14 12 ll 10 7 6 6 5 5 4 4 22
24 344 196 125 86 65 49 38 31 27 24 21 17 14 12 11 10 7 6 5 5 4 4 4 24
26 346 194 124 87 64 Chi 39 31 26 23 20 18 15 13 ll 10 7 6 5 ts a 4 3 26
28 344 195 125 88 63 49 40 31 26 22 19 17 16 13 By 10 7 5 5 4 4 3 3 28
30 345 194 125 86 64 49 40 32 26 22 19 17 15 14 12 10 " 5 4 4 3 3 3 30
32 344 194 124 86 65 48 39 32 26 22 18 16 15 13 12 ll 7 5 4 4 3 3 3 32
34 345 195 124 87 64 49 38 32 26 22 18 16 14 13 12 11 7 5 4 4 3 3 2 34
36 344 194 125 87 63 49 38 31 27 22 18 16 14 12 11 10 8 5 4 3 3 3 2 36
38 345 194 124 86 63 49 38 31 26 22 19 16 14 12 ul 10 8 6 4 3 3 3 2 38
40 344 194 124 86 64 49 39 31 26 22 19 16 14 12 i 10 8 6 4 3 3 2 2 40
42 345 194 125 86 64 48 39 31 26 22 19 16 14 12 11 10 8 6 4 3 3 2 2 42
44 344 194 124 a7 63 49 39 31 26 22 19 16 14 12 12 10 7 6 4 3 3 2 2 44
46 345 194 124 86 63 49 38 32 26 22 19 16 14 12 lt 10 7 6 5 4 3 2 2 46
48 344 194 124 86 63 49 36 31 26 22 18 16 14 12 11 10 7 6 5 4 3 2 2 48

6-90

TABLE 6-5.

THICKNESS@=H EQUALS 061875 INCHES

FIBERGLASS POLYESTER LAMINATES

CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED (Cont'd)

LENGTH=B WIOTH=A Gites
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 1270 667 423 317 263 232 212 199 189 183 177 173 170 168 165 164 160 158 156 155 154 153 153 6
8 1163 714 436 291 219 179 154 138 127 119 113 109 = 105 103 1co 99 95 92 90 89 88 88 87 8
10 1202 656 457 310 215 164 134 114 101 92 85 80 76 73 7 69 65 62 60 59 58 57 57 10
12 1163 667 423 317 232 167 129 106 90 19 72 66 61 58 55 53 48 46 44 43 42 41 40 12
16 1183 665 420 296 233 160 134 105 87 T4 65 58 53 49 46 44 39 36 34 33 32 31 30 14
16 1163 654 438 291 219 179 144 109 87 73 62 55 49 45 41 39 33 30 28 26 25 25 24 16
18 1174 667 423 297 214 166 141 117 91 14 62 53 47 42 38 35 29 26 24 22 21 20 20 18
20 1163 656 419 301 215 164 134 114 98 78 64 54 47 41 37 33 27 23 21 19 18 i7 17 20
22 1170 655 424 292 222 164 130 109 94 83 67 55 47 41 36 32 25 21 19 17 16 15 14 22
24 1163 661 423 291 219 167 129 106 90 79 71 58 49 42 36 32 24 20 17 15 14 13 13 24
26 1168 654 419 294 214 171 130 105 88 76 68 61 51 43 37 33 24 19 16 14 13 12 ll 26
28 1163 657 420 296 214 166 134 105 87 74 65 58 53 45 38 33 24 18 15 13 12 ll 10 28
30 1166 656 423 292 215 164 134 107 87 73 63 56 51 47 40 34 24 18 15 13 T2 10 9 30
32 1163 654 419 291 219 163 131 109 87 73 62 55 49 45 41 36 24 18 15 12 11 10 9 32
34 1165 658 419 292 215 165 129 107 89 73 62 54 48 43 40 37 25 18 14 12 10 9 8 34
36 1163 654 423 294 214 167 129 106 90 74 62 53 47 42 38 35 26 19 14 12 10 9 8 36
36 1164 655 419 291 214 166 130 105 68 76 63 53 47 41 37 34 27 19 14 12 10 9 8 38
40 1163 656 419 291 215 164 131 105 87 75 64 54 47 41 37 33 27 19 15 12 10 8 7 40
42 1164 654 420 292 216 163 a3i 105 87 14 65 54 47 41 36 33 26 20 15 12 10 8 7 42
44 1163 655 419 292 214 164 130 106 86 73 64 55 47 41 36 32 25 21 15 12 10 8 7 44
46 1164 654 418 291 214 165 129 107 87 1} 63 56 48 41 36 32 25 20 16 12 10 8 7 46
48 1163 654 419 291 214 165 129 106 a7 73 62 55 49 42 36 32 24 20 16 12 10 8 7 48
THICKNESS=H EQUALS 002500 INCHES
LENGTH=8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 3009 1582 = 1002 752 624 550 503 471 449 433 420 411 403 397 392 388 379 374 370 367 365 364 363 6
8 2756 1693 1038 689 518 423 365 328 302 283 269 258 250 243 238 234 224 218 214 212 210 208 207 8
lo 2850 1555 1083 735 510 389 317 271 240 218 202 190 181 174 168 163 153 147 143 140 138 136 135 10
12 2756 1582 1002 752 549 395 306 250 214 188 170 156 146 137 131 126 115 108 104 101 99 97 96 12
14 2803 1577 996 701 553 426 316 249 205 175 154 138 126 117 110 104 92 85 81 78 15 14 72 14
16 2756 1550 1038 689 518 423 340 259 207 172 148 130 116 106 98 91 78 7 66 62 60 58 57 16
18 2783 1582 += 1002 703 506 399 334 278 217 176 147 127 lll 100 91 84 69 61 56 52 50 48 47 18
20 2756 1555 992 713 510 389 317 271 231 184 151 126 110 97 87 19 63 55 49 45 43 41 39 20
22 2773, 1553-1006 693 525 386 308 258 224 196 158 131 v2 97 86 7 60 50 44 40 37 35 34 22
24 2756 1566 1002 689 516 395 306 250 214 188 168 137 115 99 86 7 58 47 41 36 34 31 30 24
26 2767 = 1550 992 696 508 405 309 248 208 180 160 145 120 102 88 7 56 45 38 34 31 28 27 26
28 2756 «1557 996 701 506 394 316 249 205 175 154 138 126 107 91 19 36 44 36 32 28 26 24 28
30 2764 1555 1002 691 510 389 317 253 205 173 150 133 120 lll 95 82 57 43 35 30 27 24 22 30
32 2756 1550 993 689 518 388 310 259 207 172 1468 130 116 106 98 85 58 43 34 29 25 23 21 32
34 2761 1560 993 693 510 390 307 255 211 173 147 127 113 102 94 87 59 43 34 28 24 22 20 34
36 2756 1551 1001 696 506 395 306 250 214 176 147 127 lll 100 91 84 61 44 34 28 24 21 19 36
38 2760 = 1552 994 690 507 392 308 248 209 179 149 127 110 98 89 ar 63 45 34 28 23 20 18 38
40 2756 = 1555 992 689 510 389 311 248 207 178 151 128 110 97 87 719 63 46 35 28 23 20 18 40
42 2759 1550 996 692 517 387 311 249 205 175 154 129 rh B| 97 86 78 61 47 35 28 23 19 17 42
44 2756 ©1553 994 693 507 388 308 251 205 173 151 131 112 97 86 7 60 49 36 28 23 19 17 44
46 2758 1551 992 689 506 391 306 253 206 172 149 132 113 98 86 7 59 48 37 28 23 19 17 46
48 2756 ©1550 994 689 507 391 306 250 207 172 148 130 115 99 86 17 58 47 38 29 23 19 16 48

6-911

TABLE 6-5, FIBERGLASS POLYESTER LAMINATES |
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH i)
2 OZ, MAT - LOADED EDGES SIMPLY SUPPORTED - |
REMAINING EDGES CLAMPED (Cont'd) )

THICKNESS=H EQUALS 063125 INCHES

eles et “Ne
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 4B 54 60 66 72 78
6 5250 3089 1957 1469 1219 1073 982 920 877 B45 821 B02 788 776 766 758 740 730 722 717 713 711 708 6
8 5250 3306 2027 1346 1012 827 714 640 589 552 525 504 488 475 465 456 438 426 419 413 409 406 404 8
1c 5250 3037 2116 1437 996 759 619 529 469 426 395 372 354 339 328 318 299 287 278 273 269 266 263 10
12 5250 3089 1957 1469 1073 772 598 489 417 367 331 305 284 268 256 245 224 211 203 197 193 149 187 12
14 5250 3080 1946 1369 1080 832 618 487 401 342 301 270 247 229 215 204 180 166 157 75a 147 144 141 14
16 5250 3028 2027 1346 1012 827 664 507 405 336 288 253 227 207 191 178 153 138 129 122 117 114 lll 16
18 5250 3089 1957 1373 989 779 653 543 423 343 287 247 217 195 177 163 135 119 109 102 97 94 91 18
20 5250 3037 1938 1392 996 759 619 529 452 359 295 249 215 190 170 155 124 107 96 a8 83 80 77 20
22 5250 3034 1964 1354 1026 759 602 503 437 382 309 256 218 190 168 150 117 98 86 78 73 69 66 22
24 5250 3058 1957 1346 1012 7172 598 489 417 367 327 268 225 193 169 150 112 92 79 71 65 61 58 24
26 5250 3028 1938 1359 993 791 604 484 406 352 313 283 235 199 172 151 110 a8 74 66 60 55 52 26
28 5250 3041 1946 1369 989 770 618 487 401 342 301 270 247 208 178 155 110 86 71 62 55 51 48 28
30 5250 3037 1957 1350 996 759 619 494 401 337 293 260 235 216 185 160 111 84 69 59 52 47 44 30
32 5250 3028 1939 1346 1012 157 606 507 405 336 288 253 227 207 191 166 113 84 67 57 50 45 41 32
34 5250 30467 1940 1354 996 762 599 497 413 339 287 249 221 200 183 170 116 85 67 55 48 42 39 34
36 5250 3029 1956 1359 989 772 598 489 417 343 287 247 217 195 a7, 163 119 86 66 54 46 4. 37 36
38 5250 3030 1941 1348 990 766 601 485 409 350 290 247 216 192 173 158 124 88 67 54 45 40 35 38
40 5250 3037 1938 1346 996 159 608 484 403 348 295 249 215 190 170 155 124 90 68 54 45 39 34 40
42 5250 3027 1946 1351 998 757 608 487 401 342 301 252 216 189 168 152 120 92 69 54 45 38 33 42
44 5250 3034 1942 1354 991 159 602 491 400 339 295 256 218 190 168 150 117 96 70 55 44 38 33 44
46 5250 3030 1937 1347 988 764 599 495 402 337 291 257 221 191 168 150 114 95 72 55 45 37 32 46
48 5250 3028 1941 1346 990 764 598 489 405 336 288 253 225 193 169 150 112 92 74 56 45 37 32 48
THICKNESS=H EQUALS 003750 INCHES
LENGTH=8 WIDTH=A LENGTH=B8_
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 6640 5338 3382 2539 2106 1855 1697 1590 1515 1460 1416 1386 1361 1340 1323 1309 1279 1261 1248 1239 1232 1228 1224 6
8 6640 5713 3502 2325 1749 1428 1233 1105 1018 954 907 872 843 821 803 788 756 736 724 714 707 702 697 8
10 6640 5247 3656 2482 1722 1312 1069 914 810 736 683 642 611 586 566 550 516 495 481 471 464 459 455 10
12 6640 5338 3382 2539 1854 1334 1033 845 721 635 573 526 491 464 442 424 387 365 350 340 333 327 323 12
14 6640 5321 3363 2365 1866 1438 1068 841 693 591 519 466 426 396 371 352 312 288 272 262 254 248 244 14
16 6640 5232 3502 2325 1749 1428 1148 875 700 581 498 437 392 357 33 308 264 239 222 211 203 197 193 16
18 6640 5338 3382 2372 1709 1346 1129 938 731 593 497 427 376 337 306 262 234 206 189 177 168 162 158 18
20 6640 5247 3348 2405 1722 1312 1069 914 781 621 510 430 372 328 294 267 214 184 165 153 144 138 133 20
22 6640 5243 3394 2340 1773 1311 1040 869 755 660 533 443 377 328 290 260 202 169 149 135 126 119 1146 22
24 6640 5284 3382 2325 1749 1334 1033 B45 721 635 565 463 389 334 291 258 194 159 137 123 113 106 101 24
26 6640 5232 3348 2349 1716 1367 1044 837 701 608 541 490 406 345 297 261 191 152 129 113 103 96 90 26
28 6640 5254 3363 2365 1708 1330 1068 B41 693 591 519 466 426 359 307 267 190 148 123 107 96 88 82 28
30 6640 5247 3382 2332 1722 1312 = 1069 854 693 583 506 449 406 374 320 276 191 146 119 102 90 82 76 30
32 6640 5232 3351 «2325. «1749-1308 = 1047 875 700 581 498 437 392 357 330 287 195 145 116 98 B6 77, 71 32
34 664U 5264 3352 2340 1721 1316 ©1036 B59 713 585 495 430 382 345 316 293 200 146 115 95 82 73 67 34
36 6640 5234 3380 2348 1709 1334 1033 B45 721 593 497 427 376 337 306 282 206 148 115 94 80 7 64 36
38 6640 5236 3353 2329 1710 1324 1039 838 706 605 502 427 373 331 299 274 214 151 115 93 78 68 61 38
40 6640 5247 3348 2325 1722 1312 1050 837 697 601 510 430 372 328 294 267 214 NEE 117 93 77 67 59 40
42 6640 5231 3363 2335 1725 1308 1051 841 693 591 519 436 374 327 291 263 207 160 119 93 (a 66 58 42
44 6640 5243 3356 2340 1712 1311 1040 849 692 585 509 443 377 328 290 260 202 165 121 94 77 65 57 44
46 6640 5236 3348 2327 1768 1320 1034 855 694 582 502 444 382 330 290 259 197 163 124 96 77 65 56 46
48 6640 5232 3354 2325 1711 1321 1033 B45 700 581 498 437 389 334 291 258 194 159 128 97 78 65 55 48
6-92

TABLE 6-5.

CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

FIBERGLASS POLYESTER LAMINATES

2 OZ. MAT - LOADED EDGES SIMPLY SUPPORTED -
REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 064375 INCHES

= LENGTH=6
fairy winches meres
6 6 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7740 7740 5370 4032 3344 2946 2695 2525 2606 2319 2252 2201 2161 2128 2101 2079 2031 2002 1982 1967 1957 1950 1943 6
8 7740 77460 5561 3692 2777 2268 1988 1755 1616 1516 1441 1384 1339 1304 1275 1282 1201 1169 1149 1134 1123 1115 1107 8
10 7740 7740 5806 3942 2734 2083 1697 1452 1286 1169 1084 1020 970 931 899 874 820 787 164% 748 738 729 123 10
12 7740 7740 5370 4032 2943 2119 1641 1343 1145 1008 909 836 780 736 702 674 615 580 556 540 529 520 514 12
14 7740 7740 5340 3756 2962 2283 1696 1335 1100 939 825 741 677 628 389 558 495 457 432 415 403 394 387 14)
16 7740 7740 5561 3692 2777 2268 1823 1390 1111 923 791 694 622 567 524 490 420 379 353 335 322 313 306 16
18 7740 7740 5370 3767 2714 2138 1792 1490 1161 942 789 678 0597 534 486 448 372 327 299 261 267 258 250 18
20 7740 7740 5317 3819 2734 2083 1697 = 1452. -1240 985 809 683 591 521 467 424 340 292 262 243 229 218 ail 20
22 7740 7740 5390 3715 2815 2081 1651 1380 1200 1048 847 704 599 520 460 413 320 268 236 215 200 190 182 22
24 7740 7740 5370 3692 2777 2119 1641 1343 1145 1008 898 736 618 530 463 410 309 252 218 195 180 168 160 24
26 7740 7740 «5317 «3730-2724 02171 «1658 = 13291114 965 859 778 645 547 472 414 303 241 204 180 164 152 143 26
28 7740 7740 5340 3756 2713 2113 1696 1335 1100 939 825 741 677 571 42 424 301 235 195 169 152 140 131 28
30 7740 7740 5370 3703 2734 2083 1697 1356 1100 926 803 713, 645 593 508 438 304 231 189 161 143 130 120 30
32 7740 7740 5321 3692 2777 2077 «1662 «1390-1211 923 791 694 = 622 567 524 456 309 231 185 156 136 122 112 32
34 7740 7740 5322 3715 2733 2090 1644 1365 1132 929 786 683 606 548 = 502 466 317 232 183 152 131 117 106 34
36 7740 7740 5367 3729 2714 «2119 164113431145 942 789 678 ©5597 534 486 448 327 235 182 149 127 112 101 36
38 7740 7740 5325 3698 2715 2103 1650 1331 1122 961 797 679-592 526 475 434 339 240 183 148 125 109 97 38
40 7740 7740 5317 3692 2734 2083 1668 1329 1107 955 809 683591 521 467 424 340 246 185 148 123 106 94 40
42 7740 7740 5340 3708 2740 2077 1669 1335 1100 939 825 692 593 519 462 417 329 254 188 148 122 104 92 42
44 7740 7740 «5329 3715 «271920811651 = 1348 = 1099 929 809 704 599 520 460 413 320 262 192 150 122 103 90 44
46 7740 7740 5316 3695 2712 2096 1642 1358 1103 924 798 706 607 524 460 411 314 259 197 152 123 103 89 46
48 7740 7740 5327 3692 2718 2098 1641 1343 1111 923 791 694 618 530 463 410 309 252 203 154 123 103 88 48
THICKNESS=H EQUALS 005000 INCHES
LENGTH-8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9600 9600 8016 6019 4992 4397 4022 3769 3592 3461 3362 3286 3226 3177 3136 3103 3032 2988 2958 2936 2921 2910 2900 6
8 9600 9600 8301 $512 4145 3386 2923 2620 2412 2262 2151 2066 1999 1947 1904 18669 1793 1746 1716 1693 1676 1664 1653 8
10 9690 9600 8667 5884 4081 3109 2534 2167 1920 1745 1618 1522 1448 1389 1343 1304 1226 1174 1141 1117 1101 1088 1079 10
12 600 9600 8016 6019 4394 3163 2450 2004 1709 1505 1358 1248 1164 1099 1047 1006 918 865 831 806 789 776 767 12
14 9600 9600 7971 5606 4422 3408 2532 1993 1642 1402 1231 1106 10121 938 880 834 739 682 645 620 602 589 578 14
16 9600 9600 8301 5512 4145 3386 2721 2075 1659 1378 1180 1036 929 846 782 731 627 566 526 500 481 467 457 16
18 9600 9600 8016 5624 4051 3191 2675 2223 1734 1406 1177 «2»1013 agl 798 726 669 555 489 447 419 399 385 374 18
20 9600 9600 7937 5700 4081 3109 2534 2167 1851 1471 1208 1020 882 777 «697 633 508 436 392 362 341 326 315 20
22 9600 9600 8046 5546 4202 3107 2465 2061 1791 1565 1264 1050 894 777-687 616 478 401 353 321 299 283 271 22
24 9600 9600 8016 5512 4145 3163 2450 2004 1709 1505 1340 1098 922 791 690 612461 376 325 291 268 251 239 24
26 9600 9600 7937 5567 4067 3241 2475 1984 1662 1441 1262 1i61 964 817 705 619 452 360 305 269 245 227 214 26
28 9660 9600 7971 5606 4049 3153 2532 1993 1642 1402 1231 1106 1011 852 728 633-450 350 291 253 227 208 195 28
30 9600 9600 8016 5528 4081 3109 2533 2024 1642 1382 1198 1064 963 885 759 654 453 345 282 241 213 194 180 30
32 5600 9600 7943 5511 4145 3100 2481 2075 1659 1378 1180 1036 929 846 782 680 461 344 276 232 203 183 168 32
34 9600 9600 7945 5546 4080 3120 2455 2037 1690 1387 1174 1020 905 318 750 696 473 347 273 226 195 174 158 34
36 9600 9600 8012 5567 4051 3163 2450 2006 1709 1406 1177 1013 3891 798 726 669 488 351 272 223 190 167 151 36
38 9600 9600 7949 5520 4053 3139 2462 1987 1674 1434 1189 1013 883 7285 708 648 506 359 274 221 186 162 145 38
40 9600 9600 7937 5512 4081 3109 2490 1984 1653 1425 1208 1020 882 777 697 633 508 368 277 220 184 158 140 40
42 9600 9600 7971 5536 4099 3100 2492 1993 1642 1402 1231 1033 886 775 690 623 491 379 281 221 182 156 137 42
46 9600 9600 7955 5546 4058 3107 2465 2011 1640 1387 1207 1050 894 777 687 616 478 391 287 223 182 154 134 44
46 9600 9600 7935 5516 4049 3128 2452 2027 1646 1379 1191 1053 906 782 687 613 468 387 294 227 183 153 132 46
48 9600 9600 7951 5512 4057 3131 2449 2004 1659 1378 1180 1036 922 791 690 612 461 376 302 231 184 153 131 43

6-93

TABLE 6-5. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - LOADED EDGES SIMPLY SUPPORTED
REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 065625 INCHES

ia LENGTH=8
aces wTNCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 8570 7107 6261 5727 5367 5114 4928 4786 4678 4593 4524 4466 4419 431742554212 41804159 4144 4130 6
8 10800 10800 108CO 7848 5902 4621 4162 3731 3434 3221 3063 2982 2847 2772 2711 «2661 «25532485 2443 2411-2387 2369 ©2354 8
10 10800 10800 10800 68378 5810 4427 3607 3085 2733 2485 2304 2167 2062 1978 1912 1857 1742 1672 1624 1591 1568 1549 1536 10
12 10800 10800 10800 8570 6256 4506 3688 2853 2433 2142 1933 1777 1658 1565 1491 1432 1308 1232 1183 1148 =1124 = 11051091 12
14 10800 10800 10800 7982 6296 4852 3605 2837 2337 1996 1753 1574 1439 1335 1253 1187 1052 971 918 883 857 838 823 14
16 10800 10800 10800 7848 5902 4821 3875 2955 2362 1962 1680 1476 1323 1205 1113 1040 892 805 750 712 685 665 650 16
18 10800 10800 10800 8007 5768 4544 3809 3166 2469 2002 1677 1442 1268 1136 1033 952 790 696 636 595 568 548 532 18
20 10800 10800 10800 8116 5810 4427 3607 3085 2635 2094 1720 1453 1256 1107 992 902 723 621 558 515 486 464 448 20
22 10800 10800 10800 7897 5983 4424 3510 2934 2550 2228 1800 1496 1273 1106 978 877 681 570 502 457 426 403 386 22
24 10800 10800 10800 7848 5902 4504 3488 2853 2434 2142 1909 1564 1313 1126 983 872 656 536 462 415 382 358 340 24
26 10800 10800 10800 7927 5790 4615 3523 2825 2367 2051 1826 1653 1372 1163 1004 881 643 513 434 383 348 323 305 26
28 10800 10800 10800 7982 5766 4490 3605 2837 2337 1996 1753 1574 1439 1213 1037 901 641 499 414 360 323 297 277 28
30 10800 10800 10800 7871 5810 4427 3607 2883 2338 1968 1706 1515 1371 1261 1081 931 646 492 401 343 304 276 256 30
32 10800 10800 10800 7847 5902 4414 3533 2955 2362 1962 1680 1476 1322 1205 1113 969 657 490 393 331 289 260 239 32
34 10800 10800 10800 7897 5809 4442 3495 2900 2407 1974 1671 1452 1289 1165 1068 991 674 494 388 322 278 248 225 34
36 10800 10800 10800 7926 5768 4504 3488 2853 2433 2002 1677 1442 1268 1136 1033 952 695 500 388 317 270 238 215 36
38 10800 10800 10800 7859 5771 4469 3506 2829 2384 2042 1693 1443 1258 1117 1009 923 721 511 390 314 265 231 206 38
40 10800 10800 10800 78468 5810 4427 3545 2825 2353 2029 1720 1453 1256 1107 992 902 723 524 394 314 261 225 200 40
42 10800 10800 10800 7882 5823 4413 3548 2837 2337 1996 1753 1471 1261 1103 982 887 700 539 401 315 260 222 195 42
44 10800 10800 10800 7897 5778 4424 3510 2864 2335 1974 1719 1496 1273 1106 978 877 681 557 409 318 259 219 191 44
46 10800 10800 10800 7854 5764 4454 3491 2886 2343 1964 1695 1500 1291 1114 978 873 667 551 419 323 260 218 188 46
48 10800 10800 10800 7848 5776 4458 3488 2853 2362 1962 1680 1476 1313 1126 983 872 656 536 431 328 262 218 187 48
THICKNESS=H_ EQUALS 046250 INCHES
LENGTH=8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 12000 12000 12000 11756 9749 8588 7856 7362 7016 6760 6566 6417 6300 6205 6126 6061 5921 5837 5778 5734 5704 5684 5665 6
8 12000 12000 12000 10765 8096 6613 5709 5117 4711 4419 4201 4036 3905 3602 3718 3650 3502 3409 3351 3307 3274 3250 3229 8
10 12000 12000 12000 11492 7970 6073 4948 4232 3750 3408 3160 2973 2828 2714 2622 2547 2390 2293 2228 2182 2150 2125 2107 10 |
12 12000 12000 12000 11756 8581 6178 4784 3914 3338 2939 2651 2437 2274 2147 2046 1964 1794 1690 1622 1575 1541 1515 1497 12
146 12000 12000 12000 10949 8637 6656 4944 3892 3206 2737 2404 2159 1974 1831 1718 1628 1443 1332 1260 1211 1176 1150 1129 14
16 12000 12000 12000 10765 8096 6613 5315 4053 3240 2691 2305 2024 1814 1653 1527 1427 1224 1105 1028 976 940 913 892 16
18 12000 12000 12000 10984 7912 6233 5225 4343 3386 2746 2300 1978 1740 1558 1418 1306 1083 954 873 818 780 751 730 18
20 12000 12000 12000 11133 7970 6073 4948 4232 3615 2873 2360 1993 1722 1518 1361 1237 992 852 765 707 666 637 615 20
22 12000 12000 12000 10832 8207 6068 4814 4025 3496 3056 2469 2052 1746 1517 1341 1204 934 782 689 627 584 553 530 22
24 12000 12000 12000 10765 8096 6178 4784 3914 3338 2939 2618 2145 1601 1545 1349 1196 900 735 634 569 523 491 467 24
26 12000 12000 12000 10874 7943 6330 4833 3875 3247 2614 2504 2268 1882 1595 1377 1208 883 703 595 525 478 444 418 26
28 12000 12000 12000 10949 7909 6159 4944 3892 3206 2737 2404 2159 1974 1664 1423 1236 879 684 568 494 443 407 381 28 |
30 12000 12000 12000 10797 7970 6073 4948 3954 3207 2699 2340 2078 1881 1729 1482 1277 886 675 550 470 417 379 351 30
32 12000 12000 12000 10764 8096 6055 4846 4053 3240 2691 2305 2024 1614 1653 1527 1329 901 673 538 454 397 357 328 32
34 12000 12000 120CO 10832 7968 6093 4794 3978 3302 2708 2293 1992 1768 1597 1464 1359 924 677 533 442 382 340 309 34
36 12000 12000 120C0 10872 7912 6178 4784 3914 3338 2746 2300 1978 1740 1558 1418 1306 953 686 532 435 x Irbh 327 ra 36
38 12000 12000 12000 10781 7916 6130 4809 3881 3270 2801 2323 1979 1725 1533 1384 1266 989 700 534 431 363 317 283 38
40 12000 12000 12000 10765 7970 6073 4863 3875 3228 2783 2360 1993 1722 1518 1361 1237 992 718 540 431 359 309 274 40
42 12000 12000 12000 10812 7988 6054 4866 3892 3206 2737 2404 2017 1730 1514 1347 1217 960 740 549 432 356 304 267 42 |
44 12000 12000 12000 10832 7926 6068 4B14 3929 3203 2708 2358 2052 1746 1517 1341 1204 934 764 561 437 356 301 262 44 |
46 12000 12000 12000 10773 7907 6110 4788 3959 3214 2693 2325 2057 1770 1527 1342 1197 914 756 575 443 357 299 258 46
48 12000 12000 12000 10765 7923 6116 4784 3914 3240 2691 2305 2024 1801 1545 1349 1196 900 735 591 450 360 299 256 48

6-94

TABLE 6-6.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ, MAT - LOADED EDGES CLAMPED -
REMAINING EDGES SIMPLY SUPPORTED

FIBERGLASS POLYESTER LAMINATES

PHYSICAL CONSTANTS:

Ey = Ey = 0.86x10® PSI

Gxy = 0.40x10® PSI

Pp Oxy = Oyvx = 0.37

THICKNESS=H EQUALS 000625 INCHES FMCTIEE

THe

SINCHES. “INCHES INCHES

6 8 10 12 16 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 39 31 27 26 25 24 24 23 23 23 23 23 23 23 23 23 22 22 22 22 22 22 22 6
8 33 22 18 16 15 14 14 14 14 13 13 13 13 13 13 13 13 13 13 13 13 13 13 8
10 33 19 14 12 ll 10 10 9 9 9 9 9 9 8 8 8 8 8 8 8 8 8 8 10
12 29 18 12 10 9 8 1 7 7 6 6 6 6 6 6 6 6 6 6 6 6 6 6 12
14 27 18 12 9 1 6 6 5 5 5 5 5 5 5 5 4 4 4 4 4 4 4 4 14
16 27 16 12 8 7 6 5 5 4 4 4 4 4 4 4 4 3 3 3 3 3 3 16
18 26 16 11 8 6 5 4 4 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 18
20 26 15 10 8 6 5 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 20
22 26 15 10 8 6 5 4 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 22
24 25 15 10 7 6 5 4 3 3 2 2 2 2 2 2 2 2 2 2 2 1 1 24
26 25 15 10 7 6 5 4 3 3 2 2 2 2 2 2 2 1 i 1 1 1 al 1 26
28 25 15 10 7 5 4 4 3 2 2 2 2 2 2 2 1 1 Z 1 1 1 1 1 28
30 26 15 10 7 5 4 4 3 2 2 2 2 2 1 1 1 1 1 1 7 1 il 1 30
32 26 14 9 7 5 4 3 3 2 2 2 2 1 1 1 1 1 1 1 1 Z 1 | 32
34 27 14 9 7 5 4 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 34
36 28 14 9 7 5 4 3 3 2 2 2 2 1 1 pt 1 1 1 1 1 1 1 1 36
38 29 14 9 7 5 4 3 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 i 38
40 30 15 9 6 5 4 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 40
42 31 15 9 6 5 4 3 3 2 2 2 it it it 1 1 1 1 1 1 1 1 1 42
a4 33 15 9 7 5 4 3 3 2 2 2 1 1 1 1 1 1 1 1 1 1 1 ° 44
46 34 15 9 6 5 4 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 ° 0 46
48 36 16 9 6 5 4 3 2 2 2 2 1 1 fy 1 1 1 1 1 1 ° ° ° 48
THICKNESS-H EQUALS 0¢1250 INCHES
He
ae ieee fg
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 315 247 220 206 198 193 190 187 186 184 183 183 182 182 181 181 180 179 179 179 179 179 179 6
8 264 177 1465 130 121 116 112 110 108 107 106 105 104 104 103 103 102 102 101 101 101 101 101 8
10 260 152 114 96 86 81 7 1% 72 71 70 69 68 68 67 67 66 66 65 65 65 65 65 10
12 231 145 99 19 68 62 58 55 53 51 50 50 49 48 48 47 47 46 46 46 45 45 45 12
14 220 141 94 70 58 51 46 44 41 40 39 38 37 37 36 36 35 34 34 34 34 33 33 14
16 219 130 93 66 52 44 40 36 34 32 31 30 30 29 28 28 27 27 26 26 26 26 26 16
18 211 124 88 65 49 40 35 32 29 27 26 25 24 24 23 23 22 21 21 21 21 20 20 18
20 208 123 83 65 48 38 32 28 26 24 23 22 21 20 20 19 18 18 17 17 17 17 17 20
22 208 123 80 61 48 37 30 26 23 21 20 19 18 17 17 16 16 15 15 14 14 14 14 22
24 204 119 19 58 47 36 29 25 22 20 18 17 16 15 15 14 13 13 12 12 12 12 12 24
26 203 117 19 56 44 37 29 24 rh 18 17 16 15 14 13 13 12 ll ll ll 10 10 10 26
28 204 117 78 55 42 35 29 23 20 18 16 16 13 13 12 12 ll 10 10 9 9 9 9 28
30 207 116 76 55 41 34 29 23 19 17 5 14 13 12 ll il 10 9 9 8 8 8 8 30
32 211 115 75 55 41 32 28 23 19 16 14 13 12 2 10 10 9 8 8 7 if 7. 7 32
34 217 114 75 54 40 32 26 23 19 16 14 13 ll ll 10 9 8 7 7 7 6 6 6 34
36 224 114 75 53 40 31 26 22 19 16 14 12 11 10 9 9 8 7 6 6 6 6 36
38 232 115 1% 52 40 31 25 21 19 16 14 12 11 10 9 8 7 6 6 6 5 5 5 38
40 241 116 73 52 39 31 25 21 18 16 14 12 ll 9 9 8 7 6 6 5 5 5 5 40
42 251 118 73 52 39 31 24 20 18 16 14 12 10 9 8 8 6 6 5 5 5 4 4 42
44 262 120 73 52 38 31 24 20 ly. 15 14 12 10 9 8 8 6 5 5 4 4 4 44
46 274 123 73 51 38 30 24 20 17 15 13 12 10 9 8 7 6 5 5 4 4 4 4 46
48 286 126 74 51 38 30 24 20 17 14 13 12 10 9 8 7 6 5 4 4 4 4 3 48

6-95

TABLE 6-6. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ, MAT - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS“H EQUALS 001875 INCHES

LensTins wip tHe MINCHES.
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 1065 834 742 695 669 652 641 633 627 623 619 617 615 613 611 610 607 606 605 604 603 603 603 6
8 890 599 490 438 409 391 379 371 365 360 357 354 352 350 349 348 345 343 342 341 341 340 339 8
10 878 513 383 324 291 272 259 250 244 239 236 233 231 229 227 226 223 222 220 220 219 219 218 10
12 780 491 335 266 230 208 195 185 179 174 170 167 165 163 lol 160 157 156 155 154 153 152 152 12
14 741 476 316 237 196 172 157 147 140 135 131 128 125 123 122 120 118 116 215 114 113 113 112 14
16 736 439 ehle 222 176 150 133 123 115 110 105 102 100 98 96 95 92 90 89 88 87 87 87 16
138 714 420 298 218 166 136 118 107 98 93 88 85 82 80 19 ad. 7% 72 7 70 70 69 69 18
20 702 414 281 220 161 128 109 96 87 81 76 73 70 68 66 65 62 60 59 58 57 57 56 20
22 702 414 271 205 160 124 102 89 79 73 68 64 61 59 Li? 56 52 51 49 48 48 47 47 22
24 686 402 266 195 158 123 99 84 74 67 61 57 54 52 50 49 45 43 42 41 41 40 40 24
26 6384 396 265 189 149 123 97 81 70 62 57 53 49 47 45 43 40 38 37 36 35 35 34 26
28 687 395 263 185 143 119 97 719 67 59 ok) 49 46 43 41 39 36 34 32 31 31 30 30 28
30 697 392 257 184 139 114 98 78 66 57 51 46 43 40 38 36 32 30 29 28 27 27 26 30
32 713 387 254 185 137 110 93 719 65 56 49 44 40 37 35 33 30 27 26 25 24 24 23 32
34 732 385 253 182 135 107 89 78 65 55 48 42 39 36 33 31 27 25 24 23 22 21 21 34
36 756 385 253 178 135 105 87 75 65 55 47 41 37 34 32 30 26 23 22 21 20 19 19 36
38 734 388 250 177 136 104 85 72 64 55 47 41 36 33 30 28 24 22 20 19 18 18 ny 38
40 814 392 248 176 133 104 83 70 61 55 46 40 36 32 29 27 23 20 19 18 17 16 16 40
42 848 398 246 176 132 104 82 69 59 53 47 40 35 31 29 26 22 19 17 16 16 15 15 42
44 885 406 246 176 130 103 82 68 58 51 46 40 35 31 28 26 ral 18 16 15 14 14 13 44
46 924 415 247 173 129 102 82 67 57 50 45 40 35 31 28 25 20 17) 16 14 14 13 13 46
48 966 425 249 172 129 100 62 66 56 49 43 39 35 31 27 25 20 17 15 16 13 12 12 48
THICKNESS“H EQUALS ©2500 INCHES
LENGTH=8 WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 2524 1976 1758 1648 1585 1545 1519 1500 1486 1476 1468 1462 1457 1452 1449 1446 1439 1435 1434 1431 1430 1429 1429 6
8 2109 1420 «1162 ~=—-1038 970 927 899 879 B65 854 846 840 834 830 827 824 817 813 811 809 807 806 804 8
10 2082 «1216 909 767 690 644 614 593 578 567 559 552 547 542 539 536 530 526 523 520 519 518 517 10
12 1848 = 1163 794 631 545 494 462 439 424 412 403 396 391 386 383 380 373 369 366 364 363 361 361 12
14 1757-1128 750 561 464 407 372 348 331 319 310 303 297 292 289 286 279 275 272 270 268 267 266 14
16 1750 1040 746 527 417 355 316 291 273 260 250 242 237 232 228 225 218 214 211 209 207 206 205 16
18 1692 996 707 517 392 323 260 253 233 220 209 201 195 190 186 183 176 172 169 167 165 164 163 18
20 1665 982 665 520 381 304 257 227 207 192 161 173 166 161 157 153 146 142 139 137 135 134 133 20
22 1665 980 641 485 380 294 243 210 188 172 160 152 145 140 135 132 124 120 117 115 113 112 lll 22
24 1631 252 630 462 374 291 234 199 175: 158 145 136 129 124 119 115 108 103 100 98 96 95 94 24
26 1621 938 629 447 354 292 230 191 166 147 134 125 117 lll 107 103 95 90 87 85 83 82 81 26
28 1629 937 623 439 339 282 230 187 160 140 126 116 108 102 97 93 85 80 7 74 73 71 70 28
30 1653 930 609 436 330 269 231 186 156 135 120 109 101 94 89 85 77 72 68 66 64 63 62 30
32 1689 917 602 438 324 260 220 187 154 132 116 104 96 89 83 79 70 65 61 59 Chi 56 55 32
34 1736 912 399 431 321 253 212 184 154 130 an) 101 91 a4 793 74 65 59 56 54 52 51 50 34
36 1793 912 621 423 321 249 205 177 155 129 lll 98 88 81 75 70 61 55 51 49 47 46 45 36
38 1858 719 593 416 322 246 201 171 a51 129 110 96 86 78 72 67 57 51 47 45 43 42 41 38
40 1930 930 587 416 315 245 197 166 145 130 110 95 84 76 69 64 54 48 44 42 40 38 37 40
42 2010 944 384 416 311 246 195 163 141 125 ill 95 83 75 68 62 52 45 41 39 37 35 34 42
44 2097 963 584 416 348 245 194 160 137 121 110 95 83 74 66 61 49 43 39 36 34 33 32 44
46 2190 984 525 411 306 241 194 159 135 118 106 96 83 73 65 59 4B 41 37 34 32 31 30 46
48 2289 1008 589 “cB 306 238 194 158 133-50 3216 103 93 83 73 65 59 46 39 35 32 30 29 28 48

6-96

TABLE 6-6. FIBERGLASS POLYESTER LAMINATES

CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

2 OZ. MAT - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 003125 INCHES

FINCHES. “INCHES “INCHES
6 8 10 12 14 16 18 20 22 24 26 26 30 32 34 36 42 48 54 60 66 72 78
6 4930 3860 3433. «3219 «3095.««3018 «2967 «2930-2903 2883. 2866 «= 2855 2845 2837 = 2829) 28232811 = 2804 = 28002795 2794 = 2792-2792 6
8 4119 2773. «2270»«2028:~«S («1894 1811 1756 1717 1690 1669 1652 1640 1629 1622 1615 1610 1596 1588 1585 15860 1577 1575 1571 8
10 4066 2375 1775 1498 1349 1258 1199 1159 1130 1108 1091 1079 1068 1059 1053 1047 1034 1027 1021 1016 1014 1012 1010 10
12 3610 2271 1551 1232 1064 965 901 858 827 805 788 774-763 755 748 742 729 721 715 711 708 106 705 12
14 3432 2202 «1465 =: 1095 905 796 726 680 647 623 605 591 580 571 564 558 545 536 531 527 524 522 520 14
16 3419 2030 «1458 =1030 615 693 618 567 532 507 488 473, 462 453 445 439 425 417 4il 407 405 402 401 16
168 3305 1945 1382 1009 766 631 548 493 456 429 409 393 381 372 364 358 344 335 330 326 323 320 318 18
20 3252-1918 «61299-1017 745 594 503 444 403 375 353 337 9-325 315 306 300 286 emt 271 267 264 262 260 20
22 Se5e0 19S 252 948 742 574 474 410 367 336 313 296 283 273 264 257 243 234 228 224 221 218 217 22
a 24 3185 = 18591231 902 730 568 458 388 341 308 284 266 = 252 241 233 225 210 201 195 191 188 185 184 24
26 3165 1833 1228 874 691 571 450 374 323 288 263 243 229 217 208 201 185 176 170 165 162 160 158 26
a 28 3182 1829 1217 858 663 551 449 366 312 274 247 226 09211 199 189 182 166 156 149 145 142 139 138 28
30 3228 ©1817 + 1190 852 644 526 452 363 304 264 235 213 197 185 175 166 150 140 133 129 126 123 121 30
32 3299 1792-1175 855 633 508 430 364 301 257 227 204 187 173 163 154 137 127 120 115 112 110 108 32
34 3391 1781 1170 B41 627 495 414 360 300 254 221 197-178 165 154 145 127 116 109 104 101 99 97 34
36 3502 1783 1173 826 626 486 401 345 302 252 217 192 172 158 146 137 118 107 100 95 92 89 88 36
38 3628 1795 1159 817 629 481 392 334 294 253 215 188 168 152 140 131 lll 100 93 88 84 82 80 38
Ry 3770 «1816 =1147 813 616 479 385 325 284 254 215 186 165 148 136 126 105 94 86 81 78 75 73 40
| 42 3926 «1845 1141 813 607 480 381 318 275 245 216 185 9-163 146 132 122 101 88 81 76 72 69 67 42
44 4096 1880 1140 813 601 479 379 313 268 237 214 186 = 162 144 130 119 97 84 76 71 67 64 62 44
46 4277 1922-1143 803 598 471 379 310 263 231 207 187 =: 161 142 128 116 93 80 72 67 63 60 58 46
| 48 4470 1970 1151 796 597 465 380 308 259 226 201 183 162 142 127 114 91 qt 69 63 1c) 56 ch 48
THICKNESS=H EQUALS 003750 INCHES
LENGTH=8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
| 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
|
6 6640 6640 5932 5562 5349 5215 5127 5063 5017 4981 4953 4933 4916 4901 4889 4879 4857 4844 4839 4830 4828 48246 4824 6
8 6640 4791 3922 3505 3272 3129 3034 2967 2920 2884 2855 2834 2815 2802 2790 2781 2758 2744 2738 2731 2725 2722 2715 8
10 6640 4104 3067 2589 2330 2174 2072 2002 1952 1914 1886 1864 1846 1831 1819 1809 1787 1774 1763 1756 1753 1748 1745 10
12 6237 3924 «= 2681 92130-1839 1668 = 1558 =: 1483143001391 13610-1337 «1319-1304 = 1292-1282) -1260)S 1245) 1236) = 1229-1224 =-1220—Ss:1218 12
14 5931 3806 2531 1892 1565 1375 1255 1175 1118 1077 1046 1022 1002 987 97% 964 942 927 917 911 906 902 899 va
16 5908 3508 2519 1779 1408 1198 1067 981 920 876 843 818 798 782 769 759 735 721 71 704 699 695 692 16
18 5710 3361 2388 1744 1324 1090 946 853 788 741 706 680 659 643 629 618 594 aig, 570 563 557 553 550 18
20 5619 3314 2245 1757 1287 1026 869 767 697 647 611 583 561 544 530 518 494 479 468 461 456 452 449 20
22 5619 3309 2164 1638 1283 993 619 709 634 580 541 512 489 471 457 445 420 404 394 386 381 377 374 22
24 5504 3212 2127 1559 1262 981 791 670 589 532 491 460 436 417 402 389 364 348 ceM 336 326 320 317 24
26 5469 3167 2122 1510 1194 986 777 646 559 498 454 421 395 376 360 347 320 304 293 286 280 276 273 26
28 5498 3161 2162 1483 1146 951 175 633 538 473 426 391 365 344 327 314 286 269 258 251 245 241 238 28
30 5578 3140 2056 1473 1113 908 781 628 526 456 406 369 341 319 302 288 i259 242 230 222 air 213 210 30
32 5701 3096 2030 1477 1094 a77 743 630 520 445 391 352 322 299 281 267 237 219 207 200 194 190 186 32
34 5860 3078 2022 1453 1084 355 715 622 519 438 381 340 308 284 265 250 219 201 189 181 alg ES 171 167 34
36 6051 3081 2027 1428 1082 840 693 597 522 436 375 331 298 272 253 237 204 185 173 165 159 155 pie 36
38 6270 3102 2002 1412 1087 832 677 577 508 437 372 325 290 263 242 226 192 173 160 151 145 141 138 38
40 6515 3138 1981 1405 1065 829 666 561 490 439 371 322 285 256 235 217 182 162 149 140 134 130 126 40
42 6640 3187 1971 1405 1049 830 659 550 475 423 373 3200-281 252 228 210 174 153 139 131 124 120 116 42
44 6640 3249 1969 1405 1039 827 655 541 464 409 370 321 279 248 224 205 167 145 131 122 116 111 108 44
46 6640 3321 1976 1388 1033 813 655 535 455 399 357 323-279 246 221 201 161 139 125 115 109 104 100 46
48 6640 3403 1989 1376 1032 803 656 532 448 390 347 316 280 245 219 198 156 133 119 109 102 97 94 48

6-977,

TABLE 6-6. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ, MAT - LOADED EDGES CLAMPED -
REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS*H EQUALS 004375 INCHES

LENGTH=8 WIDTH=A LENCO
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7746 7740 7740 7740 7740 7740 7740 7740 7740 7740 7740 7740 7740 7740 7740 7740 7713 7693 7684 7670 7666 7661 7661 6
8 77a0. 7609 6228. 45565. +5197 4968 4818 4712 4637 4579 4534 4500 4471 4449 4630 4416 4380 4358 © 4348 4336 4327 4322 4311 g
10 776¢ 6517» 4#B7O A111 3700 3452 3290 3180 3100 3080 2995 2959 2931 2907 2869 2872 2838 2617 2800 2789 2783) 2776 2771 ag
12 71s0 6231 4257 3382 2921 2648 2476 2355 2270 2208 2161 2123 2094 2070 2052 2035 2000 1978 1963 1952, 1944 861937 1934 12
14 =a ie Gn Len SEL SEALE PRL TAl np aUrrn eC ELTA erm EER DUTTA Serr) GE. GE SAE eee hy 14
16 77405571. 4000 2826 2237 1902 1695 1557 1661 1392 1339 1299 1268 1242 1221 1205 1168 1145 1129 1118 1110 ©1104 ~—-1099 16
18 7746 5338) 3791 27e9N 2103 173i) 50a) 1354 9251) 177) 4222 080 1067 ‘1020 999! | [sai 944 920 {905 893) Baa B12 BT 18
20 7740. 5263. 3566 2789 2043 «41629 «241379 «21217 °«21107°«1028,-s'i«‘«isi2 BH] B28 784 7607447330724 728713 20
22 77405255. 3637 2601 42037.°:1576 1301 1125 «1006 922 860 813 777 748 725 706 666 642 625 614 606 599 59% Ge
24 7740 5101 3377 2476 2004 1558 1256 1064 936 B45 780 730 692 662 638 618 577 552 535 524 515 509 504 24
26 77h0 S029 S370 2398 MNBOsTnSé6 MN z3au doze 9 B87. 790) 720 0 sesm 620) 596 8 S71) 551, (5097 9482) 562454500 Bho 838 Sas 26
28 7740 5019 3338 2355 1819 1511 1231 1005 855 751 677 621 579 546 520 498 454 428 410 398 389 383 378 28
30 7740. 4986 3266 2339 «421768 41443 1260 997 835 724 665 586 541 506 479 457 411 384 366 353 344 338 333 ag
32 7740 4916 3224 2345 1737 1393 1180 1000 826 706 622 559 512 476 447 424 376 348 329 317 308 301 296 32
34 7740 4887 3210 2308 1721 1358 1135 988 824 696 606 540 490 451 421 397 348 319 300 287 278 271 266 34
36 7740 4892 3219 «-2267')S:1719 1334 = 1100 948 829 692 596 526 473 433 491 376 325 294 275 262 252 245 240 36
38 7740 4925 3180 =. 2242,-«:1726)=S 13211075 916 807 694 591 516 461 418 385 359 305 274 254 241 231 224 219 38
40 7740 4983 3146 2231 1690 1316 1058 891 778 697 590 511 452 407 372 345 289 257 236 223 213 206 200 40,
42 7740 5062 3130 2231 1666 1317 1046 873 755 671 592 509 447 399 363 334 276 243 221 207 197 190 185 42
44 7740 5159 3127 2231 1649 1314 1041 859 737 650 587 509 4a 394 356 325 265 230 209 194 184 177 171 a
46 7740 5274 3137 2203 1640 1291 1039 850 723 633 568 512 443 391 350 319 256 220 198 183 172 165 159 46
48 7740 5405 3158 2185 1638 1275 1042 844 712 619 552 501 444 389 347 314 249 211 188 173 162 155 149 48
THICKNESS=H EQUALS 065000 INCHES
LENGTH=8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9606 9600 9600 9600 9600 9609 9606 9600 9600 6
8 9600 9600 9297 8308 7757 7416 7192 7034 6921 6836 6768 6718 6674 6642 6613 6592 6539 6505 6491 6472 6459 6452 6436 8
10 9600 9600 7269 6137 5523 5153 4912 4746 4628 4537 4470 4418 4375 4339 4312 4287 4236 4205 4180 4163 4154 4144 4136 10
12 9600 9301 6355 5048 4360 3953 3692 3515 3389 3296 3226 3170 3126 3091 3062 3038 2986 2952 2930 2913 2902 2891 2888 12
14 9600 9021 5999 4485 3709 3259 2976 2785 2651 2553 2479 2422 2376 2340 2309 2285 2232 2197 2174 2159 2147 2139 2130 14
16 9600 8316 5970 4218 elche he 2839 2530 2324 2161 2077 1999 1939 1892 1854 1823 1798 1743 1709 1685 1668 1657 1648 1641 16
18 9600 7968 5659 4134 3139 2583 2243 2021 1867 1757 1675 1612 1562 1523 1491 1465 1409 1374 1350 1333 1321 1312 1304 18
20 9600 7855 5322 4164 3050 2432 2059 1817 1652 1534 1447 1381 1329 1288 1255 1228 1170 1134 1110 1094 1081 1072 1065 20
22 9600 7844 5130 3883 3041 2353 1942 1680 1502 1376 1283 1214 1160 1117 1082 1054 995 958 933 916 904 394 887 22
24 9600 7614 5041 3696 2992 2325 1875 1589 1397 1262 1164 1090 1033 988 952 923 862 824 799 782 769 760 752 24
26 9600 7506 5031 3579 2829 2337 1843 1532 1324 1180 1075 997 937 890 853 823 759 720 695 677 664 654 647 26
28 9600 7492 4983 3515 2716 eens 1838 1500 1276 Li2i 1010 927 B64 815 776 744 678 638 612 594 581 Birt: 564 28
30 9600 7442 4873 3491 2639 2153 1851 1488 1247 1061 962 874 808 756 1S, 682 614 573 546 S27 514 504 497 30
32 9600 7338 4813 3501 2592 2079 1762 1493 1232 1054 928 835 764 710 667 ~=— 632 562 519 492 473 460 450 442 32
34 9600 7295 4792 3445 2569 2027 1694 1475 1230 1039 904 805 731 674 629 593 519 476 447 428 414 404 396 34
36 9600 7303 4806 3384 2565 1992 1643 1415 1238 1033 890 785 706 646 599 561 484 439 410 391 AT: 366 358 36
38 9600 7352 4746 3347 2576 1972 1605 1367 1204 1035 882 771 «688 624 575 535 456 409 379 359 345 334 326 38
40 9600 7438 4697 3330 2523 1964 1579 1331 1161 1041 881 763. 675 608 556 515 432 384 353 332 318 307 299 40
42 9600 7556 4672 3330 2486 1966 1562 1303 1127 1002 884 759 667 596 542 498 412 362 331 309 295 284 275 42
44 9600 7702 4668 3330 2462 1961 1553 1283 1100 971 876 760 662 538 931 486 396 444 312 290 275 264 255 44
46 9600 7873 4683 3289 2449 1928 1552 1269 1079 945 847 765 661 583 523 476 382 329 295 273 257 246 238 46
48 9600 6067 4715 3262 2445 1903 1556 1260 1063 924 823 748 663 581 518 469 Srl S15 281 258 242 231 222 is

6-98

TABLE 6-6.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

FIBERGLASS POLYESTER LAMINATES

2 OZ, MAT - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 005625 INCHES

“enorics ae ee.
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10600 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 6
8 10800 10800 10800 10800 10800 10559 10241 10015 9855 9733 9637 9565 9502 9457 9416 9387 9310 9262 9242 9216 9196 9186 9163 8
10 10800 10800 10350 8738 7864 7338 6994 6758 6589 6460 6365 6290 6229 6179 6139 6104 6032 5987 5952 5928 5915 5901 5890 10
12 10800 10800 9048 7187 6208 5628 5257 5005 4825 4693 4593 4513 4451 4401 4360 4326 4251 4203 4172 4148 4132 4116 4111 12
14 10800 10800 8542 6387 5280 4640 4237 3966 3775 3636 3529 3448 3383 3331 3288 3253 3178 3128 3095 3074 3057 3045 3033 16
16 10800 10800 8501 6006 4754 4043 3602 3309 3105 2957 2846 2761 2694 2640 2596 2560 2481 2433 2400 2376 2359 2347 2336 16
18 10800 10800 8058 5886 4469 3678 3194 2878 2659 2502 2384 2295 2225 2169 2123 2086 2006 1956 1923 1898 1881 1868 1857 18
20 10800 10800 7578 5929 4343 3463 2931 2587 2352 2185 2061 1966 1893 1834 1787 1748 1667 1615 1581 1557 1540 1526 1516 20
22 10800 10800 7304 5528 4329 3350 2766 2392 2138 1959 1827 1728 1651 1590 1541 1501 1416 1364 1329 1304 1287 1273 1263 22
24 10800 10800 7178 5263 4259 3311 2669 2262 1989 1797 1657 1552 1471 1607 «1356 «1314 = 1227, 1173. -1138)=1113. 1095S 1081S 1071 24
26 10800 10687 7163 5096 4028 3328 2623 2181 1886 1680 1531 1420 1334 1268 1214 1171 1081 1025 989 964 946 932 921 26
28 10800 10668 7095 5004 3866 3211 2617 2136 1817 1597 1438 1320 1230 1160 «1104 1059 966 909 872 B46 827 813 803 28
30 10800 10596 6938 4971 3758 3066 2635 2119 1775 1539 1370 1245 1150 1076 ~=—:1018 971 B74 B15 177 751 732 718 707 30
32 10800 10449 6852 4985 3691 2960 2509 2125 1755 1501 1321 1188 1088 =1011 950 900 800 739 700 674 654 640 629 32
34 10800 10387 6823 4905 3658 2886 2412 2101 1751 1480 1288 1147 1041 959 895 B44 739 677 637 609 590 575 564 a4
36 10800 10398 6842 4818 3653 2836 2339 2014 1762 1471 1267 1117 1005 919 B52 799 690 625 584 556 536 521 510 36
38 10800 10468 6758 4765 3668 2808 2286 1947 1715 1474 1256 1097 979 889 818 762 649 582 540 511 491 476 465 38
40 10800 10591 6687 4741 3593 2796 2248 1895 1654 1482 1254 1086 961 866 792 733 615 546 503 473 452 437 426 40
42 10800 10758 6652 4741 3540 2800 2224 1855 1605 1427 1259 1081 949 B49 m7 710 587 516 471 441 419 404 392 42
44 10800 10800 6647 4741 3505 2792 2212 1826 1566 1362 1247 1082 943 837 756 691 563 490 444 413 391 375 363 44
46 10800 10800 6668 4683 3486 2745 2209 1806 1536 1345 1206 1089 942 831 745 678 54a 468 420 389 366 350 338 46
48 10800 10800 6713 4644 3481 2710 2215 1795 1513 1316 1172 1065 945 828 738 667 528 449 400 368 345 329 316 48
THICKNESS=H EQUALS 0206250 INCHES
LENGTH=B WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 6
8 12000 12000 12006 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 8
10 12000 12000 12000 11986 10788 10065 9593 9270 9038 8862 8731 8628 8545 8475 8422 8373 8274 8212 8164 8131 8114 8094 8079 10
12 12000 12000 12000 9859 8515 7721 7212 6866 6619 6438 6300 6191 6106 6036 5981 5934 5832 5765 5723 5690 5668 5647 5640 12
14 12000 12000 11718 8761 7243 6365 5812 5440 5178 4987 4841 4730 4640 4569 4510 4463) 4359 42914246 4217-4193) 4177 4161 14
16 12000 12000 11661 8238 6521 5546 4941 4540 4260 4056 3904 3788 3695 3621 3561 3512 3404 3338 3292 3259 3236 3219 3205 16
18 12000 12000 11053 8074 6130 5045 4382 39467 3647 3431 3271 3148 3052 2975 «2913. 2861 =. 2751S 2683-2637 «= 2604 «= 2581 = 2562) 2548 18
20 12000 12000 10395 8133 5958 4750 4021 3549 3227 2997 2827 2697 2596 2516 2452 2398 2286 2215 2166 2136 2112 2093 2080 20
22 12000 12000 10020 7583 5939 4595 3794 3281 2933 2687 2507 2370 2265 2181 2114 2059 1963 1871 1823 1789 1765 1746 1732 22
24 12000 12000 9847 7219 5843 4542 3661 3103 2728 2465 2273 2129 2018 1930 1860 1803 1683 1609 1561 1526 1502 1483 1469 24
26 12000 12000 9825 6991 5526 4565 3599 2991 2587 2305 2100 1947 1631 1739 1666 1607 1683 14607 1357 1322 1297 1278 1264 26
28 12000 12000 9733 6865 5304 4405 3590 2929 2493 2190 1973 1811 1688 =1591 1515 1453 1325 1247 196 1160 1135 1116 1101 28
30 12000 12000 9517 6819 5155 4206 3614 2907 2435 2111 1879 1708 1577 14676 «6.1396 = 1332, 1199 «1118 = 1066 = 1030S 1004 985 970 30
32 12000 12000 9399 6838 5063 4061 34461 2915 2407 2060 1812 1630 1493 1386 1302 1235 1097 1014 961 924 898 878 863 32
34 12000 12000 9360 6728 5018 3958 3308 2882 2402 2030 1766 1573 1428 = 1316 «1228 «61158 1014 929 874 836 809 789 774 34
36 12000 12000 9386 6609 5010 3891 3208 2763 2417 2019 1737 1533 1379 1261 1169 1095 946 858 801 763 735 715 700 36
38 12090 12000 9270 6537 5031 3851 3135 2671 2352 2022 1723 1505 1343 1219 1122 ©1045 890 799 741 701 673 653 637 38
40 12060 12000 9173 6504 4929 3836 3084 2599 2268 2033 1720 1489 1318 1188 1086 1005 843 749 689 649 621 600 584 40
42 12060 12000 9125 6504 4856 3840 3051 2545 2201 1958 1727 1483 1302 1164 +=1058 973 805 707 646 604 575 554 538 42
44 12000 12000 9118 6504 4808 3830 3034 2505 2148 1896 1711 1485 1294 1149 = 1037 948 773 672 609 566 536 515 498 44
46 12000 12000 9147 6424 4782 3765 3031 2478 2106 1845 1655 1493 1292 1139-1022 929 746 642 576 533 503 481 464 46
48 12000 12000 9208 6370 4776 3718 3039 2462 2075 1805 1608 1461 1296 «11351012 915 725 616 549 504 473 451 434 48

6-99

TABLE 6-7. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES CLAMPED

PHYSICAL CONSTANTS:
Ex = Ey = 0.86x10® PS|

Gxy = 0.40x10® PS]

- Oxy = Oyx = 0.37
THICKNESS=H EQUALS 000625 INCHES
LENGTH=8 WIDTH=A arnenese
INCHES INCHES
6 8 10 12 14 16 18 20 22 246 26 28 30 32 34 36 42 48 54 60 66 T2 78
6 62 39 31 28 26 25 24 24 24 23 23 23 23 23 23 23 23 22 22 22 22 22 22 6
8 54 35 24 19 17 16 15 14 14 14 14 13 13 13 13 13 13 13 13 13 13 13 13 8
lo 50 31 22 16 13 12 11 1) 10 9 9 9 9 9 9 9 8 8 8 A 8 8 8 10
12 48 29 21 15 12 10 9 8 7 7 1 7 6 6 6 6 6 6 c 6 & i s oe
16 47 28 19 15 ll 9 8 Zi 6 6 5 5 5 5 5 5 4 4 zs i is ef E a
16 46 27 18 13 ll 9 "8 6 5 5 4 4 “ od + % % 2 = @ : 3 2 as
18 46 27 18 13 10 9 7 6 5 4 4 4 3 3 3 3 3 3 3 3 ; Z 3 1
20 47 26 17 13 10 8 xf 6 5 4 4 3 E} 3 5) 3 2 2 2 2 2 2 2 ZO
22 49 26 17 12 9 7 6 6 5 4 3 3 3 3 2 2 2 2 2 2 2 g 2 22
24 52 26 17 12 9 7 6 5 5 4 3 3 3 2 2 2 2 2 2 2 2 2 2 ee
26 56 26 17 12 9 7 6 5 4 4 3 3 3 2 2 2 2 2 1 1 1 1 2 a2
28 61 27 16 12 9 7 6 5 4 4 3 3 2 2 2 2 2 1 1 1 1 1 1 28
30 66 28 17 12 9 7 6 5 4 3 3 3 2 2 2 2 1 1 it 1 1 i 1 30
32 TL 30 17 11 9 7 6 5 4 3 3 3 2 2 2 2 1 1 1 1 1 1 1 32
34 17 31 17 ll 9 7 5 5 4 3 3 3 2 2 2 2 1 1 1 i 1 1 1 34
36 83 33 18 ll 9 7 5 5 4 3 3 3 2 2 2 2 1 if 1 1 1 1 1 36
38 90 35 18 12 8 7 5 4 4 3 3 2 2 2 2 2 1 1 1 1 1 : ig 2g
40 97 37 19 12 8 7 5 4 4 3 3 2 2 2 2 2 1 1 1 1 1 1 1 40
42 105 39 20 12 8 6 5 4 4 3 3 2 2 2 2 2 1 a 1 il 1 1 1 42
44 113 42 21 12 8 6 5 4 4 3 3 2 2 2 2 2 1 1 1 1 1 1 1 44
46 122 44 21 13 z 6 5 4 4 3 3 2 2 2 2 2 1 DY 1 1 1 1 if 46
48 131 47 23 13 9 6 5 4 4 3 3 2 2 2 2 1 1 1 1 1 1 1 ) 48
THICKNESS-H EQUALS 001250 INCHES
LENGTH=8 WIDTH=-A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 268 30 32 34 36 42 48 54 60 66 72 78
6 495 312 251 224 209 ~=201 196 192 189 187 186 185 184 183 182 182 181 180 180 180 179 179 179 6
8 428 278 191 155 136 126 119 115 112 110 108 107-106 105 105 104 103 102 102 101 101 101 101 8
10 402251 178 130 106 93 86 81 17 75 73 71 70 70 69 68 67 66 66 65 65 65 65 10
12 385 229 166 124 94 78 69 63 ae) 56 54 yd pe 50 49 49 48 47 46 46 46 45 45 12
14 S72: 227 150 118 91 Wa. 60 53 48 45 43 41 40 39 38 37 36 ee) 35 34 34 34 34 14
16 368 217 145 107 88 70 56 48 42 39 36 34 33 31 31 30 28 27 27 27 26 26 26 16
18 367 213 145 102 80 69 55 45 39 35 32 30 28 27 26 25 23 22 22 21 21 21 21 18
20 377210 139 101 16 63 55 45 37 32 29 27 25 23 22 21 20 19 18 18 17 17 17 20
22 395 206 136 100 14 59 50 45 37 31 27 25 23 21 20 19 7, 16 15 15 15 14 14 22
24 420 207 137 96 1% 57 48 4. 37 31 27 23 21 20 18 17 15 14 13 13 12 12 12 24
26 450 210 133 95 73 57 46 39 35 31 26 23 20 18 17 16 14 12 12 ll ll ll 10 26
28 485 217 132 95 TH 57 45 38 33 29 Cid 23 20 18 16 15 13 11 10 10 10 9 9 28
30 525 225 132 93 70 55 45 37 31 28 25 23 20 17 16 14 12 10 10 9 9 8 8 30
32 568 236 134 92 70 54 45 36 pt 27 24 22 20 17 15 14 ll 10 9 8 8 7 Tt 32
34 616 249 137 92 69 53 44 36 30 26 23 ar 19 17 15 14 ll 9 8 7 7 ii Z 34
36 667 263 141 92 638 53 43 36 30 25 22 20 18 17 15 14 10 9 8 id 7 6 6 36
38 722 278 146 93 67 53 42 35 30 25 22 19 18 16 15 14 10 8 u z 6 6 6 38
40 780 295 151 94 67 53 42 35 30 25 22 19 17 16 15 14 10 8 7 6 6 5 5 40
42 841 313 157 96 67 52 42 34 29 25 27 19 17 15 14 13 10 8 if 6 5 5 5 42
44 906 333 164 99 68 52 42 34 29 25 21 1s 16 15 14 13 10 8 6 6 5 5 4 46
46 975 353 172 102 69 51 41 34 28 24 22 18 16 15 13 12 10 8 6 5 5 4 4 46
4B 1046 375 180 105 70 52 41 34 28 24 21 18 16 14 + Me} 12 10 8 6 5 5 4 4 48

6-100

TABLE 6-7;

THICKNESS=H * EQUALS 001875 INCHES

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES CLAMPED (Cont'd)

LENGTH=8 oes rENenee:
INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 76
6 1670 1054 847 755 707 678 660 647 639 632 627 623 620 617 615 613 610 608 606 605 604 604 604 6
8 1446 939-645 522 460 425 403 389 379 371 366 361 358 355 353 352 348 345 344 343 342 341 340 8
10 1357 48-601 838359315 289272 260 252 266 = 241238 235 232 230 226 224 222 221 220 219 219 10
12 1300 774 560 417 317 264 232 212 198 189 182 177173 170 167 165 161 158 156 155 154 153 153 12
14 1280 766 508 398 307 = 241 203 179 163 152 144 139134 131 128 126 121 118 117 115 114 114 113 14
16 1242 731 490 362 298 235 189 161 143 130 122 115 110 106 103 101 96 93 a1 90 89 88 87 16
18 1239. °«719°~*=«C«BSCiHHSCTZSs3Ssi«dBHSC«d‘SSs=—(i‘iaBSs=—(ia'.”s—=—“(ié«itSs«éidtD 94 90 87 84 19 75 3 72 1 79 vhs oe
20 1273 710-468 339 «= -.257 212 185 150 126 109 98 90 83 79 75 ue 66 63 61 59 58 58 3 ee
22 1334 696 460 336 250 200 170 151126 10693 83 76 71 67 64 58 54 52 50 49 =8 Ou ae
24 1617697, 4461-325. 250194 161140126104 90 79 72 66 61 58 51 47 45 43 ae eh nu ay
26 1519 710 449 320 246 191 155 132 117 105 89 7 69 62 58 54 46 42 39 38 37 36 35 26
28 16380731445. 320s 239,192 5227) 99 90 7 67 60 55 51 43 38 35 34 32 31 aa a
| 30 1771 761 446 316 235 187 151 124 106 94 86 77 67 59 53 49 40 35 32 30 29 28 27 30
| 32 1918 797 452 311 235 183 152 122 103 90 81 74 67 59 52 47 38 33 29 28 26 25 24 32
34 2078 839 462 309 234 180 147 122 102 a8 78 71 65 che} 52 47 36 ax 27 25 24 aa 22 34
36 2251 887 = 475 310 230 180 144 122. 101 86 76 68 62 58 52 46 35 29 26 24 22 21 20 36
| 38 2435 939 491 313.228 180 143 119 101 85 74 66 60 55 52 47 35 28 24 22 20 19 19 38
} 40 2632 996 510 318 227 177 142 117 101 85 73 64 58 oie) 49 46 34 rae 23 21 a 18 17 40
42 2840 1057 532 325 228 175 142 116 98 85 72 63 56 51 47 44 34 27 23 20 18 17 16 42
. 44 2980 ©1123 555 334 230 174 141 11s 97 84 72 63 55 50 46 43 34 26 22 9 17 16 15 44
| 46 2980 ©1193 581 343 233 174 139 115 96 82 73 62 55 49 45 41 34 26 21 18 17 15 14 46
48 2980 1266 608 354 237 174 136 115 95 81 7 62 54 48 44 40 33 26 al 18 16 14 14 48
THICKNESS=H EQUALS 0462500 INCHES
| LENGTH=8 WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 3958 2499 2008 1790 1675 1607 1564 1534 1514 1498 1486 1477 1470 1463 1458 1454 1445 1440 1437 1435 1433 1431 1431 6
8 3428 2226 1529 1236 1090 1007 955 921 897 880 867 857 849 843 837 833 824 818 815 812 810 809 ats 8
10 3216 2009 1425 1037 850 747 685 644 617 597 583 572 563 556 551 546 537 531 526 2a 522 520 D7! 10
12 3081 1835 1326 990 752 625 550 502 470 447 431 419 409 402 396 391 381 374 370 367 365 364 363 12
14 3034 1815 1204 943 727 571 481 424 387 361 343 329 318 310 303 298 267 261 276 273 271 270 268 14
16 2945 1733 1160 857 705 SST 449 382 339 309 268 273 261 252 245 239 227 220 215 212 210 208 207 16
18 2937 1703 1159 816 644 548 440 362 312 278 254 236 223 213 205 199 186 179 174 170 168 166 165 18
20 3017 1683 1109 804 609 502 438 356 298 259 232 212 198 187 178 171 157 149 144 141 138 137, 135 20
22 3162 1650 1091 797 593 474 404 358 294 250 219 197 181 169 159 151 136 128 122 119 116 114 113 22
24 3360 1652 1093 770591 459 381 332 298 247 213 188 = -170 156 146 137 121 1l2 106 102 100 98 96 24
26 3601 1682 1065 758 582 453 367 313 277 250 211 183.163 148 136 127 110 100 94 90 87 85 83 26
28 3882 1734 1055 758 566 454 360 301 262 236 212 182 159 143 130 120 101 90 84 80 77 75 73 28
30 4198 1804 1057 748 558 444 357 294 252 223 203 183-158 140 126 115 94 83 76 72 69 66 65 30
32 4200 1890 1072 736 556 433 359 290 245 214 192 176 159: 139. 124 112 90 77 70 65 62 60 58 32
34 4200. 1990 1095 732 555 428 349 290 241 208 185 168-155 140 123 110 86 73 65 60 57 54 52 34
36 4200 2102 1126 734 545 426 342 290 239 204 179: 161 147 137 124 110 84 69 61 56 52 50 48 36
38 4200 2226 1165 742 539 428 338 282 240 202 175 156 142 be yh 122 110 82 67 58 52 49 46 44 38
40 4200 2361 1209 754 538 421 337 277 238 201 173 152.0137 126 117 110 81 65 55 49 46 43 Pet ra
42 4200 2507 1260 TTY 540 415 337 274 233 202 171 150 134 122 112 105 81 63 53 47 43 40 38 42
44 4200 2662 1316 791 544 412 335 273 229 199 171 1480131 119 19 101 81 63 52 45 41 38 36 44
46 4200 2827 1376 814 551 412 330 273 227 195 172 148-130 116 106 98 B82 62 51 44 39 36 34 46
48 4200 3001 1441 B40 561 413 327 273 226 193 169 148 129 115 104 95 78 62 50 42 38 34 32 48

(yes (O

TABLE 6-7. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES CLAMPED (Cont'd)

THICKNESS*H EQUALS 003125 INCHES

LENGTH=8 WIOTH=A tener
INCHES IHSUES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 5250 4880 3921 3496 3271 3139 3055 2997 2956 2926 2902 2884 2870 2858 2849 2840 2823 2813 2607 2803 2799 2796 2795 6
8 5250 4348 2986 2415 2129 1966 1866 1799 1752 1719 1693 1674 1658 1646 1635 1628 1609 1598 1592 1586 1582 1579 1576 8
10 5250 3924 2783 2026 1660 1459 1337 1258 1205 1166 1138 1117 1100 1086 1076 1067 1048 1037 © 1028 1022 1019 1016 1013 10
12 5250 3584 2591 1933 1469 1220 1073 980 918 B74 B42 818 799 785 773 764 744 731 723 718 14 710 709 12
14 5250 3545 2351 1842 1420 1115 939 829 756 705 669 642 621 605 593 582 561 548 539 534 529 526 524 14
16 5250 3385 2266 1674 1378 1087 876 746 662 604 563 532 509 492 478 466 443 430 421 414 410 407 404 16
18 5250 3327 2264 1593 1257 1070 859 707 609 542 495 461 436 416 401 388 363 349 339 333 328 325 322 18
20 5250 3287 2166 1571 1190 981 856 696 583 507 453 415 386 365 348 334 307 292 282 275 270 267 264 20
22 5250 3222 2131 1557 1159 926 788 700 575 488 428 385 353 329 311 296 267 250 239 232 227 224 221 22
24 $250 3227 2136 1504 1155 896 744 648 581 483 415 367 332 305 284 268 237 218 207 200 195 191 188 24
26 5250 3285 2081 1481 1137 884 717 612 542 488 412 358 9-318 289 = 266 «= 249 2:14 195 183 175 170 166 163 26
28 5250 3386 2060 1461 1105 B86 702 588 512 460 415 355 311 re) 254 235 197 176 164 155 150 146 143 28
30 5250 3523 2065 1461 1090 867 698 573 492 436 396 357 309 273 246 225 184 162 149 140 134 130 126 30
32 5250 3691 2093 1438 1087 846 702 567 479 418 376 344 311 272 242 219 175 151 137 127 121 117 113 32
36 5250 3886 2138 1430 1084 835 683 566 471 406 361 327-302 273 241 216 168 142 127 117 lll 106 103 34
36 5250 4106 2200 1434 1065 832 669 566 467 398 350 314 288 268 242 215 163 136 119 109 102 97 94 36
38 5250 4348 2275 1449 1054 835 660 551 468 394 342 304 276 255 239 216 160 130 113 102 95 90 86 38
40 5250 4612 2362 1473 1050 822 657 542 465 393 337 297 268 245 228 214 158 127 108 97 89 84 80 40
42 5250 4896 2461 1505 1054 811 658 535 455 394 335 293 261 238 219 205 158 124 104 92 84 78 74 42
44 5250 5199 2570 1544 1063 806 654 533 448 389 335 290 257 232 212 197 158 122 101 88 80 74 70 44
46 5250 5250 2688 1589 1077 B04 645 533 443 382 336 289 254 227 207 191 159 121 99 a5 76 70 66 46
48 5250 5250 2815 1640 1095 807 639 534 440 376 331 289 252 224 203 186 153 121 97 83 74 67 63 48
THICKNESS=H EQUALS 003750 INCHES
LENGTH-B WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 26 30 32 34 36 42 48 54 60 66 72 76
6 6640 6640 6640 6041 5653 5425 5279 5179 5108 5055 5014 4984 4960 4939 4922 4908 4878 4860 4851 4843 4836 4831 4830 6
8 6640 6640 5159 4173 3679 «= 3398 «= 3224 3108 )= 3028 «= 2970 2925 2892 2864 «= 2844) 2826 ©2813. 2781 )=— 2761 20275102741 027330 «272922725 8
10 6640 6640 94809 93501 2868 2520 2310 2175 2082 2015 1967 1930 1900 1877 1859 1843 1611 1791 1777 1767 1761 1755 1752 10
12 6640 6194 4476 3340 2538 2108 1855 1694 1586 1510 1455 1413 1361 1356 1336 1320 1285 1264 1250 1240 1233 1227 1224 12
14 6640 6126 4063 3182 2454 1927 1622 1432 1306 1219 1156 1109 1074 1046 1024 1v06 970 947 932 922 915 910 905 14
16 6640 5848 3916 2892 2381 1879 1514 1290 1143 1043 972 920 880 849 825 806 766 742 727 716 709 703 699 16
18 6640 5749 3912 2753 2172 1850 1484 1222 1052 937 856 797 753 719 692 671 628 603 587 575 568 562 557 18
20 6640 5679 3743 2714 2056 1695 1479 1202 1007 875 783 717 668 630 601 578 531 504 487 475 467 461 456 20
22 6640 5568 3682 2691 2003 1601 1362 1210 994 B44 740 666 611 569 537 511 461 432 413 401 393 386 382 22
24 6640 5577 3691 2599 1996 1548 1285 1119 1004 835 718 635 573 527 492 464 409 378 358 345 336 330 325 24
26 6640 5677 3596 2559 1965 1528 1238 1057 937 843 711 618 550 499 460 430 370 336 316 302 293 286 261 26
28 6640 5852 3559 2560 1910 1531 1213 1016 886 796 717 613 538 482 439 405 341 305 283 268 259 252 246 28
30 6640 6088 3569 2524 1883 1498 1206 991 850 753 685 618 534 472 425 389 319 280 257 242 231 224 219 30
32 6640 6378 3616 2485 1878 1462 1213 979 827 723 649 595 538 470 416 378 302 261 236 220 209 202 196 32
34 6640 6640 %695 2471 1874 1443 1179 978 ai3 702 623 566 523 #72 416 373 290 246 219 202 191 183 177 34
36 6640 6640 3601 2478 1839 1437 1155 978 808 688 604 543 497 462 418 371 262 234 206 188 176 168 162 36
38 6640 6640 3931 2504 1821 14643 1141 953 809 681 591 526 478 441 412 373 277 225 195 177 164 155 149 38
40 6640 6640 4082 2546 1815 1420 1136 936 804 678 583 514 463 426 394 370 274 219 187 167 154 144 138 40
42 6640 6640 4252 2601 1821 1402 1138 925 786 681 579 506 451 410 379 354 273 214 180 159 145 ED 128 42
44 6640 6640 4440 2668 1836 1392 1131 920 773 673 578 501 443 400 367 340 273 211 175 153 138 128 121 44
46 6640 6640 4645 2746 1861 1390 1115 920 765 659 581 499 438 392 357 330 275 209 17 147 132 121 114 46
48 6640 6640 4865 2835 1892 1394 1104 923 761 650 571 499 435 387 350 321 265 209 168 143 127 116 108 48

6-102

TABLE 6-7.

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 004375 INCHES
LENGTH=B WIDTH=A CNG Tey
INCHES INCHES
6 8 10 12 14 16 18 29 22 24 26 28 30 32 34 36 42 48 54 60 66 72 76
6 7740 7740 «-7740=- 774077407740 7740-=- 7740-7740. 7740-7740, 7740-7740 77400 7740-7740 7740-7718 = 770376917679 = 7672 7670 6
8 7740 7740 7740 6627 5842 5396 5120 4936 4809 4716 4645 4592 45468 4515 4487 4466 4415 4384 4368 4352 4340 4333 4326 8
10 7740 7740 7637 5559 4555 4002 3669 3453 3306 3200 3123 3064 3018 2981 2952 2927 2876 2844 2821 2806 2797 2787 2780 10
12 7740 7740 7108 5303 4030 3348 2945 2690 2518 2398 2311 2244 2194 2154 2122 2096 2041 2007 1985 1969 1958 1948 1944 12
14 7740 7740 6452 5053 3696 3060 2575 2273 2074 1935 1436 1762 1705 1661 1626 1598 1540 1503 1480 1465 1453 1445 1437 14
16 7740 7740 6219 4593 3781 2983 2404 2048 1816 1657 1544 1460 1398 1369 1311 1280 1216 1179 1154 1137 1125 1117 1110 16
18 7740 7740 6213 4371 3449 2937 2357 1940 1670 1488 1359 1266 1196 1142 1100 1066 997 957 931 914 901 B92 B85 18
20 7740 7740 5944 4309-3264 = 26922348) = 1909-1598 = «13901244 = 1139, 10601001 954 917 843 800 773 754 741 732 725 20
22 7740 7740 5846 4273 3180 2542 2163 1921 1578 1340 1175 1057 970 903 852 612 732 685 656 637 624 613 606 22
24 7740 7740 5860 4128 3170 2459 2041 1777 1595 1326 1140 1008 910 837 781 736 649 600 569 548 534 524 516 24
26 7740 7740 5710 4064 3120 2426 1966 1678 1487 1338 1130 982 874 793 731 682 587 534 501 480 465 454 446 26
28 7740 7740 5652, 4065 3033. 2432, «1927 «1613. 1406 = 12631139 974 854 765 697 644 541 484 449 426 411 400 391 28
30 7740 7740 «5667 «4008 §=. 2990 2378) «=: 1915. 1574 =1350 1196 = 1087 981 849 750 676 618 506 445 408 384 367 356 347 30
32 7740 7740 5743 3945 2982 2322 1926 1555 1313 1148 1031 945 854 746 664 601 480 414 375 349 332 320 all 22
34 7740-7740 «5868 «= 3923. 2976 «= 22911873. :1552,1291 1114 989 898 830 750 66: 592 461 390 348 322 303 291 281 34
36 7740 7740 «= 6036 = 3936) 29210 2282) 1834 «61553-1283 =) :1093 959 862 790 734 664 589 448 372 327 299 280 266 2a, 36
38 7740-7740 6242, 3977-289) 229118121513. 1284 = 1081 939 835 759 700 655 592 439 358 310 280 260 246 236 38
40 7740, 7740 6482 4042288202255 180% «61486 «= 1277 = 1077 926 816 735 673 625 587 434 347 297 265 244 229 219 40
42 7740-7740 «6752 4130-2892 2226 = 1807 = 1469S :1248 1081 919 803 717 652 601 561 433 340 286 253 230 215 204 42
44 7740 7740 «©7051 «4237-2916 = 2210-1796 = 1462-1228 = 1068 918 795 704 635 582 541 434 335 278 242 219 203 191 44
46 7740 7740 7376 4361 2954 2207 1770 1462 1215 1047 922 792 696 623 568 524 437 332 272 234 210 193 181 46
48 7740 7740 «= 7725-4501 = 30052214 = :1753 1465) = 1209-1032 907 792 691 615 556 510 420 331 267 228 202 184 172 48
THICKNESS=H EQUALS 065000 INCHES
LENGTH=8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9600 9600 9600 9600 9600 9600 9660 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 6
8 9600 9600 9600 9600 8720 8054 7642 7367 7178 7039 6933 6855 6789 6740 6698 6667 6591 6544 6521 6496 6478 6468 6456 8
10 9600 9600 9600 8299 6799 5974 5476 5155 4935 4777 4661 4574 4505 4449 4406 4369 4292 4246 4211 4188 4174 4161 4150 10
12 9600 9600 9600 7916 6016 4997 4396 4015 3759 3580 3449 3350 3274 3215 3167 3128 3047 2996 2963 2939 2923 2908 2902 12
14 9600 9600 9600 7543 5816 4568 3844 3394 3095 2849 2740 2630 2545 2480 2427 2386 2298 2244 2209 2186 2169 2156 2145 14
16 9600 9600 9283 6855 5644 4453 3589 3057 2710 2473 2304 2180 2086 2014 1956 1911 1816 1760 1723 1697 1680 1667 1656 16
18 9600 9600 9274 6525 5149 4384 3518 2895 2493 2221 2029 1889 1785 1704 1641 1591 1489 1429 1390 1364 1345 1331 1321 18
20 9600 9600 8872 6433 4872 4018 3505 2850 2386 2075 1857 1700 1583 1494 1424 1369 1259 1194 1153 1126 1107 1092 1082 20
22 9600 600 8727 6379 «4747 «= 3794 = 3228 «= 2867 = -2355 2001 = 1755) 01578 = 1447 1349-1272) 1212) 10921023 980 951 931 916 904 22
24 9600 9600 8748 6161 4731 3670 3047 2653 2381 1979 1702 1504 1359 1249 1165 1099 969 895 849 819 798 782 770 24
26 9600 9600 8523 6067 4657 3621 2935 2505 2220 1997 1646 1465 1304 1183 1091 1018 877 797 749 717 694 678 666 26
28 9600 9600 8437 6068 4527 3630 2876 2408 2099 1886 1700 1454 1275 1142 1040 961 807 722 670 636 613 596 584 28
30 9600 9600 8460 5983 4463 3550 2859 349 2015 1786 1623 1464 1267 1120 1008 922 755 664 608 573 548 531 518 30
32 9600 9600 8572 5889 4451 3466 2875 2321 1960 1714 1539 loll 1274 1113 991 897 TUT 618 559 522 496 478 464 32
34 9600 9660 8759 5857 4442 3420 2796 2317 1928 1664 1477 1341 1239 1119 986 884 688 583 520 480 453 434 420 34
36 9600 9690 9010 5875 4360 3407 2738 2319 1915 1631 1432 1287 1179 1096 991 880 668 555 488 446 418 398 383 36
38 9600 9600 9318 5936 4316 3420 2705 2259 1917 1614 1401 1247 1132 1045 977 683 656 534 463 418 388 368 352 38
40 9600 9600 9600 6034 4303 3366 2692 2218 1906 1608 1382 1218 1097 1005 933 876 648 519 443 396 364 342 326 40
42 9600 9600 9600 6165 4316 3322 2697 2193 1863 1613 1372 1198 1070 973 898 838 646 508 427 377 344 321 304 42
44 9600 9600 9600 6324 4353 3300 2680 2162 1833 1595 1371 1187 1051 949 869 807 648 500 415 362 327 303 286 44
46 9600 9600 9606 6510 4410 3294 2642 2162 1614 i563 1377 1182 1038 930 B47 782 653 496 405 350 313 288 270 a6
48 9600 3600 9600 6719 4485 3305 2617 2187 1804 1540 1354 1183 1031 918 830 762 627 495 399 340 301 275 256 48

6-103

TABLE 6-7, FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
2 OZ. MAT - ALL EDGES CLAMPED (Cont'd)

THICKNESS*H EQUALS 005625 INCHES

LENGTH=8 Denes Tnenegy
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10600 10800 10800 10600 10800 10800 10800 10800 10800 10800 10800 10800 10800 6
8 10800 10800 10800 10800 10800 10800 10800 10490 10220 10022 9872 9760 9667 9597 9537 9493 9384 9317 9284 9250 9224 9210 91961 8
10 10800 10800 10800 10800 9680 8506 7797 7339 7027 6801 6637 6512 6414 6335 6274 6220 6112 6045 5996 5963 5944 5924 5910 1c
12 10800 10800 10800 10800 6566 115: 6260 S7ar 5352 5097 4911 4770 4662 4577 4510 4454 4338 4265 4219 4185 4162 4141 4132 12
14 10800 10800 10800 10740 8281 6504 5474 4832 4407 4114 3901 3745 3624 3531 3456 3397 3273 3195 3145 3113 3088 3070 3054 14
16 10800 10800 10800 9761 8036 6340 5110 4353 3859 3521 3261 3104 2971 2867 2785 2720 2585 2506 2453 2417 2392 2373 2358 16
18 10800 10800 10800 9290 7331 6243 5009 4123 3550 3162 2889 2690 2541 2426 2337 2265 2120 2034 1980 1942 1916 1896 1880 18
20 10800 10800 10800 9159 6937 5722 4991 4058 3397 2954 2644 2620 2253 2127 2028 1949 1792 1700 1642 1604 1576 1555 1540 20
22 10800 10800 10800 9082 6759 5402 4596 4082 3353 2848 2498 2247 2061 1920 1611 1726 1555 1457 1395 1354 1325 1304 1288 22
24 10800 10800 10800 8773 6737 5226 4338 3777 3390 2818 2423 2142 1935 1779 1659 1565 1380 1274 1209 1166 1136 1114 1097 24
26 10800 10800 10800 8638 6631 5156 4179 3567 3161 2844 2401 2087 1857 1685 1553 1450 1249 1135 1066 1020 989 966 949 26
28 10800 10800 10800 8639 6445 5169 4095 3428 2989 2685 2420 2070 1816 1626 1481 1368 1150 1028 954 906 873 849 831 28
30 10800 10800 10800 8519 6354 5054 4071 3345 2869 2543 2310 2084 1803 1594 1436 1313 1076 945 866 815 781 756 737 30
32 10800 10800 10800 68385 6338 4935 4094 3304 2791 2440 2191 2009 1814 1585 1411 1277 1020 880 796 743 706 680 661 32
34 10800 10800 10800 8339 6324 4870 3981 3299 2745 2369 2103 1909 1764 1593 1404 1258 980 830 740 683 645 618 598 34
36 10800 10800 10800 8365 6208 4851 3899 3301 2726 2323 2039 1833 1679 1561 1411 1252 952 791 696 635 595 566 546 36
38 10800 10800 10800 8452 6145 4870 3852 3216 2730 2297 1995 1776 1612 1488 1391 1258 933 761 660 596 553 523 502 38
40 10800 10800 10800 8592 6126 4792 3833 3158 2714 2290 1967 1734 1562 1430 1328 1248 923 738 631 563 519 487 465 40
42 10800 10800 10800 8778 6146 4731 3840 3123 2653 2297 1953 1706 1524 1385 1278 1193 920 723 608 537 490 457 433 42
44 10800 10800 10800 9005 6198 4698 3816 3106 2610 2271 1952 1690 1497 1351 1238 1149 923 712 591 515 466 431 407 44
a6 10800 10600 10800 9269 6279 4691 3762 3107 2583 2226 1960 1683 1479 1325 1206 1113 930 706 577 498 445 410 384 46
48 10800 10800 10800 9567 6386 4705 3727 3114 2569 2193 1928 1684 1469 1306 1182 1085 893 704 568 484 429 391 365 48
THICKNESS*H EQUALS 006250 INCHES
LERGTH-8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 6
8 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 8
10 12000 12000 12000 12000 12000 11669 10696 10068 9639 9329 9104 8933 8799 8690 8606 8533 8383 8292 8226 8180 68153 8127 8106 10
12 12000 12000 12000 12000 11751 9761 8586 7842 7342 6991 6737 6543 6395 6279 6186 6110 5950 5851 5787 5740 5709 5680 5668 12
14 12000 12000 12000 12000 11359 8921 7509 6628 6045 5643 5352 5137 4972 4844 4741 4659 4489 4383 4315 4270 4236 4212 4190 14
16 12000 12000 12000 12000 11023 8697 7009 5971 5294 4830 4500 4258 4075 3933 3821 3732 3546 3437 3365 3315 3281 3255 3235 16
18 12000 12000 12000 12000 10056 8563 6872 5655 4870 4338 3963 3690 3486 3328 3206 3107 2908 2790 2716 2664 2628 2600 2579 18
20 12000 12000 12000 12000 9516 7849 6846 5566 4660 4052 3627 3320 3091 2917 2782 2674 2458 2332 2253 2200 2162 2133 2112 20
22 12000 12000 12000 12000 9271 7410 6305 5600 4600 3907 3427 3082 2827 2634 2485 2367 2133 1998 1914 1857 1618 1788 1766 22
24 12000 12000 12000 12000 9241 7168 5951 5181 4650 3865 3324 2938 2654 2440 2276 2147 1892 1748 1659 1599 1558 1528 1505 24
26 12000 12000 12000 11849 9096 7073 5733 4893 4336 3901 3293 2862 2547 2311 2130 1989 1713 1557 1462 1400 1356 1325 1302 26
28 12000 12000 12000 11851 8841 7090 5618 4703 4100 3683 3320 2840 2491 2230 2032 1877 1577 1411 1309 1243 1198 1165 1140 28
30 12000 12000 12000 11686 8716 6933 5584 4588 3936 3488 3169 2859 2474 2187 1970 1801 1475 1297 1188 1119 1071 1037 + 1012 30
32 12000 12000 12000 11503 8694 6769 5615 4532 3828 3347 3006 2756 2489 2174 1936 1752 14600 1207 1093. 1019 969 933 906 32
34 12000 12000 12000 11439 8675 6681 5460 4526 3765 32469 2885 2619 2419 2186 1926 1726 1344 1138 1016 937 885 848 820 34
36 12000 12000 12000 11474 8516 6654 5348 4528 3740 3186 2797 2514 2303 2141 1935 1718 1306 1085 954 871 816 777 749 36
38 12000 12000 12000 11594 8429 6680 5284 4412 3745 3151 2736 2436 2212 2041 1908 1725 1280 1044 905 817 759 718 688 38
40 12000 12000 12000 11785 8404 6573 5258 4332 3722 3141 2698 2379 2142 1962 1822 1712 1266 1013 865 773 711 668 638 40
42 12000 12000 12000 12000 8430 6489 5267 4283 3639 3151 2680 2341 2090 1900 1753 1637 1262 991 834 736 672 627 595 42
44 12000 12000 12000 12000 8502 6445 5235 4261 3580 3115 2677 2318 2053 1853 1698 1576 1266 977 810 707 639 592 558 44
46 12000 12000 12000 12000 8614 6435 5160 4262 3543 3053 2689 2308 2028 1817 1655 1527 1275 969 792 683 611 562 527 46
48 12000 12000 12000 12000 8760 6454 5112 4271 3523 3008 2645 2310 2014 1792 1621 1488 1225 966 779 663 588 537 500 48

6-104

TABLE 6-8.

FIBERGLASS POLYESTER LAMINATES

CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ, WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED

PHYSICAL CONSTANTS:
1.81x108 PSI

m
x
"

m
<
1

1,54x10® PS!

Gyy = 0245x108 PSI
Oxy = Oyx = 0.19

THICKNESS*H EQUALS 060625 INCHES

- NGTH=

eee “INCHES “INCHES.

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 33 20 15 13 12 ar ql 10 10 lo 10 10 9 9 9 9 9 9 9 9 9 9 9 6
8 38 19 12 10 8 7 7 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 8
To 34 20 12 9 7 6 5 5 a 4 4 & 4 4 4 4 4 3 3 3 3 3 3 10
12 33 20 13 8 6 5 4 4 4 3 3 3 3 3 3 3 3 2 2 2 2 2 2 12
14 35 19 13 9 6 5 4 3 3 3 3 2 2 r 2 2 2 2 2 2 2 2 2 14
16 34 19 12 9 6 5 4 3 3 2 2 2 2 2 2 2 2 1 1 1 1 1 i 16
18 33 19 12 9 7 5 4 3 3 2 2 2 2 2 2 1 1 1 1 1 1 1 1 18
20 34 19 12 9 "i 5 4 3 2 2 2 2 2 i 1 1 ik 1 1 1 1 1 1 20
22 33 19 12 8 6 5 4 3 2 2 2 2 1 1 1 1 1 1 1 ‘j 1 z 1 22
24 33 19 12 8 6 5 4 3 3 2 2 2 1 1 st 1 1 1 1 1 1 1 1 24
26 34 19 12 8 6 5 4 3 3 2 2 iz 1 1 1 1 1 1 1 1 1 1 1 26
28 33 19 12 9 6 5 4 3 3 2 2 2 1 1 i 1 1 1 1 if 1 1 ° 28
30 33 19 12 9 6 5 4 3 3 2 2 2 a 1 1 1 1 1 1 1 ° 0 () 30
32 34 19 12 8 6 5 4 3 3 2 2 2 1 1 1 1 1 1 1 t) C) 0 0 32
34 33 19 12 8 6 5 4 3 3 2 2 2 1 1 1 1 1 1 1 0 0 0 0 34
36 33) ah) 12 8 6 5 4 3 3 2 2 2 1 1 1 By Z ut (0) ° i) ic} ° 36
38 33 19 12 8 é 5 4 3 3 2 2 2 1 1 1 1 1 a ° ) 0 ° ° 38
40 33 19 12 9 6 b 4 3 2 2 2 2 2 1 1 1 1 ii 0 0 0 ( ) 40
42 33 19 12 8 6 5 4 3 2 2 2 2 1 1 1 1 1 1 ) ) ° ) 0 42
44 33 19 12 8 6 5 4 3 2 2 2 2 1 u 1 1 1 1 t) t) ) to) ° 44
46 33 19 12 8 6 5 4 3 2 2 2 2 1 T 1 1 1 1 0 ty) 0 ° to) 46
48 33 19 12 8 6 5 4 3 3 2 2 2 1 1 7 1 it 1 t) ° 0) 0 0 48
THICKNESS=H EQUALS 041250 INCHES

LENGTH-8 WIDTH=A LENGTH=8

INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 268 30 32 34 36 42 48 54 60 66 72 78

6 267 161 123 105 95 89 Bs 82 8c 79 77 7 76 75 75 m4 14 73 73 72 72 72 72 6
8 301 150 100 77 66 59 54 51 49 48 46 46 45 44 44 43 42 42 42 41 41 41 4. 8
10 273 162 96 68 54 46 41 38 35 34 32 31 31 30 29 29 28 27 27 27 27 26 26 10
12 267 161 102 67 5c 40 34 31 28 26 25 24 23 22 22 21 20 20 19 19 19 19 18 12
14 279 152 108 70 49 38 31 27 24 22 20 19 18 18 17 17 16 15 15 14 14 14 14 14
16 269 150 100 75 51 38 30 25 22 19 18 16 15 15 14 14 13 12 12 11 17 ll ll 16
18 267 154 96 72 54 39 30 24 20 18 16 15 14 13 12 12 ll 10 9 9 9 9 9 18
20 273 154 96 68 54 41 30 24 20 oT, 15 14 12 12 ll 10 9 8 8 8 7 7 7 20
22 267 150 98 67 51 43 32 25 20 17 14 13 12 ll 10 9 8 7 7 U 6 6 6 22
24 267 150 100 67 50 40 33 25 20 27, 14 12 ll 10 9 9 7 7 6 6 5 5 5 24
26 270 153 97 68 49 39 33 27 21 17 14 12 ll 10 9 8 7 6 5 5 5 5 4 26
28 267 152 96 70 49 38 31 27 22 17 14 12 ll 9 9 8 6 5 5 5 4 4 4 28
30 267 150 96 68 50 38 30 26 23 18 15 12 a1 9 8 8 6 5 5 4 4 4 4 30
32 269 150 97 67 51 3e 3c 25 22 19 15 13 11 9 8 zi 6 5 4 4 4 3 3 32
34 267 152 98 67 ER 38 30 24 21 19 16 13 aip 9 8 7 6 5 4 4 3 3 3 34
36 267 151 96 67 50 39 30 24 20 18 16 43 11 10 8 7 6 4 4 3 3 3 3 36
38 268 150 96 67 49 39 30 24 20 17 15 14 12 10 9 7 5 4 4 3 3 3 3 38
40 267 150 96 68 49 38 30 24 20 17 a5 14 12 10 9 8 5 4 4 3 3 3 2 40
42 287 151 97 67 49 38 31 24 20 17 15 13 12 10 9 8 5 4 3 3 3 2 2 42
44 267 Neh) 97 67 49 38 31 25 20 17 14 ats} 12 ll 9 8 5 2 3 3 3 2 2 44
46 267 150 96 67 50 38 30 25 20 17 14 13 apt 10 9 8 6 oo 3 3 2 2 2 46
46 267 150 96 67 50 38 30 25 20 17 14 12 vl 10 9 8 6 4 3 3 2 2 2 48

6-105

TABLE 6-8.

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

25-27 OZ, WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS*H ECUALS 001875 INCHES
ie “Roe! ae
6 6 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 902 543 414 353 320 299 286 277 270 265 262 259 256 254 253 251 249 246 245 245 244 243 243 6
8 1017 507 337 261 222 199 184 173 166 161 57) 154 151 149 148 146 143 141 140 139 139 138 138 8
10 921 548 325 230 183 155 138 127 119 113 109 106 103 101 99 98 95 93 91 91 90 89 89 10
12 902 543 343 226 168 136 116 103 95 88 84 80 7 75 73 72 68 66 65 64 63 63 62 12
14 940 512 363 235 166 128 ics 91 81 74 69 65 62 -¥) 57 56 53 50 49 48 47 47 46 14
16 907 507 337 254 71 127 lol 84 73 65 60 55 52 50 48 46 42 40 39 38 37 37 36 16
18 902 521 326 241 182 130 10c 81 69 60 54 49 46 43 41 39 36 33 32 31 30 29 29 18
20 921 518 325 230 183 137 103 81 67 58 51 46 42 39 36 35 31 28 27 26 25 24 24 20
22 903 508 332 226 173 144 107 83 67 56 49 43 39 36 33 31 27 25 23 22 21 rat 20 22
24 902 507 337 226 168 136 112 86 68 56 48 42 37 34 31 29 25 22 20 19 18 18 Ne) 24
26 911 515 326 229 166 131 lo 90 7 57 48 41 36 33 30 27 23 20 18 17 16 16 15 26
238 901 512 324 235 166 128 105 91 73 59 49 41 36 ae 29 26 21 18 17 15 15 14 14 28
30 902 507 325 230 168 127 102 87 76 61 50 42 36 32 28 26 20 17 15 14 13 13 12 30
32 907 507 328 227 uri 127 101 84 73 64 51 43 36 32 28 25 20 16 14 13 12 11 ll 32
34 901 512 330 225 171 128 100 82 71 63 53 44 37 32 28 25 19 16 14 12 11 ll 10 34
36 902 5c9 326 226 168 130 100 81 69 60 54 46 38 33 28 25 19 15 13 11 11 10 9 36
38 904 506 324 227 166 132 101 81 68 59 52 47 39 33 29 25 18 15 12 ll 10 9 9 38
40 900 507 325 230 165 130 103 81 67 58 51 46 41 34 29 26 18 14 12 10 9 9 8 40
42 902 Sad 327 227 166 128 104 82 67 om 50 44 40 35 30 26 18 14 12 10 9 8 8 42
44 903 508 327 226 167 127 103 83 67 56 49 43 39 36 31 27 19 14 ll 10 9 8 7 44
46 900 506 325 225 169 127 102 84 68 56 48 43 38 35 32 27 19 14 ll 10 8 8 7 46
48 902 507 324 226 168 127, lol 84 68 56 48 42 37 34 31 28 19 14 ll 9 8 7 a 48
THICKNESS=H_ EQUALS 002500 INCHES
LENGTH=8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 16 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 2138 ©1287 980 837 758 71¢ 678 656 641 629 620 613 608 603 599 596 589 584 581 580 578 576 576 6
8 2410 1203 798 620 526 471 435 411 394 362 372 365 355 354 350 347 340 335 332 330 328 327 326 8
10 2184 1299 770 546 432 368 326 301 282 269 258 250 244 239 235 232 224 220 217 215 213 212 211 10
12 2138 ©1287 813 535 398 322 275 245 224 209 198 189 183 177 173 170 162 157 154 152 150 149 148 12
14 2229 «1212 860 557 393 2ca 250 215 192 175 163 154 146 141 136 133 125 120 116 114 112 lll 110 14
16 2149 1203 798 602 406 3c1 239 200 173 155 142 131 124 118 113 109 101 95 92 90 88 87 86 16
18 2138 «61235 772 572 432 3c9 238 193 163 143 128 117 109 102 97 93 84 79 75 73 Ta 70 69 18
20 2184 1229 770 546 432 325 243 192 159 137 120 108 99 92 86 82 73 67 64 61 59 58 57 20
22 2139-1203 785 535 419 340 253 196 159 134 116 103 93 85 79 74 64 59 55 52 50 49 48 22
24 2138 =1203 798 535 398 322 268 203 162 134 114 99 89 80 74 69 58 52 48 46 44 42 41 24
26 2160 ©=1221 778 542 392 310 260 213 167 136 114 98 86 77 71 65 54 47 43 41 39 37 36 26
28 2136 = 1212 769 357 393 303 250 215 174 139 115 98 85 76 68 62 51 44 39 37 35 33 32 28
30 2138 = =1201 770 546 397 320 243 206 181 144 118 99 86 75 6? 61 48 41 36 33 31 30 29 30
32 2149 1203 778 537 406 301 239 200 173 et 122 iol 86 75 66 60 46 39 34 31 29 27 26 32
34 2135 «1215 782 534 495 304 237 195 16E 148 127 104 88 76 67 59 45 37 32 29 27 25 24 34
36 2138 1206 772 535 393 309 238 193 163 143 128 108 90 77 67 59 44 36 31 27 25 23 22 36
38 2143 =1200 768 539 394 313 240 192 161 139 124 112 93 79 68 60 44 35 29 26 23 22 20 38
40 2134 1203 770 546 392 307 243 192 159 137 120 108 96 81 70 61 44 34 28 25 22 21 19 40
42 2138 =«1211 775 539 393 303 248 194 159 135 118 105 96 B4 71 62 44 34 28 24 21 19 18 42
44 2129 = 1203 775 535 395 301 245 196 159 134 116 103 93 85 4 63 44 33 ch) 23 20 19 17. 44
46 2134 1200 770 333 400 300 241 199 160 133 115 lol 90 83 76 65 44 33 27 23 20 18 16 46
48 2138 ©1203 768 535 396 301 239 200 162 134 114 99 89 80 4 67 45 33 27 22 19 17 16 48

6-106

TABLE 6-8.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

FIBERGLASS POLYESTER LAMINATES

25-27 OZ. WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 003125 INCHES

LENGTH=8 WIDTH=A a CHeaE
INCHES INCHES
6 8 10 12 14 16 18 20 22 26 26 28 30 32 34 36 42 48 54 60 66 72 78
6 41762514 «1915. «163414801386 01325. -:1282.«s«1252Ss1229s2dd=s1297 «21287 | «1178 «11701164 9128212411136 113211301125 1:24 6
8 4707-2349 «1559. «1210. «1027S's«919S's«SOSs«iOSsiTTOsi«‘“THSSi72HsC“‘TAZ:==CTO- 691 883 TT 663 55 849 645 B41 639 637 Q
10 4266 2538 1503 1066 846 719 641 588 551 525 505 489 477 S67 899 453 438 429 423 419 = 416413411 at
12 4176 2514 1588 1064 777 628 538 479 438 408 387 370 357 347 338 331 316 307 301 297 293 291 oe he
14 4353 2368 1680 1088 767 592 487 420 374 342 318 300 286 275 266 259 243 234 227 223 220 217 215 14
16 4197 2349 1559 1177 «7930-587 = 466390339303, 276) 287) 2k? 2300 2200212196 = 186 180 175 172 169 167 16
18 4176 2413. 1508 «1117 «843. 603. BHT) 319, 279, 25k) 229219 200-190 182164154 147142139 13T 135 us
20 4266 2399 1503 1066 846 634 475 376 311 267 235 211 19 180 169 160 142 131 124 219 126 113° 111 20
22 4178 2350 «1533 = 1045 802 665 495 383 311 261 226 200 181 166 155 145 126 115 107 102 99 76 me EZ
24 4176 2349 «1559 1044 «=o 777s «2B 823-397 316 261022217357 145 13H 114102 94 89 86 83 81 24
26 4219 2384 1519 1060 766 605 508 416 326 265 222 192 169 151 138 127 105 93 85 79 75 3 aN 26
28 4172. 2368 «1502, 1088 = 7767S 5892s BT )~=— 420.—Ss339°-Sss272,—Ss—s225siaSsidSTSsCidBSCdBs1:2D 99 85 7 72 68 65 63 28
30 4176 2346 «1503. 1066 776 586 474 42 354 282 231 194 167 147 131 118 94 80 1 65 61 58 56 30
32 4197 2349 «1520 -1049'Ss«793,'s«587) = 466390 338 = 294 = 238 S198 S169) 47) 130117 90 76 66 60 56 53 51 32
34 4169 2372 1527 1042 «792 «593. #63. 3820327) 289 247) 204 = 172~Ssia B11 88 72 63 56 52 49 47 34
36 41762356 «1508-1084 ~=S777/=S'«s«O3.ss!HS377—Ss319Ss279.S25Ls2ddSsid‘7%6~SS«‘SDSsSs6 86 70 60 53 49 45 43 36
38 4185 2345 1501 1053 769 612 468 375 314 272 242 219 162 154 133° 117 85 68 57 51 46 42 40 38
40 4168 2349 1503 1066 766 600 475 376 311 267 235 211 186 159 136 119 85 67 56 48 44 40 37 40
42 4176 2366 1514 1052 167 592 484 379 310 263 230 205 187 164 140 121 85 66 54 47 42 38 35 42
44 4178 2350 1514 1045 772 588 478 383 311 261 226 200 181 166 144 124 86 65 53 45 40 36 34 a
46 4168 2344 1504 1042 781 586 471 389 313 260 224 197 177 161 148 127 87 65 52 44 39 35 32 46
48 4176 2349 «1500 1644 777 587 466 390 316 261 222 19 (173 157 165 131 88 65 52 43 38 34 31 48
THICKNESS=H EQUALS 063750 INCHES
LENGTH=8 WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 19 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7200 4344 3308 2822 2558 2395 2289 2215 2162 2123 2092 2069 2050 2035 2022 2012 1989 1971 1962 1956 1952 1945 1943 6
8 7200 4059 2694 2091 1775 1588 1469 1388 1330 1288 1255 1230 1211 1194 1181 1170 1147 1131 1121 #1114 1108 1104 1101 8
10 7200 4385 2598 1843 1461 1243 1107 1016 953 907 872 845 824 807 794 782 757 «+742. «2731 + «724 ~«#2718 «71H 711 10
12 7200 4344 2744 1804 1363 1086 929 827 757 706 668 639 617 599 586 572 547 531 520 513 507 $03 499 12
14 eoO 4092 2903 1880 1325 1023 B42 726 647 591 550 519 494 475 460 447 420 404 393 385 379 375 372 14
16 7200 4059 2694 2022 1370 1015 806 674 585 523 478 446 418 397 381 367 339 322 311 9303 297 + 292 °© 289 16
18 7200 4169 2605 1931 1457 1062 802 651 552 483 433 396 368 345 328 3146 284 266 254 246 240 236 232 18
20 7200 4146 2598 1843 1461 1096 820 649 538 461 406 365 335 311 292 277 246 227 214 206 200 «196 ~+# 192 20
22 7250 4061 2648 «61805 1385. «1149. 855 H2si*dS37)——s«S2391Ss3H6 S313 287)~Ss2T)S2S1~Si218)~S—i«a298~S:=«iSSCi«dL'TG—~<“i«é‘«~iTNSC*C«édNSSSC~“C«*‘«iCD 22
24 7200 4059 2694 1804 1343 1086 904 686 546 451 384 336 299 272 250 232 197 1176 163 156 148 163 139 24
26 7220 4119 2624 1831 1324 1046 878 719 563 458 384 331 292 261 238 219 «©1182 160 166 137 130 126 ~~» 122 26
28 7200 4092 2595 1880 1325 1023 @42 726 586 470 389 331 286 256 230 211 #21171 «212168 +~«2133 «2126 +#«117 ~~ «112.~«108 28
30 7200 4054 2598 1843 1341 1013 819 695 611 487 399 335 289 253 226 205 162 «138 «123 «#2113 «2106 ©1023 97 30
32 7200 4059 2626 1813 1370 1015 806 674 585 508 411 342 292 254 224 «2201 186 «131 «2115 +~«106 97 92 88 32
34 7200 4099 2638 1801 1368 1025 800 659 565 500 427 382 297 256 225 200 «1152 «2125 ~~» 108 97 90 a4 80 34
36 7200 4071 2605 1804 1343 1042 802 651 552 483 433 3646 305 261 227 «2200 «2149 + «2121 ~«2103 92 84 78 1% 36
38 7200 4051 2593 1819 1328 1057 808 648 $43 470 418 378 314 267 230 202 «148 117 99 87 79 73 69 38
40 7200 4059 2598 1843 1323 1037 820 649 $38 461 406 365 325 278 235 205 147 115 96 84 75 69 65 40
42 7200 4088 2617 1819 1325 1023 836 654 536 455 397 355 323 283 21 209 1467 114 94 81 72 66 61 a2
44 7200 4061 2616 1805 1334 1018 825 662 $37 451 391 3466 313 287 268 218 148 2113 92 78 69 63 58 a
46 7200 4051 2598 1800 1349 1013 814 673 $60 450 387 340 305 279 «256 219 «©1150 °#«113 90 16 67 60 55 46
48 7200 4059 2593 1804 1343 1015 806 674 $66 451 384 336 299 272 280 226 182° «113 90 75 65 58 53 48

6-107

TABLE 6-8, FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ, WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 004375 INCHES

& NGTH=B
tENCHES. wTNCHES “INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 8400 6898 5254 4483 4062 3803 3635 3518 3434 3371 3322 3285 3256 3231 3211 3194 3158 3130 3116 3106 3100 3088 3085 6
8 B400 6445 4278 3321 2818 2522 2332 2204 2113 2045 1993 1954 1923 1896 18675 1858 1821 1797 1781 1769 1760 1753 1748 8
10 8400 6963 4125 2926 2320 1976 1758 1614 1513 1440 1385 1342 1309 1282 1260 1242 1203 1178 1161 1150 1140 1134 1129 10
abr) 8400 6898 4358 2865 2132 1725 1476 1313 1201 1121 “1061 1015 979 951 928 909 868 843 826 614 805 799 793 12
14 8400 6498 4611 2986 2105 1624 1337 1153 1027 938 373 B23 785 755 730 710 668 641 624 612 602 596 590 14
16 8400 6445 4278 3229 2175 1611 1280 1070 929 830 758 704 663 630 604 583 539 511 493 481 471 464 459 16
18 8400 6621 4137 3066 2314 1655 1273 1034 876 766 687 629 584 549 521 498 451 423 404 391 382 375 369 18
20 8400 6584 4125 2926 2320 1741 1302 1031 854 732 644 580 531 493 464 440 390 360 341 327 318 310 305 20
22 8400 6449 4206 2866 2200 1824 1358 1051 852 717 620 550 497 456 424 398 346 314 294 280 270 263 257 22
24 8400 64465 4278 2865 2132 1725 1435 1089 867 716 610 533 475 431 397 369 313 280 259 245 235 227 221 24
26 8400 6541 4167 2907 2103 1661 1394 1142 894 727 610 526 463 415 378 348 289 254 232 218 207 199 194 26
28 8400 6498 4121 2986 2105 1624 1337 1153 931 T47 618 526 458 406 366 334 271 235 212 196 185 178 172 28
30 8400 6437 4125 2926 2130 1609 1301 1104 971 774 633 532 458 402 359 325 258 219 195 179 168 160 154 30
32 8400 6445 4170 2879 2175 1611 1280 1070 929 807 653 544 463 403 356 320 248 208 182 166 154 146 139 32
34 8400 6509 4189 2860 2172 1627 1271 1047 898 794 678 559 472 407 357 318 241 198 172 155 143 134 128 34
36 8400 6464 4137 2865 2132 1655 1273 1034 876 766 687 578 484 414 360 318 237 192 164 146 133 125 118 36
38 8400 6434 4118 2889 2109 1679 1284 1029 862 746 663 601 499 423 366 321 234 187 158 139 126 127, 110 3e
40 8400 6445 4125 2926 2101 1646 1302 1031 854 732 644 580 517 435 — 373 326 233 183 152 133 119 110 103 40
42 8400 6492 4155 2888 2105 1624 1327 1039 851 722 630 563 512 449 383 332 234 180 149 128 114 104 97 42
44 8400 6449 4153 2866 2119 1612 1311 1051 852 717. 620 550 497 456 394 339 235 179 146 124 110 100 92 44
46 8400 6433 4126 2859 2143 1608 1292 1068 $58 715 614 540 485 442 407 349 238 179 144 121 106 96 88 46
48 8400 6445 4117 2865 2132 1611 1280 1070 867 716 610 533 475 431 397 359 242 179 142 119 103 92 84 48
THICKNESS=H EQUALS 065000 INCHES
LENGTH=8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 a4 36 42 48 54 60 66 72 78
6 9600 9600 7842 6692 6063 5677 5426 5251 5125 5032 4959 4904 4860 4823 4794 4768 4714 4673 4651 4637 4628 4609 4605 6
8 9600 9600 6386 4957 4206 3764 3481 3290 3154 3052 2975 2916 2870 2831 2799 2773 2718 2682 2658 2640 2627 2616 2609 8
10 9600 9600 6158 4368 3464 2946 2624 2499 2259 2150 2067 2003 1953 1913 1681 1854 1795 1759 1734 1717 1702 1693 1685 10
12 9600 9800 6505 4276 3183 2574 2203 1960 1793 1673 1584 1516 1662 1419 1385 1356 1296 1258 1232 1215 1202 1192 1184 12
14 9600 9600 6882 4457 3142 2425 1996 1721 1534 1401 1303 1229 1172 1127 1090 1060 997 957 931 913 899 889 881 14
16 9600 9600 6386 4820 3247 2405 1910 1597 1337 1239 1132 1052 990 941 902 870 804 763 736 718 704 693 685 16
18 9600 9600 6176 4576 3454 2471 1900 1544 1308 1144 1026 938 871 819 777 744 674 631 603 583 569 559 551 18
20 9600 9600 6158 4368 3464 2598 1944 1539 1274 1092 962 866 793 737 692 656 582 537 508 468 474 463 455 20
22 9600 9600 6278 4279 3284 2723 2027 1569 1272 1070 926 821 742 681 633 594 516 469 439 418 404 393 384 22
24 9600 9600 6386 4276 3183 2574 2142 1626 1294 1069 911 796 710 644 592 551 467 418 387 366 350 339 331 24
26 9600 9600 6221 4340 3140 2479 2080 1705 1334 1085 911 785 691 620 564 520 431 380 347 325 309 298 289 26
28 9600 9600 6151 4457 3142 2425 1996 1721 1390 1114 923 7385 683 606 546 499 405 350 316 293 277 265 256 28
30 9600 9600 6158 4368 3179 2402 1941 1648 1449 1155 945 795 684 601 536 485 385 327 292 268 251 239 230 30
32 9600 9600 6224 4298 3247 2405 1910 1597 1386 1205 975 812 692 601 532 478 370 310 272 247 230 218 208 32
34 9600 9600 6253 4269 3243 2429 1897 1563 1340 1185 1013 835 705 607 533 474 360 296 257 231 213 200 191 34
36 9600 9600 6176 4276 3183 2471 1900 1544 1308 1144 1026 863 723 618 538 475 354 286 245 218 199 186 176 36
38 9600 9600 6146 4312 3149 2506 1916 1537 1286 1114 990 897 745 632 546 479 350 278 235 207 188 17% 164 38
40 9600 9600 6158 4368 3136 2457 1944 1539 1274 1092 962 B66 771 650 357 486 348 273 228 198 178 164 153 40
42 9600 9600 6203 4311 3142 2428 1981 1551 1270 1078 941 B41 765 670 572 495 349 269 222 191 170 156 145 42
44 9600 9600 6200 4279 3163 2407 1957 1569 1272 1070 926 821 742 681 588 507 351 267 217 1865 164 149 137 4a
46 9600 9600 6159 4268 3199 2401 1929 1595 1280 1067 916 806 724 660 607 520 355 267 214 181 158 143 131 46
48 9600 9600 6145 4276 3183 2405 1910 1597 1294 1069 911 796 710 644 592 536 361 267 212 177 154 138 126 48

6-108

TABLE 6-8.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

FIBERGLASS POLYESTER LAMINATES

THICKNESS*H EQUALS 065625 INCHES
6 LENGTH-8
“INCHES “INCHES INeHeS
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 9529 8632 8084 7725 7477 7298 7165 7061 6983 6920 6867 6825 6789 6712 6653 6623 6602 6589 6563 6556 6
8 1080C 10600 9093 7058 5989 5360 4957 4684 4490 4346 4236 4152 4086 4031 3986 3948 3869 3819 3785 3759 3740 = 3725 3715 8
10 10800 10800 8767 6219 4932 4195 3737 3430 3216 3061 2943 2852 2781 2724 2678 2639 2556 2504 2469 2444 2423 2411 2400 10
12 10800 10800 9261 6088 4532 3665 3157 2791 2553 2382 2255 2158 2082 2021 1972 1931 1845 1791 1755 1730 1711 1697 1685 12
14 10800 10800 9799 6347 4673 3453 2842 2450 2183 1994 1856 1750 1669 1604 1552 1509 1419 1363 1326 1300 1280 1266 1255 14
16 10800 10800 9093 6863 4623 3425 2720 2273 1974 1765 1612 1497 1409 1340 1284 1239 1145 1086 1048 1022 1002 987 976 16
18 10800 10800 8796 6516 4917 3518 2706 2198 1862 1629 1461 1336 1241 1166 1107 1059 959 898 658 831 811 796 785 16
20 10800 10800 8767 6219 4932 3700 2768 2192 1814 1555 1370 1233 1129 1049 985 934 829 765 724 695 675 660 646 20
22 10800 10800 8938 6092 4676 3878 2886 2235 1811 1523). 1319 1169 1056 969 901 846 735 668 625 596 575 559 S47 ad
24 10800 10800 9093 6088 4532 3665 3050 2315 1842 1522 1297 1133 1010 916 B43 784 665 596 551 520 499 483 471 24
26 10800 10800 8857 6179 4470 3530 2962 2427 1899 1545 1297 1118 984 882 803 740 614 541 494 463 440 424 411 26
28 10800 10800 8759 6347 4473 3453 2842 2450 1979 1587 1314 1118 o73 863 778 711 576 499 450 417 394 377 365 28
30 10800 10800 8767 6219 4526 3420 2764 2346 2064 1644 1346 1132 974 855 163 691 548 466 415 381 357 340 327 30
32 10800 10800 8863 6119 4623 3425 (2720 2273) 1978 Ivl65 2389 1156 985 856 157 680 527 441 388 352 328 310 296 32
34 10800 10800 8903 6079 4617 3459 2702 2226 1909 1688 1442 1189 1003 865 758 675 513 422 366 329 304 285 271 34
36 10800 10800 8793 6088 4531 3518 2706 2198 1862 1629 1461 1229 1029 880 765 676 504 407 349 310 284 265 251 36
38 10800 10800 8751 6139 4483 3568 2729 2188 1832 1586 1409 1277 1061 900 777 682 498 396 335 295 267 248 233 38
40 10800 10800 8767 6219 4465 3498 2768 2192 1814 1555 1370 1233 1098 925 794 692 496 389 324 282 254 234 219 40
42 10800 10800 8831 6138 4473 3453 2821 2208 1808 1534 1340 1197 1089 954 814 705 497 384 316 272 243 222 206 42
44 10800 10800 8827 6092 4503 3427 2786 2235 1811 1523 1319 1169 1056 969 837 722 500 381 310 264 233 212 196 44
46 10800 10800 8769 6076 4554 3418 2746 2271 1823 1519 1305 1148 1030 940 864 741 506 380 305 258 226 203 187 46
48 10800 10800 8750 6088 4532 3425 2720 2273 1842 1822 1297 1133 1010 916 843 763 514 381 302 253 219 196 179 48
THICKNESS=H EQUALS 046250 INCHES
LENGTH-8 WIDTH=A LENGTH=6
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 12000 12000 12000 12000 11841 11088 10597 10256 10010 9829 9686 9579 9493 9420 9363 9313 9207 9127 9085 9057 9039 9003 8993 6
8 12000 12000 12000 9682 8215 7353 6799 6425 6159 5961 5811 5695 5606 5529 5467 5416 5308 5238 5192 5157 5131 5110 5096 8
10 12000 12000 12000 8531 6765 5755 5126 4706 4412 4199 4037 3912 3815 3737 3674 3621 3507 3435 3386 3353 3324 3308 3292 10
12 12000 12000 12000 8352 6216 5028 4303 3829 3503 3268 3094 2960 2856 2772 2705 2649 2531 2457 2407 2373 2347 2328 2312 12
14 12000 12000 1200C 8706 6136 4736 3899 3361 2995 2736 2545 2401 2289 2200 2129 2070 1946 1870 1819 1783 1756 1736 1722 146
16 12000 12000 12000 9414 6341 4698 3731 3118 2708 2421 2211 2054 1933 1838 1762 1700 1571 1490 1438 1401 1374 1354 1339 16
18 12000 12000 12000 8938 6745 4826 3712 3016 2554 2235 2004 1833 1702 1599 1518 1452 1316 1232 1177 1140 1112 1092 1076 18
20 12000 12000 12000 8531 6765 5075 3797 3007 2489 2133 1879 1691 1549 1439 1351 1281 1137 1050 993 954 926 905 889 20
22 12000 12000 12C00 8357 6414 5319 3959 3065 2485 2089 1809 1604 1449 1330 1236 1161 1008 916 857 817 788 767 751 22
24 12000 12000 12000 9352 6216 5028 4184 3176 2527 2088 1779 1554 1386 1257 1156 1076 913 817 755 714 684 662 646 24
26 12000 12000 12000 8476 6132 4842 4063 3329 2605 2119 1779 1533 1350 1211 1102 1016 843 742 678 634 604 581 564 26
28 12000 12000 12000 8706 6136 4736 3899 3360 2714 2176 1803 1534 1335 1184 1067 975 790 684 617 572 541 518 500 28
30 12000 12000 12009 8531 6209 4692 3792 3218 2831 2256 1846 1552 1336 1173 1047 948 752 639 570 523 490 467 449 30
32 12000 12000 12000 8394 6341 4698 3731 3118 2708 2353 1905 1585 1351 1174 1039 933 724 605 532 483 450 425 407 32
34 12000 12000 12000 8338 6333 4745 3706 3053 2618 2315 1978 1630 1376 1186 1040 926 704 579 502 451 416 391 372 34
36 12000 12060 12000 8352 6216 4826 3712 3016 2554 2235 2004 1686 1412 1206 1050 928 691 559 478 425 389 363 344 36
38 12000 12000 12000 8422 6150 4894 3743 3001 2513 2175 1933 1752 1455 1234 1066 936 683 544 459 404 367 340 320 38
40 12000 12000 12000 8531 6125 4799 3797 3007 2489 2133 1879 1691 1506 1269 1089 949 681 533 445 387 348 320 300 40
42 12000 12000 12000 8420 6136 4736 3869 3029 2480 2105 1838 1642 1494 1309 1116 967 682 526 433 373 333 304 283 42
44 12000 12000 12000 6357 6177 4701 3822 3065 2485 2089 1809 1604 1449 1330 1149 990 686 522 425 362 320 290 268 44
46 12000 12000 12000 8335 6247 4689 3767 3115 2501 2084 1790 1575 1414 1290 1185 1016 694 521 419 353 310 279 256 46
48 12000 12000 12000 8352 6216 4698 3731 3118 2527 2088 1779 1554 1386 1257 1156 1046 705 522 415 346 301 269 246 48

G09)

TABLE 6-9.

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ, WOVEN ROVING - LOADED EDGES SIMPLY SUPPORTED -
REMAINING EDGES CLAMPED

PHYSICAL CONSTANTS;
Ex = 181x106 PS|
Ey = 1.54x10® PSI
p Gxy 4 0.45x10® PSI
THICKNESS“H EQUALS 00625 INCHES Gap = Ora = 0819
TINCHES, “TRCHES MINCHES
é a 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 68 37 23 iz, 14 13 12 11 ll 10 10 10 10 10 10 9 9 9 9 9 9 9 9 6
a 64 38 25 16 12 10 8 7 rf 7 6 6 6 6 6 6 o G 5 5 5 5 5 8
10 65 36 25 18 12 9 7 6 S 1 5 4 4 4 4 CP 4 4 3 3 3 3 3 10
12 64 37 23 17 13 9 7 6 5 4 4 4 3 3 3 3 3 3 Z 2 2 2 2 12
14 64 26 23 16 13 10 7 6 5 4 3 3 3 3 3 2 2 2 2 2 2 2 2 14
16 64 36 24 16 12 lo 8 6 5 4 3 3 2 2 2 2 2 2 1 1 1 1 16
18 64 36 23 16 12 9 8 7 5 4 3 3 3 2 4 2 2 1 1 1 1 1 a 18
20 64 36 23 16 12 9 7 6 5 4 4 3 3 2 2 2 1 1 sl 1 1 1 1 20
22 63 36 23 16 12 9 i 6 5 5 4 3 3 2 2 2 1 1 1 1 1 1 1 22
24 64 36 23 16 12 9 7 6 5 4 4 3 3 2 1 1 1 1 1 1 a 24
26 63 36 23 16 12 9 7 6 5 4 4 3 3 2 2 2 1 1 1 1 1 1 1 26
28 64 36 23 16 12 9 7 6 5 4 3 3 3 3 2 2 1 1 1 1 1 1 1 28
30 63 36 23 16 12 9 7 6 5 4 3 3 3 3 2 2 1 1 2 1 1 1 1 30
32 64 36 23 16 12 9 7 6 5 4 3 3 3 2 1 1 2 1 1 1 ° 32
34 63 36 23 16 12 9 v 6 5 4 3 3 3 2 2 1 1 a 1 1 C) ° 34
36 64 36 23 16 12 9 7 6 5 4 3 3 3 2 2 2 1 1 1 1 1 0 ° 36
38 63 36 23 16 12 9 7 6 5 4 3 3 3 2 2 2 2 1 1 1 a to) ° 38
40 63 36 23 16 12 9 7 6 5 4 4 3 2 2 1 1 1 1 1 ) 0 40
42 63 36 23 16 12 9 z, 6 5 4 3 3 3 2 2 2 1 1 it 1 1 0 ° 42
44 63 36 23 16 12 9 7 6 5 4 3 3 3 2 2 2 1 a 1 1 1 0 ° 44
46 63 36 23 16 12 9 7 6 5 4 3 3 3 2 ri 2 1 1 1 1 1 ° ° 46
48 63 36 23 16 12 9 7 6 5 4 3 3 3 2 2 2 1 1 1 1 1 ° ° 48
THICKNESS-H EQUALS 061250 INCHES
LENGTH=8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 19 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 546 297 183 137 114 101 93 88 a5 82 81 79 78 7 76 76 75 74 73 73 73 72 72 6
8 509 307 197 127 94 77 67 60 56 53 50 49 47 46 46 45 43 43 42 42 41 41 41 8
10 5168 285 197 141 95 71 58 49 44 40 37 35 34 32 32 31 29 28 28 27 27 27 27 10
12 509 297 183 137 106 7% 57 46 39 34 31 28 27 25 24 23 22 21 20 20 19 19 19 12
14 511 287 1385 128 100 82 60 46 38 32 28 25 23 21 20 19 17 16 15 15 14 14 14 14
16 509 286 199 127 94 7 66 49 39 32 27 24 2. 19 18 17 14 13 12 12 ll ll ll 16
18 508 290 183 132 93 73 61 53 41 33 27 23 20 18 16 15 13 ll 10 10 9 9 9 18
20 599 285 183 130 95 124 58 49 44 35 28 24 20 18 16 14 12 10 9 8 8 8 u 20
22 507 288 187 127 98 72 56 47 41 36 30 25 21 18 16 14 ll 9 8 7 7 7 6 22
24 509 286 183 127 94 74 57 46 39 34 31 26 22 19 16 14 10 9 7 7 6 6 6 24
26 507 285 183 130 93 74 58 46 3u 33 29 26 23 19 17 14 10 8 ua 6 6 5 5 26
28 509 287 185 128 93 72 59 46 38 32 28 25 23 21 17 15 10 8 7 6 5 5 4 28
3c 507 285 183 127 95 1 58 47 38 32 27 24 22 20 18 16 ll 8 6 5 5 4 4 30
32 509 286 182 127 94 72 57 47 39 32 27 24 21 19 18 16 11 8 6 5 5 4 4 32
34 506 286 184 129 93 73 56 46 40 32 27 23 21 19 17 16 uy 8 6 5 4 4 4 34
36 508 285 183 127 93 73 57 46 39 33 27 23 20 18 16 15 12 8 6 5 4 4 3 36
33 506 236 182 127 94 72 57 46 38 33 28 23 20 18 16 15 12 8 6 5 4 4 3 38
40 5028 235 182 127 94 7 58 46 38 32 28 24 20 18 16 16 12 9 6 5 4 4 3 40
42 506 285 183 128 93 71 57 46 38 32 28 24 21 18 16 14 ll 9 ui 5 4 * 3 42
44 507 285 182 127 93 72 56 47 38 32 27 24 21 18 16 14 ll 9 7 5 4 4 3 44
46 507 285 183 127 93 72 56 46 38 32 27 24 21 18 16 14 ql 9 7 5 4 4 3 46
4e 507 286 183 127 94 1 57 46 39 32 27 24 21 19 16 14 10 9 7 5 4 4 3 48

25-27 OZ, WOVEN ROVING - LOADED EDGES SIMPLY SUPPORTED -

TABLE 6-9.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

FIBERGLASS POLYESTER LAMINATES

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 001875 INCHES

a LENGTH-B
“INCHES, “INCHES INCHES
6 8 10 12 4 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 1844 1002 618 461 384 341 315 298 286 278 272 267 263 260 258 256 252 249 247 246 245 244 244 6
8 1716 = 1037 665 429 318 259 225 202 188 177 170 164 160 156 154 rE | 147 144 142 141 140 139 138 8
10 1750 962 664 475 321 240 194 166 147 135 125 119 114 110 106 104 99 96 94 92 91 90 90 10
12 1716 = 1002 618 461 356 250 191 154 131 115 104 96 90 85 82 79 73 70 67 66 65 64 63 12
14 1725 970 624 431 339 278 202 156 127 108 94 85 78 72 68 65 58 54 52 50 49 48 47 14
16 1716 965 641 429 318 259 222 166 131 107 91 80 72 65 6c 56 49 44 42 40 39 38 37 16
18 1716 980 618 445 314 245 205 180 139 ill 92 79 69 61 56 51 43 38 35 33 32 31 30 18
20 1716 962 618 437 321 240 194 166 147 119 96 80 69 60 54 49 39 34 30 28 27 26 25 20
22 1712 971 632 428 330 243 190 158 137 123 102 B4 71 61 53 48 37 31 27 25 23 22 22 22
24 1716 965 618 429 318 250 191 154 131 115 104 89 74 63 54 48 35 29 25 22 21 20 19 24
26 i711 963 616 438 314 249 195 154 128 110 98 89 78 66 56 49 35 28 23 21 19 18 17 26
28 1716 970 624 431 315 243 201 156 127 108 94 85 78 69 59 50 35 27 22 19 17 16 15 28
30 1710 962 618 427 321 240 194 160 128 107 92 82 74 68 62 53 36 27 22 18 16 15 4 30
32 1716 965 616 429 318 241 191 160 131 107 91 80 71 65 60 56 37 27 21 18 16 14 13 32
34 1709 964 620 435 315 245 190 156 134 109 91 79 ri) 63 57 53 38 27 21 17 15 13 12 34
36 1716 962 618 429 314 245 191 154 131 lll 92 79 69 61 56 51 40 28 21 17 15 13 12 36
38 1710 967 615 427 316 242 193 154 129 112 94 79 68 60 54 50 41 29 21 17 14 12 ll 38
40 1714 962 618 429 318 240 194 154 127 109 96 80 69 60 54 49 39 30 22 a | 14 12 ql 40
42 1710 964 618 431 315 241 192 156 127 108 94 82 69 60 53 48 38 31 22 17 14 12 10 42
44 1712 963 615 428 314 243 190 158 128 107 93 82 71 61 53 48 37 31 23 18 14 12 10 44
46 1710 962 617 427 315 243 190 156 129 107 92 al 72 62 54 47 36 30 24 18 14 12 10 46
48 1711 965 618 429 317 241 191 154 131 107 91 80 7 63 54 48 35 29 25 18 15 12 10 48
THICKNESS=H EQUALS 0+2500 INCHES
LENGTH=B WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 3950 2374 1464 1093 911 809 T47 707 679 659 644 633 624 617 611 607 597 589 586 583 581 578 577 6
8 3950 2459 1575 1017 755 615 532 480 445 420 402 389 379 371 364 359 348 341 337.334 331 329 328 8
10 3950 2280 1574 1125 760 570 461 393 349 319 297 281 269 260 252 246 234 226 222 218 216 214 213 10
12 3950 2374 1464 1093 845 594 452 366 311 273 247 228 213 202 194 187 173 165 160 156 153 152 150 12
14 3950 2300 1480 1022 803 658 478 370 301 256 224 201 184 171 161 153 137 128 123 119 116 114 112 14
16 3950 2288 1519 1017 755 615 527 394 310 254 216 189 169 154 142 133 115 105 99 nbs 92 90 6B 16
18 3950 2323 1464 1055 745 581 486 426 330 264 216 186 163 145 132 121 101 90 83 79 75 TE 72 18
20 3950 2280 1465 1037 760 570 461 393 349 281 228 190 163 142 127 115 92 80 72 67 64 62 60 20
22 3950 2302 1499 1015 782 576 451 375 325 291 242 199 167 144 126 113 87 73 65 59 56 53 51 22
24 3950 2288 1464 1017 155 594 452 366 all 273 247 211 175 148 128 113 84 68 59 53 49 47 45 24
26 3950 2282 1460 1039 745 589 462 365 303 262 233 212 186 155 133 115 83 6s 55 bx 45 42 40 26
28 3950 2300 1480 1022 747 575 475 370 301 256 224 201 184 164 139 119 83 64 53 46 41 38 36 28
30 3950 2280 1464 1013 760 570 461 380 304 253 218 193 175 161 147 125 84 63 51 44 39 35 a3 30
32 3950 2288 1459 1017 755 572 453 380 310 254 216 189 169 154 142 132 87 64 50 42 37 33 31 32
34 3950 2284 1470 1030 746 580 450 371 319 258 216 186 165 149 136 126 90 64 50 41 35 32 29 34
36 3950 2280 1464 1017 745 581 452 366 311 264 218 186 163 145 132 lai 94 66 50 41 35 30 27 36
38 3950 2292 1459 1013 750 573 458 365 305 265 222 187 162 143 129 118 96 68 51 41 34 29 26 38
40 3950 2280 1465 1017 755 570 461 366 302 259 228 190 163 142 127 115 92 70 52 41 34 29 25 40
42 3950 2284 1464 1022 747 571 454 370 301 256 224 194 164 143 126 114 89 73 53 41 33 28 25 42
44 3950 2283 1459 1015 744 576 451 375 303 254 220 195 167 144 126 113 87 73 55 42 34 28 24 44
46 3950 2280 1462 1013 746 577 450 369 305 253 217 191 a7 146 127 113 85 70 56 43 34 28 24 46
48 3950 2288 1464 1017 751 572 452 366 310 254 216 189 169 148 128 113 84 68 59 44 34 28 24 48

syEIE AL

TABLE 6-9. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ, WOVEN ROVING - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS-H EQUALS 003125 INCHES

STNMES “TRches “INCHES,
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 76
6 4940 4637 2860 2134 1779 1580 1460 1381 1326 1287 1258 1236 1219 1205 1194 1185 1165 1151 1144 1138 1135 1130 1128 6
8 49460 4803 3077 1987 1474 1201 1039 937 869 821 786 760 740 724 711 701 680 666 658 651 647 643 641 8
10 4940 4452 3074 2197 1485 1113 900 768 682 623 580 549 525 507 493 481 457 442 433 426 421 418 415 10
12 4940 4637 286C 2134 1650 1159 883 715 607 534 482 445 417 395 378 365 338 322 312 305 300 296 293 12
14 4940 4492 2891 1996 1568 1285 934 723 589 499 437 392 359 334 314 299 268 250 239 232 226 223 220 14
16 4940 4470 2966 1986 1474 1201 1029 769 605 497 422 369 330 300 278 260 225 205 193 185 179 175 172 16
18 4940 4537 2869 2061 1454 1134 949 833 645 515 426 364 318 284 257 237 198 176 162 153 147 143 140 18
20 4940 4452 2861 2025 1485 1113 900 768 682 549 445 371 318 278 248 225 180 156 141 131 125 120 117 20
22 4940 4496 2927 1982 1527 1124 881 732 635 569 474 388 326 281 247 220 170 142 126 116 109 104 100 22
24 4940 4469 2860 1986 1474 1159 883 715 607 534 482 413 342 290 251 22l 164 133 115 104 97 91 87 24
26 4940 4456 2852 2029 1455 1151 902 713 592 511 455 414 363 304 259 225 162 128 108 96 88 82 78 26
28 4940 4492 2891 1996 91459-1123 929 723 589 499 437 392 359 321 271 233 162 125 103 90 81 75 70 28
30 4940 4452 2860 1979 1485 1113 900 742 593 495 426 378 342 314 287 244 165 124 100 85 76 69 64 30
32 4940 4470 2850 1986 1474 1117 885 742 605 497 422 369 330 300 278 257 170 124 98 82 72 65 60 32
34 4940 4462 2871 2012 1457 1133 879 724 623 504 422 364 322 290 266 247 176 126 98 80 69 62 56 34
36 4940 4454 2860 1986 1454 1134 883 715 607 515 426 364 318 284 257 237 183 129 98 79 67 59 54 36
38 4940 4477 2849 1979 1464 1119 894 mle, 596 518 434 366 317 280 252 230 188 133 99 Te} 66 58 51 38
40 4940 4452 2861 1986 1474 1113 900 715 590 506 445 371 318 278 248 225 180 137 101 79 66 56 50 40 |
42 4940 4461 2860 1996 1459 1115 887 723 589 499 437 379 321 279 247 222 174 143 104 89 65 55 49 42 |
44 4940 4459 2849 1982 1454 1124 881 732 591 495 429 382 326 281 247 220 170 142 107 82 66 BS 48 44 |
46 4940 4453 2855 1979 1457 qa27! 880 721 597 495 424 374 333 285 248 220 166 137 110 83 66 55 47 46
48 4940 4469 2860 1986 1467 1117 883 715 605 497 422 269 330 290 251 221 164 133 114 35 67 55 47 48
THICKNESS=H EQUALS 003750 INCHES
LENGTH=B WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7200 7200 4942 3688 3074 2731 2522 2386 2292 2224 2174 2136 2106 2082 2063 2047 2013 1989 1976 1567 1961 1952 1949 6
8 7200 7200 5316 3433 2548 2075 1796 1620 1502 1419 1358 1313 1279 1251 1229 1211 #1174 1151 1137 1126 1118 1112 1107 8
10 7200 7200 5311 3797 2565 1923 1555 1328 1179 1076 1003 949 908 876 851 831 789 764 748 737 728 723 718 10
12 7200 7200 4942 3688 2851 2003 1526 1236 1048 922 833 768 720 683 654 631 584 556 538 527 518 512 507 12
14 7200 7200 4995 3450 2710 2220 1613 1249 1017 B62 755 677 620 577 543 516 463 433 413 401 391 385 380 14
16 7200 7200 5125 3433 2548 2075 1779 1329 1046 858 729 637 569 519 480 449 389 355 334 320 310 303 298 16
18 7200 7200 4942 3561 2513 1960 1639 1439 12115 890 737 628 549 490 445 410 342 303 280 265 255) 247 242 18
20 7200 7200 4943 3499 2565 1923 1555 1328 1179 949 768 641 549 481 429 389 311 269 244 227 216 208 202 20
22 7200 7200 505¢ 3425 2638 1942 1522 1264 1097 983 818 671 564 486 426 381 293 246 218 200 188 179 173 22
24 7200 7200 4942 3433 2548 2003 1526 1236 1048 922 833 713 591 501 433 381 283 231 200 180 167 158 151 24
26 7200 7200 49286 3505 2513 1988 1558 1232 1024 BB4 786 715 626 524 448 389 279 221 187 166 Pol 141 134 26
28 7200 7200 4995 3450 2522 1940 1605 1249 1017 B62 755 677 620 555 469 403 280 216 178 155 140 129 121 28
30 7200 7200 4942 3419 2565 1923 1555 1282 1025 855 737 652 590 543 495 422 285 214 173 148 131 120 lll 30
32 7200 7200 4924 3433 2548 1931 1528 1281 1046 858 729 637 569 519 480 445 293 215 170 142 124 112 104 32
34 7200 7200 4961 3477 2518 1959 1519 1252 1076 870 729 629 556 501 459 427 304 218 169 139 120 107 97 34
36 7200 7200 4942 3432 2513 1960 1526 1236 1048 890 737 628 549 490 445 410 317 223 170 137 116 102 93 36
38 7200 7200 4923 3419 2530 1934 1544 1231 1030 894 750 632 547 483 435 397 325 229 172 137 114 99 89 38
40 7200 7200 4943 3433 2548 1923 1555 1236 1020 875 768 641 549 481 429 389 311 237 175 137 113 97 86 40
42 7200 ©7200 4942 3450 2521 1927 1533 1249 1017 B62 755 654 555 482 426 383 301 247 179 139 113 96 B4 42
44 7200 7200 4923 3424 2512 1942 1522 1264 1021 856 742 660 564 486 426 381 293 246 185 141 113 95 82 44
46 720C 7200 4934 3420 2517 1947 1520 1246 1031. 855 733 646 576 492 429 380 287 237 191 144 115 95 81 46
48 7200 7200 4942 3433 2535 1931 1526 1236 1046 858 729 637 569 501 433 381 283 231 198 148 116 95 81 48

6-112

TABLE 6-9. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ, WOVEN ROVING - LOADED EDGES SIMPLY SUPPORTED

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 04375 INCHES

MINCHES. “INCHES “INCHES.
6 € 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 8400 6400 7848 5857 4881 4337 4005 3788 3639 3532 3452 3392 3345 3306 3276 3251 3197 3159 3138 «3124 = 3114 = 3100-3095 6
8 3400 8400 8400 5451 4046 3294 2852 2572 2385 2253 2157 2085 2031 1987 1952 1923 1865 1828 1805 1788 1775 1765 1758 L
10 8400 B4CO 8400 6030 4074 3054 2470 2108 1872 1709 1593 1507 1442 1391 1352 1320 1253 1214 1168 1170 1156 1148 1140 10
12 400 8400 7808 5857 4528 3181 2423 1962 1665 1466 1323 1220 1243 1084 1038 1001 927 883 855 836 822 813-805 12
14 8400 8400 7933 5478 4303 3526 2562 1983 1615 1370 1199 1076 985 916 662 820 736 687 657 636 621 611 603 14
16 8400 8400 8139 5451 4046 3294 2824 2111 1661 1363 1158 loll 904 824 762 713 618 563 530 508 492 481 472 16
18 8400 8400 7848 5655 3990 3112 2603 2285 1770 1614 1170 998 872 778 (707 651 542 482 445 421 404 — 392 384 18
20 8400 8400 7849 «5557 «4074 «= 3054 = 2470s 2108 ~=sa872Ss«1507 =«1220.«1018 = 872764 BL 617 495 427 387 360 343 330 320 20
22 8400 8400 8032 5438 4189 3085 2417 2008 1743 1562 1299 1065 896 771 677 604 465 390 346 317 298 284 274 22
24 8400 ©8400 7848 «= 45451 4046 = 3181 = 2423-1962 «16651464 «= :323«1:32Ss«938B 795 688 606 459 366 317 286 265 250 240 24
26 8460 8400 7826 5566 3991 3157 2474 1957 1626 1403 1248 1135 995 833 711 618 443 351 297-263. 240225 213 26
28 8400 8400 7933 5478 4005 3041 2548 1983 1615 1369 1199 1076 985 881 745 640 445 342 283. «246 = 222 205 193 28
30 8400 8400 7848 5430 4074 3054 2470 2036 1628 1357 1170 1036 937 862 786 670 453 339 274 234 208 190 177 30
32 8400 8400 7819 5451 4046 3066 2427 2035 1660 1363 1158 loll 904 824 762 706 465 341 270-226 198 178 164 32
34 8400 8400 7877 5521 3998 3110 2413 1987 1708 1382 1158 999 883 796 730 678 482 346 268 221 190 169 155 34
36 8400 8400 7848 5450 3990 3112 2423 1962 1665 1416 1170 998 872 778 ‘107 651 503 353. 269° = 218 185 163 147 36
38 8400 8400 7818 5429 4017 3071 2452 1955 1635 1420 1191 1004 869 768 691 631 516 364 272 217 182 158 ds Be
40 8400 8400 7869 5451 4046 3054 2470 1962 1619 1389 1220 1018 872 764 681 617 495 377 «278 = 218 180 154 137 40
42 8400 8400 7848 5478 4004 3060 2435 1983 1615 1369 1199 1039 881 765 677 609 478 392 285 220 179 152 133 42
44 8400 8400 7817 5438 3988 3085 2417 2008 1622 1360 1178 1047 896 771 677 604 465 390 293 224 180 151 131 44
46 8400 8400 7835 5430 3997 3092 2413 1979 1637 1358 1164 1026 915 781 681 603 456 377 303 229 182 151 129 Ede
48 8400 8400 7848 5451 4026 3066 2423 1962 1660 1363 1158 1011 904 795 688 606 450 366 314 2.235 185 151 129 48
THICKNESS“H_ EQUALS 065000 INCHES
LENGTH=B WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9600 9600 9600 8743 7286 6473 5979 5655 5432 5273 5153 5063 4993 4936 4890 4852 4773 4716 4684 4663 4649 4627 4619 6
8 9600 9600 9600 8137 6039 4918 4257 3839 3560 3363 3220 3113 3032 2966 2914 2871 2784 2729 2694 2668 2649 2635 2624 8
10 9600 9600 9600 9001 6081 4559 3687 3147 2794 2551 2377 2249 2152 2077 2018 1970 1871 1812 1773 1747 1726 1713 1702 10
12 9600 9600 9600 8743 6759 4749 3617 2929 2485 2186 1975 1621 1706 1618 1550 1495 1384 1318 1276 1248 1228 1213 1201 12
14 9600 9600 9600 8177 6423 5263 3824 2961 2411 2044 1789 1606 1470 1367 1287 1224 1098 1026 980 950 927 912 900 14
16 9600 9600 9600 8137 6039 4918 4216 3150 2479 2034 1728 1510 1350 1229 1137 1064 922 841 791 758 735 «718 705 16
18 600 9600 9600 8442 5957 4646 3886 «3410 2643-2110 «1747 «agg s:1302S1161 «1055 971 810 719 664 628 604 586 573 18
20 9600 9600 9600 8295 6081 4559 3686 3147 2794 2250 1821 1520 1302 1140 1017 ~~ 922 738 638 577 538 5ll 492 478 20
22 9600 9600 9600 8117 6254 4604 3608 2997 2601 2331 1939 1590 1337 1151 1010 902 695 583 516 473 445 424 409 22
24 9600 9600 9600 8137 6039 4749 3616 2929 2485 2186 1975 1690 1400 1187 1027 904 671 546 473 427 396 374 358 24
26 9600 9600 9600 8309 5958 4713 3693 2921 2426 2095 1862 1694 1485 1243 1062 923 662 524 443 392 359 335 318 26
28 9600 9600 9600 8177 5978 4599 3803 2960 2411 2044 1789 1606 1470 1316 1111 956 664 511 423 367 331 306 = 288 28
30 9600 9600 9600 8105 6081 4559 3687 3039 2431 2026 1747 1546 1399 1287 1174 1000 676 507 410 350 310 283 264 30
32 9600 9600 9600 8137 6039 4577 3623 3037 2478 2034 1728 1510 1350 1229 1137 1054 695 509 403 337 295 266 245 32
34 9600 9600 9600 8241 5968 4643 3602 2967 2550 2063 1729 1a92 1319 1189 1089 1011 720 516 400 330 284 253 231 34
36 9600 9600 9600 8135 5957 4646 3616 2929 2485 2110 1747 1489 1302 1161 1055 971 751 528 402 325 276 243 219 36
38 9600 9600 9600 8104 5996 4584 3661 2918 2441 2120 1778 1499 1297 1146 1031 942 770 543 407 324 271 236° 2il 38
40 9600 9600 9600 8137 6039 4559 3686 2929 2417 2074 1821 1520 1302 1140 1017 922 9738 563° 415 325 269 «= 230-204 40
42 9600 9600 9600 8177 5977 4568 3634 2960 2411 2044 1789 1551 1316 1142 1010 909 714 585 425 329 268 227 199 42
44 9600 9600 9600 8117 5954 4604 3608 2997 2621 2029 1758 1563 1337 1151 1010 902 695 583 437 334 269 225 195 44
46 9600 9600 9600 8106 5967 4616 3602 2954 2644 2026 1738 1532 1366 1166 1016 901 681 563 452 341 272225 193 46
48 9600 9600 9600 8137 6010 4576 3616 2929 2478 2034 1728 1510 1350 1187 1027 904 671 546 468 350 275 226 192 48

6-113

TABLE 6-9. FIBERGLASS POLYESTER LAMINATES |
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - LOADED EDGES SIMPLY SUPPORTED -
REMAINING EDGES CLAMPED (Cont'd)

THICKNESS-H EQUALS 005625 INCHES

LENGTH=8 WIDTH=A LENGTH-B
INCHES INCHES MES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 10800 10374 9217 8512 8051 7734 7507 7336 7209 7109 7028 6963 6909 6795 6714 6670 6639 6619 6588 6577 6
8 10800 10800 10800 10800 8599 7002 6062 5467 5069 4788 4585 4432 4317 4223 4148 4088 3963 3686 3836 3799 3772 3752 3737 8
10 10800 10800 10800 10800 6658 6492 5249 4481 3978 3633 3385 3202 3064 2957 2872 2805 2664 2580 2525 2487 2458 2439 2423 10
12 10800 10800 10800 10800 9623 6761 5149 4170 3539 3112 2812 2593 2430 2304 2206 2128 1970 1877 1817 1777 1748 1727 1710 12
14 10800 10800 10800 10800 9145 7494 544% 4215 3633 2911 2548 2286 2093 1946 1833 1743 1564 1460 1396 1352 1321 1298 1281 14
16 10800 10800 10800 10800 8599 7002 6003 4486 3529 2897 2460 2150 1922 L75i 1619 Isis 1312 1197 1126 1079 1046 1022 1004 16
18 10800 10800 10800 10800 8481 6615 5532 4856 3763 3005 2487 2120 1853 1654 1502 1383 1153 1024 946 895 859 834 815 18
20 10800 10800 10800 10800 8658 6491 5249 4481 3978 3204 2593 2164 1854 1623 1448 1312 1051 908 822 766 728 701 681 2c
22 10800 10800 10800 10800 8904 6556 5137 4268 3704 3319 2762 2263 1904 1639 1439 1284 989 830 735 674 633 604 583 22
24 10800 10800 10800 10800 8598 6761 5149 4170 3539 3112 2812 2406 1994 1690 1462 1287 955 778 674 607 563 532 509 24
26 10800 10800 10800 10800 8483 6710 5258 4159 3455 2982 2652 2413 2114 1770 1512 1314 943 746 631 559 $11 477 453 26
28 10800 10800 10800 10800 8511 6549 5415 4215 3433 2911 2548 2286 (2093 1873 1583 1361 946 728 602 523 472 436 410 28
30 10800 10800 10800 10800 8658 6491 5249 4327 3461 2885 2487 2202 1992 1833 1671 1424 962 721 583 498 442 404 376 30
32 10800 10800 10800 10800 8598 6517 5159 4324 3529 2896 2460 2150 1922 1751 1619 1501 989 724 573 480 420 379 350 32
34 10800 10800 10800 10800 8497 6610 5128 4224 3631 2938 2462 2124 1877 1692 1551 1440 1025 734 570 469 404 360 329 34
36 10800 10800 10800 10800 8481 6615 5149 4170 3539 3005 2487 2120 1853 1654 1502 1383 1069 751 572 463 393 346 312 36
38 10800 10800 10800 10800 8538 6527 5212 4154 3475 3018 2531 2134 1846 1632 1468 1341 1096 174 579 462 386 335 300 38
40 10800 10800 10800 10800 8598 6491 5249 4171 3442 2953 2593 2164 1854 1623 1448 1312 1051 801 590 463 382 328 290 40 |
42 10800 10800 10800 10800 8510 6503 5174 4215 3433 2911 2548 2208 1873 1626 1438 1294 1016 833 605 468 381 323 283 42
44 10800 10800 10800 10800 8477 6556 5137 4268 3447 2889 2503 2226 1904 1639 1439 1284 989 830 623 476 383 321 278 44
46 10800 10800 10800 10800 8496 6572 5129 4206 3479 2885 2475 2181 1944 = 1661 1447 1282 969 801 644 486 387 321 275 46
48 10800 10800 10800 10800 8557 6516 5149 4170 3529 2896 2460 2150 1922 1690 1462 1287 955 778 667 498 392 322 273 48
THICKNESS=H EQUALS 006250 INCHES
LENGTH=8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 12000 12000 12000 12000 12000 12000 11677 11044 10609 10298 10064 9889 9752 9640 9552 9477 9321 9210 9149 9107 9080 9037 9022 6
8 12000 12000 12000 12000 11796 9605 8315 7499 6953 6568 6289 6080 5921 5793 5691 5608 5437 5331 5262 5212 5175 5146 5126 8
10 12000 12000 12000 12000 118676 8905 7201 6147 54657 4983 4643 4393 4204 4057 3942 3848 3654 3539 3463 3412 3372 3346 3324 10
12 12000 12000 12000 12000 12000 9275 7064 5720 4854 4269 3857 3557 3333 3161 3026 2919 2702 2575 2492 2438 2398 2369 2346 12
14 12000 12000 12000 12000 12000 10280 7468 5782 4710 3993 3495 3136 2871 2670 2514 2391 2145 2003 1914 1855 1811 1781 # 1758 14
16 12000 12000 12000 12000 11796 9605 8234 6153 4841 3973 3375 2949 2636 2401 2229 2079 1800 1642 1544 1480 1435 1402 1377 16
18 12000 12000 12000 12000 11634 9074 7589 6661 5162 4122 3412 2908 2542 2268 2060 1897 1581 1405 1297 1227 #1179 1144 1118 18
20 12000 12000 12000 12000 11876 8904 7200 6147 5457 4395 3558 2969 2543 2226 1986 1800 1442 1246 1128 1051 999 962 934 20
22 12000 12000 12000 12000 12000 8993 7046 5854 5080 4553 3788 3105 2612 2248 1973 1762 1357 1138 1008 925 869 829 800 22
24 12000 12000 12000 12000 11795 9275 7063 5720 4854 4269 3857 3300 2735 2319 2006 1766 +1311 + «1067 924 833 773 730 699 24
26 12000 12000 12000 12000 11636 9204 7212 $705 4739 4091 3637 3310 2900 2428 2074 1803 1293 1023 865 766 701 655 622 26
28 12000 12000 12000 12000 11676 8983 7428 5782 4710 3993 3495 3136 2871 2570 2171 1867 1297 998 825 718 647 598 562 28
30 12000 12000 12000 12000 11876 8904 7200 5936 4748 3958 3411 3020 2732 2514 2293 1953 1320 989 800 683 606 554 516 30
32 12000 12000 12000 12000 11795 8939 7076 5932 4841 3973 3375 2949 2636 2401 2221 2059 1356 993 786 659 576 520 479 32
34 12000 12000 12000 12000 11656 9067 7034 5794 4981 4030 3377 2914 2575 2321 2127 1975 1406 1007 782 644 554 494 451 34
36 2000 12000 12000 12000 11634 9074 7063 5720 4854 4122 3411 2908 2542 2268 2069 1897 1467 1031 785 636 539 474 429 36
38 12000 12000 12000 12000 11712 8953 7150 5698 4767 4140 3472 2928 2533 2238 2014 1840 1503 1061 794 633 530 460 411 38
40 12000 12000 120¢0 12000 11795 8904 7200 5721 4721 4050 3558 2969 2543 2226 1986 1800 1442 1099 810 636 525 450 398 40
42 12000 12000 12000 12000 11674 8921 7098 5782 4709 3993 3495 3026 2570 2230 1973 1774 1394 1142 830 642 523 O44 388 42
44 12000 12000 12000 12000 11628 6993 7046 5854 4728 3964 3433 3054 2612 2248 1973 #1762 «1357 + «21138 854 653 525 440 382 44
46 12000 12000 12000 12000 11654 9015 7036 5770 4773 3958 3395 2992 2667 2278 1984 1759 1330 1099 883 667 530 440 377 46
46 12000 12000 12000 12000 11738 8938 7063 5720 4841 3973 3375 2949 2636 2319 2006 1766 1311 1067 915 684 538 441 375 48

6-114

TABLE 6-10.

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED

P PHYSICAL CONSTANTS:
Ex = 1.81x10® PSI
Ey. = 1.54x10® PSI
Gxy = 0.45x10® PSI
P Re ctr nek
THICKNESS-H EQUALS 020625 INCHES
“INCHES “INCHES “INCHES.
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 57 45 42 40 38 38 37 37 37 37 37 37 37 37 37 37 37 37 37 37 She 37 37 6
8 49 33 26 24 23 23 23 21 21 2a 21 21 21 21 21 21 21 21 21 21 21 21 21 8
10 47 28 21 7 16 16 14 14 14 14 14 14 14 14 14 14 14 14 12 12 12 12 le 10
12 40 26 17 14 12 12 10 10 10 10 10 10 9 9 9 a 9 9 9 9 9 9 9 le
14 38 24 17 12 10 9 9 9 7 7 7 7 7 if 7 vi 7 © 7 x 7 7 7 14
16 38 23 17 12 9 9 7 7 7 7 5 5 5 5 5 5 5 5 5 5 5 5 5 16
18 37 23 16 12 9 ih Us 5 5 5 5 5 5 5 5 5 3 3 3 3 3 3 3 18
20 37 23 14 12 9 7 5 5 5 5 3 3 3 3 3 3 3 3 3 3 3 3 3 20
22 37 21 14 10 9 7 5 5 3 3 3 3 3 3 :} 3 3 3 3 3 3 3 3 22
24 35 21 14 10 9 i} 5 ss 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 24
26 35 21 14 10 7 7 5 5 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 26
28 37 21 14 10 7 7 5 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 28
30 37 21 14 10 7 5 5 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 30
32 38 19 14 10 i 5 5 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 32
34 40 19 14 9 ii 5 5 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 34
36 42 21 14 9 1 5 5 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 36
38 43 21 12 9 a 4 5 = a 3 2 2 2 rs 2 2 2 2 ie 2 2 2 2 38
40 45 21 12 9 iv ei 5 mS 3 3 2 2 2 2 2 2 2 2 re 2 2 2 2 40
42 49 21 a2 9 Rf 5 3 3 3 3 2 2 2 2 G 2 2 2 2 73 ) t) 0) 42
44 50 23 12 9 7 5 3 3 2) 3 2 2 2 2 2 2 2 2 2 ) ° ) Co) 44
46 54 23 12 9 1 5 3 3 3 2 2 2 2 2 2 2 2 2 C) O) 0 t) ° 46
48 56 23 14 9 i 5 3 3 3 2 2 2 2 2 2 2 2 2 ° ) ° ° 0 48
THICKNESS-H EQUALS 061250 INCHES
LENGTH=B WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 461 369 334 316 308 302 299 296 294 292 292 290 290 289 289 289 287 287 287 287 287 285 285 6
8 384 259 216 195 184 179 174 172 169 169 167 165 165 165 163 163 163 162 162 162 162 162 162 8
10 369 221 165 141 129 122 116 115 lll 1lo 110 108 108 106 106 106 104 104 104 104 104 104 103 10
12 azo) 214 144 115 101 92 87 83 82 80 78 76 76 75 75 75 73 73 73 73 73 71 te! 12
14 aul 200 137 103 85 75 70 66 63 61 59 59 57 57 56 56 56 54 54 54 54 54 54 14
16 308 183 137 96 76 64 57 54 50 49 47 47 45 45 43 43 42 42 42 42 42 42 40 16
18 296 176 125 96 1 59 50 47 43 42 40 38 37 37 37 35 35 33 33 33 33 33 33 18
20 292 174 116 92 70 56 47 42 38 35 33 33 31 EDI 30 30 28 28 28 26 26 26 26 20
22 289 170 113 85 70 54 43 38 35 31 30 28 28 26 26 24 24 23 23 23 23 23 23 22
24 283 167 li 82 66 54 43 37 31 30 26 24 24 23 23 21 21 19 19 19 19 19 19 24
26 283 165 113 78 63 54 42 35 30 26 24 23 21 21 19 19 17 17 17 16 16 16 16 26
28 287 165 108 78 59 50 42 35 30 26 23 21 19 19 17 17 16 16 14 14 14 14 14 28
30 294 162 106 78 57 47 42 35 28 24 23 19 19 17 16 16 14 14 12 12 12 12 12 30
32 304 160 106 76 57 45 38 35 28 24 21 19 17. 16 16 14 14 12 12 12 10 lo 10 32
34 316 160 106 75 57 45 37 33 28 24 21 19 17 16 14 14 12 10 10 10 10 10 10 34
36 330 160 104 73 57 43 37 31 28 24 21 17 16 14 14 12 10 10 1o 9 9 9 9 36
38 346 163 103 73 56 43 35 30 26 24 21 17 16 14 14 12 10 9 9 9 9 9 9 38
40 365 165 103 73 56 43 35 30 26 23 21 17 16 14 12 12 10 i 7 7 7 40
42 384 170 103 73 54 43 35 28 24 23 21 17 16 14 12 12 9 9 u 7 if 7 rz 42
44 405 174 103 71 54 43 35 28 24 21 19 17 16 14 12 10 9 9 7 7 7 7 7 a4
46 428 181 103 io 54 42 35 28 24 21 19 17 16 14 12 10 9 7 7 7 5 5 5 46
48 450 186 104 7 54 42 35 28 23 21 17 17 16 14 12 10 9 7 7 5 5 5 5 48

6-115

TABLE 6-10. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 061875 INCHES

Lene “rpc “ikgoes®
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 1552. 1243. 1126 «61071-1040 1020-1006 «= 998 = 991 987 = 984 = 980 579-977 9S 9730 -87200«C 968 9660966 966 965 965 6
8 1297 874 727 659 624 601 588 579 572 567 563 560 558 555 553 553 549 548 546 546 544 544 544 8
10 1246 746 569 478 436 412 396 386 377 372 369 365 363 360 358 358 355 353 351 351 349 349 349 10
12 1099 721 487 388 339 311 294 282 273 268 262 259 257 256 254 252 249 247 245 245 243 243 243 12
14 1048 673 462 344 285 252 233 221 212 205 200 196 193 191 189 188 184 183 183 181 179 179 179 4
16 1040 617 466 325 256 219 196 181 172 165 160 156 153 151 148 148 144 141 141 139 139 137 137 16
18 996 593 421 322 242 198 172 156 146 137 132 129 125 123 120 118 115 113 111 111 110 110 1lo 18
20 987 589 395 311 236 186 158 139 129 120 113 110 106 103 lol 99 96 94 92 90 90 89 89 20
22 973 577 382 289 238 181 149 129 115 106 99 96 92 89 87 83 80 78 76 76 75 75 75 22
24 958 561 377 275 224 181 144 122 108 97 90 85 80 78 75 73 70 66 66 64 Ss 63 63 2h
26 958 555 379 266 210 179 143 118 101 90 83 76 73 70 66 64 61 57 57 56 54 de 34 26
28 970 556 367 262 202 169 143 116 97 85 78 7 66 63 61 59 54 50 50 49 47 47 47 28
30 994 544 358 262 196 160 139 115 96 83 73 68 63 59 56 54 49 45 43 43 42 42 42 30
32 1027 539 356 261 193 155 132 116 96 82 al 64 59 54 52 49 43 42 40 38 38 37 37 32
34 1069 537 356 254 193 151 125 110 96 80 70 63 56 52 49 45 40 38 37 35 33 33 33 34
36 1116 541 353 249 193 148 122 106 94 80 68 61 54 49 45 43 38 35 33 31 30 30 30 36
38 1170 549 348 247 189 148 120 101 90 82 68 59 52 49 43 42 a5 31 30 28 28 28 26 38
40 1231 560 344 247 186 148 118 99 87 78 68 59 52 47 42 40 33 30 28 26 26 24 24 40
42 1295 574 344 247 183 148 116 97 83 75 68 59 52 45 42 38 31 28 26 24 24 23 23 42
44 1366 589 346 243 183 144 116 96 82 73 66 59 52 45 40 37 30 26 24 23 23 21 21 44
46 1441 607 348 240 181 143 116 94 80 70 63 57 52 45 40 37 30 26 23 21 21 19 19 46
48 1521 628 353 240 183 141 115 94 78 68 61 56 52 45 40 37 28 24 23 21 19 19 17 48
THICKNESS-H EQUALS 042500 INCHES
LENGTH-8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 3682 2945 2670 2538 «= 2463. 2416 «= 2387 )=— 2366 «= 2350 = 23400-23310 2324 «= 2319) 2314 «= 2310 2308 «= 2302, «2295 229122912291 02288) 2284 6
8 3075 2070 1723 1563 1478 1427 1394 1372 1356 1342 1333 1326 1321 1316 1312 1309 1302 1299 1295 1293 1290 1288 1288 8.
10 2953 1768 =1325 1133 ©1033 975 939 913 895 883 873 B66 859 855 850 847 840 836 833 831 829 827 827 10
12 2602 1710 1154 920 803 737 695 668 648 634 624 615 610 605 600 596 589 584 582 579 579 577 575 12
14 2486 1594 1097 815 676 600 553 521 501 485 475 466 459 454 450 447 438 433 431 428 426 426 424 14
16 2465 1464 1104 768 607 518 464 431 407 391 379 370 362 356 353 348 341 335 332 330 329 327 327 16
18 2362 1406 1000 761 570 469 409 370 346 327 315 304 297 290 285 282 273 268 266 262 261 261 259 18
20 2340 1398 937 739 558 442 374 332 302 283 269 259 250 243 238 235 226 221 217 216 214 212 210 20
22 2308 1366 904 685 563 429 353 306 275 252 236 226 216 210 203 200 191 186 183 179 177 176 176 22
24 2268 ©1328 893 650 530 428 342 269 254 229 214 200 191 184 179 174 163 158 155 153 151 149 148 24
26 2268 1316 899 631 499 424 337 278 240 214 196 183 172 165 158 153 144 137 134 132 130 129 127 26
28 2300 1319 869 622 478 398 339 275 231 203 184 169 158 149 143 137 127 122 118 115 113 ql 111 28
30 2357 = 1290 850 621 464 379 329 275 228 196 174 158 148 139 132 125 115 108 104 101 99 97 97 30
32 2435 1276 843 615 457 367 311 276 226 193 169 151 139 129 122 116 104 97 94 90 89 87 85 32
34 2533 1274 843 600 455 356 299 261 228 189 165 146 132 122 115 108 96 89 85 82 80 78 76 34
36 2646 1283 836 591 457 351 289 250 223 189 162 143 129 116 110 103 89 82 76 75 7 71 70 36
38 2774 1300 824 586 448 349 283 242 214 191 162 141 125 113 104 97 83 76 71 68 66 64 63 38
40 2917 1326 817 586 440 349 278 235 205 184 162 139 123 ql 1o1 94 78 7 66 63 61 59 57 40
42 3072 ©1358 815 588 435 349 276 229 198 177 162 139 122 108 99 90 75 66 61 57 56 54 52 42
44 3238 8©61396 819 577 431 342 276 226 193 170 155 141 122 108 97 89 71 63 57 54 52 50 49 44
46 3416 1439 826 570 429 335 276 224 189 167 149 137 122 106 96 87 70 61 54 50 49 47 45 46
48 3605 1488 834 567 431 332 275 223 188 163 146 132 123 108 96 85 68 57 52 49 45 43 42 48

6-116

THICKNESS-H

TABLE 6-10.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ, WOVEN ROVING - LOADED EDGES CLAMPED -

FIBERGLASS POLYESTER LAMINATES

REMAINING EDGES SIMPLY SUPPORTED

EQUALS 043125 INCHES

(Cont'd)

“INCHES "INCHES “INCHES.
5 A 10 io ve 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 4940 4940 4960 4940 4812 4721 4662 4620 4591 4568 4551 4539 4528 4520 4313 4507 4495 4481 4476 4474 4474 = 446T 4462 C
8 4940 4045 3364 3054 2887 2788 2722 2679 2647 2621 2604 2590 2580 2569 2562 2555 2543 2536 2529 2524 252125172515 LW
10 4940 3452 2588 + «-2213.«2018+~=«1903.-1332S«1783.S«1749=S«724+~=s«1705.-S«1690.-Ss «dS T77 = 1669) 16621655) 164116321627) 16221618 = 16171615 10
12 4940 3343 2255 1797 1568 1438 1358 1304 1265 1239 1219 1203 1292 1180 1172 1165 1151 1142 1135 1132-1128 11261125
14 4855 3115 2142 1591 1321 1170 1079 1020 979 949 927 gil 897 887 = 878 = 8710 857 B47 841 8360 8330 B32 829 a
16 4813 2860 2157 1502 1184 1012 907 841 796 763 741 721 707 697 688 681 666 655 650 645 641 640 638 ue
18 4613 2747 «1959 1486-1114 916 800 725 674 640 614 594 579 568 558 551 535 525 518 513 509 508 506 18
20 4570 2729 1839 1443 1092 B64 730 647 591 a53) 525 504 488 476 466 459 442 431 424 419 415 414 412 20
22 4507 2670 1766 1337 1099 8460 688 596 535 492 462, 440 422 410 398 391 372 362 355 349 346 ane 342 a2
24 4431 2595 1745 i271 1034 836 668 563 495 450 T3393 374 360 348 339 322 309 302 297 294 292 289 24
26 4431 2571 «1754 ~—«:1232 973 831 659 544 469 419 382 356 337 322 309 301 282 269 262 257 254 250 249 26
28 4492 2578 «1697-1213 933 779 664 535 454 398 358 330 309 292 280 269 249 236 229 224 221 217 216 28
30 4603 2521 «1662-1213 907 741 641 535 445 384 341 all 287 269 257 245 224 212 203 198 195 191 189 30
32 4756 2493 1646 = 1203 893 714 608 539 442 375 329 296 27 252 238 228 203 191 183 177 174 170 169 32
34 4940 2489 = 1648-1173 890 697 582 511 443 372 322 285 259 240 224 212 188 174 165 160 155 153 149 34
36 4940 2505 1632 1154 893 687 565 488 436 372 318 278 250 229 212 200 174 160 151 144 141 137 136 36
38 4940 2540 1608 1144 876 681 553 47 415 374 316 275 243 221 203 189 163 148 139 132 129 125 123 38
40 4940 2588 1596 1142 859 681 544 457 400 360 318 273 240 216 196 183 155 139 129 122 118 115 113 40
42 4940 2653 1592 1146 848 683 539 448 388 346 316 273 238 212 193 177: 146 130 120 113 110 106 103 42
44 4940 2726 1597 1126 B41 668 539 442 379 334 302 275 238 210 189 172 141 123 113 106 101 97 96 44
46 4940 2811 1611 1114 840 657 541 438 370 325 292 268 238 209 186 169 136 116 106 99 94 90 89 46
48 4940 2906 1631 1107 B41 648 535 436 365 318 283 259 240 209 186 167 132 113 101 94 89 85 82 48
THICKNESS-H_ EQUALS 063750 INCHES
LENGTH-B WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 +7200 7200 7200 7200 #7200 «7200 +#«7200 6
8 7200 6988 5811 5277 4989 4817 4704 4627 4573 4532 4500 4476 4459 4441 4427 4417 4396 4381 4372 4361 4356 4351 4347 8
10 7200 5966 = 44473, 3823-3487 «=. 3.291 3167 = 3082-3023. 2979 2946 «= 2920 2899 2884 = 2872) 28600-2835 0S 282102811 = 2804 »=— 2795S 2793S 2790 10
12 7200 5776 3896 3106 2710 2486 2345 2253 2189 2140 2105 2079 2056 2039 2025 2015 1989 1973 1963 1956 1950 1947 1943 12
14 7200 5382 «370102748 = 2282-2023, 1865 1761 = 1690 1639 1603. 1573. 1551015311518 = 1505 147914641453 1446) 14391434) 1432 14
16 7200 4940 = 3727) 2594 = 2046) 1747) 1568 = 1453) 1375 1319-1278) «= 1246 = 1224S 1205S 1189) 1177) 11491133. -1121)0S«1114~=S-1109+~=S«:1104~=«21100 16
18 7200 44746 «©3372 «2567 «891926 «691584 1380 1252 1165 1104 1060 1027 1001 980 965 5 923 906 895 887 881 878 874 18
20 7200 4714 3162 24691 1884 1491 1262 1118 1022 956 907 873 845 822 805 791 763 746 734 725 720 714 711 20
22 7200 4613 «3052, 2312)s-1898 )= 1450-1191 031 925 852 798 760 730 707 688 674 643 626 614 605 600 594 591 22
24 7200 4485 3014 2195 1787 1445 1152 973 857 777 720 678 645 621 601 586 555 535 523 515 508 504 501 24
26 7200 4441 3032 2129 1683. 1434 1140 940 812 723 662 617 582 556 535 518 485 466 452 443 436 433 429 26
28 7200 4455 2931 2098 1613 1345 1146 925 784 687 619 570 534 506 483 466 431 410 396 388 381 377 372 28
30 7200 4354 2870 2095 1570 1281 1107 925 768 662 589 Sa 497 468 443 424 388 365 351 342 335 330 327 30
32 7200 4306 2844 2079 1545 1236 1050 932 763 648 568 511 469 436 412 393 353 330 315 306 299 294 290 32
34 7200 4301 28467 2027 1538 1205 1008 881 767 641 556 494 448 414 388 365 325 301 285 275 268 264 259 34
36 7200 44330 42821 1994 1544 1187 975 843 754 641 548 482 433 396 367 346 301 276 261 250 243 238 235 36
38 7200 44389 2778 1976 1516 1179 954 814 720 647 546 475 422 382 353 329 282 256 240 229 221 216 212 38
40 7200 4474 2755 1975 1485 1179 940 791 692 622 548 471 415 374 341 316 266 238 223 210 203 198 195 40
42 7200 4582 2752 1980 1464 1179 932 774 669 598 546 471 412 367 332 306 254 224 207 196 188 183 177 42
44 7200 4711 «2760 194714531152 930 763 654 577 523 475 410 362 327 297 243 212 195 183 174 169 165 44
46 7200 4859 2785 1926 «61450-1133 933 756 641 561 506 464 412 362 322 292 235 203 184 172 163 156 153 46
48 7200 5022 2818 1914 1453 1121 925 754 633 549 490 447 414 362 320 289 228 195 174 162 153 146 143 48

6-117

TABLE 6-10. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 064375 INCHES

= NGTH=
“INCHES. “INCHES “INCHES,
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 8400 8400 8400 8800 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 6
8 8400 8400 8400 8380 7921 7649 7469 7348 7263 7195 7146 7108 7080 7052 7031 7012 6979 6957 6941 6927 6917 6908 6903 e
10 8400 8400 7103 6072 5538 5225 5029 4895 4799 4732 4678 4638 4605 4579 4560 4542 4504 4480 4462 4452 4440 4436 4429 10
12 8400 8400 6185 4932 4304 3946 3723 3577 3475 3400 3344 3301 3266 «63238 «63216 = 33198 = 3158 = 3134 8603117) 3106 = 3098 = 33092 3085 12
14 8400 8400 5877 4365 3624 3212 2960 2797 2684 2604 2543 2498 2461 2434 24609 2390 2350 2324 2308 2296 2286 2279 2274 14
16 B400 7847 5917 4120 3249 2774 2491 2307 2183 2095 2030 1980 1942 1912 1888 1867 1825 1799 1782 1770 1761 1754 1749 16
18 8400 7536 5354 4076 3059 2514 2192 1987 1850 1754 1683 1631 15911558 =61531 = 15111467) 1439) 14220 1408 = 1399 1392-1387 18
20 8400 7487 5022 3956 2993 2369 2004 1775 1624 1518 1441 1384 1340 1305 Ler) 1257 1212 1184 1165 1151 1142 1135 1130 20
22 8400 7325 4848 3670 3014 2302 1891 1636 1467 1351 1269 1206 1159 1123 1095 1071 1022 994 973 961 951 946 939 22
24 8400 7122 4787 3487 2837 2293 1830 1545 1361 1232 1142 1076 1026 987 956 932 880 850 829 817 807 800 794 24
26 8400 7052 4815 3381 2674 2277 1810 1493 1288 1149 1050 979 925 883 850 824 770 739 718 704 694 687 681 26
28 8400 7075 4653 3331 2562 2136 1820 1469 1243 1092 984 906 848 803 768 Tal 685 650 629 615 605 598 591 28
30 8400 6915 4558 3327 2491 2034 1759 1467 1219 1053 937 852 789 742 704 674 615 581 558 544 534 525 520 30
32 8400 6838 4516 3303 2454 1961 1667 1479 1212 1029 904 812 744 694 654 622 560 523 501 485 475 468 461 32
34 8400 6828 4521 3218 2442 1912 1599 1401 1217 1019 883 784 711 657 614 581 515 476 454 438 426 419 412 34
36 8400 6875 4480 3165 2453 1884 1551 1338 1198 1019 871 765 687 629 584 548 478 438 414 398 386 377 372 36
38 8400 6969 4412 3139 2406 1870 1516 1292 1142 1027 867 753 669 607 560 521 448 407 381 363 351 344 337 38
40 8400 7104 4377 3136 2357 1872 1493 1255 1099 989 871 749 659 593 541 501 422 379 353 335 323 315 308 40
42 8400 7277 4368 3145 2326 1872 1481 1229 1064 949 867 749 654 582 527 485 403 356 329 311 299 289 283 42
44 8400 7482 4384 3092 2308 1830 1478 1212 1038 918 831 754 652 575 518 473 386 337 309 290 276 268 261 44
46 8400 7715 4420 3058 2303 1801 1483 1201 1017 892 803 737 654 574 511 464 372 322 292 271 259 249 242 46
48 8400 7975 4476 3039 2308 1780 1467 1198 1003 873 779 709 657 574 508 457 362 308 276 256 243 233 226 48
THICKNESS-H_ EQUALS 065000 INCHES
LENGTH=B8 WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9609 6
8 9600 9600 9600 9600 9600 9600 9600 9605 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 8
10 9600 9600 9600 9062 8266 7800 7506 7306 7165 7064 6983 6922 6873 6835 6805 6779 6722 6686 6661 6646 6626 6621 6612 10
12 9600 9600 9232 7363 6423 5891 5559 5340 5185 5074 4992 4926 4876 4834 4801 4773 4716 4678 4652 4638 4624 4615 4605 12
14 9600 9600 8773 6515 5410 4794 4420 4175 4007 3887 3796 3729 3675 3631 03598 = 3569 = 33508 = 3470 3445 3428 34123402 03395 14
16 9600 9600 8834 6148 4850 4141 3716 3444 3259 3127 3030 2957 2899 2854 2818 2788 2726 2686 2660 2642 2628 2618 2609 16
18 9600 9600 7993 6084 4567 3753 3271 2967 2762 2618 2514 2434 2373 2324 2286 2255 2190 2149 2121 2103 2089 2079 2072 18
20 9600 9600 7496 5907 4469 3536 2992 2651 2423 2265 2152 2067 2001 1950 1969 1877 1808 1766 1738 1719 1705 1695 1686 20
22 9600 9600 7235 5479 4500 3437 2823 2442 2190 2018 18693 1801 1731 1677 1634 1599 1526 1483 1455 1434 1420 1410 1401 22
24 9600 9600 7146 5206 4236 3423 2733 2308 2030 1841 1705 1606 1531 14720-1427 1391 1314 1269! 1239) l2to) 1205 1194 1186 24
26 9600 9600 7186 5046 3989 3400 2701 2230 1924 1716 «1568 =. 1460 1380 41318 1269 1229 1151 1102-1073 1052 1036 1026 =1017 26
28 9600 9600 6946 4972 3824 3190 2717 2194 1857 1629 1469 1352 1265 1199 1147-1106 = 1020 972 940 918 904 892 883 28
30 9600 9600 6804 4966 3720 3037 2625 2190 182¢ 1571 1398 1272 +1179 1107 1052 1006 918 867 834 812 796 786 775 30
32 9600 9600 6743 4930 3663 2927 2489 2208 1808 1537 1349 1213 1113 1036 977 930 836 782 747 725 709 697 688 32
34 9600 9600 6748 4803 3645 2856 2388 2089 1817 1521 1318 1170 1062 980 918 867 768 713 676 654 636 624 615 34
36 9600 9600 6687 4725 3661 2813 2314 1997 1787 1521 1300 1142 1026 939 871 819 714 655 617 593 575 563 555 36
38 9600 9600 6586 4686 3591 2793 2262 1928 1705 1533 1295 1125 1000 907 834 779 669 607 568 542 525 513 502 38
40 9600 9600 6533 4680 3518 2793 2229 1874 1639 1476 1300 1118 984 883 808 747 631 567 527 501 482 469 459 40
42 9600 9600 6520 4693 3471 2795 2209 1836 1589 1417 1295 1118 975 869 787 723 601 532 492 464 445 431 422 42
44 9600 9600 6545 4617 3445 2734 2206 1810 1549 1370 1241 1125 972 859 772 706 575 504 461 433 414 400 389 44
46 9600 9600 6599 4565 3438 2689 2213 1794 1519 1332 1198 1099 975 855 763 692 556 480 435 407 386 372 362 46
48 9600 9600 6680 4537 3445 2658 2190 1787 14698 1302 1161 1059 982 855 758 683 539 461 414 382 362 348 337 46

6-118

TABLE 6-10,

25-27 OZ. WOVEN ROVING - LOADED EDGES CLAMPED -
REMAINING EDGES SIMPLY SUPPORTED

THICKNESS-H EQUALS 005625 INCHES

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

(Cont'd)

= NGTH=
“tncHes. “INCHES MINCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 10800 10800 10800 10800 10809 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 6
8 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 8
10 10800 10800 10800 10800 10800 10800 10689 10404 10202 10058 9943 9856 9787 9733 9691 9653 9571 9519 9486 9463 9435 9429 9415 10
12 10800 10800 10800 10684 9145 8387 7916 7602 7384 7224 7108 7016 6941 6882 6837 6797 6713 6661 6625 6604 6585 6571 6557 12
14 10800 10800 10800 9277 7702 6826 6294 5945 5705 5533 5406 5309 5232 5171 5123 5081 4994 4940 4905 4879 4857 4843 4834 14
16 10800 10800 10800 8754 6905 5896 5293 4906 4640 4452 4314 4208 4128 4064 4012 3969 3880 3823 3786 3762 3741 3727 3716 16
18 10800 10800 10800 8664 6503 5344 4659 4224 3932 3727 3577 3466 3379 3310 3256 3211 3119 3059 3021 2993 2974 2960 2950 18
20 10800 10800 10673 8410 6362 5034 4261 3774 3451 3226 3063 2943 2849 2776 2719 2672 2574 2514 2475 2448 2428 2413 2401 20
22 10800 10800 10303 7800 6407 4893 4019 3477 3119 2872 2696 2564 2465 2387 2326 2275 2173 2112 2070 2043 2022 2008 1996 22
24 10800 10800 10174 7412 6030 4872 3890 3285 2891 2621 2428 2286 2180 2096 2030 1978 1870 18606 1764 1735 1716 1698 1688 24
26 10800 10800 10232 7184 5681 4841 3847 3174 2740 2442 2234 2081 1964 1876 1806 1750 1637 1570 1526 1497 1476 1460 1448 26
28 10800 10800 9891 7080 5444 4540 3868 3124 2644 2319 2091 1926 1801 1707 1632 1573 1453 13864 1338 1307 1286 1271 1259 28
30 10800 10800 9688 7071 5297 4323 3737 3119 2592 2237 1990 1811 1677 1575 1497 1434 1307 1234 1187 1156 1133 1118 1106 30
ae 10800 10800 9601 7019 5215) 4168 3544 S145 2574 2189 AB AC) 1726 1584 1474 1391 1323 1191 1113 1064 1033 1010 993 980 32
34 10800 10800 9608 6838 5191 4066 3400 2976 2587 2166 1876 1667 1512 1396 1305 1234 1095 1013 963 930 906 888 876 34
36 10800 10800 9522 6727 5211 4003 3294 2846 2545 2166 1851 1625 1460 1337 1239 1165 1017 932 880 845 820 803 7389 36
38 10800 10800 9376 6672 5112 3977 3219 2745 2427 2183 1844 1601 1424 1292 1189 1109 953 B64 808 774 747 730 716 38
40 10800 10800 9302 6665 5010 3977 3172 2668 2335 2103 1851 1591 21401 1259 1149 1066 899 807 749 713 687 668 654 40
42 10800 10800 9284 6684 4942 3981 3146 2613 2262 2018 1844 1591 1389 1236 1121 1031 855 758 699 661 634 615 601 42
4a 10800 10800 9317 6573 4905 3892 3139 2576 2206 1950 1768 1601 1385 1224 1100 1005 820 718 657 617 589 568 555 44
46 10800 10800 9396 6500 4895 3828 3150 2554 2162 1896 1705 1564 1389 1217 1086 986 791 683 619 579 549 530 515 46
48 10809 10800 9512 6460 4905 3784 3120 2543 2133 1853 1653 1507 1398 1219 1079 973 767 655 588 544 516 495 480 48
THICKNESS-H EQUALS 046250 INCHES
LENGTH-B WIDTH-A LENGTH=8
INCHES INCHES. INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 6
8 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 8
10 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 10
12 12000 12000 12000 12000 12000 11504 10857 10428 10129 9910 9748 9623 9522 9441 9378 9323 9210 9138 9088 9058 9032 9015 8996 12
14 12000 12000 12000 12000 10565 9364 8632 8156 7826 7589 7416 7282 7176-7094 = 7026 «= 6971 = 6851 6776 «= 6729 6694 = 6663 6644 = 6390 14
16 12000 12000 12000 12000 9472 8088 7261 6727 6366 6108 5919 5773 5663 5575 = 5503 5444 5323 5244 5194 5161 5133 5111 5097 16
18 12000 12000 12000 11885 8921 7330 6392 5795 5394 5112 4909 4754 4634 4540 4466 4405 4276 4196 4144 4108 4080 4061 4045 18
20 12000 12000 12000 11537 8728 6906 5844 5177 4733 4426 4203 4036 3909 3809 3729 3666 3530 3449 3395 3357 3331 3310 3294 20
22 12000 12000 12000 10701 8789 6712 5512 4768 4278 3941 3697 3518 3381 63275-3190 3122-2981 = 2896 «= 2840) 28022774 «=s2 755 2738 22
24 12000 12000 12000 10167 8273 6686 5337 4507 3967 3595 3331 3136 2990 2877 2786 2715 2566 2477 2420 2380 2352 2331 2315 24
26 12000 12000 12000 9854 7793 6640 5277 4354 3756 3351 3063 2853 2694 2573 2479 2401 2246 2154 2095 2053 2023 2003 1987 26
28 12000 12000 12000 9712 7469 6228 5307 4285 3626 3181 2868 2640 2472 2341 22392159 1994 1898 = 1836 = 1794 «1764 «= «1 7H2~S «1726 28
30 12000 12000 12000 9701 7264 5929 5128 4278 3555 3070 2729 2684 2302 2161 2053 1966 1794 1693 1629 1585 1556 1533 1516 30
32 12000 12000 12000 9628 7155 5719 4862 4313 3532 3002 2634 2368 2171 2022 1907 1815 1632 1526 1660 1415 1386 1361 1344 32
34 12000 12000 12000 9362 7120 5576 4664 4082 3548 2971 2573 2286 2074 1914 1790 1695 1502 1391 1321 1276 1243 1220 1203 34
36 12000 12000 12000 9229 7150 5493 4518 3902 3491 2971 2538 2230 2004 1832 1702 1597 1394 1278 1206 1159 1125 1100 1083 36
38 12000 12000 12000 9152 7014 5455 4417 3763 3329 2995 2529 2197 1954 1771 1631 1521 1305 1184 1109 1060 1026 1002 982 38
40 12000 12000 12000 9142 6871 5457 4351 3661 3202 2884 2538 2182 1921-1726 1577 1460-1234 = 1106 = 1029 977 942 916 897 40
42 12000 12000 12000 9168 6779 5460 4316 3584 3101 2769 2529 2183 (1903 1697 1537 1413 1173 1041 960 906 869 843 824 42
44 12000 12000 12000 9017 6729 5336 4308 3532 3025 2675 2425 2197 1900 1677 1509 1378 1125 986 900 B45 808 780 761 44
46 12000 12000 12000 68916 6713 5251 4321 3503 2967 2600 2340 2147 1905 1671 1491 1352 = 1085 939 850 793 754 727 706 46
48 12000 12000 12000 8860 6731 5191 4280 3489 2926 2541 2268 2069 (1917 1671 1481 1335 1052 899 807 747 707 678 657 48

6-119

TABLE 6-11. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - ALL EDGES CLAMPED

ij PHYSICAL CONSTANTS:
+
ao) Ex = 1.81x106 PSI
fea)
"| Ey = 1.54x10® PS]
Gxy = 0.45x10® PS|
Bi
Oxy = Oyx = 0.19
THICKNESS=H EQUALS 000625 INCHES
“ines “inches “ines
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 96 59 47 43 40 38 38 38 37 37 37 37 37 37 37 37 37 a7 37 37 30 37 37 6
8 80 54 37 30 26 24 23 23 23 21 21 21 21 21 21 21 21 21 21 21 21 21 21 8
10 76 47 35 24 21 17, 16 16 16 14 14 14 14 14 14 14 14 14 14 12 12 12 12 10
12 7 43 31 24 17 16 14 12 10 10 10 10 10 10 10 9 9 9 9 9 9 9 9 12
14 71 42 28 23 17 14 12 10 9 9 9 9 7 7 7 7 an 1 7 i 7 7 14
16 68 40 28 19 16 iv 10 9 9 7 7 7 7 5 5 5 5 5 5 5 5 5 5 16
18 70 40 26 19 16 12 10 9 7 7 5 5 5 5 5 5 5 3 3 3 3 3 3 18
20 71 38 26 19 14 12 10 9 7 7 5 5 5 5 3 3 eg! 3 3 3 2 5) 20
22 76 38 26 19 14 10 9 9 7 5 5 5 3 3 3 3 3 3 3 3 3 3 3 22
24 83 38 24 17 14 10 9 7 7 5 5 5 3 3 3 3 3 3 2 2 2 2 2 24
26 90 40 24 17 14 10 9 7 7 5 5 5 3 3 3 3 2 2 2 2 2 2 2 26
28 99 42 24 17 14 10 9 7 7 5 5 5 3 3 3 3 2 2 2 2 2 2 2 28
30 108 43 24 17 12 10 9 iz 5 5 5 5 3 3 3 3 2 2 2 2 2 2 2 30
32 118 47 26 17 14 10 9 7 5 5 5 3 3 3 3 3 2 2 2 2 2 2 2 32
34 130 50 26 17 12 10 9 7 5 5 3 3 3 3 3 3 2 2 2 2 2 2 2 34
36 143 54 28 17 12 10 9 7 5 5 3 3 3 3 B 3 2 2 2 2 2 2 36
38 155 57 28 17 12 10 9 7 5 5 3 3 3 3 3 3 2 2 2 2 2 2 2 38
40 169 61 30 aly? 12 10 9 id i Eh e 3 3 3 3 2 2 2 2 2 2 2 2 40
42 183 66 31 19 12 10 9 7 5 5 3 3 3 3 2 2 2 2 2 2 2 2 42
44 198 70 33 19 12 9 7 7 5 5 3 3 3 3 2 2 2 2 2 2 2 2 ° 44
46 216 15 35 19 14 10 7 7 5 5 3 3 3 3 2 2 2 2 2 2 2 C) ° 46
48 231 80 37 21 14 10 7 x4 5 5 3 3 3 3 2 2 2 2 2 2 2 ° to) 48
THICKNESS-H EQUALS 061250 INCHES
LENGTH-8 WIDTH-A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 770 475 382 344 323 313 306 301 297 296 294 292 292 290 290 290 289 287 287 287 231 287 285 6
8 638 433 292 235 209 193 184 179 176 172 170 169 167 167 165 165 163 163 162 162 162 162 162 8
1o 608 374 276 198 162 143 130 123 118 116 113 lll 110 110 108 108 106 106 104 104 104 104 104 10
12 570 344 247 193 144 118 104 96 90 85 83 82 80 78 76 76 75 75 73 73 73 73 73 12
14 565 339 224 176 141 110 92 80 73 70 66 63 61 59 59 57 56 56 54 54 54 54 54 14
16 544 322 219 160 130 108 87 73 64 59 56 52 50 49 47 47 43 43 42 42 42 42 42 16
18 551 320 214 153 120 103 85 70 59 52 49 45 42 40 40 38 37 a5 35 33 33 33 33 16
20 575 309 205 151 113 94 82 70 Sir 50 43 40 38 35 35 33 30 30 28 28 28 26 26 20
22 614 306 203 148 lll 89 75 66 57 49 42 38 35 31 30 30 26 24 24 23 23 23 23 22
24 662 309 202 143 113 85 1 61 56 49 42 37 33 30 28 26 23 21 2l 19 19 19 19 24
26 721 320 196 141 108 85 68 57 52 47 42 35 31 28 26 24 21 19 17 17 17 7 16 26
28 789 334 196 141 104 85 68 56 49 43 40 35 31 28 24 23 19 17 16 1é 16 14 14 28
30 B66 351 198 137 104 82 68 56 47 42 38 35 31 26 24 23 LT 16 14 14 14 12 12 30
32 949 372 203 136 104 80 66 54 45 40 37 33 31 28 24 21 17 14 14 12 12 12 10 32
34 1040 398 209 136 103 80 64 56 45 38 35 31 30 28 24 21 16 14 12 12 10 10 10 34
36 1137 424 217 137 101 80 63 54 45 38 33 30 28 26 24 21 16 14 12 10 10 9 9 36
38 1241 455 228 141 99 78 63 52 45 38 33 30 26 24 23 21 16 iz 10 10 9 :) 9 38
40 1351 487 2368 144 101 78 63 52 43 38 33 28 26 23 21 21 16 12 10 g) S| 9 9 40
42 1467 521 250 148 101 76 63 50 43 38 aa 28 24 23 2. 19 16 12 10 9 9 7 Ul 42 -
44 1591 560 264 153 103 76 61 50 42 37 33 28 24 23 ai 19 16 12 10 9 7) 7 7 ra
46 1719 598 280 160 104 76 61 50 42 37 31 28 24 21 19 17 16 12 10 9 7 4 7 46
4B 1740 640 296 165 108 78 61 50 42 37 31 28 24 21 19 17 14 12 10 9 7 if 7 48

6-120

TABLE 6-11, FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - ALL EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 061875 INCHES

eal aii “nents?
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 2599 1604 1292 1159 1093 1055 1033 1017 1006 998 993 987 986 982 980 979 973 970 968 968 779 966 965 6
8 2150 1462 984 793 702 652 622 603 589 581 574 568 565 561 560 556 553 549 548 548 546 544 544 8
10 2053 1259 935 669 546 480 442 417 402 391 382 375 372 369 365 363 358 355 353 353 351 349 349 10
12 1926 = 1159 831 650 487 402 353 323 302 290 280 273 268 264 261 257 252 250 247 247 245 245 243 12
14 1905 1146 756 591 478 370 309 273 249 233 221 214 207 202 198 196 189 186 184 183 181 181 161 14
16 1837 ©1083 737 537 443 365 290 245 217 198 184 176 169 163 158 155 149 146 143 141 141 139 139 16
18 1858 §=1078 72. 515 403 344 289 235 202 179 163 NED 144 137 132 129 122 116 115 113 111 ill 110 18
20 1940 1045 694 513 384 315 275 235 193 167 149 136 127 120 115 110 103 97 96 92 92 90 90 20
22 2069 = =1033 688 497 375 297 252 224 193 163 1461 127 116 108 103 97 89 83 80 78 76 76 75 22
24 2237 1045 678 482 379 290 238 209 188 162 139 122 110 101 94 89 78 73 70 68 66 64 64 24
26 2437 = 1078 664 478 363 289 231 196 174 158 139 120 106 96 87 82 71 64 61 59 57 56 56 26
28 2600 1125 662 476 355 287 228 189 165 148 136 120 104 92 83 76 64 57 54 52 50 49 49 28
30 2600 «1186 669 464 351 276 228 186 158 139 127 118 104 90 82 7 61 54 49 47 45 43 42 30
32 2600 = 1259 685 459 353 271 224 184 155 134 120 ll 103 92 80 73 57 50 45 42 40 38 38 32
34 2600 1340 706 461 344 269 217 186 153 130 116 104 97 90 82 71 56 47 42 38 37 35 35 34
36 2600 1434 734 464 339 269 214 181 153 129 113 101 92 85 82 73 54 45 40 37 33 33 31 36
38 2600 1535 768 473 337 266 212 176 153 129 lll 97 89 82 76 73 54 43 37 33 31 30 28 38
40 2600 = 1644 805 485 339 261 212 174 148 129 110 96 85 78 73 70 52 42 35 31 30 28 26 40
42 2600 1761 847 501 341 259 212 172 146 127 110 94 83 76 70 66 54 42 35 30 28 26 24 42
44 2600 1886 893 518 346 259 209 172 143 123 110 94 83 75 68 62 54 40 33 30 26 24 23 44
46 2600 2018 942 537 353 259 205 172 143 122 108 94 82 73 66 61 50 40 33 28 24 23 21 46
48 2600 2159 996 560 362 261 203 170 143 120 106 94 82 73 66 59 49 40 33 28 24 23 21 48
THICKNESS-H EQUALS 042500 INCHES
LENGTH-B8 WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 3950 3803 3059 2768 2592 2501 2448 2411 2385 2366 2352 2343 2335 2328 2322 2817 2308 2300 2296 2295 1846 2289 2286 6
8 3950 3464 2331 1881 1664 1545 1474 1429 1399 1377 1359 1349 1338 1332 1325 1319 1311 1304 1300 1295 1293 1292 1290 8
10 3950 2985 2216 1585 1292 1137 1046 989 951 925 906 892 881 873 B66 860 848 841 838 834 831 831 829 10
12 3950 2747 1971 1540 1152 951 836 765 718 687 664 648 634 626 617 612 600 591 586 5B4 581 579 577 12
14 3950 2713 1794 1401 1132 876 732 645 589 551 525 504 490 480 S71 464 450 442 436 433 429 428 426 14
16 3950 2567 1747 1274 1048 866 688 582 515 469 438 415 400 386 377 369 353 344 339) 335 332 330 329 16
18 3950 2554 1709 1220 956 815 685 556 476 422 386 360 341 325 315 306 289 278 271 268 264 262 261 18
20 3950 2479 1643 1217 909 746 652 ebb 459 396 353 323 301 283 271 261 242 231 224 221 217 216 214 20
22 3950 2448 1631 1177 892 706 600 534 459 386 335 301 275 256 242 231 209 196 189 186 183 179 177 22
24 3950 2477 1606 1142 897 687 567 492 445 384 329 289 259 238 221 209 184 172 163 158 155 153 151 24
26 3950 2554 1573 1132 859 683 548 466 412 375 329 283 250 226 207 193 167 153 144 139 136 132 130 26
28 3950 2667 1568 1130 838 678 541 448 389 351 323 283 247 219 198 183 153 137 129 123 118 116 113 28
3c 3950 2811 1585 1102 831 655 541 440 375 332 301 280 247 216 193 176 144 127 116 110 106 103 102 30
32 3950 2981 1622 1090 836 641 532 436 367 318 285 262 245 217 19. 172 136 118 106 99 96 92 90 32
34 3950 3178 1674 1090 817 636 516 440 362 309 275 249 229 216 191 170 132 Td 99 92 87 83 82 34
36 3950 3397 1740 1100 805 638 508 428 362 306 266 240 219 203 193 170 129 106 92 85 80 76 73 36
38 3950 3637 1818 1121 800 631 504 417 362 304 262 231 210 195 183 172 127 103 89 80 75 70 68 38
40 3950 3897 1909 1149 801 619 504 410 351 304 259 228 203 186 174 163 125 99 83 75 70 66 63 40
42 3950 3950 2008 1186 808 614 502 409 B44 301 259 224 200 181 167 156 125 97 82 71 66 61 59 42
44 3950 3950 2117 1226 822 612 492 407 339 294 259 223 196 177 162 149 127 96 80 70 63 57 54 44
46 3950 3950 2234 1272 838 614 487 409 337 289 256 223 195 174 158 146 122 96 78 66 59 54 52 46
48 3950 3950 2361 1325 859 619 485 402 337 285 250 224 195 172 155 141 116 96 76 64 57 52 49 48

6-121

TABLE 6-11, FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - ALL EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 063125 INCHES

“INCHES. “INCHES “INCHES,
6 8 10 12 1s 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 4940 4940 4940 4940-4940 4886-47794 707 4657) = 4622 4594 = 4575 4560 4546 4535 4527 4509 = 4490 4483 4480 3605 4471 4466 6
8 4940 4940 4554 3673 3269 3019 2680 2792 2733 2689 2656 2634 2616 2600 2588 2578 2559 2547 2538 2531 2526 2522 2519 8
10 4940 4940 4330 3098 2524 2220 2044 1933 1858 1808 1770 1742 1721 41704 1691 1681 1658 1644 1636 1629 1624 1622 1618 10
12 4940 4940 3849 3007 2249 1857 1632 1493 1405 1342 1299 1265 1241 1222 1206 1194 1170 1156 1146 1140 1135 1132 1128 12
14 4940 4940 3504 2738 2209 1710 1431 1260 1151 1076 1024 986 958 935 920 906 878 862 852 845 840 836 833 14
16 4940 4940 3412 2489 2049 1691 1345 1139 1006 918 857 812 780 754 735 720 690 673 661 654 648 645 641 16
18 4940 4940 3339 2385 1869 1592 1337 1086 930 826 753 702 664 636 614 596 563 542 530 523 518 513 511 18
20 4960 4839 3211 2376 1775 1457 1272 1083 897 114 690 631 588 555 530 511 473 452 438 429 424 421 417 20
22 4940 4782 3185 2298 1742 1378 1172 1041 895 753 655 588 537 501 473 450 409 386 370 362 355 351 348 22
24 4940 4839 3139 2229 1752 1342 1106 963 869 753 640 563 506 464 433 409 362 335 320 309 304 299 296 24
26 4940 4960 3073 2211 1677 1333 1069 909 805 735 641 553 488 442 405 377 327 297 282 271 262 259 254 26
28 4940 4940 3063 2206 1637 1325 1055 876 761 685 629 553 480 428 388 358 299 269 250 240 231 226 223 28
30 4940 4940 3098 2150 1624 1279 1055 859 732 648 589 546 482 422 377 344 280 247 228 216 207 202 196 30
32 4940 4940 3169 2128 1632 1253 1038 854 714 622 558 513 478 422 374 337 266 229 209 195 186 181 176 32
34 4940 4940 3271 2129 1594 1245 1008 859 706 605 535 487 450 422 375 334 257 216 193 179 170 163 158 34
36 4940 4940 3400 2150 1570 1246 991 834 706 596 521 468 428 398 375 334 250 207 181 165 156 149 144 36
38 4940 4940 3553 2190 1561 1231 984 815 706 593 511 454 410 379 355 335 247 198 172 155 144 137 132 38
40 4940 4940 3727 2246 1566 1210 984 803 687 594 506 443 398 365 339 318 245 193 165 148 136 127 122 40
42 4940 4940 3922 2314 1580 1199 980 196 673 589 504 438 389 353 325 304 245 189 158 141 129 120 113 42
44 4940 4940 4134 2395 1604 1196 963 796 664 574 508 436 384 344 315 292 249 188 155 134 122 113 106 44
46 4940 4940 4363 2486 1637 1199 951 800 659 565 499 436 3al 339 308 283 236 188 151 130 116 106 101 46
48 4940 4940 4610 2588 1677 1210 946 784 657 558 488 438 379 335 302 276 228 188 149 127 ll 103 96 48
THICKNESS=H EQUALS 003750 INCHES
LENGTH-B WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 7200 6230 7200 7200 6
8 7200 7200 7200 6347 5615 5217 4977 4824 4721 4645 4591 4549 4520 4492 4471 4454 4422 4400 4386 4374 4365 4358 4353 8
10 7200 7200 7200 5352 4361 3836 3530 3339 3211 3122 3058 3009 2972 2945 2922 2903 2865 2840 2826 2816 2806 2802 2797 10
12 7200 7200 6651 5196 3887 3209 2821 2581 2425 2319 2242 2187 (2143 2110 2086 2065 2022 1997 1980 1969 1961 1956 1950 12
14 7200 7200 6054 4730 3817 2957 2472 2176 1987 1858 1770 1704 1655 1617 1587 1564 1518 1490 1472 1460 1450 1445 1439 14
16 7200 7200 5896 4301 3541 2924 2326 1968 1738 1587 1481 1405 1347 1304 1271 1245 1192 1161 1142 1130 «1121 «1114 = 1109 16
18 7200 «7200 «45769 4120 3228 2752 2310 1879 1606 1425 1302 1213 1147 1099 1060 1031 972 939 918 904 893 888 881 18
20 7200 7200 5547 4106 3066 2519 2201 1870 1549 1338 1192 1090 1015 960 916 883 817 780 758 T44 734 727 720 20
22 7200 7200 5503 3970 3011 2363 2023 1801 1545 1300 1133 1015 928 866 517 779 706 666 641 626 614 607 601 22
24 7200 7200 5423 3852 3030 2317 1912 1662 1500 1299 1107 972 Big 801 747 706 624 579 553 535 525 516 509 24
26 7200 7200 5309 3819 2899 2305 1848 1571 1392, :1271)—=—«1107 954 843 761 701 654 563 S15 485 468 455 447 440 26
28 7200 7200 5291 3810 2830 2289 1822 1514 1316 1182 1968 954 831 739 671 617 518 464 433 414 400 391 384 28
30 7200 7200 5352 3716 2806 2211 1825 1483 1265 1119-1017 944 831 730 654 594 485 426 393 370 356 348 339 30
32 7200 7200 5476 3677 2820 2166 1792 1474 1234 1076 965 885 826 730 647 581 461 396 360 337 322 311 304 32
34 7200 7200 5651 3678 2755 2149 1742 1483 1220 1046 927 840 TTT 730 647 575 443 374 334 309 294 282 275 34
36 7200 7200 5875 3716 2713 2154 1712 1443 1219 1031 900 807 739 688 648 577 431 356 313 287 269 257, 249 36
38 7200 7200 6140 3764 2698 2128 1698 1408 1220 1024 883 782 709 655 614 581 426 344 297 269 250 238 229 38
40 7200 7200 6440 3880 2705 2091 1700 1387 1186 1026 874 767 688 629 5u4 549 422 334 285 254 235 221 212 40
42 7200 7200 6776 3998 2731 2072 1693 1377 1161 1017 873 756 673 610 563 525 424 329 275 242 221 207 196 42
44 7200 7200 7143 4139 2773 2065 1664 1375 1146 993 876 753 662 596 546 506 428 325 268 233 210 195 184 44
46 7200 7200 7200 4297 2828 2072 1664 1382 1139 975 862 753 657 586 232 490 410 323 262 224 200 184 174 46
48 7200 7200 7200 4473 2898 2091 1634 1356 1137 963 843 758 655 579 321 478 393 325 225) 219 193 176 165 48

6-122

THICKNESS~H

TABLE 6-11.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
(Cont'd)

25-27 OZ. WOVEN ROVING - ALL EDGES CLAMPED

EQUALS 064375 INCHES

FIBERGLASS POLYESTER LAMINATES

MINCHES “INCHES “INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 8400 6
8 8400 8400 8400 8600 8400 68285 7904 7661 7496 7377 7290 7224 7177 7134 7101 7073 7021 6986 6964 6945 6931 6920 6913 8
10 8400 8400 8400 8400 6925 6093 5608 5302 5098 4959 4855 4779 4721 4676 4641 4612 4549 4511 4488 = 4471 4455 444B 4441 10
12 8400 8400 8400 8252 6173 5095 4480 4099 3852 3682 3562 3473 3405 3353 3311 3278 3211 3171 3145 3127 3115 3105 3096 12
14 8400 8400 8400 7511 6063 4695 3923 3457 3155 2952 2809 2705 2627 2567 2522 2434 2409 2364 2338 2319 2303 2293 2286 14
16 8400 8400 8400 6830 5622 4641 3694 3124 2762 2519 2350 2229 2140 2070 2018 1976 1893 1844 1815 1794 1780 1768 1761 16
18 8400 8400 8400 6543 5126 4368 3668 2983 2550 2265 2067 1926 1822 1744 1684 1636 1544 1490 1457 1436 1420 1410 1401 18
20 8400 8400 8400 6520 4869 4000 3494 2971 2461 2124 1895 1731 1613 1523 1455 1401 1299 1239 1205 1180 1165 1152 1144 20
22 8400 8400 8400 6305 4780 3784 3212 2860 24654 2065 1799 1611 1476 1373 1297 1236 1121 1057 1019 993 975 963 954 22
24 8400 8400 8400 6117 4810 2680 3035 2640 2383 2063 1757 1544 1389 1274 1187 1119 991 921 878 852 833 820 810 24
26 8400 8400 8400 6065 4605 3659 2936 2494 2209 2016 1757 1514 1338 1210 1113 1038 895 817 772 742 723 709 699 26
28 8400 8400 8400 6051 4494 3635 2894 24046 2089 1877 1730 1516 1319 1173 1064 980 822 739 688 657 636 621 610 28
30 8400 8400 8400 5903 4457 3511 2898 2355 2009 1778 1615 1498 1321 1158 1038 944 770 676 622 589 567 551 539 30
32 8400 8400 8400 5837 4478 3440 2847 2341 1961 1707 1531 1406 1312 1161 1026 923 730 629 572 535 511 494 482 32
34 8400 8400 8400 5841 4375 3412 2766 2354 1938 1662 1471 1335 1234 1158 1927 914 704 593 530 490 466 447 435 34
36 8400 8400 8400 5902 4309 3421 2719 2291 1936 1636 1429 1281 1173 1092 1029 916 687 567 497 455 428 409 396 36
38 8400 8400 8400 6011 4285 3378 2698 2235 1938 1625 1403 1243 1126 1040 973 921 676 546 471 426 396 377 363 38
40 8400 8400 8400 6162 4295 3320 2700 2202 1883 1631 1389 1217 1093 1000 928 873 673 532 452 403 372 351 335 40
42 8400 8400 8400 6350 4335 3289 2689 2185 1844 1617 1385 1201 1069 968 893 834 674 521 436 384 351 329 313 42
44 8400 8400 8400 6571 4403 3280 2640 2185 1820 1577 1392 1194 1052 946 866 803 680 516 424 369 334 309 292 44
46 8400 8400 8400 6823 4492 3291 2609 2194 1808 1547 1368 4196 1043 930 845 779 652 515 415 356 318 294 276 46
48 8400 8400 8400 7103 4603 3320 2595 2154 1804 1530 1338 1203 1041 520 829 760 624 516 410 348 308 280 261 48
THICKNESS-H EQUALS 065000 INCHES
LENGTH-B WIDTH-A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

,

6 9600 9600 9600 9600 9600 9600 9600 9604 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 6

8 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 9600 8
10 9600 9600 9600 9600 9600 9093 8370 7914 7610 7402 7247 7134 7047 6979 6927 6884 6792 6734 6699 6675 6651 6640 6628 10
12 9600 9600 9600 9600 9215 7605 6686 6119 5750 5497 5317 5184 5983 5005 4944 4893 4792 4733 4693 4669 4648 4636 4622 12
14 9600 9600 9600 9600 9050 7007 5858 5159 4711 4407 4193 4038 3922 3833 3763 3708 3595 3530 3489 3461 3438 3423 3412 14
16 9600 9600 9600 9600 8393 6929 5514 4664 4123 3760 3510 3327 3193 3091 3012 2950 2826 2753 2708 2679 2656 2640 2628 16
18 9600 9600 9600 9600 7652 6520 5474 4454 3807 3379 3085 2875 2720 2602 2514 2442 2303 2223 2175 2142 2119 2103 2091 18
20 9600 9600 9600 9600 7270 5969 5215 4434 3673 3172 2828 2585 2408 2274 2171 2093 1936 1851 1797 1763 1738 1721 1707 20
22 9600 9600 9600 9411 7136 5649 4796 4268 3664 3082 2686 2406 2202 2051 1935 1846 1672 1578 1519 1481 14657 1438 1424 22
24 9600 9600 9600 9131 7179 5495 4532 3941 3557 3080 2623 2303 2072 1902 1771 1672 1479 1373 1311 1271 1243 1224 1210 24
26 9600 9600 9600 9053 6873 5462 4382 3723 3299 3011 2623 2260 1999 1806 1669 1549 1335 1220 1151 1107 1078 1057 + 1043 26
28 9600 9600 9600 9032 6708 5427 4320 3588 3119 2802 2581 2263 1968 1752 1589 1464 1227 1102 1027 980 949 927 911 28
30 9600 9600 9600 8811 6652 5241 4325 3517 3000 2653 2411 2237 #1971 1730 1549 1410 1349 1010 930 880 845 822 805 30
32 9600 9600 9600 8714 6684 5137 4250 3494 2927 2548 2286 2098 1959 1731 1531 1378 1092 940 854 798 763 737 720 32
34 9600 9600 9600 8719 6531 5095 4130 3515 2893 2481 2195 1992 1843 1728 1535 1366 1050 887 791 734 695 668 648 34
36 9600 9600 9600 8810 6433 5105 4059 3619 2891 2442 2133 1912 1752 1631 1537 1368 1024 845 742 680 640 610 591 36
38 9600 9600 9600 8971 6397 5043 4026 3338 2894 2427 2093 1857 1683 1552 1453 1375 1008 815 704 636 593 563 542 38
40 9600 9600 9600 9197 6413 4956 4029 3287 2811 2434 2072 1817 1631 1493 1387 1304 1003 793 674 601 555 523 501 40
42 9600 9600 9600 9479 6472 4909 4014 3263 2753 2413 2069 1794 1594 1446 1333 1246 1005 779 650 574 523 490 466 42
44 9600 9600 9600 9600 6573 4897 3942 3261 2717 2352 2077 1783 1571 1411 1292 1199 1015 770 633 551 497 461 436 44
46 9600 9600 9600 9600 6706 4912 3896 3275 2698 2310 2043 1785 1558 1389 1260 1161 972 768 621 532 476 438 412 46
48 9600 9600 9600 9600 6870 4956 3873 3214 2694 2282 1999 1796 1552 1373 1238 1133 932 770 612 518 459 417 389 48

6-123

TABLE 6-11. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
25-27 OZ. WOVEN ROVING - ALL EDGES CLAMPED (Cont'd)

THICKNESS-H EQUALS 005625 INCHES

WIDTH=A LENGTH-B

MINCHES, INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 6
8 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 10800 8
lo 10800 10800 10800 10800 10800 10800 10800 10800 10800 10539 10320 10157 10033 9938 9863 9801 9670 9588 9538 9503 9469 9455 9437 10
12 10800 10800 10800 10800 10800 10800 9519 8712 8186 7826 7570 7381 7237 7125 7038 6967 6825 6739 6682 6647 6619 6600 6581 12
14 10800 10800 10800 10800 10800 9978 8340 7346 6706 6274 5971 5749 5583 5458 5359 5281 5119 5025 4968 4928 4895 4872 4859 14
16 10800 10800 10800 10800 10800 9865 7850 6640 5870 5354 4996 4737 4547 4401 4288 4200 4024 3920 3856 3814 3783 3758 3743 16
18 10800 10800 10800 10800 10800 9284 7795 6340 5422 4813 4393 4094 3873 3706 3579 3478 3280 3167 3098 3051 3018 2995 2978 18
20 10800 10800 10800 10800 10350 8500 7426 6314 5231 4516 4028 3680 3426 3237 3092 2979 2759 2635 2559 2508 2475 2449 2430 20
22 10800 10800 10800 10800 10159 8043 6828 6075 5218 4389 3823 3424 3136 2920 2755 2628 2381 2246 2164 2110 2074 2048 2027 22
24 10800 10800 10800 10800 10223 7822 6453 5611 5064 4384 3736 3280 2952 2707 2522 2380 2105 1956 1867 1810 1770 1742 1721 24
26 10800 10800 10800 10800 9788 7777 6239 5302 4697 4287 3736 3219 2847 2571 2364 2204 1902 1737 1639 1577 1535 1505 1485 26
28 10800 10800 10800 10800 9552 7727 6150 5109 4441 3991 3675 3221 2802 2494 2263 2084 1749 1568 1462 1396 1351 1319 1297 28
30 10800 10800 10800 10800 9472 7464 6159 5006 4271 3777 3433 3186 2806 2461 2204 2008 1636 1439 1325 1252 1205 1172 1147 30
32 10800 10800 10800 10800 9517 7313 6051 4975 4168 3630 3256 2986 2788 2467 2189 1963 1554 1338 1215 1137 1086 1050 1024 32
34 10800 10800 10800 10800 9298 7254 5881 5003 4120 3532 3125 2837 2623 2461 2185 1945 1495 1262 1126 1043 989 951 925 34
36 10800 10800 10800 10800 9159 7270 5778 4867 4115 3477 3037 2724 2494 2321 2189 1949 1458 1203 1057 968 909 869 841 36
38 10800 10800 10800 10800 9107 7179 5733 4753 4120 3456 2979 2642 2395 2211 2069 1959 1436 1159 1003 907 B45 801 772 38
40 10800 10800 10800 10800 9130 7057 5736 4680 4003 3464 2952 2588 2322 2124 1975 1857 1429 1128 960 857 791 744 713 40
42 10800 10800 10800 10800 9215 6990 5716 4646 3920 3435 2945 2554 2270 2060 1898 1773 1432 1109 927 817 746 697 664 42
44 10800 10800 10800 10800 9357 6972 5613 4643 3868 3350 2959 2540 2237 2011 1839 1707 1445 1097 902 784 707 657 621 44
46 10800 10800 10800 10800 9548 6995 5547 4662 3842 3291 2908 2541 2218 1976 1796 1655 1384 1093 885 758 678 624 586 46
48 10800 10800 10800 10800 9783 7056 5514 4575 3836 3251 2846 2555 2211 1956 1763 1613 1328 1097 873 737 652 594 555 48
THICKNESS-H EQUALS 026250 INCHES
LENGTH-B WIDTH=A LENGTH=-B
INCHES INCHES INCHES
6 8 10 12 4 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 12000 12000 12000 12000 12000 12000 12000 12006 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 6
8 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 8
10 12000 12000 12000 12000 12000 12000 12000 12004 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 12000 1200q 12000 10
12 12000 12000 12000 12000 12000 12000 12000 11951 11229 10734 10385 10124 9927 9773 9655 9559 9361 9244 9166 9117 9079 9053 9027 12
14 12000 12000 12000 12000 12000 12000 11440 10077 9199 6606 6191 7887 7659 7487 7351 7243 7023 6894 6814 6760 6715 6684 6665 14
16 12000 12000 12000 12000 12000 12000 10767 9109 8052 7344 6854 6500 6237 6039 5884 5761 5519 5377 5290 5232 5187 5156 5133 16
18 12000 12000 12000 12000 12000 12000 10692 8697 7436 6602 6025 5615 5312 5083 4909 4772 4500 4344 4248 4184 4139 4108 4083 18
20 12000 12000 12000 12000 12000 11661 10186 8660 7174 6195 5524 5048 4700 4440 4241 4087 3784 3614 3510 3442 3395 3360 3334 20
ae 12000 12000 12000 12000 12000 11035 9366 8335 7158 6020 5244 4697 4301 4005 3779 3605 3268 3080 2967 2894 2844 2809 2781 22
24 12000 12000 12000 12000 12000 10731 8851 7697 6946 6015 5125 4499 4049 3713 3459 3265 2889 2684 2561 2482 2428 2390 2361 24
26 12000 12000 12000 12000 12000 10668 8558 7273 6442 5879 5125 4415 3904 3527 3244 3025 2607 2381 2249 2164 2107 2065 2036 26
28 12000 12000 12000 12000 12000 10600 8436 7009 6091 5474 5041 4419 3845 3421 3105 2860 2399 2152 2006 1916 1853 1811 1778 28
30 12000 12000 12000 12000 12C00 10239 8448 6868 5858 5182 4711 4370 3849 3378 3023 2753 2244 1973 1817 1717 1651 1606 1573 30
32 12000 12000 12000 12000 12000 10032 8299 6825 5717 4978 4466 4097 3826 3383 2992 2693 2131 1836 1665 1559 1490 1441 1405 32
34 12000 12000 12000 12000 12000 9950 8066 6865 5651 4845 4288 3890 3598 3376 2997 2667 2051 1731 1545 1432 1356 1305 1267 34
36 12000 12000 12000 12000 12000 9973 7927 6679 5646 4770 4167 3736 3421 3185 3002 2674 1999 1650 1451 1328 1248 1192 1154 36
38 12000 12000 12000 12000 12000 9847 7864 6519 5651 4740 4088 3624 3287 3033 2839 2687 1969 1591 1375 1243 1158 1100 1059 38
40 12090 12000 12000 12000 12000 9681 7869 6420 5491 4753 4049 3550 3186 2915 2708 2547 1959 1549 1316 1175 1083 1022 979 40
42 12000 12000 12000 12000 12000 9588 7841 6373 5378 4711 4040 3504 3115 2825 2604 2434 1964 1521 1271 1119 1022 956 911 42
44 12000 1200C 12000 12000 12000 9564 7699 6369 5305 4596 4059 3484 3068 2759 2524 2341 1983 1505 1238 1074 972 900 852 44
46 12000 12000 12000 12000 12000 9595 7610 6395 5269 4513 3989 3485 3042 2712 2461 2268 1898 1500 1213 1040 928 855 803 46
48 12000 12000 12000 12000 12900 959679 7565 6277 5262 4459 3902 3506 3033 2682 2418 2213 1822 1504 1196 1012 895 815 761 48

6-124

TABLE 6-12.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - ALL EDGES SIMPLY SUPPORTED

FIBERGLASS POLYESTER LAMINATES

PHYSICAL CONSTANTS:

Ex 1.96x10° PSI

Ey = 1.70x10® PSI

Gxy = 0.52x10® PSI
F Oxy = Oyx = 0420
THICKNESS=H EQUALS 000625 INCHES
LENGTH=-8 WIDTH=A SiniCes
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 37 23 17 15 ig 12 12 11 11 Ly 11 11 11 10 10 10 10 10 10 10 10 10 10 6
8 42 21 14 11 9 8 8 7 i, 7 6 6 6 6 6 6 6 6 6 6 6 6 6 :
10 38 23 13 10 8 6 6 5 5 5 5 4 4 C) 4 4 4 A) 4 a 4 a es 10
12 oF 23 14 9 Fd 6 5 4 4 4 3 3 3 | 3 3 | 3 eh 3 3 3 3 12
14 39 21 15 10 7 5 4 4 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 4
16 38 21 14 10 a 5 4 3 3 3 2 a 2 2 2 2 2 2 2 2 2 2 i 16
18 37 22 14 10 8 5 4 3 3 3 2 2 2 2 2 2 1 1 1 1 1 1 i 18
20 38 22 13 10 8 6 4 3 3 2 2 2 2 2 2 1 Hh 1 1 1 1 1 1 20
22 37 21 14 9 7 6 4 3 3 2 2 2 2 1 1 1 i 1 x 1 1 1 1 22
24 37 21 14 9 7 6 5 4 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 24
26 38 21 14 9 7 5 5 4 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 26
28 37 21 13 10 7 5 4 4 3 2 2 2 1 1 1 1 1 1 1 i 1 1 1 28
30 37 21 13 10 iz 5 rs 4 3 3 2 2 1 1 2 1 1 1 1 a af 1 i 30
32 38 21 14 9 7 5 4 3 3 3 2 2 2 1 1 1 1 1 1 ii 1 ° ) 32
34 37 21 14 9 7 5 4 3 3 3 2 2 2 1 1 1 1 1 i fi ° ° 0 a4
36 a7 21 14 9 7 5 4 3 3 3 ‘4 2 2 at 1 1 a 1 1 (o) io) te) ° 36
38 38 21 13 9 7 5 4 3 3 2 2 2 2 1 1 1 1 1 1 0 0 0 0 38
40 37 21 13 10 7 5 4 3 3 2 2 2 2 1 1 1 1 1 8 o a 9 2 oY
42 37 21 14 9 7 5 4 3 3 2 2 2 2 1 1 nt 1 rt 0 0 0 0 0 42
44 37 21 14 9 5 4 3 3 2 2 2 2 1 1 1 1 1 0 0 ° 0 ° 44
46 37 2. 13 9 us 5 4 3 3 2 2 2 2 1 a il 1 1 ) ° ° ° ° 46
48 37 21 13 9 i 5 4 3 4 2 2 2 2 1 z 1 1 1 ° ° ° ) ° 48
THICKNESS=H EQUALS 041250 INCHES
LENGTH=B WIDTH=A LENGTH=-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 299 181 137 117 106 99 94 91 89 a7 86 85 84 84 83 83 82 81 81 80 80 80 80 6
8 336 168 112 87 1% 66 61 57 55 53 52 51 50 49 49 48 47 47 46 46 46 45 45 8
10 306 181 108 ia 61 52 46 42 39 38 36 35 34 ce 33 32 ehh 31 30 30 30 29 29 10
12 299 181 114 75 56 45 39 34 31 29 28 26 26 25 24 24 23 22 21 21 21 21 21 12
14 311 170 121 78 55 42 35 30 27 25 23 21 20 20 19 18 17 17 16 16 16 15 15 14
16 301 168 112 84 57 42 33 28 24 22 20 18 17 16 16 15 14 13 13 12 12 12 12 16
18 299 173 108 80 60 43 33 27 23 20 18 16 15 14 14 13 12 1 10 10 10 10 10 18
20 306 172 108 77 61 45 34 27 22 19 17 15 14 13 12 11 10 9 9 9 8 8 8 20
22 300 169 110 75 58 48 35 27 22 19 16 14 13 12 il 10 9 8 8 7 T 7 il 22
24 299 168 112 75 56 45 37 28 23 19 16 14 12 11 10 10 8 7 7 6 6 6 6 24
26 303 a7 109 76 55 43 36 30 23 19 16 14 12 ql 10 9 8 7 6 6 5 5 5 26
28 299 170 108 78 55 42 35 30 24 19 16 14 12 ql 10 9 7 6 6 5 5 5 4 28
30 299 168 108 77 56 42 24 29 25 20 17 14 12 ll 9 9 7 6 5 5 4 4 4 30
32 301 168 109 75 57 42 33 28 24 21 17 16 12 1 9 8 6 5 5 4 4 4 4 32
34 299 170 110 Re) 57 42 33 27 24 21 18 15 12 at, 9 8 6 5 =) 4 4 3 3 34
36 299 169 108 75 56 43 33 2a 23 20 18 15 13 ll 9 8 6 >) 4 4 3 3 3 36
38 300 168 108 pA 55 44 34 er 23 20 17 16 13 Np 10 8 6 Le} 4 4 El 3 3: 38
40 299 168 108 76 55 43 34 27 22 19 17 15 13 11 10 8 6 5 4 3 3 3 3 40
42 299 170 108 76 55 42 35 27 22 19 16 15 13 12 10 9 6 5 4 3 3 3 3 42
44 200 169 109 75 55 42 34 27 22 19 16 14 13 12 10 9 6 5 4 3 3 3 2 44
46 299 168 108 75 56 42 34 28 22 19 16 14 he} 12 ll 9 6 DB 4 2 =| 3 3 46
48 299 168 108 75 56 42 33 28 23 19 16 14 12 11 10 9 6 5 4 3 3 2 2 48

lA)

TABLE 6-12. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 001875 INCHES

LENGTH=8 WIDTH=A LenGTHag

INCHES INCHES

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78 |
6 1010 609 464 395 357 334319 308 301 295 291 287 = 285 282 280 279 276 274 272 271 270 270 269 6
a 1133 568 378 293.249 222 205 194 185 179 175 171-168 166 164 163 159 157 156 154 154 153 153 8
10 1034 612 364 258 205 174 155 142 133 127 122 11g s115 112 110 109 105 103 102 100 100 99 99 10
12 1010 = 609 383 253 188 152 130 116 106 99 93 89 86 84 81 80 76 14 72 71 70 70 69 12
14 1051 574 407 263 186 143 118 102 91 83 77 73 69 66 64 62 59 56 55 54 53 52 52 14
16 1017 568 378 283 191 142 113 94 82 73 67 62 58 56 53 51 47 45 43 42 41 41 40 16
18 1010 583 365 271 203 146 112 91 17 68 61 56 52 48 46 44 40 37 35 34 33 33 32 18
20 1032 582 364 258 205 153 115 91 75 65 57 51 a7 44 4. 39 34 32 30 29 28 27 27 20
22 1012 569 370 253 194 161 119 93 75 63 55 49 44 40 37 35 30 28 26 25 24 23 23 22
24 1010 568 378 253 188 152 126 96 76 63 54 47 42 38 35 33 28 25 23 22 al 20 19 24
26 1022 576 368 256 186 147 123 100 79 64 54 46 41 37 33 31 26 22 20 19 18 18 17 26
28 1010-574 364 263 186 143 118 102 82 66 54 46 40 36 32 30 24 21 19 17 16 16 15 28
30 1010 568 364 258 188 142 115 97 86 68 56 47 40 36 32 29 23 19 17 16 15 14 14 30
32 1017 568 367 254 191 142 113 94 82 71 57 48 41 36 31 28 22 18 16 15 14 13 12 32
34 1010 514 370 252 192 143 112 92 79 70 60 49 42 36 31 28 21 18 15 14 13 12 ll 34
36 1010 571 365 253 188 146 112 91 77 68 61 51 43 36 32 28 21 i? 14 13 12 ll 10 36
38 1014 568 363 255 186 148 113 a1 76 66 59 53 44 37 32 28 21 16 14 12 11 10 10 38
40 1009 568 364 258 185 145 115 91 75 65 57 51 45 38 32 29 21 16 13 12 ll 10 9 40
42 1010 572 366 255 186 143 117 92 75 64 56 50 45 39 34 29 21 16 13 ql 10 9 9 42
44 1012 569 367 253 187 142 116 93 75 63 55 49 44 40 35 30 21 16 13 ll 10 9 8 44
46 1009 568 364 252 189 142 114 94 76 63 54 4B 43 39 36 <hl 21 16 13) ay 9) 8 8 46
48 1010 568 363 253 188 142 113 94 76 63 54 47 42 38 35 31 al 16 13 10 9 8 7 48

THICKNESS-H EQUALS 062500 INCHES
LENGTH=B WIDTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 2395 1444 1099 936 B47 792 756 731 713 699 689 681 675 669 665 661 654 649 645 643 641 640 638 6
8 2685 1347 896 695 589 527 487 459 440 425 414 406 399 393 389 385 377 372 369 366 364 363 362 8
10 2450 1450 862 613-486 413 367 337 316 300 288 279272 266 262 258 250 244 9 241 238 236 235 234 10
12 2395 1444 = 908 599 446 361 309 275 251 234 221 212-204 198 193 189 180 175 171 169 167 165 164 12
14 2490 1360 965 623. 440 340 280 241 215 196 182 172164 157 152 148 139 133 130 127 125 123 122 14
16 2410 1347 896 671 454 337 268 224 194 174 159 147-139 132 126 122 112 106 102 100 98 96 95 16
18 2395 1381 866 642481 345 266 = 216 183 160 144 132 22 115 109 104 94 88 84 81 19 78 17 18
20 2446 = 1378 862 613 486 362 272 216 179 153 135 121 111 103 97 92 81 75 71 68 66 64 63 20
22 2399 1349 878 600 461 382 283 219 17h 150 130 115.104 95 89 83 T2 66 61 58 56 55 53 22
24 2395 1347 896 599 446 361 298 227 181 150 128 112-100 90 83 77 65 59 54 51 49 47 46 24
26 2423 1366 872 607 440 AGA 292 238 186 152 128 110 97 87 7 t2) 60 53) 49 45 43 42 40 26
28 2395 1360 862 623. 440 340 280 241 194 156 129 110 96 85 77 70 57 49 44 41 39 37 36 28
30 2395 1346 862 613.445 337 272 231 203 161 132 ii 96 84 15 68 54 46 41 37 35 33 32 30
32 2410 1347 871 602 454 337 268 224 194 168 136 113 97 84 75 67 52 43 38 35 32 30 29 32
34 2393 1359 877 598 455 340 266 219 188 166 141 bh Wed 98 85 75 66 51 42 36 afl 30 28 27 34
36 2395 1353 866 599 446 345 266 216 183 160 144 120 iol Be 75 67 50 40 34 31 28 26 25 36
38 2402 1346 861 603 441 351 268 215 180 156 139 125 104 88 76 67 49 39 33 29 26 24 23 38
40 2392 1347 B62 611 O39 345 272 216 i179 153 135 121 107 91 78 68 49 38 32 28 25 rx} 21 40
42 2395 1356 868 604 440 340 277 217 178 151 132 118 107 93 80 69 49 38 31 27 24 22 20 42
44 2399 1349 869 600 443 337 274 219 178 150 130 115 104 95 82 7 49 37 30 26 23 21 19 44
46 2392 1345 863 598 447 336 270 223 179 149 128 113 102 93 85 73 50 37 30 25 22 20 18 46
48 2395 1347 861 599446 337 268 224 181 150 128 112 100 90 83 75 50 37 30 25 22 19 18 48

6-126

TABLE 6-12.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - ALL EDGES SIMPLY SUPPORTED

THICKNESS=H EQUALS 0463125 INCHES

FIBERGLASS POLYESTER LAMINATES

(Cont'd)

tats pee oon
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 4678 2821 «2166-1829 «1654 «1547-1477: 1428 «1393-1366 = 1347 «1332-1328 «1307 1298) 12921277) 1267) 12611256) 125212501247 6
8 5245 2631 1749 1358 1151 1029 950 897 859 831 809 792 179 768 760 752 737 727 720 715 711 709 706 8
10 4786 2832 1684 1197 949 807 718 658 617 546 563 546 532 520 511 504 487 477 470 465 461 459 457 10
12 4678 2821 1774 1169 872 705 603 537 490 457 432 413 399 387 377 369 352 B42 334 330 326 323 321 12
14 4864 2656 1885 1216 859 664 547 471 420 383 356 336 320 307 297 289 271 260 253 248 244 241 239 14
16 4707 2631-1750 :1311 886 658 523 437 380 339 310 288 271 257 246 238 219 208 200 195 191 188 186 16
18 4678 2698 1691 1254 940 675 520 423 358 313 281 257 = 238 224 213 203 184 172 164 159 155 152 150 18
20 47772692, 1684 =—1197 949 708 531 421 349 299 264 237 217 202 189 179 159 147 138 133 129 126 124 20
22 4685 2635 1714 1171 900 746 553 429 3468 293 254 225 203 187 173 163 141 128 120 114 110 107 104 22
24 4678 2631 1750 1169 872 705 583 443 353 292 249 218 194 176 162 151 128 114 106 100 95 92 90 24
26 4733 2667 1704 1186 859 679 570 464 364 296 249 215 189 170 155 142 118 104 95 89 84 81 79 26
28 4677 2656 1684 1216 859 664 547 471 378 304 252 215-187 166 150 137 ill 96 86 80 76 72 70 28
30 4678 2630 1684 1197 869 657 532 451 396 315 258 217-187 164 147 133 105 90 80 73 69 65 63 30
32 4707 2631 1701 = 1177 886 658 523 437 380 328 266 222 189 164 146 131 101 85 75 68 63 59 57 32
34 4674 2655 1712 1168 888 664 519 428 367 325 276 228 ©6192 166 146 130 99 81 70 63 58 55 52 34
36 4678 2642 «1691 ~=—-1169 872 675 520 423 358 313 281 235 197 169 147 130 97 78 67 60 54 51 48 36
38 4693 2628 1682 1178 862 687 524 421 352 305 271 244 203 172 149 131 96 16 64 57 51 48 45 38
40 4672 2631 1684 1194 858 673 531 421 349 299 264 237-210 177 152 133 95 75 62 54 49 45 42 40
42 4678 2649 1695 1181 859 664 540 424 347 295 258 230 209 182 156 135 95 14 61 52 47 43 40 42
44 4685 2635 1698 1171 865 659 536 429 348 293 254 225 203 187 160 138 96 73 60 51 45 41 38 44
46 4671 2628 1686 1168 874 657 528 435 350 292 251 221 «198 181 165 142 97 73 59 50 43 39 36 46
48 4678 2631 1682 1169 872 658 523 437 353 292 249 218° 194 176 162 146 98 73 58 49 42 38 34 48
THICKNESS-H EQUALS 043750 INCHES
LENGTH-8 WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7090 4875 = 33709 3160 2857 =. 2673-2552 2467 «= 2407 = 2361 02327 2300-2278 )=— 2259S 2244 «= 2232, 2207) «2190S 2178 = 2170 216321600 2155 6
8 7090 4547 3023 2346 1989 1777 1642 1550 1484 1435 1399 1369 1347 1328 1313 1300 1273 1256 1244 1235 1229 1225 1220 8
10 7090 4893 2910 2068 1640 1394 1240 1138 1065 1013 973 943-919 899 883 870 B42 824 812 804 797 793 790 10
12 7090 4875 3065 2021 1506 1219 1043 927 847 790 747 714 689 668 652 638 609 590 578 569 563 558 555 12
14 7090 4590 3258 2101 1485 1148 945 814 726 662 616 580 553 531 513 499 469 450 437 428 422 417 413 14
16 7090 4547 3023 2266 1531 1137 904 756 656 586 535 497 468 444 426 411 379359 346 337 330 325 321 16
18 7090 4662 2922 2167 1625 1166 898 730 619 542 486 444 412 387 367 351 317 297 284 274 267 262 259 18
20 7090 4652 2910 2068 1639 1223 917 727 603 517 455 410 375 348 327 310 275 253 239 230 223 218 214 20
22 7090 4554 2963 2024 1555 1289 955 741 601 506 438 389 9351 322 299 281 244 221 207 197 190 185 180 22
24 7090 4547 3023 2021 1506 1219 1007 766 611 505 431 377-336 305 280 261 221 197 182 172 165 159 155 24
26 7090 4609 2944 2049 1485 1174 985 802 629 512 430 chp VET 293 267 246 204 179 164 153 146 140 136 26
28 7090 4590 2909 2101 1485 1148 945 814 654 525 436 371 323 287 259 236 191 166 149 138 130 125 120 28
30 7090 4544 2910 2068 1501 1136 919 780 685 544 446 375-323 284 254 230 182 155 138 126 118 113 108 30
32 7090 4547 2939 2033 1531 1137 904 756 656 566 459 383-327 284 252 226 175 147 129 117 109 103 98 32
34 7090 4588 «2959 2019 1535 1147 897 740 635 561 476 393 332 287 252 224 171 140 122 109 101 94 90 34
36 7090 4565 2922 2021 1506 1166 898 730 619 542 486 406 341 291 254 225 167 135 116 103 94 88 83 36
38 7090 4541 2907 2036 1490 1186 905 727 609 527 469 421 351 298 258 226 166 132 lll 98 89 82 77 38
40 7090 4547 2910 2064 1483 1163 917 Tet 602 517 455 410 362 306 263 229 165 129 108 94 84 78 72 40
42 7090 4577 2929 «2040 «14851147 934 732 600 510 445 398 362 315 269 233 165 128 105 90 81 7% 68 42
44 7090 4554 2934 2024 1494 1138 926 741 601 506 438 389 351 322 277 239 166 126 103 88 78 70 65 44
46 7090 4546 2913 2018 1510 1135 913 752 605 504 434 382 343 313 285 245 168 126 101 86 75 68 62 46
48 7090 4547 2906 2021 1506 1137 904 756 611 505 431 377-336 305 280 252 170 126 100 84 73 65 59 48

G=l27

TABLE 6-12. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 004375 INCHES

LENGTH-8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 a 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 8270 7741 5889 5018 4537 4244 4052 3918 3822 3748 3695 3652 3617 3587 3563 3545 3504 3477 3459 3445 3434 3431 3422 6
8 8270 7220 48C1 3725 3158 2822 2608 2461 2356 2279 2221 2174 2139 2108 2085 2065 2021 1994 1976 1961 1952 1946 1938 6
10 8270 7770 4621 3283 26046 2214 1969 1806 1692 1609 1546 1497 1459 1428 1403 1382 1337 1309 1290 1276 1266 1259 1254 10
12 8270 7741 4867 2209 2392 1935 1656 1472 1346 1254 1187 1134 1094 1061 1035 1013 966 937 918 904 894 886 861 12
14 8270 7289 5173 3337 2358 1822 1501 1293 1152 1052 978 922 878 843 815 793 744 714 694 680 670 662 656 14
16 8270 7220 48C1 3598 2431 1805 1435 1200 1042 931 850 790 743 706 676 652 601 570 549 535 524 516 510 16
16 8270 7404 4646 3440 2580 1851 1426 1160 983 860 771 705 654 615 583 558 504 472 450 435 425 416 411 18
20 8270 7387 4621 3283 2603 1943 1456 1155 957 821 723 651 596 553 520 492 436 402 380 365 354 346 339 20
22 8270 7231 4705 3214 2469 2047 1516 1176 955 803 696 617 558 512 476 446 387 351 328 313 301 293 287 22
24 8270 7220 4801 3209 2392 1935 1599 1217 970 802 684 598 533 484 445 414 351 314 290 273 262 253 247 24
26 8270 7319 4675 3253 2358 1864 1564 1273 998 813 684 590 519 466 424 391 324 285 260 243 231 222 216 26
28 8270 7288 4620 3337 2358 1822 1501 1293 1038 834 692 589 hig) 456 411 375 304 263 237 219 207 198 191 28
30 8270 7216 4621 3283 2384 18046 1459 1239 1088 863 708 596 513 451 403 365 289 246 219 201 188 179 172 30
32 8270 7220 4667 3229 2431 1805 1435 1200 1042 899 729 608 519 451 399 359 278 233 204 186 172 163 156 32
34 8270 7285 4699 3206 2438 1821 1425 1175 1008 891 756 624 528 455 400 356 271 223 193 173 160 150 143 34
36 8270 7249 4640 3209 2392 1851 1426 1160 983 860 771 645 541 463 403 357 266 215 184 164 150 139 132 36
38 8270 7212 4615 3234 2365 1884 1437 1154 967 837 744 669 557 473 409 359 263 209 177 156 141 130 123 38
40 8270 7220 4621 3277 2355 1847 1456 1155 957 821 723 651 576 486 417 364 262 205 171 149 134 123 115 40
42 8270 7268 4652 3239 2358 1822 1483 1163 953 810 707 632 575 501 427 371 262 202 167 144 128 117 109 42
44 8270 7231 4659 3214 2372 1808 1471 1176 955 803 696 617 558 512 439 379 264 201 163 139 123 112 103 44
46 8270 7210 4626 3204 2397 1802 1449 1194 960 801 688 606 544 496 453 389 266 200 161 136 119 107 98 46
48 8270 7220 4614 3209 2392 1805 1435 1200 970 802 684 596 533 484 445 400 270 201 159 133 116 103 94 48
THICKNESS=H EQUALS 065000 INCHES
LENGTH=B WIOTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 9450 9450 8791 7490 6773 6335 6048 5848 5705 5595 5515 5452 5400 5355 5318 5292 5231 5190 5163 5143 5126 5121 5108 6
8 9450 9450 7166 5561 4714 4213 3892 3673 3517 3402 3315 3246 3193 3147 3113 3082 3017 2977 2949 2927 2914 2904 2893 8
10 9450 9450 689T 4901 3887 3304 2940 2696 2526 2401 2308 2234 2177 2132 2094 2063 1996 1953 1925 1905 1890 1879 1871 10
12 9450 9450 7265 4790 3570 2889 2471 2198 2009 1872 1771 1693 1632 1584 1545 1512 1443 1399 1370 1350 1334 1323 1314 12
14 9450 9450 7722 4981 3519 2720 2240 1931 1720 1570 1459 1376 1310 1259 1217 1183 1111 1066 1036 1015 999 988 979 14
16 9450 9450 7166 5370 3629 2694 2142 1791 1556 1390 1269 1179 1109 1053 1009 973 897 851 820 798 782 770 762 16
18 9450 9450 6926 5136 3852 2763 2129 1731 1468 1284 1151 1052 977 918 870 832 753 704 672 650 634 622 613 18
20 9450 9450 6897 4901 3886 2900 2174 1726 1429 1225 1079 972 890 826 776 735 651 600 567 544 528 516 506 20
22 9450 9450 7022 4797 3685 3056 2263 1756 1425 1199 1039 921 832 764 T1o 666 578 525 490 467 450 437 428 22
24 9450 9450 7166 4790 3571 2889 2387 1816 1447 1197 1021 893 796 722 664 618 524 468 432 408 391 378 368 24
26 9450 9450 6979 4856 3520 2782 2334 1901 1490 1214 1020 880 775 695 633 584 484 425 388 363 345 332 322 26
28 9450 9450 6896 4981 3519 2720 2240 1930 1550 1245 1033 880 766 680 613 560 454 393 354 328 309 296 286 28
30 9450 9450 6897 4901 3558 2693 2178 1849 1624 1289 1056 889 766 673 601 545 432 367 327 300 281 267 256 30
32 9450 9450 6966 4820 3629 2694 2142 1792 1556 1343 1089 907 774 674 596 536 416 348 305 277 257 243 233 32
34 9450 9450 7014 4786 3639 2719 2127 1753 1504 1330 1129 932 788 680 597 532 404 332 288 259 239 224 213 34
36 9450 9450 6926 4790 3571 2763 2129 1731 1468 1284 1151 963 807 691 602 532 397 321 275 244 223 208 197 36
38 9450 9450 6890 4827 3531 2812 2145 1722 1443 1250 1111 999 831 706 611 536 392 312 264 232 210 195 183 38
40 9450 9450 6897 4892 3515 2757 2174 1724 1429 1225 1079 972 859 725 623 544 391 306 255 222 200 184 172 40
42 9450 9450 6944 4835 3519 2720 2214 1736 1423 1209 1056 542 858 747 638 553 391 302 249 215 191 174 162 42
54 9450 9450 6954 4797 3541 2699 2196 1756 1425 1199 1039 921 832 764 656 566 393 300 244 208 184 167 154 44
46 9450 9450 6906 4783 3578 2691 2164 1783 1433 1196 1028 905 812 741 676 580 398 299 240 203 178 160 147 46
48 9450 9450 6887 4790 3571 2694 2142 1792 1447) 1197-1021 893 796 722 664 597 403 299 238 199 173 154 141 48

6-128

TABLE 6-12. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS=H EQUALS 005625 INCHES

hens" “et “inet
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10630 10630 10630 16630 9644 9021 8612 8326 8123 7967 7853 7762 7688 7624 7573 7534 7448 7390 7352 7322 7299 7292 7272 6
8 10630 10630 10203 7917 6712 5999 5542 5230 5008 4844 4720 4621 4546 4481 4432 43868 4296 4238 4199 4167 4149 4135 = 4119 8
10 10630 10630 9821 6978 5534 4705 4185 3839 3596 3419 3266 3181 3100 3035 2961 2938 2843 2781 2741 2712 2691 2676 2665 10
12 10636 10630 10344 6820 5084 4113 3519 3129 2860 2666 2522 2411 2324 2255 2199 2153 2054 1992 1950 1922 1900 1884 1871 12
14 10630 10630 10630 7092 5011 3873 3189 2749 2449 2236 2078 1959 1866 1793 1733 1684 1582 1518 1475 1445 1423 1406 1394 14
16 10630 1C630 10203 7647 5167 3836 3050 2551 2215 1979 1807 1678 1578 1500 1437 1385 1278 1211 1167 1136 1114 1097 1085 16
18 10630 10630 9661 7312 5484 3934 3031 2465 2090 1828 1639 1498 1391 1306 1239 1185 1072 1002 957 925 903 885 873 1e
20 10630 10630 9821 6978 5533 4129 3095 2455 2034 1744 1537 1383 21267 (‘1176 1104 1046 927 855 807 775 752 734 72h 20
22 10630 10630 9999 6831 5247 4351 3222 2500 2029 1708 1479 1312 1185 1088 1011 949 822 747 698 665 641 623 609 22
24 10636 16630 10203 6820 5084 4113 3398 2586 2061 1705 1454 1271 1134 1028 946 880 746 667 616 581 556 538 524 24
26 10630 10630 9936 6914 5012 3961 3324 2706 2122 1729 1453 1253 1104 990 901 831 689 606 553 517 491 473 459 26
26 10630 10630 9819 7092 5011 3873 3189 2749 2207 1773 1471 1253 1091 968 873 797 646 559 504 466 440 421 407 28
30 10630 10630 9821 6978 5066 3834 3101 2632 2312 1835 1504 1266 1091 959 856 775 615 523 465 427 400 380 365 30
32 10630 10630 9919 6862 5167 3836 3050 2551 2215 1912 1550 1292 1102 959 849 763 592 495 435 395 367 346 331 32
34 10630 10630 9987 6814 5181 3871 3029 2497 2142 1893 1607 1327 1122 968 B5c 757 576 473 410 369 340 319 303 34
36 10630 16630 9861 6820 5084 3934 3031 2465 2090 1628 1639 1371 1149 983 857 758 565 457 391 348 318 296 280 36
38 10630 10630 9810 6872 5027 4004 3054 2452 2055 1779 1581 1422 1183 1005 869 764 559 445 376 331 300 277 261 38
40 10630 10630 9821 6965 5005 3925 3095 2455 2034 1744 1537 1383 1223 1032 887 774 556 436 364 317 285 262 245 40
42 10630 10630 9886 6885 5011 3873 3152 2472 2027 1721 1503 1343 1222 1064 908 788 557 430 354 305 272 248 231 42
44 10630 10630 9902 6831 5042 3842 3126 2500 202 1708 1479 1312 1185 1088 934 806 560 427 347 296 262 237 219 44
46 10630 10630 9832 6811 5095 3831 3081 2533 2041 1703 1463 1288 1156 1055 963 826 566 426 342 289 253 228 209 46
48 10630 10630 9607 6820 5084 3836 3050 2551 2061 1705 1454 1271 1134 1028 946 850 574 426 339 283 246 220 201 48
THICKNESS=H EQUALS 0«6250 INCHES
LENGTH=8 WIOTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 11810 11810 11610 11810 11810 1181¢ 11810 11422 11142 10928 10772 10648 10546 10459 10388 10335 10216 10137 10085 10045 10012 10002 9976 6
8 11810 11810 11810 10860 9207 8229 7602 7174 6870 6645 6475 6339 6236 6147 6080 6019 5893 5814 5760 5717 5691 5673 5650 8
10 11610 11810 11810 9572 7591 6454 5741 5266 4933 4690 4507 4364 4253 4163 4089 = 4030, 3899-3815 3760 3721 03692 3671 = 3655 10
12 11810 11810 11810 9355 6973 5642 4827 4293 3923 3657 3459 3307 3188 =93093. «3017 «2953. 2817 «=. 2732S 2675 «= 2637 = 2606 = 2584 =. 2567 12
14 11810 11810 11810 9728 6873 5313 4375 3771 3359 3067 2850 2667 2559 2459 2377 2311 2170 2082 2024 1982 1952 1929 1912 14
16e 11810 11810 11810 10489 7088 5262 4184 2499 3039 2715 2475 2302 2165 2057 1971 1901 1753 1661 1601 1559 1528 1505 1488 16
18 11810 11810 11810 10630 7523 5396 4158 3382 2866 2508 2249 2056 1908 =61792, «1700-1625. 1470-1375: 1313. 1269-1238 = 12141197 18
20 11810 11810 11810 9572 7590 5663 4246 3368 2791 2393 2108 1898 1738 16130-1515) 1435-1271, 1173, 1108 = 1063. 1031 = 1008 989 20
22 11610 11810 11810 9370 7198 5968 4420 3429 2783 2343 2029 1799 1626 1492 1386 1302 1128 1025 958 912 879 854 825 22
24 11810 11810 11810 9355 6974 5642 4662 3547 2827 2339 1994 1743 1555 1410 1297 = 1207 = 1023 914 B45 797 763 738 719 24
26 11810 11810 11810 9484 6875 5433 4559 3712 2911 2371 1993 1719 1514 1358 1237 1140 945 831 758 709 674 648 629 26
26 11810 «11810 11810 9728 6873 5313 4375 3771 3027 2432 2017 1718 1497 1328 =61197' 1094 887 767 691 640 604 578 558 28
30 11810 11810 11810 9572 6949 5260 4254 3611 3172 2517 2063 1737 1497 13151174 1064 B43 717 638 585 548 521 501 30
32 11€1C 11610 11810 9413 7088 5262 4184 3499 3039 2622 2126 1772 1512. 1316 = =61165 = 1046 812 679 596 541 503 475 454 32
24 11810 11810 11810 9347 7107 5310 4154 3425 2938 2597 2205 1820 1539-1328) «=61165 = 1039 790 649 563 506 466 437 416 34
36 11810 «11816 «611810 ©9355 «6974 5396 4158 3342 2866 2508 2249 1881 1577-1349 1175 1039 175 627 536 477 436 406 384 36
36 11810 11610 11810 9427 6896 5492 4190 3364 2818 2441 2169 1951 1623. 1379 «1192 1048 766 610 515 453 411 380 358 38
40 11610 11616 11810 9554 6865 5384 4246 3368 2791 2393 2108 1898 1678 81416 = =1216 = 1062 763 598 499 434 399 359 336 40
42 11610 11810 11810 9444 6873 5312 4324 3390 2780 2361 2062 1842 1676 «914659 1246 ~=1081 764 590 486 419 373 341 317 42
44 11810 11810 11810 9370 6916 5271 4288 3429 27€3 2342 2029 1799 1626 14692 1281 1105 768 586 476 406 359 325 301 44
46 11810 11810 11810 9342 6989 5255 4226 3482 2800 2336 2007 1767 1586 1447 1320 1133 777 584 470 397 347 313 287 46
48 1181011810 «11810 = 9355) 6974 = 52624184 = 34992827) 2339 1994 1743 1555 1411 1297 1165 788 585 465 389 338 302 275 48

G-12g

TABLE 6-13. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED

ig PHYSICAL CONSTANTS:
A | Ex = 1.96x10® PS|
fea}
| Ey = 1.70x10® PSI
Gxy = 0.52x10® PSI
i Opp Oye = 10520
THICKNESS=H EQUALS 000625 INCHES
Lense te eae
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72
6 76 4) 25 19 16 14 13 12 12 TW il ll 11 11 11 11 10 10 10 10 10 10
8 7 43 27 18 13 ll 9 8 8 7 7 7 7 6 6 6 6 6 6 6 6 G
10 72 40 27 19 13 10 8 7 6 6 5 5 5 5 4 4 4 4 4 4 4 4
12 71 41 25 19 15 10 8 6 5 5 4 4 4 4 3 3 3 3 3 3 3 3
14 7 40 26 18 14 ll 8 6 5 4 4 3 3 3 3 3 2 2 2 2 2 2
16 1 40 26 18 13 ll 9 7 5 4 Oe 3 3 3 2 2 2 2 2 2 2 2
18 71 40 25 18 13 10 8 7 6 5 4 3 E) 3 2 2 2 2 1 1 1 1
20 1 40 25 18 13 10 8 7 6 5 4 zi a 2 2 2 2 1 1 1 1 1
22 71 40 26 18 14 10 8 7 6 5 4 3 3 2 2 2 2 1 1 1 1 1
24 7 40 25 18 13 10 8 6 5 5 4 4 3 3 2 il 1 i 1 1 1
26 1 40 25 18 13 10 8 6 5 5 4 4 3 a) 2 z 1 1 1 1 1
28 72 40 26 18 13 10 8 6 5 4 4 a 3 3 2 2 1 1 1 1 1 1
30 apt 40 25 18 13 10 8 7 5 4 4 3 3 3 3 2 1 1 1 i 1 1
32 7 40 25 18 ie) 10 8 7 5 4 4 3 3 g) 2 2 2 1 1 1 1 at
34 70 40 26 18 13 10 8 6 6 4 4 3 3 E] 2 2 2 1 1 1 1 1
36 7 40 25 18 13 10 8 6 5 5 4 3 3 3 2 2 2 1 1 1 iT 1
38 70 40 25 18 13 10 8 6 5 5 4 3 3 2 2 2 2 1 1 1 1 1
40 7 40 25 18 13 10 8 6 5 5 4 3 3 2 2 2 2 1 1 1 1 1
42 70 40 25 18 13 10 8 6 5 4 4 3 3 2 2 2 2 1 1 1 1 Cy)
44 7 40 25 18 13 10 8 7 5 4 4 3 3 2 2 2 2 a Hf 1 1 °
46 70 40 25 18 13 10 8 6 5 4 4 3 3 3 2 2 1 1 af 1 1 0
48 7 40 25 18 13 10 8 6 5 4 4 3 3 3 2 2 1 1 1 1 1 °
THICKNESS=H_ EQUALS 001250 INCHES
LENGTH-8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 610 330 204 152 127 113 104 98 95 92 90 88 87 86 85 84 83 82 81 81 80 80 80 6
8 566 343 218 142 105 86 1% 67 6z 59 56 54 53 52 51 50 48 47 47 46 46 46 45 8
10 578 317 220 156 106 19 64 BG 49 44 41 39 37 36 35 34 33 31 31 30 30 30 30 10
12 566 330 204 152 117 a2 63 51 43 38 34 32 30 28 27 26 24 23 22 22 21 21 21 72
14 570 321 206 142 112 a1 66 51 42 36 31 28 26 et 22 21 19 18 17 16 16 16 16 14
16 566 318 212 142 105 86 73 55 43 35 30 26 24 21 20 19 16 15 14 13 13 12 12 16
18 567 324 204 147 104 81 68 59 46 37 30 26 23 20 18 17 14 13 12 11 Ty 10 10 18
20 566 317 204 145 106 79 64 55 49 39 32 26 23 20 18 16 13 ll 10 9 9 9 8 20
22 565 320 209 141 109 80 63 52 45 41 34 28 23 20 18 16 12 10 9 8 8 7 7 22
24 566 319 204 142 105 82 63 51 43 38 34 29 24 21 18 16 12 10 8 7 7 7 6 24
26 565 318 203 144 104 82 64 51 42 37 32 30 26 22 18 16 12 9 8 7 6 6 6 26
28 566 321 206 142 104 80 66 51 42 36 31 28 26 23 19 17 12 9 7 6 6 5 5 28
30 564 317 204 141 106 19 64 53) 42 35 30 27: 24 22 20 17 12 9 7 6 5 5 5 30
32 566 318 203 142 105 80 63 53 43 35 30 26 24 21 20 18 12 9 7 6 5 5 4 32
34 564 318 204 143 104 81 63 52 44 36 30 26 23 21 19 18 12 9 7 6 5 4 4 34
36 566 317 204 142 104 81 63 51 43 37 30 26 23 20 138 17. 13 9 7 6 5 4 4 a
38 564 319 203 141 104 80 64 51 43 37 31 26 23 20 18 16 13 9 7 6 5 4 4 38
40 566 317 204 142 105 79 64 51 42 36 32 26 23 20 18 16 13 10 7 6 5 4 4 40
42 564 318 204 142 104 79 63 51 42 36 31 27 23 20 18 16 12 10 7 6 S 4 3 42
44 565 318 203 141 104 80 63 52 42 35 31 27 23 20 18 16 12 10 8 6 5 4 3 44
46 564 317 203 141 104 80 63 51 42 35 30 27 24 20 18 16 12 10 8 6 5 4 3 46
48 565 318 204 142 104 80 63 51 43 35 30 26 24 21 18 16 12 10 8 6 5 4 3 ae

6-130

TABLE 6-13. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS“H EQUALS 061875 INCHES

MINCHES "TNcHes “Ncres
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 2058 = 1113 689 515 429 381 352 332 319 309 302 297 293 289 286 284 279 276 274 273 272 271 270 6
8 1911-1158 737 478 355 289 25) 226 209 198 189 183 178 174 171 168 163 160 158 156 155 154 153 8
10 1952-1072 741 526 357 268 217 185 164 150 140 132 127 122 119 116 110 106 104 102 101 100 100 10
12 19il 1113 689 515 395 278 212 172 146 129 116 107 100 95 91 88 81 7 75 73 72 Wa 70 12
14 1923 1082 695 481 378 307 224 174 142 120 105 95 87 80 76 72 65 60 58 56 54 53 53 14
16 1911-1075 715 478 355 289 246 184 145 119 102 89 19 72 67 63 54 49 46 44 43 42 41 16
18 1913 1093 689 495 350 273 229 201 155 124 102 87 TT 68 62 57 48 42 39 37 35 34 34 18
20 1911 =:1072 688 488 356 268 217 185 164 132 107 89 16 67 60 54 43 38 34 32 30 29 28 20
22 1908 =©1081 705 477 368 270 212 176 153 137 113 93 78 68 59 53 41 34 30 28 26 25 24 22
24 1911 1076 689 478 355 278 212 172 146 129 116 99 82 70 60 53 39 32 28 25 23 22 21 24
26 1906 =1072 686 487 350 277 216 172 143 123 110 100 87 73 62 54 39 31 26 23 21 20 19 26
28 1911 = 1082 695 481 351 270 224 174 142 120 105 95 87 7 65 56 39 30 25 22 19 18 17 28
30 1905 1072 689 476 357 268 217 178 143 119 103 91 82 76 69 58 40 30 24 21 18 17 16 30
32 1911-1075 686 478 355 269 213 179 145 119 102 89 19 72 67 62 41 30 24 20 17 16 14 32
34 1905 1074 690 484 351 272 212 174 149 121 102 88 78 70 64 60 42 30 24 19 17 15 14 34
36 19111071 689 478 350 273 212 172 146 124 102 87 7 68 62 57 44 31 24 19 16 14 13 36
38 1904 1078 686 476 352 269 215 171 144 125 104 88 76 67 61 55 45 32 24 19 16 14 12 38
40 1910 = 1072 688 478 355 268 217 172 142 122 107 89 76 67 60 54 43 33 24 19 16 14 12 40
42 1904 = 1073 689 481 351 268 214 174 142 120 105 91 na 67 59 53 42 34 25 19 16 13 12 42
44 1908 1073 686 477 350 270 212 176 142 119 103 92 78 68 59 53 4. 34 26 20 16 13 ql 44
46 1904 1071 687 476 350 271 212 174 143 119 102 90 80 68 60 53 40 33 26 20 16 13 11 46
48 1907-075 689 478 353 269 212 172 145 119 102 89 19 70 60 53 39 32 27 20 16 13 11 48
| THICKNESS-H EQUALS 0+2500 INCHES
LENGTH=8 WIDTH=A LENGTH-B
. INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 aa 34 36 42 48 54 60 66 72 78
4730 2638 1632 1220 1017 903 833 788 756 733 717 704 694 685 679 673 662 655 650 647 644 643 641 6
4529-2745) 17481132 842 686 594 536 496 469 449 433 422 412 405 399 387 379 374 370 367 366 364 8
4626 2540 1756 1247 845 635 514 439 390 356 332 314 300 289 281 274 260 252 246 242 240 238 236 10
4529 2637 1632 1220 936 659 503 408 347 305 276 254 238 226 216 208 193 183 197 173 170 168 167 12
4559 2564 1646 1140 896 729 531 412 336 285 250 224 205 191 180 171 153 143 136 132 129 127 125 14
4529 2547 1694 1132 B42 686 583 437 344 283 241 210 188 172 159 149 129 T17. 110 105 102 100 98 16
4534 2591 1632 1172 829 648 542 476 366 293 243 207 181 162 147 136 113 100 93 88 84 81 80 18
4529 2540 1630 1157 B45 635 514 439 390 312 253 211 181 159 142 129 103 89 80 7S 71 69 67 20
4523 2561 1672 1131 872 640 503 418 363 325 269 221 186 160 141 126 97 81 72 66 62 59 57 22
4529 2550 1632 1132 B42 659 503 408 347 305 276 234 194 165 143 126 94 76 66 60 55 52 50 24
4518 2541 1626 1155 830 657 513 407 338 292 260 236 206 172 147 128 92 73 62 cb 50 47 44 26
4529 2564 = 1646 =—1140 832 641 531 412 336 285 250 224 205 182 154 133 92 7 59 51 46 43 40 28
4515 2540 1632 1129 B45 635 514 422 338 282 243 216 195 180 162 139 94 71 57 49 43 40 37 30
4529 2547 1625 1132 842 637 505 424 344 283 241 210 188 172 159 146 96 1 56 47 4. 37 34 32
4514 2546 1636 1147 831 645 502 414 354 287 241 208 184 166 152 141 100 72 56 46 40 35 32 34
4529 2540 1632-1134 829 648 503 408 347 293 243 207 181 162 147 136 104 73 56 45 39 34 31 36
4514 2554 1625 1128 834 639 *09 406 340 296 247 209 161 160 144 131 107 75 57 45 38 33 29 38
4528 2540 1630 1132 842 635 514 408 337 289 253 211 181 159 142 129 103 78 58 45 37 32 28 40
4514 2543 1632-1140 833 636 507 412 3360285 250 215 183 159 141 127 100 81 59 46 37 32 28 42
4523 2544 1625 1131 829 640 503 418 337 283 245 218 186 160 141 126 97 81 61 46 37 31 27 44
4514 2539 1627 1128 830 643 502 412 340 282 242 216 190 162 141 125 95 79 63 47 38 31 27 46
4520 2547 1632 1132 836 638 503 408 344 283 241 210 188 165 143 126 94 76 65 49 38 31 27 48

loyealsial

TABLE 6-13. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 003125 INCHES

LENGTH=8 WIDTH=A LENGTH=6
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 5900 5152 3188 2382 1985 1763 1628 1538 1477 1432 1400 1375 1355 1339 1325 1315 1293 1279 1270 1263 «1257 12551251 6
8 5900 5360 3413 2211 1645 1340 1160 1046 970 916 876 846 824 806 792 780 755 740 730 722 718 714 711 8
10 5900 4961 3431 2436 1650 1240 1004 858 761 695 648 613 586 565 549 536 508 492 481 474 468 464 461 10
12 $900 5151 3188 2382 1828 1288 983 797 677 596 538 496 465 441 422 407 376 358 346 339 333 329 326 12
14 5900 5008 3216 2226 1750 1423 1036 B04 656 557 487 438 401 373 351 333 299 279 266 258 252 247 244 14
16 5900 4975 3310 2211 1645 1340 1139 853 673 553 470 411 368 335 310 290 251 229 215 206 200 195 192 16
18 5900 5061 3188 2289 1620 1265 1059 929 716 572 474 405 354 316 287 265 221 196 161 171 164 159 156 18
20 5900 4961 3184 2259 1650 1240 1004 858 761 609 494 413 354 310 277 251 201 174 157 146 139 134 130 20
22 5900 5002 3265 2208 1704 125% 981 816 709 635 525 431 363 313 275 245 189 159 141 129 121 115 111 22
24 5900 4981 3188 2211 1645 1288 983 797 677 596 538 457 379 322 279 246 183 149 129 116 108 102 97 24
26 5900 4963 3176 2255 1621 1284 1002 794 660 571 507 462 402 337 288 251 180 143 121 107 98 91 87 26
28 5900 5008 3216 2226 1625 1252 1036 B04 656 556 487 438 401 356 301 259 181 139 115 100 90 83 78 28
30 5900 4961 3188 2205 1650 1240 1004 824 660 551 476 421 381 351 317 271 183 138 112 95 85 7 72 30
32 5900 4975 3174 2211 1645 1244 986 827 673 553 470 411 368 335 310 285 188 138 110 92 80 73 67 32
34 5900 4973 3195 2240 1624 1260 980 808 691 560 470 406 359 324 297 276 195 140 109 90 7 69 63 34
36 5900 4960 3188 2214 1620 1265 983 797 677 572 474 405 354 316 287 265 203 143 109 89 75 66 60 36
38 5900 4989 3174 2204 1629 1248 994 793 664 577 482 407 353 312 281 257 210 147 110 88 14 64 57 38
40 5900 4961 3184 2211 1645 1240 1004 796 658 565 494 413 354 310 277 251 201 152 112 868 73 63 56 40
42 5900 4966 3188 2226 1627 1242 989 804 656 556 487 421 357 310 275 247 194 158 115 89 73 62 54 42 |
44 5900 4989 3174 2208 1620 1251 982 B16 658 552 479 426 363 313 275 245 189 159 118 91 73 61 53 44
46 5900 4959 3179 2204 1622 1257 980 804 664 551 473 417 370 317 276 245 185 153 122 93 74 61 53 46
48 5900 4975 3188 2211 1632 1245 983 797 673 553 470 411 368 322 279 246 183 149 127 95 75 61 52 48
THICKNESS“H_ EQUALS 003750 INCHES |
LENGTH=8 WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 7090 7090 5509 4117 °3431 3047 2813 2658 2552 2475 2419 2376 2341 2313 2290 2273 2235 2210 2194 2182 2173 2169 2162 6
8 7090 7090 5898 3821 2842 2316 2005 1808 1675 1582 1514 1463 1424 1392 1368 1347 1304 1278 1261 1248 1240 1234 1228 8
10 7090 7090 5928 4209 2852 2143 1735 1482 1316 1201 1119 1058 1013 977 948 926 878 849 831 818 809 802 197 10
12 7090 7090 5509 4117 3158 2225 1698 1377 1170 1029 930 858 803 762 729 703 650 619 599 585 575 568 563 12
14 7090 7090 5557 3846 3025 2459 1791 1389 1133 962 842 756 692 644 606 576 517 482 460 445 435 428 422 14
16 7090 7090 $719 3821 2842 2316 1969 1474 1162 955 812 710 635 579 535 501 434 396 372 356 345 337 331 16
18 7090 7090 5509 3956 2799 2186 1830 1606 1236 989 820 700 612 547 496 457 381 339 313 295 284 275 269 18
20 7090 7090 $502 3904 2852 2143 1735 1482 1316 1052 853 713 61l 536 478 434 348 300 272 253 240 231 225 20
22 7090 7090 5643 3816 2944 2161 1696 1411 1225 1098 907 744 627 540 475 424 327 274 243 223 209 200 192 22
24 7090 7090 5509 3821 2842 2225 1698 1377 1170 1029 930 790 655 556 482 425 316 257 223 201 186 176 168 24
26 7090 7090 5488 3897 2801 2218 1732 1372 1141 986 877 798 694 582 497 433 311 246 209 185 169 158 150 26
28 7090 7090 5557 3846 2807 2164 1791 1389 1133 962 842 756 692 615 520 448 312 240 199 173 156 144 135 28
30 7090 7090 5509 3810 2852 2143 1735 1424 1141 952 822 728 659 606 548 468 317 238 193 165 146 133 124 30
32 7090 7090 5484 3821 2842 2149 1704 1430 1162 955 812 710 635 579 535 492 325 239 189 159 139 125 116 32
34 7090 7090 $520 3871 2806 2178 1693 1396 1195 968 812 701 620 560 513 476 337 242 188 155 134 119 109 34
36 7090 7090 5509 3826 2799 2186 1698 1377 1170 989 820 700 612 547 496 457 351 247 189 153 130 114 103 36
38 7090 7090 5484 3808 2815 2156 1717 1371 1148 998 834 704 609 539 485 444 363 254 191 152 128 lll 99 38
40 7090 7090 5502 3821 2842 2143 1735 1376 1137 976 853 713 611 536 478 434 348 263 194 153 126 108 96 40
42 7090 7090 5509 3846 2811 2145 1710 1389 1133 962 B42 727 617 536 475 427 336 273 199 154 126 107 94 42
44 7090 7090 5485 3816 2799 2161 1696 1411 1137 954 827 736 627 540 475 424 327 274 205 157 126 106 92 44
46 7090 7090 5493 3809 2802 2172 1693 1390 1147 952 817 721 640 547 477 423 320 265 211 160 127 106 91 46
48 7090 7090 5509 3821 2821 2152 1698 1377 1162 955 812 710 635 556 482 425 316 257 219 164 129 106 90 48

6-132

TABLE 6-13. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 004375 INCHES

LENGTH=8 WIDTH=A LENGTH=8
INCHES INCHES INCHES
6 8 10 12 16 16 18 20 22 24 26 28 30 32 34 36 42 46 54 60 66 O72 78
6 8270 8270 8270 6537 5448 4839 4466 4221 4053 3930 3841 3773 3718 3673 3637 3609 3549 3510 3484 3465 3451 3444 3433 6
8 8270 8270 8270 6068 4512 3677 3184 2871 2660 2512 2405 2323 2261 2211 2172 2139 2071 2030 2003 1982 1969 1960 1950 8
10 8270 8270 8270 6683 4529 3403 2755 2353 2089 1908 1778 1681 16098 1551 1506 1470 1395 1349 1320 1299 1285 1274 1266 10
12 8270 8270 8270 6537 5015 3534 2€97 2187 1858 1634 1477 1362 1276 1210 1158 1117 1032 982 951 930 914 902 894 12
14 8270 8270 8270 6108 4803 3904 2844 2206 1799 1527 1337 1201 1099 1022 962 915 820 766 731 707 691 679 670 14
16 8270 8270 8270 6068 4512 3677 3126 2341 1846 1517 1290 1128 1009 919 850 796 689 628 590 565 548 535 526 16
18 270 8270 8270 6282 4464 3472 2905 2550 1963 1571 1302 1112 972 868 788 726 605 538 496 469 450 437 427 18
20 8270 8270 8270 6199 4529 3403 2755 2353 2089 1671 1355 1132 971 851 760 689 552 477 431 402 382 367 357 20
22 8270 8270 8270 6060 4675 3432 2693 2240 1945 1743 1440 1182 996 858 754 673 519 436 386 354 332 317 305 22
24 8270 8270 8270 6068 4512 3534 2697 2187 1858 1634 1477 1254 1041 883 765 674 501 409 354 319 296 279 267 24
26 8270 8270 8270 6188 4447 3522 2750 2179 1812 1565 2393 1267 1102 924 790 688 494 391 331 293 268 251 238 26
28 8270 8270 8270 6108 4458 3436 2843 2206 1799 1527 1337 1201 1099 976 826 711 495 382 316 275 248 229 215 28
30 8270 8270 8270 6050 4529 3403 2755 2262 1812 1512 1305 1156 1046 963 871 743 503 378 306 261 232 212 198 30
32 8270 8270 8270 6068 4512 3413 2706 2270 1846 1517 1290 1128 1009 919 850 782 517 379 301 252 221 199 184 32
34 8270 270 8270 6148 4456 3458 2688 2217 1897 1537 1290 1114 985 889 814 756 535 384 299 246 212 189 173 34
36 8270 8270 8270 6075 4444 3472 2697 2187 1858 1571 1302 1111 972 868 788 726 557 393 300 243 206 182 164 36
38 8270 8270 8270 6047 4470 3423 2727 2177 1823 1585 1324 1118 968 856 m7 704 576 404 303 242 203 176 157 38
40 8270 8270 8270 6068 4512 3403 2755 2184 1805 1550 1355 1132 971 B51 759 689 552 418 309 243 201 172 152 40
42 8270 8270 8270 6108 4463 3407 2715 2206 1799 1527 1337 1154 980 852 754 679 534 434 316 245 200 170 149 42
44 8270 8270 8270 6060 4444 3432 2693 2240 1805 1515 1313 1169 996 858 754 673 519 436 325 249 201 168 146 44
46 8270 8270 8270 6048 4450 3449 2688 2207 1821 1512 1298 1145 1016 869 758 672 509 421 336 254 202 168 144 46
48 8270 8270 8270 6068 4479 3417 2697 2187 1846 1517 1290 1128 1009 883 765 674 501 409 347 260 205 169 143 48
THICKNESS=H EQUALS 025000 INCHES
LENGTH=8 WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 9450 9450 9450 9450 8132 7223 6667 6301 6050 5866 5734 5631 5550 5483 5429 5388 5297 5239 $201 5173 5151 5141 5125 6
8 9450 9450 9450 9057 6736 5489 4753 4285 3971 3750 3589 3467 3375 3300 3242 3193 3092 3030 2990 2959 2940 2926 2911 8
10 9450 9450 9450 9450 6760 = 5080 = 4112, 3513. 3119 2848 «= 2653-2509 «240023152248 «202194 += 2082, 2014 «1970-1940 1918 §=1902 1890 10
12 9450 9450 9450 9450 7486 = 5275 = 4026 «= 3265 2773) 2440-2205) 2033. «1904 §=1806 = 1728 «= 1667 = 1541 1467 = 1419-1388 = 1364 = 1347) 1334 12
14 9450 9450 9450 9117 7169 5828 4245 3293 2686 2280 1996 1792 1641 1526 1436 1366 1225 1143 1091 1056 1032 1013 1000 14
16 9450 9450 9450 9057 6736 5489 4667 3495 2755 2264 1926 1684 1506 1372 1269 1188 1029 938 6881 B44 817 798 785 16
18 9450 °9450 9450 9377 6634 5182 4337 3807 2931 2345 1963 1659 1451 1296 1177 1084 904 803 Tal 700 672 652 637 168
20 9450 9450 9450 9253 6760 5080 4112 3513 3119 2494 2023 1690 1449 1270 1134 1028 B24 712 644 600 570 549 532 20
22 9450 9450 9450 9045 6978 5122 4020 3344 2903 2602 2149 1764 1486 1281 1125 1005 775 651 576 528 496 473 456 22
24 9450 9450 9450 9057 6736 5275 4026 3265 2773 2440 2204 1872 1553 1319 1142 1006 748 610 528 476 441 417 399 24
26 9450 9450 9450 9236 6639 5257 4105 3252 2705 2337 2079 1a92 1645 1379 1179 1026 738 5B4 495 438 400 374 355 26
28 9450 9450 9450 9117 6654 5129 4244 3293 2686 2279 1996 1792 1641 1457 1232 1061 739 570 472 410 370 341 321 28
30 9450 9450 9450 9031 6760 5080 4112 3376 2705 2258 1948 1725 1561 1437 1300 1108 751 564 457 390 347 316 295 30
32 9450 9450 9450 9057 6736 5095 4039 3389 2755 2264 1926 1684 1506 1372 1269 1167 TT 566 44g 377 329 297 274 32
34 9450 9450 9450 9177 6651 5162 4013 3309 2832 2294 1925 1663 1470 1326 1216 1129 798 574 44e 368 317 282 258 34
36 9450 9450 9450 9068 6634 5182 4026 3265 2773 2344 1943 1658 1451 1296 1177 1084 832 586 447 363 308 271 245 36
38 9450 9450 9450-9027 = 6672-5110 40713250 2722-2365 «1976 «= 1668 «= 1444 = 127711501052 859 603 452 361 302 263 235 38
40 9450 9450 9450 9057 6736 $080 4112 3261 2694 2313 2023 1690 1449 1270 1134 1028 824 624 461 362 299 257 227 40
42 9450 9450 9450 9117 6662 5085 4052 3293 2686 2279 1996 172g 1464 1271 1126 1013 797 648 472 366 298 253 222 42
44 9450 9450 9450 9045 6634 5122 4020 3344 2695 2261 1961 1745 1486 1261 1125 1005 775 651 485 372 299 251 218 44
46 9450 9450 9450 902866435148 4012, «3295-2718 = 2257 «1938 ~=1709 «1817-1297 «1131 1003 760 628 501 379 302 251 215 46
48 9450 9450 9450 9057 6686 5101 4026 3265 2755 2264 1926 1684 1506 1319 1142 1006 748 610 519 388 306 252 214 48

6-133

TABLE 6-13. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - LOADED EDGES SIMPLY SUPPORTED -

REMAINING EDGES CLAMPED (Cont'd)

THICKNESS=H EQUALS 005625 INCHES

LENGTH=B WIDTH=A LENGTH=a_
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10630 10630 10630 10630 10630 10284 9492 8971 8614 8353 8164 8018 7902 7807 7729 7671 7542 7460 7405 7365 7334 7320 7297 6
8 10630 10630 10630 16630 9591 7815 6768 6101 5654 5339 5111 4936 4805 4698 4616 4546 4403 4315 4257 4213 4186 4166 4144 E)
10 10630 10630 10630 10630 9626 7233 5855 5002 4441 4055 3778 3572 3417 3297 3200 3124 2964 2867 2805 2762 2730 2708 2691 1c
12 10630 10630 10630 10630 10630 7511 5732 4648 3948 3474 3139 2895 2712 2571 2461 2373 2194 2088 2021 1976 1942 1918 1900 12
14 10630 10630 10630 10630 10208 8298 6044 4689 3824 3246 2843 2552 2336 2173 2045 1945 1743 1627 1554 1504 1469 1443 1424 14
16 1063C 10630 10630 10630 9591 7815 6645 4976 3922 3224 2742 2398 2145 1954 1807 1692 1464 1335 1255 1201 1164 1137 1117 16
18 10630 10630 10630 10630 9445 7379 6175 5420 4173 3338 2767 2361 2066 1845 1676 1544 1287 1143 1055 997 957 928 907 18
20 10630 10630 10630 10630 9625 7233 5855 5002 4441 3551 2880 2406 2063 1808 1614 1464 1174 1014 917 854 811 781 758 20
22 10630 10630 10630 10630 9936 7294 5724 4761 4134 3705 3060 2512 2116 1823 1602 1431 1104 926 820 752 706 673 649 2?
24 10630 10630 10630 10630 9591 7510 5732 4648 3948 3474 3139 2665 2212 1878 1626 1433 1066 868 752 678 628 593 568 24
26 10630 10630 10630 10630 9452 7485 5845 4631 3852 3327 2960 2693 2342 1963 1679 1461 1050 832 704 624 570 533 506 26
28 10630 10530 10630 10630 9475 7302 6043 4689 3824 3245 2842 2552 2337 2075 1755 1511 1053 811 671 584 526 4B6 457 28
30 10630 10630 10630 1C630 9626 7233 5855 4807 3851 3215 2773 2457 2223 2046 1851 1578 1070 804 651 556 493 451 420 30
32 10630 10630 10630 10630 9591 7254 5751 4825 3922 3224 2742 2398 2145 1954 1807 1661 1098 B06 639 536 469 423 390 32
34 10630 10630 10630 10630 9470 7350 5713 4711 4032 3267 2741 2368 2094 1888 1731 1607 1137 817 635 523 451 402 367 34
36 10630 10630 10630 10630 9446 7379 5732 4648 3948 3338 2766 2361 2066 1845 1676 1544 1184 835 637 516 439 386 349 36
38 10630 10630 10630 10630 9501 7276 5796 4627 3875 3368 2814 2375 2057 1819 1638 1497 1223 858 644 514 431 374 335 38
40 10630 10630 10630 1C630 9591 7233 5855 4643 3836 3294 2880 2406 2063 1808 1614 1464 1173 888 656 516 426 366 324 40
42 10630 10630 10630 10630 9486 7241 5770 4689 3824 3245 2842 2452 2084 1810 1603 1442 1134 922 672 521 425 361 316 42
44 10630 10630 10630 19630 9445 7294 57246 4761 3837 3220 2791 2484 2116 1823 1602 1431 1104 926 691 529 426 358 310 44
46 10630 10630 10630 10630 9458 7329 5713 4691 3871 3213 2759 2433 2159 1846 1610 1428 1081 894 713 540 430 357 307 46
48 10630 10630 10630 10630 9520 7263 5732 4648 3922 3224 2742 2398 2145 1878 1626 1433 1066 868 738 553 436 358 305 48
THICKNESS=H EQUALS 006250 INCHES
LENGTH=B WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 1810 11810 11810 11810 11819 11810 11810 11810 11810 11458 11199 10999 10840 10709 10603 10523 10346 10233 10158 10103 10060 10041 10009 6
8 11810 11810 11810 11810 11810 10721 9283 8369 7756 7324 7010 6771 6591 6445 6332 6236 6039 5919 5839 5779 5742 5714 5685 8
10 11810 11810 11810 11810 11810 9921 8032 6861 6092 5562 5182 4900 4688 4522 4390 4285 4066 3933 3847 3788 3745 3714 3692 10
12 11810 11810 11810 11810 11810 10393 7862 6376 5416 4765 4306 3971 3720 3527 3376 3255 3010 2864 2772 2710 2664 2631 2606 12
14 11810 11810 11810 11810 11810 11383 8290 6432 5246 4453 3899 3501 3205 2981 28606 2667 2392 2232 2131 2062 2015 1979 1953 14
16 11610 11810 11810 11810 11810 10721 9115 6826 5381 4423 3761 3269 2942 2680 2479 2321 2009 1831 1721 1648 #1597 1559 1532 16
18 11810 11810 11810 11810 11810 10122 8471 7436 57246 4579 3795 3239 2834 2530 2299 2118 1765 1567 14467 1367 1313 1273 1244 18
20 11610 11810 11810 11810 21810 9921 8032 6861 6092 4871 3950 3301 2830 2480 2214 2008 1610 ©1391 1258 1172 1113 1071 1040 20
22 11810 11810 11810 11810 11810 10005 7852 6531 5670 5083 4198 3446 2903 2501 2198 1963 1514 1271 1125 1032 969 924 891 22
24 11810 11810 11810 11810 11810 10302 7862 6376 5416 4765 4305 3655 3034 2576 2231 1966 1462 1191 1031 930 862 814 779 24
26 11810 11810 11810 11810 11810 10268 8018 6352 5284 4564 4060 3694 3212 2693 2303 2004 1441 1141 966 856 782 731 693 26
28 11810 11810 11810 11810 11810 10017 8290 6432 5246 4452 3899 3501 3205 2846 24607 2073 1444 1113 921 801 722 667 627 28
30 11810 11810 11810 11810 11810 9921 8032 6594 5283 4410 3804 3270 3049 2807 2539 2165 1467 1102 892 762 677 618 576 30
32 11810 11810 11810 11810 11810 9951 7889 6619 5381 4423 3761 3289 2942 2680 2479 2279 1506 1106 877 736 643 580 535 32
34 11610 11810 112810 11810 11810 10082 7837 6462 5530 4481 3761 3248 2872 2591 2374 2205 1560 1120 871 718 619 5a 503 34
36 11810 11810 11810 11810 11810 10122 7862 6376 5416 4579 3795 3239 2834 2530 2299 2118 1625 1145 874 708 602 529 478 36
38 11610 11810 11810 11810 11810 9980 7951 6347 5316 4620 3860 3258 2821 2495 2246 2053 1678 1178 B84 705 591 513 459 38
40 11810 11810 11810 11810 11810 9921 8031 6369 5262 4518 3950 3301 2830 2480 2214 2008 1610 1218 900 708 585 502 444 40
42 11810 11810 11810 11810 11810 9932 7915 6432 5246 4452 3899 3364 2859 2483 2199 1979 1556 1265 921 715 583 495 433 42
44 11810 11610 11810 11810 11810 10005 7852 6531 5263 4417 3829 3407 2903 2501 2198 1963 1514 1271 947 726 585 491 426 44
46 11810 11810 11810 11810 11810 10054 7837 6435 5310 4408 3784 3338 2962 2532 2209 1959 1483 1227 978 740 590 490 420 46
48 11810 11810 13810 11810 11810 9963 7862 6376 5381 4423 3761 3289 2942 2576 2230 1966 1462 1191 1013 758 598 491 418 48

6-134

TABLE 6-14.

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED

-PHYSICAL CONSTANTS:

p
- Ey = 1.96x10® PSI
A
ao Ey = 1.70x10® PSI
Gxy = 0.52x10® PSI
THICKNESS-H EQUALS 000625 INCHES 5 Oeai0ye =.0-20
MINCHES. “INCHES INCHES
6 8 10 12 146 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 65 52 46 a4 42 42 42 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 6
8 53 36 31 27 25 25 25 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 8
10 52 31 23 19 17 17 17 15 15 15 15 15 8 8 8 8 8 8 8 8 8 8 8 14
12 46 31 21 15 13 13 ll 11 11 11 ll il 6 6 6 6 6 6 6 6 6 6 6 16
14 44 29 19 13 ll 10 10 10 10 8 8 8 6 6 6 6 4 4 4 4 4 a 4 18
16 44 28 19 13 2i 10 8 8 8 8 6 6 4 4 4 4 4 4 4 4 4 4 4 20
18 42 25 17 13 10 8 8 6 6 6 6 6 4 4 4 4 4 4 4 4 4 4 4 22
20 40 25 17 13 10 8 6 6 6 6 4 4 4 4 4 4 2 2 2 2 2 2 2 24
22 40 25 15 11 10 8 6 6 6 4 4 4 4 4 2 2 2 2 2 2 2 2 2 26
24 40 23 15 11 10 8 6 6 4 4 4 * 2 2 2 2 2 2 2 2 2 2 2 28
26 40 23 15 il 10 8 6 6 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 30
28 40 23 15 11 8 8 6 6 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 32
30 42 23 15 11 8 6 6 4 6 4 4 2 2 2 2 2 2 2 2 2 2 2 2 34
32 42 23 15 Te 8 6 6 6 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 36
34 44 23 15 1 8 6 6 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 38
36 46 23 15 10 8 6 6 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 20
38 48 23 15 10 8 6 6 4 4 4 2 2 2 2 2 2 2 2 2 2 2 i} 0 42
40 50 23 13 10 8 6 6 4 4 4 2 2 2 2 2 2 2 2 2 C) 0 ° ° 44
42 53 23 13 10 8 6 6 4 4 4 2 2 2 2 2 2 2 2 C) 0 ° ) 0) 46
aa 55 25 13 10 8 6 6 4 4 4 2 2 2 2 2 2 2 2 0 Cy) 0 ° ° 48
46 59 25 15 10 8 6 6 4 4 4 2 2
48 63 27 15 10 8 6 6 4 4 2 2 2
THICKNESS=H EQUALS 061250 INCHES
LENGTH-8 WIOTH=A LENGTH-8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 513 410 372 353 342 336 332 328 326 324 323 323 321 321 321 321 319 319 319 317 317 317 317 6
8 429 288 240 218 206 198 193 191 189 187 185 183 183 183 181 181 181 179 179 179 179 179 179 8
lo 412 246 185 158 143 135 130 128 124 122 122 120 118 118 118 118 116 116 114 114 114 114 114 10
12 364 239 160 128 113 103 97 9% 90 88 86 86 84 84 84 82 82 80 80 80 80 80 80 12
14 367 223 153 114 94 84 76 73 71 67 67 65 63 63 63 61 61 61 SF 59 59 59 59 14
16 345 204 155 107 84 73 65 59 57 55 53 52 50 50 50 48 48 46 46 46 46 46 46 16
18 330 197 139 105 80 65 57 52 48 46 44 42 42 40 40 40 38 38 36 36 36 36 36 18
20 326 195 132 103 78 61 52 46 42 40 38 36 34 34 32 32 31 31 31 31 29 29 29 20
22 323 191 126 95 78 59 50 42 38 34 32 31 31 29 29 29 27 25 25 25 25 25 25 22
26 317 185 124 92 1% 59 48 40 36 32 31 29 27 25 25 25 23 23 21 21 21 21 21 24
26 317 183 126 Be 7 59 48 38 34 31 27 25 25 23 23 21 19 19 19 19 17 17 7, 26
28 321 185 122 88 67 55 48 38 32 29 25 23 23 21 19 19 17 17 17 15 15 15 15 28
30 328 181 118 86 65 53 46 38 32 27 25 23 21 19 19 17 15 15 15 13 13 13 13 30
32 340 179 118 86 65 52 44 38 31 27 23 21 19 17 17 15 15 13 13 13 11 ll ll 32
34 353 177 118 84 63 50 42 36 32 27 23 21 19 17 15 15 13 ll 1 11 11 11 a 34
36 366 179 116 82 63 50 40 34 31 27 23 19 17 17 15 13 13 11 11 10 10 10 10 36
38 385 181 114 82 63 50 40 34 31 27 23 19 17 15 15 13 11 Ta 10 10 10 10 10 38
40 405 185 1M 82 61 50 38 32 29 27 23 19 17 iS 13 13 ll 10 10 10 8 8 8 40
42 426 189 114 82 61 50 38 32 29 25 23 19 17 15 13 13 10 10 8 8 8 8 8 42
4s 448 195 114 80 61 48 38 32 27 25 21 19 17 15 rye) ll 10 10 8 8 8 8 8 44
46 an 200 116 80 59 48 38 31 27 23 21 19 17 15 13 ll 10 8 8 8 8 6 6 46
48 498 206 116 80 61 46 38 31 27 23 21 19 17 15 13 il 10 8 8 6 6 6 6 48

6-135

TABLE 6-14. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - LOADED EDGES CLAMPED -

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 001875 INCHES

- NGTH=|
prucnte. ee “TNCHESM
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 1733. 1385 1254 + «21191 «21185-1134 «©1118 «1107 «1201. «1095S 1092 p88 = 1086 = 1082 1080) 1078 = 1076 «= 1074 = 107210721072 = 10711071 6
8 1446 975 811 735 695 670 655 643 635 630 624 620 618 616 614 613 609 607 605 605 603 603 603 8
10 1395 832 624 532 487 458 441 429 420 414 408 405 403 401 399 397 393 391 389 389 387 387 387 10
12 1229 803 544 433 378 345 326 313 303 298 292 288 286 282 281 279 277 273 273 271 271 269 269 12
14 1174 754 515 384 319 282 260 246 235 229 223 219 216 214 210 210 206 202 202 200 200 198 198 4
16 1164 691 $19 361 286 244 219 202 191 183 177 174 170 168 166 164 160 156 156 155 155 153 153 16
18 1116 664 471 357 269 221 193 174 162 155 147 143 139 135 134 132 128 126 124 122 122 122 122 18
20 1105 658 643 349 263 208 176 156 143 134 126 122 118 114 113 127 107 103 101 101 99 99 99 20
22 1092 647 427 323 263 202 166 143 130 118 lll 107 101 3g 95 94 90 88 86 84 84 82 82 22
24 1072 628 422 307 250 200 160 135 120 109 lol 95 90 86 84 82 76 14 73 71 71 71 69 24
26 1071 622 424 298 235 200 158 132 113 101 92 86 82 78 UG? 73 67 65 63 61 61 59 59 26
28 1084 624 410 294 225 189 160 130 109 95 86 80 74 71 67 65 59 57 55 53 53 52 52 28
30 dll 611 403 292 219 179 755 128 107 92 82 74 69 65 61 59 53 52 50 48 46 46 46 30
32 1145 603 399 292 216 174 147 130 107 90 80 7 65 61 57 55 50 46 44 42 42 40 40 32
34 1189 601 399 284 216 168 141 124 107 90 78 69 63 57 53 52 46 42 40 38 38 36 36 34
36 1240 605 395 279 216 166 137 118 105 90 76 67 61 55 52 48 42 38 36 34 34 32 32 36
38 1300 613 389 277 212 164 134 114 101 90 76 67 59 53 50 46 40 36 32 32 31 31 29 38
40 1364 624 385 ZiT 208 164 132 111 97 88 76 65 57 52 48 44 36 32 31 29 29 27 27 40
42 1435 639 385 277 204 166 130 109 94 84 76 65 57 52 46 42 36 31 29 27 27 25 25 42
44 1511 656 385 273 204 162 130 107 92 80 73 67 57 50 46 4234 31 27 25 25 23 23 44
46 1593 676 389 269 202 158 130 105 90 78 TP 65 57 50 46 40 32 29 25 25 23 21 21 46
48 1681 698 393 267 202 156 130 105 88 76 69 63 57 50 44 40 32 27 25 23 21 21 19 48
THICKNESS-H EQUALS 02500 INCHES
LENGTH-8 WIDTH-A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 4109 3282 2971 «2820-2737: 2685 = 2651 2626 «= 2609 2595-2586 «= 2578 = 2572 2565 2561 2557 = 2551 02546 = 2542 2540 2538 = 2538) 2536 6
8 3427 2311 «691920 1742) 16451588 = 15501523. 1504 1490 «61481 = 1471 1466 = 1460-1456 14520 14430 14390 14350-1431 0 14310 14290 1427 8
10 3305 1973 1479 1263 1151 1086 1044 1015 996 981 969 962 954 948 945 941 931 927 924 920 920 918 916 10
12 2912 1906 «1288 1027 895 821 775 742 721 706 693 685 677 672 666 662 655 649 645 643 641 639 639 12
14 2780 «#1784 1223 908 756 668 616 582 557 540 529 519 511 504 500 496 487 481 477 475 473 471 471 14
16 2761 «1639-1231 857 677 578 519 481 454 435 422 412 403 397 391 387 378 372 368 366 364 363 363 16
18 2645 1572 1118 847 637 523 456 414 385 364 349 340 330 323 319 313 303 298 294 292 290 288 288 18
20 2618 1561 1050 826 622 492 418 370 338 317 300 288 279 271 265 261 252 246 240 239 237 235 235 20
22 2588 1530 1011 Tea 626 479 393 342 305 281 263 252 240 233 227 223 212 206 202 198 197 197 195 22
24 2540 1488 998 729 593 47T 382 323 282 258 239 223 214 206 198 193 183 176 172 170 168 166 164 24
26 2538 1473 1004 706 559 475 376 311 269 239 219 204 193 183 177 172 160 153 149 147 143 143 141 26
28 2570 1479 973 695 534 447 378 305 260 227 204 189 177 168 160 155 143 135 130 128 126 124 122 28
30 2632 1446 952 693 521 426 366 305 254 219 195 177 164 155 147 141 128 120 116 113 lll 109 107 30
32 2716 =1429 943 691 511 410 349 307 252 214 189 170 155 145 135 130 116 109 105 101 99 97 95 32
34 2819 1426 943 672 510 399 334 292 252 212 183 164 149 137 128 120 107 99 94 92 88 86 86 34
36 2943 1435 937 662 511 393 324 279 250 212 181 158 143 132 122 114 99 92 86 82 80 78 76 36
38 3080 1452 922 656 504 391 317 269 239 214 179 156 139 126 116 109 94 84 78 76 73 71 71 38
40 3235 1481 914 655 492 389 311 261 229 206 181 156 137 124 113 105 88 78 73 71 67 65 63 40
42 3402 1513 912 656 487 391 309 258 221 198 181 156 135 120 11 101 84 14 69 65 61 59 59 42
44 3584 1555 916 647 483 384 307 254 218 191 174 156 135 120 107 99 80 71 65 61 57 55 53 44
46 3777-1603 922 639 481 376 309 250 212 187 168 155 135) 118 107 97 78 67 61 57 53 52 50 46
48 3983 1654 933 635 481 372 307 250 210 181 162 149 137 118 105 95 74 65 57 53 50 48 48 48

6-136

TABLE 6-14,
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

10 OZ. CLOTH - LOADED EDGES CLAMPED -

FIBERGLASS POLYESTER LAMINATES

REMAINING EDGES SIMPLY SUPPORTED

(Cont'd)

THICKNESS=H EQUALS 063125 INCHES

p z: ENGTH=6

sinh Hae “news

6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 g900 5900 5805 5511 5365 5240 $177 5126 P SOSSmISUEEW (SOS1 9 Bos60N 19023.) USOLD pi p002 | 14996, =47eai> ~h973 h4965)/= 9 4962" 44958) 4958). (825% 6
8 5900 4515 3752 3402 3214 3099 3027-2975 2939. 2912 2891 2076 «2662 «2851 0 28432836 = 2819 2809 2803 2798 = 2794 = 794 = 2788 8
10 5900 3853 2889 2467 2250 2120 2038 1985 1945 1916 1895 1876 1864 1853 1843 1838 1621 1809 «1803 1798 1796 1792 1790 lo
12 5689 3721 «2515 2006 «1750 = 1603 1511 1450. 1608 1378 1355 1336 1322 1311 1301 1294 1277 1267 «1259 «1256 )=-1252,S «12481246 12
14 5429 3486 2387 1775 1475 1305 1204 “1135 1090 1055 1030 1011 996 985 975 966 950 941 933 927 924 922 920 a6
16 5393 3200 2406 16746 Tage 1128 1013 937 BAT B51 B24 B03 788 775 765 756 739 727 721 716 TZ 708 7086 16
18 5166 3072 2185 1654 1244 1023 B91 809 752 712 683 662 645 632 620 613 393 582 574 571 567 563 561 18
20 $112 3048 2048 1614 1216 964 B15 723 660 616 586 563 544 531 519 510 490 IU) 471 466 462 460 456 20
22 5053 2990 1977 1498 1223 935 769 666 597 550 515 490 47 456 445 435414 403 395 389 385 382 380 22
24 4962 2906 195uU 1422 1158 931 T4464 Veo 553 502 Thee 437 416 401 387 378 457 343 336 330 326 324 321 24
26 4958 2876 1960 1378 1090 929 135) 607 525 468 427 399 376 359) 345 334 313 300 292 284 261 279 275 26
28 FEEDC UTI RI FETT ah ey eee ee Ln eer en ey nC eee eee eee 28
30 $139 2824 1861 1355 1015 830 718 595 496 427 382 347 321 302 286 275 250 235 227 221 216 214 210 30
32 5303 2792 18462 1349 1000 800 681 7 601 “492 418 wae 330 303 282 265 254 227 212 202 197 193 189 187 32
34 5507 2786 1642 1313 994 780 653 571 494 414 359 319 290 267 250 237 210 195 183 177 174 170 166 34
36 5746 2801 1830 1292 998 767 632 546 489 414 353 311 279 256 237 223 195 177 168 160 156 153 151 36
38 5900 2838 1801 1280 983 761 618 527 466 416 353 305 273 246 227 212 181 166 155 147 143 139 137 38
40 5900 2891 1786 1279 962 761 609 511 448 403 - 353 303 267 240 219 204 172 155 143 135 132 128 124 40
42 5900 2958 1782 1284 948 765 603 502 433 387 353 303 265 237 214 197 164 145 134 126 120 116 114 42
44 5900 3038 1788 1263 941 748 601 494 424 374 340 305 265 235 210 193 156 137 126 118 213) 109 105 44
46 5900 3130 1801 1248 939 735 603 490 414 364 326 300 265 233 208 189 151 132 116 11. 105 101 97 46
48 5900 3233 1822 1240 941 727 599 487 408 355 317 290 267 233 206 185 147 126 113 105 99 95 92 48
THICKNESS-H EQUALS 0423750 INCHES
“INCHES. "INCHES “INCHES
6 8 10 ie 14 16 18 20 ried 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 6
8 7090 7090 6481 5878 5553 5357 5229 5141 5078 $032 4996 4965 4946 4925 4912 4899 4872 4855 94845 48320 4828 48260 4818 8
10 7090 6656 4992 4265 3887 3664 3523 3427 3361 3311 3273 3242 3219 3202 3185 3174 3147 3128 3116 3107 3101 3097 3095 10
12 7090 6431 4347 3467 3023 2771 2612 2508 2633 2380 2341 2309 2284 2265 2250 2237 2208 2189 2177 2170 2164 2158 2154 12
14 7090 6025 4126 3069 2548 2258 2080 1964 1883 1824 1782 1748 1723, -:1702,) 168516721643 1624 1613 1603-1597 = 1592 1588 14
16 7090 5530 4156 2893 2284 1950 1750 1620 1532 1469 1426 1387 1361 1340 1322 1307 1277 1258 1246 1237 1229 1225 Leet 16
18 7090 $307 3775 2859 2149 1767 1542 1397 1300 1232 1281 1143 (1214 1092 1072 1057 1027 1008 994 985 979 973 969 18
20 7090 5267 3540 2768 2101 1664 1608 1248 1141 1067 1012 971 941 916 897 882 647 828 815 805 798 794 790 20
22 7090 5168 3414 2588 2112 1616 1328 1151 1032 950 891 847 815 788 767 752 716 695 681 672 666 660 656 22
24 7090 5023 3370 2458 2000 1609 1286 1086 956 866 803 156 719 693 670 653 616 595 580 571 565 559 555 246
26 7090 4969 3385 2382 1883 1605 1269 1050 906 807 739 687 649 620 397 578 540 517 504 492 487 481 477 26
28 7090 4990 3282 2345 1805 1506 1275 1030 B74 767 691 637 595 565 540 519 479 456 441 431 424 418 414 28
30 7090 4880 3214 2341 1756 1433 1238 1029 857 740 658 599 555 521 494 473 431 406 391 382 374 368 364 30
32 7090 4822 3183 2330 1729 1382 1176 1040 B49 723 635 571 523 489 460 437 393 368 351 340 332 326 323 32
34 7090 4813 3183 2269 1719 13467 1128 987 853 716 620 551 500 462 431 408 363 334 319 307 300 292 288 34
36 7090 4841 3162 2233 1725 1326 1092 943 B43 714 611 538 483 443 410 385 336 307 290 279 271 265 260 36
38 7090 4906 3112 2212 1696 1317 1067 910 805 9 609 529 471 427 393 366 315 286 267 256 246 240 237 38
40 7090 4994 3086 2208 1662 1317 1051 RBS 775 697 611 525 464 416 380 353 298 267 248 235 227 219 216 40
42 7090 5110 3080 2217 1639 1321 1042 866 750 670 ell 525 458 408 370 342 282 250 231 218 210 202 198 42
44 7090 5250 3088 2183 1626 1292 1040 853 731 647 586 $29 436 405 364 332 271 237 218 204 195 187 183 44
46 7090 5408 3112 2158 1622 1271 1042 B45 718 628 565 519 458 403 359 326 261 227 204 191 181 176 170 46
48 7090 5586 3149 2143 1626 1256 1036 B42 708 614 548 500 462 403 357 321 254 218 195 ig 170 164 158 48

6-137

TABLE 6-14.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - LOADED EDGES CLAMPED -

FIBERGLASS POLYESTER LAMINATES

REMAINING EDGES SIMPLY SUPPORTED (Cont'd)
THICKNESS-H_ EQUALS 004375 INCHES
STNCHES “INCHES “INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 6270 saya e270 8270 82708270 8270 6270 6270 6270 (82TO G27o (S270) ez70| e270 ez70 8270 8270 8270 8270 8270, 8270) 8270 6
8 g270. 6270 8270 8270 6270 8270 8270 8164 8064 7990 7935 7885 7855 7622 7801 7778 7736 7710 7694 7675 7668 7666 7652 8
10 8270. 8270 7929 6773 6171 5818 5595 5442 5336 5257 5198 5151 5114 5084 5059 $040 4996 4967 4946 4935 4925 4918 4914 10
12 8270 8270 6902 5505 4801 4399 4149 3983 3864 3780 3717 3668 3628 3597 3572 3551 3506 3477 3458 3446 3435 3427 = 3422 12
14 8270 8270 6551 4872 4046 3584 3301 3118 2990 2899 2830 2777 2737 2704 2677 2654 2609 2580 2561 2546 2536 2528 2521 14
16 8270. 6270 6601 4593 3626 3097 2778 2572 2433 2336 2259 2206 2160 2126 2099 2076 2029 1998 1977 1964 1952 1945 1941 16
18 270 6270 5992 4540 3414 2807 2446 2217 2065 1954 1876 1817 1769 1733 1704 1679 1630 1599 1578 1563 1553 1546 1540 18
20 8270 8270 5620 4429 3336 2643 2237 1983 1813 1693 1607 1544 1494 1454 1424 1399 1347 1315 1294 1279 1267 1259 1254 20
22 8270 8206 5423 4109 3355 2567 2111 1826 1637 1508 1414 1345 1292 1252 1219 1193 1137 1105 1082 1067 1057 1048 1042 22
24 8270 7975 5351 3902 3175 2553 2042 1725 1519 1376 1275 1200 1143 1099 10651036 979 945 924 906 897 887 882 24
26 8270 7891 5376 3782 2992 2549 2017 1666 1439 1282 1174 1092 1032 985 948 918 859 822 798 782 77 763 756 26
28 270. 7925 5213 3725 2868 2391 2027 1637 1367 1217 1099 loll 947 897 857 826 761 725 700 683 672 664 656 28
30 8270 7748 5103 3717 2788 2277 1967 1634 1359 1174 1046 950 882 828 786 7152 685 647 622 605 593 584 578 30
32 8270 7658 5055 3700 2744 2195 1866 1651 1349 1149 1008 906 832 775 729 695 624 584 557 540 529 519 511 32
34 8270 7643 5055 3605 2729 2141 1790 1567 1355 1135 985 874 794 733 685 649 574 532 506 487 475 466 458 34
36 8270 7689 5021 3544 2738 2107 1735 1498 1340 1135 971 853 767 702 651 613 534 489 462 443 429 420 412 36
38 8270 7788 4942 3513 2695 2091 1695 1445 1279 1143 966 840 748 677 624 582 500 452 424 405 391 382 374 38
40 8270 7931 4901 3507 2641 2091 1670 1405 1229 1107 969 834 735 660 603 559 471 424 393 374 359 349 342 40
42 8270 8116 4889 3523 2605 2097 1654 376 1191 1063 971 834 727 649 588 542 450 399 366 347 332 323 315 42
44 8270 8270 4904 3465 2584 2051 1651 1355 1162 1027 931 838 725 641 578 527 431 378 343 323 309 298 290 44
46 8270 8270 4942 3427 2576 2017 1654 1343 1139 998 899 824 727 637 571 517 416 359 324 303 268 8©=— 277 269 46
48 8270 8270 5000 3404 2582 1994 1645 1338 1122 975 870 794 733 637 567 510 403 343 309 286 271 260 252 48
THICKNESS=H EQUALS 065000 INCHES
“INCHES. “INCHES “INCHES.
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 6
8 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9490 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 8
10 9450 9650 9450 9450 9213 8687 8351 6126 7965 7869 7759 7687 (7633 7589 7551 7523 7458 7414 7385 7366 7351 7341 7336 10
12 9450 9450 9450 8219 7166 6566 6192 5944 5769 5643 5547 5473 416 5370 5332 5301 5233 5189 5160 5145 5128 5114 5107 12
14 9450 9450 9450 7273 6038 5349 4929 4652 4464 4326 4223 4145 4084 4036 3996 3964 3895 3851 3822 3799 3786 S775 3765 14
16 9450 9450 9450 6857 5414 4624 4147 3841 3631 3483 3374 3290 3225 3174 3133 3099 3027 2981 2952 2931 2916 2903 2897 16
18 9450 9450 8946 6776 5095 4189 3652 3311 3080 2918 2799 2710 2641 2588 2544 2508 2433 2385 2357 2334 2319 2307 2298 18
20 9450 9450 8389 6610 4979 394% 3340 2958 2704 2527 2399 2303 2229 2172 2126 2088 2009 1962 1929 1908 1893 .1882 1872 20
22 9450 9450 6095 6133 5007 3830 3149 2725 2645 2252 2112 2008 +1929 1868 1819 1780 1698 1649 1616 1593 1576 1565 1555 22
24 9450 9450 7988 5826 4740 3811 3048 2576 2267 2055 1903 1792 1708 1641 1590 1548 1462 1410 1378 1353 1338 1324 1317 24
26 9450 9450 8024 5645 4467 3805 3009 2487 2147 1916 1750 1630 1540 1469 1414 1370 1280 1227 1193 1168 1151 1139 1130 26
28 9450 9450 7782 5559 4280 3570 3025 2445 2071 1819 1639 1809 1412 1338 =6:1279 1233, «1137 1082 1046 = 1021 1004 990 981 28
30 9450 9450 7618 5549 4162 3399 2939 2439 2029 1754 1559 1420 1315 1235 1174 1124 1023 966 927 903 885 872 863 30
32 9450 9450 7545 5523 4097 3277 2786 2464 2015 1714 1504 1353 1240 1156 1090 1036 931 870 832 807 788 775 765 32
34 9450 9450 7545 5379 4074 3194 2674 2340 2023 1695 1469 1305 1185 = 1093, 1023 968 857 794 754 727 708 695 683 34
36 9450 9450 7496 5290 4088 3145 2590 2237 2000 1695 14468 1273 1145 1048 971 914 796 729 689 660 641 628 616 36
38 9450 9450 7379 5244 4023 3122 2530 2156 1908 1706 14463 1254 (‘12116 1011 931 870 746 676 = 634 605 584 571 559 38
40 9450 9450 7316 5234 3941 3122 2492 2097 1836 1653 1446 1264 1097 987 901 836 704 632 588 557 536 523 511 40
42 9450 9450 7299 5257 3887 3132 2471 2053 1779 1586 1448 1244 1086 969 878 807 672 593 548 517 496 481 469 42
44 9450 9450 7320 5173 3857 3063 2464 2023 1733 1532 1389 1252 1084 958 863 788 643 563 513 483 460 445 433 44
46 9450 9450 7377 5114 3845 3011 24671 2006 1700 1490 1340 1231 1086 abe 851 773 620 536 485 452 429 414 403 46
48 9450 9450 7463 5080 3853 2975 2454 1996 1675 1456 1300 1185 1095 952 845 761 601 513 460 427 403 387 374 48

6-138

THICKNESS-H

TABLE 6-14,

EQUALS 005625 INCHES

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - LOADED EDGES CLAMPED -
REMAINING EDGES SIMPLY SUPPORTED

(Cont'd)

= NGTH-B
oa “Incnes “news
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34° 36 42 48 54 60 66 72 78
6 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 710630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 6
8 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 8
10 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10618 10555 10515 10486 10467 10454 10444 10
12 10630 10630 10630 10630 10206 9349 0816 68463 8215 8034 7900 7793 7711 7645 7593 7547 7450 7389 7347 7324 7301 7282 7273 12
14 10630 10630 10630 10354 8597 7616 7019 6626 6355 6160 6013 5902 5815 5748 5689 5643 5546 5484 5442 5410 5391 5374 — 5360 14
16 10630 10630 10630 9763 7708 6582 5906 5469 5171 4960 $803 4685 4593 4519 4460 4412 4311 4246 ©4204 = 4173 4151 4133 4124 16
18 10630 10630 10630 9646 7253 5965 5200 4714 4367 4154 3986 3860 3761 3683 3622 3570 3464 3397 3355 3322 3301 3284 3273 18
20 10630 10630 10630 9412 7089 5616 4755 42146 3851 3599 3416 3278 3174 3091 3027 2973 2862 2794 2748 2717 2695 2677 2664 20
22 10630 10630 10630 8732 7129 5454 4485 3881 3481 3206 3007 2859 2748 2660 2590 2534 2418 2347 2301 2269 2246 2229 2214 22
24 10630 10630 10630 8295 6750 5427 4339 3668 3227 2925 2710 2551 2431 2338 2263 2204 2082 2009 1962 1927 1904 1887 1874 24
26 10630 10630 10630 8038 6360 5418 4286 3542 3057 2727 2492 2320 2193 2093 2013 1950 1822 1746 1696 1664 1639 1622 1607 26
28 10630 10630 10630 7916 6095 5082 4305 3481 2948 2588 2334 2149 2011 1904 18621 1754 1620 1540 1488 1454 1429 1410 1397 268
30 10630 10630 10630 7900 5925 4839 4183 34673 2889 2696 2221 2021 (1872 1759 1670 1599 1458 1374 1321 1286 1259 1242 1227 30
32 10630 10630 10630 7864 5832 4666 3967 3507 2868 2441 2143 1927 1767 1645 1551 1477 1326 1240 1185 1149 1122 1103 1088 32
34 10630 10630 10630 7660 5801 4549 3805 3330 2880 2414 2091 1859 1689 1559 1458 1378 1221 1130 1072 1034 1008 988 973 34
36 10630 19630 10630 7532 5820 4479 3687 3185 2847 2412 2063 1813 1630 1490 1384 1300 1134 1038 979 941 912 893 876 36
38 10630 10630 10507 7467 5729 4446 3603 3072 2717 2429 2053 1786 1590 1441 13261238 1063 964 901 861 832 811 796 38
40 10630 10630 10417 7454 5612 4444 3548 2986 2612 2353 2061 1773 1563 1405 1282 1189 1004 B99 836 794 765 742 727 40
42 10630 10630 10393 7486 5534 4460 3519 2924 2530 2259 2063 1773 1548 1380 1250 1151 956 845 780 737 706 685 668 42
44 10630 10630 10423 7366 5490 4360 3509 2882 2467 2183 1979 1782 1542 1364 1227 1120 916 601 733 687 656 634 616 44
46 10630 10630 10503 7282 5475 4288 3519 2855 2420 2122 1908 1752 1548 1357 1212 1099 884 763 691 645 613 590 ane, 46
48 10630 10630 10627 7234 5486 4236 3494 2843 2387 2074 1851 1687 1559 1357 1204 1084 857 731 656 607 574 551 534 48
THICKNESS=H EQUALS 006250 INCHES
LENGTH-B WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 11810 11610 11810 11810 11810 11810 12610 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 6
8 11610 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 112810 11810 11810 118610 11810 11810 11810 11810 11610 11610 11810 8
1o 11810 11610 11810 11810 11810 11810 11810 11810 11810 11810 11820 11810 12810 11810 11810 11810 11810 11810 11810 11810 11810 118610 11810 10
12 11810 11810 11810 118610 11810 11810 11810 11608 11269 11020 10837 10690 10578 10486 10416 10353 10219 10135 10080 10047 10015 9990 9977 12
14 11810 11810 11810 11810 11793 10448 9627 9089 8715 8450 8248 8097 7977 7883 7805 7740 7606 7523 7465 7421 7395 7370 7353 14
16 11810 11810 112810 11810 10572 9030 8101 7502 7093 6803 6587 6427 6301 6200 6118 6053 5912 5824 5765 5725 5694 5670 5656 16
18 11810 11810 11810 11810 9950 8183 7135 6467 6017 5700 5467 5294 5160 5053 4967 4899 4752 4660 4601 4559 4528 4504 4488 18
20 11810 11810 11810 11810 9725 7704 6523 5778 5282 4937 4685 4498 *355 4242 4151 4078 3925 3832 3769 3727 3696 3673 3654 20
22 11810 118610 11810 11810 9780 7482 6152 5322 4776 4397 4124 3923 3769 3649-3553) 3477) 3317 3219-3156 = 33112, 3080) 33057 = 33038 22
24 11810 11810 11810 11379 9259 7444 5952 5030 4627 4013 3717 3500 3334 3206 3105 3023 2657 2756 2691 2645 2612 2588 2570 24
26 11810 11810 11810 11026 8725 7431 5879 4857 4193 3740 3420 3185 3007 2870 2763 2677) «25022395 «2328 «0228202248 = 2223 2206 26
28 11810 11810 11810 10858 8360 6973 5906 4775 4046 3551 3202 2948 2757 = =62612, 2498 = 2406 = 222102112, 20421994 891960 19351916 28
30 11810 11810 11810 10837 68127 6637 5738 4763 3964 3424 3046 2773 2569 2412 2290-2195 2000 1885 1813-1763) 1729-1704 = 1683 30
32 11810 11810 11810 10786 8002 6400 5442 4811 3935 3347 2939 2643 2424 2258 2128 2025 1821 1700 1626 1574 1540 1513 1492 32
34 11810 11810 11810 10509 7958 6240 5221 4568 3950 3311 2868 2551 2315 2137 2000 1891 1674 1550 1471 1420 1384 1357 1336 34
36 11810 11810 11810 10333 7984 6143 5057 4368 3904 3309 2830 2488 2237 2046 =61899 1784 «= 1555 1426013431290 «125212251204 36
38 11810 11810 11810 10244 7858 6099 4942 4214 3727 3334 2817 2448 2179 1977 1821 1698 1458 1321 1237 1181 1141 1114 1093 38
40 11810 11810 11810 10225 7698 6097 4868 4097 3584 3227 2826 2431 21435 1925 «1759-1632, s:1376 1235 1147 «#1088 1048 1019 998 40
42 11810 11810 11810 10269 7591 6116 4826 4011 3473 3099 2830 2431 2122 1891 1716 1578 1311 1160 1071 1009 968 939 916 42
44 11610 11810 118610 10104 7532 5981 4813 3952 3385 2994 2716 2445 2116 1870 1683 1538 1256 1099 1004 943 899 868 B47 44
46 11810 11810 11810 9990 7511 5881 4826 3916 3320 2910 2618 2an3 2122 1861 1662 1508 1212 1048 948 884 840 809 786 he
48 11610 11810 11810 9923 7524 5813 4794 3901 3275 2845 2540 2315 2137 1861 1651 1488 1176 1004 901 834 788 756 733 48

6-139

TABLE 6-15,

10 OZ, CLOTH - ALL EDGES CLAMPED

PHYSICAL CONSTANTS:

FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH

| A | Ex = 1.96x10® PSI
| | Ey = 1.70x10® PS}
Gxy = 0.52x10® PSI
P Oxy = Oyx = 0.20
THICKNESS-H EQUALS 000625 INCHES
MINCHES “INCHES “INCHES.
6 8 10 12 146 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 107 67 53 48 46 44 42 42 42 40 40 40 40 40 40 40 40 40 40 40 34 40 40 6
8 88 59 40 32 29 27 25 25 25 25 23 23 23 23 23 23 23 23 23 23 23 23 23 8
10 84 52 38 27 23 19 19 17 17 15 15 15 15 15 15 15 15 15 15 15 15 15 15 10
12 80 48 34 27 19 17 15 13 13 ll ll oy ll a7 ll 11 10 10 10 10 10 10 10 12
14 78 48 31 25 19 15 13 11 10 10 10 10 8 8 8 8 8 8 8 8 8 8 8 14
16 76 44 31 23 19 15 il 10 10 8 8 8 8 8 6 6 6 6 6 6 6 6 6 16
18 76 44 31 21 17 13 11 10 8 8 8 6 6 6 6 6 6 6 4 4 4 4 4 18
20 80 44 29 21 15 13 ll 10 8 8 6 6 6 6 oS ui 4 Oy ce 4 4 4 4 20
22 B4 42 29 21 15 1X 10 10 8 6 6 6 6 4 4 4 4 4 4 4s S 4 4 22
24 92 44 29 19 15 ll 10 8 8 6 6 6 4 4 4 4 4 4 2 2 2 2 2 24
26 99 44 27 19 15 ll 10 8 8 6 6 6 4 4 4 4 4 2 2 2 2 2 2 26
28 109 46 27 19 15 ll 10 8 8 6 6 6 4 4 4 4 2 2 2 2 2 2 2 28
30 118 48 27 19 15 ql 10 8 6 6 6 6 4 4 4 4 2 2 2 2 2 2 2 30
32 130 52 29 19 15 ll 10 8 6 6 6 4 4 4 4 4 2 A 2 2 2 2 2 32
34 143 55 29 19 13 11 10 8 6 6 6 4 4 4 4 4 2 2 2 2 2 2 34
36 156 59 31 19 13 11 10 8 6 6 4 4 4 4 4 4 2 2 2 2 2 2 2 36
38 170 63 31 19 13 11 10 8 6 6 4 4 4 4 4 4 2 A 2 2 2 2 2 38
40 185 67 32 19 13 1l 10 8 6 6 4 4 4 4 4 2 2 2 2 2 2 2 2 40
42 200 73 34 21 13 ll 10 8 6 6 4 4 4 4 4 2 2 2 2 2 2 2 2 42
44 218 76 36 21 13 11 8 8 6 6 4 4 4 4 2 2 2 2 2 2 2 2 t) 44
46 235 82 38 23 15 ll 8 8 6 6 4 4 4 4 2 2 2 2 2 2 2 ° 46
48 254 88 40 23 15 ll 8 8 6 6 4 4 4 4 2 2 2 2 2 2 2 Cy ° 48
THICKNESS=H EQUALS 021250 INCHES
LENGTH-B WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 853 529 426 382 361 347 340 334 330 328 326 324 324 323 323 321 321 319 319 319 267 317 317 6
8 710 479 324 261 231 216 204 198 195 191 189 187 185 185 183 183 181 181 179 179 179 179 179 8
10 676 416 307 219 179 158 145 137 132 128 126 124 122 120 120 120 118 116 116 116 114 114 114 10
12 635 382 275 214 160 132 116 107 99 95 92 90 88 88 86 86 84 82 82 80 80 80 80 12
14 630 378 250 195 156 122 101 90 82 16 73 71 69 67 65 65 63 61 61 59 59 59 59 14
16 607 357 242 177 147 120 95 80 73 65 61 57 55 53 52 52 50 48 48 46 46 46 46 16
18 613 355 239 170 134 113 95 76 67 59 53 50 48 46 44 42 40 38 38 36 36 36 36 18
20 637 345 229 168 126 103 92 76 63 55 50 46 42 40 38 36 34 32 31 31 31 a1 31 20
22 679 340 227 164 124 97 84 7% 63 53 46 42 38 36 34 32 29 27 27 25 25 25 25 22
24 733 343 223 158 124 95: 78 69 61 Sa 46 40 36 32 31 29 25 rt] 23, 4c} 21 21 21 24
26 796 355 219 156 120 95 76 65 57 52 46 40 34 31 29 27 23 21 19 19 19 19 17 26
28 870 368 218 156 116 95 74 63 53 50 46 40 34 31 27 25 21 19 17 17 Ly 15 15 28
30 952 389 219 153 116 92 14 61 52 46 42 38 34 31 27 25 19 17 15 15 15 13 13 30
32 1044 412 225 151 116 90 14 61 52 44 40 36 34 31 27 25 19 17 15 13 13 13 13 32
34 1141 439 233 151 114 88 73 61 50 44 38 34 32 31 27 23 19 15 13 13 ll ll ll 34
36 1246 468 240 153 113 88 1 59 50 42 36 32 31 29 27 23 17 15 13 11 ll 11 10 36
38 1359 500 252 156 lll 88 7A 57 50 42 36 32 29 27 25 25 17 13 ll 1 10 10 10 38
40 1479 536 263 160 lll 86 72 57 50 42 36 32 29 27 25 23 17 13 11 10 10 10 10 40
42 1607 574 277, 164 113 86 71 57 48 42 36 31 29 25 23 21 17 13 11 10 10 8 8 42
44 1740 614 292 170 114 86 69 57 48 40 36 31 27 25 23 21 17 13 11 10 lo 8 8 44
46 1880 656 307 176 116 86 69 57 48 40 36 31 27 25 21 21 17 13 11 10 8 8 8 46
48 2027 700 324 183 118 86 67 55 48 40 34 31 27 25 21 19 a7 13 1 10 8 8 8 48

6-140

TABLE 6-15. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - ALL EDGES CLAMPED (Cont'd)

THICKNESS-H EQUALS 061875 INCHES

= H-'
“INCHES. “INCHES ‘INCHES.
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 2878 1782 1435 «1290 «1216 «1174 «1147 «1130-1116 «1107-12010 -1097 | = 1093-1090 1086 = 1084 = 1080 1076 = 1074 = 1074 905 1072 1071 6
8 2395 1618 1093 882 780 725 693 670 655 645 637 632 628 622 620 618 613 609 607 605 605 605 603 8
10 2280 1403 1036 Th2 607 534 490 464 447 433 426 418 412 4068 405 403 397 393 391 389 389 387 387 10
12 2145 91288 926 ng 540 47 391 359 338 323 ail 303 298 294 290 286 281 277 275 273 271 271 271 12
14 2124 ©1277 842 658 529 410 343 303 277 258 246 237 229 225 221 218 210 206 204 202 200 200 200 14
16 2046 1206 819 599 492 405 323 273 242 221 206 195 187 181 177 174 166 160 158 156 155 155 155 16
18 2065 = 1197 803 572 448 384 321 261 223 198 181 168 160 153 147 143 135 130 128 126 124 122 122 18
20 2153 1164 773 571 427 351 307 260 216 185 166 151 141 134 128 122 114 109 105 103 101 101 99 20
22 2290 1149 765 553 418 332 282 250 214 179 156 141 130 120 113 109 97 92 90 88 86 84 84 22
24 2471 1162 756 536 420 323 265 231 210 179 153 135 122 ill 103 97 86 80 76 m4 73 73 71 24
26 2689 «1195 739 531 405 321 258 219 195 177 153 132 116 105 97 92 78 71 67 65 63 61 61 26
28 2937 = 1246 737 531 393 319 254 210 163 164 151 132 114 103 94 86 73 65 61 57 55 53 53 28
30 3215-1311 744 517 389 307 254 206 176 156 141 132 114 101 90 82 67 59 55 52 50 48 48 30
32 3521 ©1389 760 511 391 302 250 204 172 149 134 124 114 101 90 80 65 55 50 48 44 44 42 32
34 3540 1479 782 511 384 300 242 206 170 145 130 116 109 101 90 80 61 52 46 44 40 40 38 34
36 3540 1580 813 517 378 300 239 200 170 143 126 113 103 95 90 80 59 50 44 40 38 36 34 36
38 3540 1689 849 525 376 296 237 197 170 143 122 109 99 92 86 80 59 48 42 38 34 32 32 38
40 3540 1809 889 538 376 292 237 193 166 143 122 107 95 88 82 76 59 46 40 34 32 31 29 40
42 3540 1935 935 553 380 288 237 191 162 141 122 105 94 86 78 73 59 46 38 34 ar 29 27 42
44 3540 2072 985 572 385 288 231 19. 160 137 122 105 92 82 76 71 59 46 36 32 29 27 25 44
46 3540 2216 1038 593 393 288 229 193 158 135 120 105 92 82 74 69 57 46 36 31 29 25 25 46
48 3540 2366 1095 618 401 290 227 189 158 134 118 105 92 80 73 67 55 46 36 31 27 25 23 48
THICKNESS-H EQUALS 002500 INCHES
LENGTH-8 WIDTH=A LENGTH-B8
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 4730 4227 3402 3055 2880 2780 2717 2675 2647 2626 2611 2599 2590 2580 2574 2569 2559 2551 2548 2544 2145 2540 2538 6
8 4730 3838 2590 2091 1851 1719 1639 1588 1553 1529 1511 1496 1487 1477 1471 1464 1452 1445 1441 1435 1433 1433 1429 8
10 4730 3324 2456 1761 1437 1265 1164 1099 1057 1029 1008 990 979 969 962 954 943 933 927 926 922 920 920 10
12 4730 3055 2195 1706 1279 1057 929 851 800 763 739 719 706 695 687 679 664 656 651 647 645 643 641 12
14 4730 3025 1996 1561 1254 971 813 718 655 613 582 561 546 532 523 515 500 490 485 479 477 475 473 14
16 4730 2859 1943 1420 1168 960 765 647 572 523 489 462 445 429 418 410 393 382 376 372 368 366 364 16
18 4730 2838 «1904 1359 1065 908 758 618 529 469 429 399 378 363 349 340 321 309 302 298 294 292 290 18
20 4730 2761 1830 1351 1011 832 727 614 510 441 393 359 334 317 302 290 269 258 250 244 240 239 237 20
22 4730 2725 1813 1311 992 786 668 593 508 427 372 334 305 284 269 256 233 219 212 206 202 200 198 22
24 4730 2754 1790 1271 996 763 632 550 496 426 364 321 288 263 246 233 206 191 181 176 172 170 168 24
26 4730 2834 = =1752 1259 958 760 609 519 460 420 363 313 277 250 231 216 1865 170 160 155 149 147 145 26
28 4730 2954 1744 =—-1259 933 756 601 500 435 391 359 313 273 242 221 204 170 153 143 135 132 128 126 28
30 4730 3109 1761 1227 926 731 601 489 418 370 336 311 273 240 216 197 160 141 130 122 118 114 113 30
32 4730 3296 1801 1212 929 716 592 485 406 355 319 292 273 240 212 191 151 130 118 lll 107 103 99 32
34 4730 3507 «18571212 910 708 574 489 403 345 305 277 256 240 212 189 145 124 lll 101 97 94 90 34
36 4730 3744 «1927 1223 895 710 565 477 401 340 298 267 244 227 214 189 141 118 103 95 90 84 82 36
38 4730 4006 2011 1244 B89 702 559 466 403 338 292 258 235 216 202 191 139 113 97 88 82 78 4 38
40 4730 4286 2109 1275 891 691 559 458 391 338 268 252 227 208 193 161 139 dll 94 84 76 73 69 40
42 4730 4588 2216 1313 899 683 559 454 384 336 288 250 221 202 185 174 139 109 90 80 73 69 65 42
44 4730 4730 2334 1357 912 681 550 454 378 328 288 248 218 197 179 166 141 107 88 76 69 65 61 44
46 4730 4730 2462-1408 929 683 542 456 376 323 284 248 216 © 193 176 162 135 107 86 74 67 61 57 46
48 4730 4730 2597 1464 952 689 538 448 374 317 279 250 216 191 172 158 130 107 86 73 63 57 53 48

6-141

TABLE 6-15. FIBERGLASS POLYESTER LAMINATES
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - ALL EDGES CLAMPED (Cont'd)

THICKNESS-H EQUALS 003125 INCHES

tenors er “fens |
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 5900 5900 5900 5900 5626 5429 5309 5227 5171 $128 5099 5076 5057 5040 5026 5017 5000 4984 4975 4969 4189 4962 4958 6m |
8 5900 5900 5059 4084 3614 3357 3202 3103 3034 2986 2950 2922 2903 2883 2872 2861 2836 2822 2813 2805 2799 2798 2794 8
10 5900 5900 4797 3439 2807 2469 2273 2149 2067 2009 1967 1935 1910 1893 1878 1866 1840 1824 1813 1807 1801 1798 1796 10
12 5900 5900 4288 3332 2498 2063 1615 1662 1561 1492 1443 1406 1380 1357 1342 1326 1300 1262 1271 1265 1259 1254 1252 12
14 5900 5900 3901 3049 2448 1899 =1590 1401 1279 1197/1139 1095 1065 1040 1021 1006 975 956 945 937 931 927 924 14
16 5900 5584 3792 2773 «228201874 1494 1265 1118 1021 952 905 B66 840 819 801 767 746 735 725 719 716 riz 16
18 5900 5542 3721 2653 2080 1775 1481 1206 1032 918 838 780 739 706 683 662 626 603 590 580 574 571 567 18
20 5900 5393 3574 2639 1975 1624 1418 1198 994 861 767 702 653 618 590 569 527 502 487 477 471 466 462 20
22 5900 5322 3542 2561 1937 1536 1303 1160 990 834 727 653 597 557 525 502 454 427 412 403 395 389 385 22
24 5900 5378 3498 2483 1946 1492 1233 1072 968 832 710 624 563 515 481 454 401 372 355 345 338 332 328 24
26 5900 5534 3422 2458 1870 1481 1191 1013 897 819 710 613 542 490 450 420 363 332 313 302 292 286 282 26
28 5900 5769 3406 2458 1824 1477 1172 975 B47 763 702 613 532 475 431 397 334 300 279 265 258 252 246 28
30 5900 5900 3443 2397 1807 1426 1174 954 815 721 656 609 532 468 420 382 311 275 252 239 229 223 219 30
32 5900 5900 3517 2368 18613 1397 1156 948 796 693 622 571 532 468 414 374 296 256 231 218 206 200 195 32
34 5900 5900 3626 2368 1777 1384 1124 952 786 674 597 542 502 469 414 370 284 240 216 198 189 181 176 34
36 5900 5900 3765 2391 1750 1385 1103 929 784 662 580 521 477 443 418 370 277 229 202 185 174 166 160 36
38 5900 5900 3929 2431 1738 1372 1093 908 788 658 569 504 458 422 395 374 273 221 191 174 160 153 147 38
40 5900 5900 4118 2490 1740 1347 1093 3893 765 660 563 494 443 406 378 355 271 216 183 164 151 141 135 40
42 5900 5900 4328 2565 1756 1334 1093 885 748 656 561 487 433 393 363 340 273 212 177 156 141 134 126 42
44 5900 5900 4559 2651 1782 1330 1072 885 739 639 563 485 427 384 351 326 275 208 172 149 135 126 118 44
46 5900 5900 4807 2750 1817 1334 1059 889 733 628 555 485 424 378 343 317 265 208 168 145 130 118 113 46
48 5900 5900 5074 2861 1859 1345 1053 B74 731 620 544 487 422 372 336 307 254 208 166 141 124 113 105 48
THICKNESS-H_ EQUALS 063750 INCHES
LENGTH-B WIDTH=A LENGTH=B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78

6 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 7090 6
8 7090 7090 7090 7057 6246 5801 5534 5360 5244 5160 5099 5049 5015 4984 4963 4942 4901 4878 4862 4845 4839 4836 4826 8
10 7090 7090 7090 5944 4849 4267 3927 3712 3570 3471 3399 3343 3301 3269 3242 3223 3179 3151 3133 3122 3112 3107 3103 10
12 7090 7090 7090 5757 4317 3567 3137 2872 2698 2578 2494 2429 2382 2345 2317 2294 2244 2216 2196 2185 2175 2168 2162 12
14 7090 7090 6740 5269 4229 3280 2746 2420 2210 2069 1967 1895 1840 1798 1763 1738 1685 1654 1634 1618 1611 1603 1597 14
16 7090 7090 6553 4790 3944 3238 2580 2185 1933 1765 1647 1561 1498 81450 1412 1384 1324 1290 1269 1254 1244 1235 1231 16
18 7090 7090 6429 4584 3595 3065 2559 2084 1784 1586 1446 1349 1277) 12210-1179 11450-1080 104210191004 992 985 979 18
20 7090 7090 6175 4559 3412 2805 2452 2072 1719 1487 1326 1212 1130 10671019 981 908 868 842 826 815 805 800 20
22 7090 7090 6120 4423 3345 2653 2254 2006 1712 1643 1258 1128 1032 962 908 866 784 740 712 695 683 674 666 22
24 7090 7090 6044 4288 3364 2578 2130 1853 1672 1439 1227 1078 971 891 830 784 695 645 614 595 582 572 567 24
26 7090 7090 5912 42468 3231 2561 2057 1750 1550 1416 1227 1057 937 847 779 727 626 572 540 519 506 496 489 26
28 7090 7090 5887 4248 3151 2551 2027 1685 1466 1317 1214 1057 922 821 744 687 576 517 483 460 445 435 427 28
30 7090 7090 5948 =64141 = 3122, 2464 = 2027) 165101408 )= 1246) 1134 =) 1051 922 809 725 660 538 473 437 412 397 385 378 30
32 7090 7090 6078 4093 3133 2412 1998 1639 1374 1197 1074 987 920 809 716 645 511 441 401 374 357 345 338 32
34 7090 7090 6267 4091 3070 2391 1941 1647 i977. 1164 =1032 937 866 813 718 639 492 416 372 343 326 313 303 34
36 7090 7090 6505 4130 3023 2395 1906 1607 1355 1145 1002 899 822 767 723 639 479 397 349 319 300 286 277 36
38 7090 7090 6792 4202 3004 2370 1889 1569 1361 1137 983 872 790 729 683 647 471 382 330 300 279 263 254 38
40 7090 7090 7090 4303 3009 2330 1889 1544 1322 1139 971 853 767 702 651 613 469 372 317 282 260 246 235 40
42 7090 7090 7090 4431 3034 2307 1887 1532 1294 1134 969 842 748 679 626 586 469 364 305 269 246 229 219 42
44 7090 7090 7090 4580 3078 2300 1853 1530 1277 1107 973 836 737 664 607 563 473 361 298 258 233 216 204 44
46 7090 7090 7090 4752 3139 2305 1830 1536 1267 1086 960 836 731 653 592 546 456 359 290 250 223 206 193 46
48 7090 7090 7090 4942 32146 2322 1819 1511 1263 1072 939 842 729 645 582 532 439 361 286 242 216 197 183 48

6-142

TABLE 6-15.
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ. CLOTH - ALL EDGES CLAMPED (Cont'd)

THICKNESS-H_ EQUALS 0+4375 INCHES

FIBERGLASS POLYESTER LAMINATES

ees “tnehes “Nees!
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 8270 6
8 8270 8270 8270 8270 8270 8270 8270 8270 8270 8194 8097 8019 7965 7914 78681 7647 7782 7744 7721 7694 7683 7679 7664 8
10 8270 8270 8270 8270 7700 6776 6234 5895 5668 5511 5397 5309 5244 5192 5151 5118 5047 5004 4975 4956 4942 4933 4925 10
12 8270 8270 68270 8270 6853 5662 4981 4559 4284 4093 3960 3859 3784 3725 «3679 3641 3563 3517 = 34BB 3469 3454 443 3435 12
14 8270 8270 8270 6270 6715 5210 4360 3843 3509 3284 3124 3007 2920 2855 2801 2759 2675 2626 2593 2570 2555 2544 2534 4
16 8270 8270 8270 7606 6263 5141 4099 3471 3070 2801 2614 2479 2380 2303 2244 2196 2103 2048 2013 1990 1975 1962 1954 16
18 8270 8270 8270 7278 5710 4868 4063 3309 2834 2517 2298 2141 2027 1939 1872 1819 1716 1654 1618 1593 1576 1563 1555 18
2¢ 8270 8270 8270 7260 5420 4454 3893 3290 2729 2359 2105 1925 1794 1695 1618 1559 1443 1378 1336 1311 1292 1280 1269 20
22 8270 8270 8270 7024 5313 4214 3578 3185 2719 2290 1998 1790 1639 1527 1443 1376 12466 1176 1132 1103 1084 1069 1059 22
24 8270 8270 8270 6811 5343 4093 3380 2941 2654 2286 1950 1714 1542 1416 «132101244 1101 1023 977 947 926 910 899 24
26 8270 8270 8270 6746 5131 4067 3267 2778 2462 2246 1946 1679 1487) «1343 123701153 994 908 857 824 803 786 775 26
28 8270 8270 8270 6746 5004 4051 3217 2675 2328 2091 1927 1679 1462 1303 1183-1090 914 821 765 731 706 691 677 26
30 8270 8270 8270 6576 4958 3912 3217 2620 2237 1981 1800 1670 1462, 1284 = 1151 1050 855 754 693 655 630 613 599 30
32 8270 8270 8270 6500 4977 3830 3172 2601 21861 1901 1706 1567 1462, 1286 = 1137 1025 813 700 635 595 569 550 536 32
34 6270 8270 8270 6498 4876 3798 3082 2614 2154 1849 1637 1487 1374 1290 1139 =1015 782 660 590 546 517 498 483 34
36 8270 8270 8270 6559 4799 3801 3027 2551 2151 1819 1592 1427 1307 1217.) «11471015 761 630 553 506 475 454 441 36
38 8270 8270 68270 6673 4769 3765 3002 2490 2160 1807 1561 1384 1256 1158 1084 1027 750 607 525 475 441 420 403 38
40 8270 68270 8270 6834 4776 3698 3000 2452 2099 1811 1544 1355 1217) 1114 1034 973 744 590 502 448 414 389 372 40
42 8270 8270 8270 7036 4818 3662 2998 2433 2055 1801 1540 1336 1189 »=-1078 994 929 746 578 485 427 389 364 347 42
44 8270 8270 8270 7274 4889 3651 2943 2429 2027 1756 1546 1328 1170 1053 964 895 752 ST2 471 410 370 343 324 4s
46 6270 8270 8270 7545 4984 3660 2906 2441 2011 1723 1525 1328 1160 = 1034 941 866 725 571 462 397 355 326 307 46
48 8270 8270 8270 7849 5103 3689 2889 2399 2008 1702 1492 1336 1156 = 1023 924 845 697 571 456 385 342 311 290 48
THICKNESS-H EQUALS 065000 INCHES
LENGTH-B8 WIOTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 6
8 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 9450 8
10 9450 9450 9450 9450 9450 9450 9307 8799 8461 8227 8055 7925 7828 7752 7687 7641 7536 7469 7427 7398 7377 7362 7353 10
12 9450 9450 9450 9450 9450 8452 7435 6805 6395 6110 5910 5761 5647 5559 5492 5435 5320 5252 5206 5179 5156 5137 5126 12
14 9450 9450 9450 9450 9450 7778 6509 5736 5238 4901 4662 4490 4359 4261 4181 4120 3994 3920 3872 3838 3815 3798 3784 14
16 9450 9450 9450 9450 9351 7675 6118 5181 4582 4181 3902 3700 3551 3437 3349 3280 3139 3057 3007 2971 2946 2929 2918 16
18 9450 9450 9450 9450 8522 7267 6065 4941 4229 3757 3431 3196 3025 2895 2794 2716 2561 2471 2416 2378 2353 2334 2320 18
20 9450 9450 9450 9450 8089 6650 5811 4912 4074 3523 3143 2874 2677 2528 2416 2326 2154 2057 1996 1956 1929 1910 1895 20
22 9450 9450 9450 9450 7931 6290 5341 4755 4059 3420 2981 2672 2448 2280 2153 2053 1861 1754 1689 1647 1616 1597 1580 22
24 9450 9450 9450 9450 7975 6110 5046 4391 3964 3412 2910 2557 2303 2112 1969 1859 1645 1529 1458 1412 1382 1359 1343 24
26 9450 9450 9450 9450 7658 6068 4876 4147 3675 3355 2906 2508 2219 2006 1845 1721 1485 1357 1280 1231 1198 1176 1158 26
28 9450 9450 9450 9450 7469 6049 4801 3994 3473 3122 2876 2506 2183 1945 1765 1628 = =61366 1225 1143 1090 1055 1030 =:1011 28
3c 9450 9450 9450 94350 7400 5839 4803 3910 3340 2956 2687 2492 2183 1918 1717 1565 1277 1124 1034 977 941 914 895 30
32 9450 9450 9450 9450 7427 5717 4736 3883 3257 2838 2548 2338 2181 1920 1698 1529 1212 1046 948 887 847 821 800 32
34 9450 9450 9450 9450 7278 5668 4601 3902 3217 2761 2445 2219 2051 1925 1700 1513 1168 985 880 815 773 742 721 34
36 9450 9450 9450 9450 7164 5675 4519 3809 3212 2716 2374 2130 1952 1817 1712 1515 1137 939 826 756 710 679 656 36
38 9450 9450 9450 9450 7120 5620 4481 3717 3225 2698 2328 2067 1874 = 1731 1620 1532, 1118 905 782 708 660 626 603 38
40 9450 9450 9450 9450 7131 5521 4479 3660 3133 2702 2305 2023 1817) 16620 1544145201113 880 750 670 616 582 557 40
42 9450 9450 9450 9450 7192 5467 4475 3630 3067 2689 2298 1996 1775 1611 1485 1387 1114 864 723 637 582 544 517 42
44 9450 9450 9459 9450 7297 5448 4393 3626 3025 2622 2307 1983 1748 1572 1439 1336 1124 855 704 613 553 513 485 44
46 9450 9450 9455 9450 7440 = 5463) 4339 «3643-3002, 2574 «= 2277) «198317321546 = 140312946 =: 1082 851 689 592 529 487 458 46
48 9450 9450 9459 9450 7616 5507 4311 3582 2996 2542 2227 1994 1725 1529 1378 1261 1038 853 679 576 510 464 433 48

6-143

THICKNESS-H

TA BER 6-1
CRITICAL BUCKLING LOADS - POUNDS PER LINEAR INCH
10 OZ, CLOTH - ALL EDGES CLAMPED (Cont'd)

EQUALS 005625 INCHES

FIBERGLASS POLYESTER LAMINATES

= NGTH=
Lenatace Bees “neve
A 8 6) 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 6
8 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 8
10 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10630 10574 10534 10505 10484 10471 10
12 10630 10630 10630 10630 10630 10630 10585 9690 9104 8702 8416 8202 8042 7916 7818 7740 7574 7477 7412 7374 7341 7315 7299 12
14 10630 10630 10630 10630 10630 10630 9267 8169 7460 6979 6639 6393 6208 6066 5954 5866 5687 5582 5513 5463 5433 5408 5389 14
16 10630 10630 10630 10630 10630 10630 8711 7376 6524 5954 5557 5269 5057 4895 4769 4670 4469 4353 4280 4233 4196 4170 4152 16
18 10630 10630 1063C 10630 10630 10345 8635 7034 6023 5349 4883 4551 4307 4122 3979 3868 3645 3519 3441 3387 3351 3322 3305 18
20 1063C 10630 10630 10630 10630 9467 8274 6994 5801 5015 4475 4091 3811 3601 3439 3313 3067 2929 2841 2786 2748 2719 2698 20
22 10630 10630 10630 10630 10630 8954 7606 6771 5780 4868 4244 3805 3485 3246 3065 2924 2649 2496 2404 2345 2303 2273 2250 22
24 10630 10630 10630 10630 10630 8700 7185 6252 5643 4857 4143 3641 3278 3009 2805 2647 2341 2175 2076 2009 1966 1935 1912 24
26 10630 10630 10630 10630 10630 8641 6942 5904 5233 4776 4139 3570 3160 2857 2628 2450 2114 1931 1822 1754 1706 1674 1649 26
28 10630 10630 10630 10630 10630 8612 6837 5687 4946 4446 4095 3569 3109 2769 2513 2317 1945 1744 1626 1551 1502 1466 1441 28
30 10630 10630 10630 10630 10536 8314 6839 5568 4755 4208 3826 3549 3109 2731 2446 2229 1819 1601 1473 1393 1338 1301 1275 30
32 10630 10630 10630 10630 10576 8141 6742 5530 4637 4042 3626 3328 3107 2733 2418 2177 1727 1488 1351 1263 1206 1168 1139 32
34 10630 10630 10630 10630 10362 8070 6549 5555 4580 3931 3481 3160 2922 2742 2420 2156 1662 1403 1254 1160 1099 1057 1027 34
36 10630 10630 10630 10630 10202 8082 6433 5425 4572 3866 3382 3034 2778 2586 2439 2158 1618 1338 1176 1076 1011 968 935 36
38 10630 10630 10630 10630 10137 8002 6379 5294 4591 3841 3317 2943 2668 2464 2305 2181 1593 1288 1114 1008 939 891 857 38
40 10630 10630 10630 10630 10154 7862 6378 5212 4460 3847 3280 2880 2586 2366 2198 2069 1584 1254 1067 952 878 828 792 40
42 10630 10630 10630 10630 10242 7784 6372 5170 4366 3828 3273 2841 2527 2294 2114 1977 1586 1231 1030 908 828 775 739 42
44 10630 10630 10630 10630 10391 7759 6255 5164 4307 3733 3284 2822 2488 2238 2050 1901 1599 1217 1002 872 788 731 691 44
46 10630 10630 10630 10630 19593 7780 6179 5187 4275 3664 3240 2822 2466 2200 1998 1842 1542 1212 981 B42 754 693 651 46
48 10630 10630 10630 10630 10630 7841 6139 5099 4265 3618 3170 2840 2458 2175 1962 1796 1479 1214 968 819 725 662 618 48
THICKNESS-H EQUALS 066250 INCHES
LENGTH=B WIDTH=A LENGTH-B
INCHES INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 42 48 54 60 66 72 78
6 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11610 11810 11810 11820 11810 11810 11810 6
8 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11610 11610 11810 11810 11610 11810 11610 11810 11810 11810 11810 8
10 1810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11610 11810 112810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 10
12 11810 11810 11810 11810 11810 11810 11810 11810 11810 11810 11543 11251 11030 10858 10727 10616 10391 10255 10167 10116 10070 10034 10013 12
14 11810 11610 11810 11810 11810 11810 112810 11206 10232 9574 9106 8769 8515 68322 8168 8045 7799 7656 7563 7496 7452 7418 7391 14
16 11810 118610 11810 11810 11810 11810 11810 10118 8950 8168 7622 7229 6937 6713 6542 6406 6131 5971 5872 5805 5757 5719 5698 16
18 11810 11810 11810 11810 11810 11810 11810 9650 8261 7337 6700 6244 5908 5654 5458 5305 5000 4826 4719 4645 4597 4557 4532 18
20 11810 11810 11810 11810 11810 11810 11351 9595 7958 6879 6139 5612 5227 4939 4717 4544 4206 4017 3899 3822 3769 3731 3700 20
22 11810 11810 11810 11810 11810 11810 10435 9286 7929 6677 5822 5219 4780 4452 4204 4009 3633 3425 3299 3215 3158 3118 3088 22
24 11810 11810 11810 11810 11810 11810 9854 8576 7740 6662 5683 4996 498 4128 3847 3630 3214 2985 2847 2757 2696 2654 2622 24
26 1810 11810 11810 11810 11810 11810 9522 8099 7177 6551 5677 4897 9334 3918 3605 3362 2901 2649 2500 2404 2341 2294 2261 26
28 11810 11810 11810 11810 11810 11810 9379 7801 6786 6099 5616 4895 4263 3798 3466 3177 2668 2393 2231 2128 2061 2011 + # 1977 28
30 11610 11810 11810 11810 11810 11406 9383 7639 6523 5773 5248 4870 4265 3746 3355 3057 2494 2195 2019 1910 1836 1786 1748 30
32 1810 12810 11810 11810 11810 11167 9250 7585 6362 5544 4975 4565 4261 3748 3317 2986 2368 2042 1853 1735 1656 1601 1561 32
34 11610 11810 11810 11810 11810 11070 8984 7620 6282 5393 4776 4334 4007 3761 3320 2958 2279 1924 1719 1592 1508 1450 1408 34
36 11810 11810 11810 11810 11810 11085 8824 7440 6271 5305 4637 4160 3611 3548 3345 2962 2219 1834 1613 1477 1387 1326 1282 36
38 11810 11810 11810 11810 11810 10977 8750 7261 6299 5269 4547 4036 3660 3380 3162 2996 2185 1767 1529 1384 1288 1223 1177 38
40 11810 11810 11810 11810 11810 10784 6748 7148 6118 5278 4500 3950 3548 3246 3017 2838 2172 1719 1464 1307 1206 1135 1088 40
42 11610 11810 11810 11810 11810 10677 8740 7091 5990 5250 4488 3897 3467 3147 2901 2710 2175 1687 1412 1264 1137 1063 1011 42
44 11610 11810 11610 11810 11810 10643 8580 7082 5908 5120 4505 3872 3412 3070 2811 2609 2195 1670 1374 1195 1080 1002 948 44
46 11810 11810 11810 11810 11810 10671 8475 7116 5862 5026 4444 3872 3382 3017 2742 2527 2114 1662 1345 1155 1032 950 893 46
48 11810 11810 11810 11810 11810 10755 68421 6996 5851 4963 4349 3895 3372 2985 2691 2464 2029 1666 1328 1124 994 908 847 48

6-144

DESIGN OF LAMINATES 6-145

Design Example 6-21 illustrates the advantage of Tables 6-4 through 6-15,

DESIGN EXAMPLE 6-21. CRITICAL COMPRESSIVE BUCKLING OF A PANEL

For the panel indicated in Fig. 6-44 assume a mat laminate with the following properties:

Width of panel a = 20 in.

Length of panel b= ThOmans

Thickness h = 0.50 in.

Moduli of elasticity Ep = E, = 0.86 x 10° psi (Table 5-10)
Foisson's ratio Oinee Sas Bore 0.37 (Average of Tables 5-8 and 5-13)
Shear modulus Gp = O40 x 10° psi (Table 5-14)

Find the critical buckling load, Poy, for all edge conditions:

Case 1, All edges are simply supported.

Case 2. Loaded edges simply supported, remaining edges clamped.
Case 3. Loaded edges clamped, remaining edges simply supported.
Case 4. All edges clamped.

Constants:
A = Ep opp + 2h Gor = 0.86x106x0,37 + 2(1-0.372)0.40x10° (6.45)
oO o
= 1.0007 x 10°
Ah? 1,0087 x 10° x 0.
x = Abe _ 1.0087 x 10° x 0650? © yar 75 ieee)
12 12(0.8631)
3 ‘ 6
Et 0.86 x 0.5
Dy = Dy = BE = 2286 x 1 x O50" _ 0376 (6. 44)
120 12(0.8631)
K 12170
«ot = Ee 1.1729 (6.47)
1 10376
(DD2)>

eb or (6.48)

6-146 DESIGN OF LAMINATES

Case 1. All Edges Simply Supported

Vn(n - 1) <2 < Vn(n + 1) n= 2

2 os ake _ 9.8696 fu. k ;
eae Aas Fon oe Sebi

1p
ee ae =e = 3.57 x Hous = 3.57 x 311.28 = 1112 lbs./in.
a 20

Case 2. Loaded Edges Simply Supported - Remaining Edges Clamped

4 Vn(n - 1)V3< 2<5 Vn (n+ 1)V3 n= 3

2 2 2
pets E ++ ] pee E +o kos 056k | = 6.3739

3} 9

Poe = Oss139 % 311.26) = 1985 Tbss/in.

Case 3. Loaded Edges Clamped - Remaining Edges Simply Supported

2
Tl 2 to 7
ae Kory = 8 Ls + 2 + 6] esd Bris)
ne 2
b Ker, =o |r ttt 20K] = 4.26 Controls

16.56

ry
=
rel
Le}
bh
"
=
col
we!
kK
nm
+
fl
+
nm
[ea]
"

7 36

lox
tan
Q
Ln}
ine)
"
ee *
Ol fm
J bh
Oo
be
Lye)
+
a6
+
6
ce |
"

2]
T pt oul
ce ok = ert + + + 10% = 7.12 Controls
q5 : 2 |

(6.

(6.

(6,

(6.

(6.

(6.

752)

51)

50)

. 52a)

. 51a)

50)

. 51b)

7 Le)

51d)

51le)

50)

, iki)

Soils)

51h)

DESIGN OF LAMINATES 6-147

2
1059
oe Kor) z tis se ee 264 = 7.88 (6551)
Pay © (ele x 311.s20-= 2217) tbs/in. (6.50)

Summary: Case 1 = 1,112 lbs./in.
Case 2 = 1,985 lbs. /in.
Gaseuse—) le 326) lbs .a/in.
Case 4 = 2,217 lbs. /in.

The critical buckling values, Per, for Design Example 6-21 can be obtained very
quickly from Tables 6-4 through 6-7. For a= 20 in., b = 40 in. andh = 0.50 in., the
values are:

Gase 1 Pa. = 211d dbs a/ine
Case 2 P,, = 1,984 lbs. /in.
Case 3 Per = 1,331 lbs. /in.
Case 4 Poy = 2,218 lbs. /in.

B. Plates Loaded In Uniform Shear

The critical shearing stresses in a rectangular plate under a uniform shear load was
investigated and reported by March (16). The discussion presented here is for loads
applied parallel to or at 90 degrees to the warp direction, Fig. 6-45.

q

yy |
|

j
| t

WARP DIRECTION | H
Wl !

U

ca

t

|
{
\
q |e
{
|
{

| |
{e} —¥ 1

Fig. 6-45. Flat Plate
in Uniform Shear
Load Parallel to Warp

The following terminology not previously given will apply:

q = uniform shearing stress and is positive when directed
as indicated in Fig. 6-45.

value of q for which buckling occurs.

Ger

6-148 DESIGN OF LAMINATES

To determine the critical shear stress in equation 6,55, the following constants are
necessary to obtain the factor ''Cq" for simply supported panels from Fig. 6-46:

n

_ A (6. 53)
an z
See
B, 2 2} 2 | 4 (6. 54)
b Ey

24 — = L —
22 lz a | +
24 + a =) V

pee 5
4

8 —. +—
ih 4
u ]
6 SS ee |e |S = |e be
fo) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Pa

REFERENCE 17

Fig. 6-46. Curves for Calculating the Buckling
Shear Stress in Orthotropic Rectangular Plates
with Simply Supported Edges Whose Axes of
Elastic Symmetry are Parallel to the Edges

For the case where the orthotropic laminate is subjected to uniform shear and the warp
is parallel to the L axis, the following relationships have been obtained:

The critical shearing stress can be calculated from:

DESIGN OF LAMINATES 6-149

2 il
Ch 3
Gears : (E,-Eo) & (6. 55)
3h a
2
Ger = on (6. 55a)
a2
Ve 1 (6. 56)
where kg ace ar E2 q
3n Er Ey,

where E] and Eg are measured parallel to the sides a and b respectively. Fora
laminate with the warp oriented parallel to the side b, the values of Ej = Ep and
E2 = Ey. The value for kg now becomes:

ic E
Sees perl q (6. 56a)
ae wey Eq
and
fe (6. 53a)
(EqEy,)2

1
Be = a eae q (6. 54a)
b | Ey

The dimensions a and b are assigned to the panel in such a way that Bg is less than or
equal to unity.

DESIGN EXAMPLE 6-22. CRITICAL SHEAR BUCKLING OF A 10 OZ, CLOTH
OR ORTHOTROPIC PANEL

Compute the critical shearing stress for the plate shown in Fig. 6-45 when:

a = ?0 in.

b = 4O in,

t = 0.50 in.

Laminate: 10 oz. cloth
Warp oarallel to side "b"

B= Ep = 1.96 x 10° E, =E,21.70x 106 (Table 5-10)

Gry, = 0.5? x 106 (Table 5-14)

on = oon = 0.20 (Average of Tables 5-8 and 5-13)

6-150 DESIGN OF LAMINATES
Determine constants:
fo) =e1n= 2 =
Cor, LT 1 - 0.20 0.96
A =3,0_, + 2G, = 1.96x106x0.20 + 2(0.96)x0.52x106 (6. 45)

= 0.392 x 10© + 0.998 x 106 = 1.39 x 10°

A 1.39 x 106 1.39 -
ae , 2 Aas 0.7596 (6. 53a)
(EqEy, )3 (W96x25;7.0)) ren HO be 1583
p= a] BEI 2 . 20 | te7ore lh . oss 0.968 = ole (6. 54a)
oes Lo | 1.96x108 a :

Referring to Fig. 6-46, for the value of Ba = 0.48 and a =0Q.76, the value of Ca is
found to be 13.7.

1
; E q 6/h
Sw | a 609s = 9 (6. 56a)
30 | Ep 3x0.96 | 1.96x106
k-Ey 12 6 5
and qor= § ERE = 4e59x1.96x10°X0. 50° eg nc on (eo554)
ae 00

This value is less than the ultimate parallel shear stress;
Fo, = 10500 psi (Table 5-14)
DESIGN EXAMPLE 6-23. CRITICAL SHEAR BUCKLING OF A MAT
OR ISOTROPIC PANEL

Compute the critical shear stress for a mat laminate with similar dimensions as those
given in Design Example 6-22.

Ep 7B, = 0.86 x 10° (Table 5-10)
Gry = 9.40 x 10° (Table 5-14)
Ort, = Opp = 0.37 (Average of Tables 5-8 and 5-13)

h =1 - 0.372 =0,863

A = 0,86x106x0.37 + 2x0.86x0.0x106 = 1,006 x 106 (6. 45)
a = 1-006x10& _ 1.17 (6. 53a)
0.86x106

DESIGN OF LAMINATES 6-151

Be = Geb ated =20.5 (6. 54a)
Ca = 15.45 from Fig. 6-46
1
= eS, | 0286 x nS ree =
a 3x 0,863 0.86 x 10° a
ee 5.99 x 0,86x10° x 0.50? . 3995 psi < 10100 psi (Table 5-14)
ele)

C. Plates Loaded Laterally

The mathematical solution of flat plates with lateral loads is much more complex and
time consuming than for flat plates in edge compression, The problem is further complicated
because of deflection considerations. When the deflection of the plate is equal to or less
than one-half the thickness of the plate, the loads are assumed transmitted mainly by bending
stresses. When the deflection exceeds one-half the thickness of the plate, direct stresses
are developed and these stresses must then be considered. Consequently for plates with
large deflections the loads are carried by both direct stresses and flexural stresses and a
new approach to the problem is necessary.

Therefore, to properly analyze plates under lateral loads, it is necessary that the
following criteria be specified:

1. Boundary Conditions

a, Simply supported edges
b. Clamped edges
Gs Combinations of above

2. Loading Conditions

Uniformly distributed load
Concentrated loads
Variable loads

: Edge moments
Combinations of above

cQA0 07 p

3. Plate Material

a, Isotropic
b. Orthotropic

4. Deflection Limitation

a. Plates with small deflections equal to or
less than one-half the thickness,
b. Plates with deflections greater than

one-half the thickness.

March (18) has developed procedures by which plywood plates under uniform or concen-
trated loads may be analyzed. Since most fiberglass laminates are orthotropic the approach
established by March will be used but the results are subject to verification by future tests.

6-152 DESIGN OF LAMINATES

Boat hulls and other marine structures are usually subject to hydrostatic or uniform
pressures. Since the preparation of plate load tables covering all conditions would be a
voluminous task, only tables for uniformly loaded plates with simply supported edges have
been completed at this time. However methods of analyses are also presented for plates
under uniform loads and clamped edges. Fig. 6-47 indicates the direction of the plate axes.
The coordinate planes are parallel to the planes of elastic symmetry.

x

WARP DIRECTION —

fo}

(nape eel

Fig. 6-47. Flat Plate Under
Uniform Lateral Load

The following terminology previously not given will apply:

p = load per unit area
€ = unit strain
My = bending moment per unit length of a

vertical section of the plate per-
pendicular to the X-axis

Myr = bending moment per unit length of a
: vertical section of the plate per-
pendicular to the Y-axis

= twisting moment per wnit length of a
vertical section of the plate per-
pendicular to either the X- or the
Y-axis

Plates With Small Deflections: For this condition, the deflection of the plate is limited
to a maximum of one-half the thickness of the plate, (w S 3 Me

Case 1. Simply Supported Plates Under Uniform Loads

The deflection of a uniformly loaded simply supported plate is obtained from the follow-
ing equation (18):

=n chy (2 = Ya) sim An # (6,57)

DESIGN OF LAMINATES 6-153

where

praltis Nye

adj” a

ont | siz ynn sing, (+n) + sinh y, (@-n) sin al

Yn =

+ V1 - x2 [cosn Ynn coséy (6-n) + cosh i ( 8-n) cosérri}}
Gave a n= ey 3; B = Eb
LQ os -

Vl-x2 cosh Y,8 + cos 6,8 ai ab

n n Sic Dy q _[ By qT
| “| ¥
et efi ara ale =
is eae = Xn? K
V DyDo
prey ea) Op = Fe
x =|SLOTL + ac. |b?
\ 12
The basic plate moment equations are given as follows (18):
. p) D
f O cw 2 OCW (6.58)
d t = 30 + OE .

bending momen My i aoe 1 One

. = 2 0 ew 3 2w (6.59)
bending moment My = -Do E 5 + D, os |
twisting moment my, = Cur en? 0ew (6. 60)

oe Ma rears as pres :
axon

The solution of these equations becomes a formidable task when more than one plate
configuration has to be investigated. To reduce the amount of work required by the designer,
Tables 6-16 through 6-18 have been established with the use of electronic digital computers.
These tables give the ultimate uniform lateral loads in psi that mat, woven roving and cloth
laminates can sustain when considered as rectangular plates with a deflection limitation of
one-half the laminate thickness or for the ultimate flexural stresses of the laminates. For
the development of these tables, the low average physical properties values previously given
were also used but the direction of the axes has been modified.

x

90 degrees and warp direction

Y

0 degrees and fill direction

The advantage of these tables is illustrated in Design Examples 6-24 and 6-25,

TABLE 6-16. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED

RHYSICAL CONSTANTS:

Ex = Ey = 0.86x108 PSI

Gxy = 0240x108 PSI
(of ORs lose
THICKNESS“H EQUALS 0,0625 INCHES
WIOTH-A
eng INCHES
6 8 10 az 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
6 el2
8 207 204
10 206 203 002
12 205 202 20)
14 20% 202 201
16 204 002 201
18 204 20) 201
20 204 201 201
22 204 201 20)
24 204 01 201
26 ry 201 201
28 Pry 201 201
30 204 201 201
32 20% 201 201
34 204 201 201
36 208 201
42 0% 201
48 204 201
54 204 201
60 204 201
66 20% 201
72 204 201
78 204 201
THICKNESS—H EQUALS 0.1250 INCHES
LENGTH-B WIOTHA
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 46
6 1290
8 1.17 260
10 290 241 25
12 077 032 18 o12
14 270 027 ols 09 206
16 266 02s o12 207 205 204
18 264% 223 ell 206 204 203 202
20 262 e21 210 206 04 203 202 202
22 61 e21 209 205 203 202 202 201
24 261 220 209 205 203 202 201 201
26 260 220 209 205 203 202 201 ool
28 260 220 208 204 203 202 201 201
30 260 019 208 204 202 202 201 201
32 260 «19 208 204 202 202 20) 201
34 260 o19 208 204 202 201 201) 2Ol
36 260 e19 208 204 202 201 201 Ol
42 260 219 208 0% 202 20) 201 201
48 260 eld 208 204 202 201 201 oO)
54 260 219 208 204 202 201 001 201
60 260 19 208 204 202 001 201 20)
66 260 019 208 04 202 201 201 201
72 260 219 208 204 202 201 201
78 260 219 208 204 202 201 20)

6-154

TABLE 6-16. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.1875 |NCHES
THICKNESS“H EQUALS 0.1675 INCHES

WIDTHHA
“Ca ate INCHES
6 8 10 12 16 16 18 20 22 24 26 28 30 32 34 36 38 40 42 ry
6 9063
8 5.93 3205
10 4656 2406 1.25
12 3089 1661 290 +60
1 3654 1.37 072 245 033
16 3434 1423 062 37 025 019
18 3022 lel 255 232 e221 015 ol2
20 Bel 1.09 250 +28 «18 013 10 208
22 Bell 1405 247 226 #16 ell 208 207 205
24 3.08 1.02 245 224 os 210 207 206 205 204
26 3206 1.00 246 223 «14 209 207 205 +04 203 203
28 3405 +99 +43 222 13 209 206 204 +04 203 202 202
30 3204 +98 242 21 213 +08 206 204 +03 203 202 202 202
32 3204 297 41 221 212 +08 205 204 203 202 202 202 201 201
34 3206 297 241 220 012 207 205 204 203 202 202 201 201 201
36 3204 297 240 220 ell 207 205 203 203 202 202 201 201 201
a2 3004 297 240 220 ell 207 204 203 202 202 +01 201 201 201
48 3004 297 239 19 el 206 204 203 202 202 201 201 201 201
56 3004 297 239 “19 210 206 204 203 202 201 201 201 201 201
60 3204 297 039 “19 «10 206 204 203 202 201 201 201 201 201
66 3204 297 239 219 210 206 204 203 202 201 201 201 201
72 3204 297 239 219 210 206 204 203 202 201 201 201 201
78 3404 297 039 “19 elo 206 +04 202 202 201 201 201 201
THICKNESS-H EQUALS 0.2500 INCHES
LENGTH-B8 WIOTH-A
INCHES: INCHES
6 8 10 12 14 16 18 20 22 26 26 28 30 32 34 36 38 40 42 44
6 30045
8 18674 9263
10 14040 6052 3695
12 12230 5.09 2065 1290
4 11420 434 2027 1.44 1.03
16 10.56 3489 1.95 1.17 +80 +60
18 10019 3061 1.73 1.01 267 +48 +38
20 9096 3043 1659 +90 258 241 on 225
22 9081 3031 1.50 82 252 236 226 21 el7
24 9072 3022 1.43 277 247 032 223 218 214 12
26 9067 3017 1.38 273 48 029 221 216 12 10 209
28 9063 3013 1435 #70 242 227 a9 ols ell 209 207 206
30 9061 3010 1.32 368 240 +26 18 013 +10 208 207 206 205
32 9e61 3208 1.30 366 238 226 217 #12 209 207 +06 205 204 204
34 9061 3406 1.29 265 <37 023 216 ell 209 207 205 205 204 203 203
36 9061 3205 1.27 +64 236 223 os ell 208 206 205 20% +04 203 203 202
42 9061 3205 1.26 262 234 221 ole #10 207 205 +04 203 203 202 202 202 202 201 201
48 9061 3005 1625 +61 033 220 o13 209 206 205 204 203 202 202 202 201 201 201 201 201
54 961 3205 1625 +60 233 #20 213 209 206 +04 203 203 202 202 201 201 201 201 201 201
60 9061 3205 1625 #60 233 019 12 208 +06 204 203 202 202 202 201 202 201 201 201 201
66 9e61 3205 1625 +60 032 19 212 208 206 204 203 202 202 201 201 201 201 201 201 201
72 9061 3005 1625 260 232 219 012 208 206 204 203 202 202 201 201 201 201 201 201 201
78 9061 3205 1.25 +60 032 019 12 208 205 206 203 202 202 201 201 201 201 201 201

6-155

TABLE 6-16. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.3125 INCHES

LENGTH-B one
INCHES
6 8 10 12 14 16 18 20 22 2 26 28 30 32 34 36 38 40 42 46 46 48
6 74034
8 45075 23052
10 35015 15.91 9063
12 30203 12043 6.95 065
14 27033 10.61 5.55 3651 2051
16 25079 9050 4676 2086 1296 1047
18 24.87 8.62 4023 2246 1063 1018 292
20 24031 8.37 3089 2420 1e41 299 275 260
22 23296 8.07 3466 2201 1626 087 064 250 241
24 23074 7087 3249 1.88 lols +78 256 043 035 029
26 23460 7073 3037 1.78 1.07 71 251 038 230 025 e2l
28 23052 7063 3029 1.71 1.01 +66 247 235 027 022 218 016
30 23046 7056 3022 1.65 297 262 243 232 225 220 016 ols 12
32 23046 7.51 3018 1.61 293 059 241 230 +230 * 018 15 12 ell 209
34 23046 7248 3016 1.58 290 257 239 228 +21 216 213 ell 209 208 207
36 23046 7.45 Bell 1.55 288 255 237 226 220 015 12 210 209 207 +06 206
42 23046 7.45 3.07 1.51 284 251 234 224 217 013 210 208 207 206 205 +04 204 203 203
468 23046 7.45 3004 1648 082 049 232 022 216 012 209 207 206 205 204 204 203 203 202 202 202 202
54 23046 7045 3204 1447 280 048 231 e2l 215 ell 208 207 205 204 204 203 203 202 202 +02 202 201
60 23046 7245 3004 1.47 280 047 230 220 014 elo 208 206 205 204 203 203 202 202 202 202 201 201
66 23046 7245 3004 1.47 079 047 230 220 214 210 207 206 205 204 203 002 202 202 202 201 201 201
72 23046 7245 3404 1.47 279 247 229 219 213 210 007 206 204 203 203 202 202 202 201 201 201 ol
78 23046 7045 3406 1.47 279 346 229 19 213 210 207 205 204 203 203 202 202 202 201 «01 201 201
, THICKNESS-H EQUALS 0.3750 INCHES
venenes* ae
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
6 154015
8 94086 48.77
10 72089 32299 19.98
12 62028 25278 14e41 9063
14 56068 21.99 11.51 7027 5020
16 53048 19070 9086 5.93 4.07 3005
18 51058 18.29 6.78 5209 3037 2045 1.90
20 50041 17.36 8.07 456 2092 2206 1.56 1.25
22 49468 16074 7259 4el7 2061 1680 1.33 1204 285
24 49623 16032 To24 3489 2039 1.61 1.17 290 272 260
26 48.94 16203 7200 3069 2023 1248 1.05 280 263 252 246
28 48.76 15062 6082 3654 2010 1.37 296 e72 356 245 238 233
30 48.65 15268 6068 3043 2001 1629 +90 266 251 241 234 028 225
32 48065 15.58 6058 3034 1693 1623 285 962 247 237 230 025 222 219
34 48065 15.50 6051 3028 1.88 118 280 258 246 234 228 023 +20 217 15
36 48065 15045 6045 3022 1663 1els 277 355 241 032 226 o21 18 215 13 212
42 48065 15445 6036 3013 1674 1206 270 249 236 027 21 ol7 214 212 210 209 +08 207 206
48 48065 15045 6031 3208 1669 1202 266 043 033 024 019 o15 212 210 209 207 +06 206 205 205 04 204
54 48065 15045 6031 3405 1067 +99 264 243 231 023 217 013 ell 209 207 206 +05 205 204 +04 +03 +03
60 48.65 15045 6e31 3206 1665 298 262 042 229 2 216 13 #10 208 207 206 205 #04 #04 203 +03
66 48065 15245 6031 300% 1.64 297 261 4 229 e2l 15 212 209 +08 +06 205 «04 204 «03 10302 202
72 48065 15.45 6031 3206 1664 297 261 240 228 220 ois ell 209 207 +06 205 204 203 203 203 402 202
78 48065 15045 6031 3004 1.64 296 260 240 028 220 15 ell 209 207 +06 205 +04 203 203 102 202 202

6-156

TABLE 6-16. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
20Z. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS—H EQUALS 0.4375 |NCHES

WIDTH-A
EINCHES. INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 cry 46 48
6 265.59
8 175674 90036
10 135404 6lell 37201
12 115238 47677 26069 17285
14 105.01 40074 21032 13648 9063
16 99209 36051 18627 10.98 72053 5065
18 95655 33.88 16027 9044 6625 4.58 3453
20 93038 32016 14.95 86am Se4) 3082 2089 2031
22 92006 31.02 14.05 7072 4083 3033 2047 1.93 1.58
24 91420 30.23 13442 Te21 4e43 2099 2017 1.67 1.34 1.12
26 90067 29269 12496 6484 412 2674 1.95 1648 1.17 +96 +81
28 90034 29031 12663 6456 3089 2.55 1.79 1.33 1.04 «84 #70 260
30 90013 29204 12.38 6.35 3072 2040 1.67 1.22 +94 275 262 053 246
32 90013 28.86 12620 6019 3058 2028 1.57 1el4 +87 269 +56 247 +40 035
| 34 90013 28.72 12406 6.07 3047 2019 1649 1.07 +81 Wass 251 243 336 Pent +28
| 36 90013 28.63 11496 5.97 3039 2012 1642 1.02 +76 +59 247 239 233 228 25 022
| 42 90613 28263 11.77 5479 3022 1.97 1.30 290 +66 +50 +40 232 +26 222 +19 217 215 13 212
| 4B 90013 26063 11.70 5.70 3014 1.89 1.22 284 +60 245 235 228 223 219 +16 214 12 +10 209 +08 +08 207
| 54 90013 28.63 11470 5266 3409 1.84 1618 280 257 942 032 225 220 16 “14 212 10 209 208 207 206 206
60 90013 28.63 11670 5063 3206 1.82 1.15 277 +54 +40 #30 023 218 +15 212 +10 209 +08 207 206 205 205
. 66 90013 28463 11.70 5263 3005 1.80 lel4 076 253 238 229 222 217 +14 ell «10 208 207 #06 205 205 204
| 72 90013 28.63 11.70 5.63 3.05 1.79 1613 075 252 037 +28 21 +17 213 ell 209 207 206 205 205 204 204
| 78 90013 28.63 11.70 5463 3005 1.78 1612 +74 251 237 227 221 16 «13 210 208 207 206 205 +04 204 203
THICKNESS-H EQUALS 0.5000 INCHES
| Sees “INCNeES
6 8 10 12 iv 16 18 20 22 26 26 28 30 32 34 36 38 40 42 44 46 48
6 434672
8 299680 154415
| 10 230037 = 104626 63014
12 196683 81.49 45053 30.45
14 179614 69250 36037 22.99 16044
16 169404 62028 31617 18474 12285 9063
18 163.00 57079 27675 16410 10066 7.74 6.02
20 159.31 54.87 25051 14440 9022 6052 4.94 3495
22 157.02 $2091 23.98 13617 Bo24 5468 421 3030 2.70
24 155658 51.58 22.90 12430 7456 5209 3470 2085 2029 1690
26 154.68 50.65 22012 11.67 7403 4068 3633 2052 1.99 1663 1038
28 154612 50200 21.55 11.20 6.64 4034 3405 2027 1.77 Lees 1620 1203
30 153676 49.55 21.13 10.84 6434 4.09 2684 2.09 1.61 1.29 1.06 290 +78
32 153476 49423 20681 10.56 bell 3689 2067 1.95 1.48 1.17 +96 280 269 260
a4 153676 49.00 20.58 10635 5493 3074 2454 1.83 1.38 1.08 +87 273 262 256 247
36 153476 48.84 20440 10619 5.78 3061 2643 1673 1.30 1.01 +81 267 +56 248 282 238
42 153476 48.84 20.09 988 5450 3036 2022 1.54 1.13 +86 268 254 245 238 233 +28 225 022 220
48 153676 48.84 19.95 9672 5035 3022 2.09 1043 1.03 277 059 “47 238 232 227 023 220 «18 aie a4 13 12
54 153676 48.84 19295 9665 5027 3014 2.01 1.36 297 o71 “54 043 234 +28 223 «20 217 «15 013 12 ell 210
6c 153676 48684 19695 9.61 5e22 3010 1.97 1632 293 +68 oS 240 PENT +26 221 +18 +15 213 ell +10 209 +08
66 153676 48.84 19295 9061 5-20 3407 1494 1.29 +90 265 49 238 230 226 220 16 214 aie 210 209 08 .07
72 153076 48.84 19495 9661 5020 3205 1.92 1627 288 +64 247 236 228 223 18 «15 213 pe 209 +08 207 206
78 153676 48684 19295 9061 5020 3204 1.91 1.26 +87 +63 046 235 227 022 +18 ols ol2 10 209 +08 207 06

6-157

TABLE 6-16. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
2 OZ. MAT - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0,5625 | NCHES

LencTH-8 Sane
INCHES
6 8 10 12 14 16 168 20 22 24 26 28 30 32 34 36 38 40 42 aa 46 “8
6 55020
8 385.69 246692
10 314.68 167200 101614
12 281625 = 130653 72.93 48077
14 259052 111033 58026 36083 26433
16 250056 99476 49.93 30001 2058 15043
16 243.44 92057 = 44045 25678 17.07 12440 9463
20 238045 87289 40486 23-06 14077 10444 7.91 6032
22 235087 84.76 38641 21610 13420 9010 6075 5028 4032
24 233201 82-61 36067 19670 12011 Bel6 5693 4056 3066 3005
26 233001 81.13 35043 18669 11626 7249 5433 4003 3019 2062 2021
28 233401 80.09 34.51 17.93 10.64 6496 4.88 3064 2.84 2230 1692 1665
30 233-01 79036 33484 17436 10016 6.55 4656 3034 2.58 2006 1270 1644 1625
32 233640 78.85 33434 16492 9679 6023 4028 3012 2.37 1.88 1653 1629 1.10 296
34 233625 78249 32296 16.58 9049 5.99 4.07 2.93 2.21 1673 1240 1016 299 286 +76
36 233016 78.28 32067 16032 9026 5679 3489 2678 2.08 1e61 1029 1.07 290 277 +68 260
42 233204 78024 32018 15-82 8.81 5.39 3454 2047 1.81 1.37 1.08 287 #72 261 252 245 240 236 233
48 233.02 78024 31096 15.58 8.57 5016 3034 2229 1.65 1623 295 +76 262 251 243 237 932 228 225 223 21 219
54 233.01 78024 31096 154045 8.44 5004 3022 2018 1.55 1eld 287 268 255 045 238 032 227 224 021 219 17 015
60 233201 T8024 31696 15439 6436 4096 3015 2011 1649 1609 282 063 250 241 234 028 224 21 18 216 ols 013
66 233001 78.24 31496 15239 8.32 4092 3ell 2207 lade 1205 278 260 247 238 23 #26 222 219 +16 214 13 ell
72 233201 78.24 31096 15439 8.32 4089 3408 2204 1042 1602 +76 258 245 236 229 224 220 017 215 13 ell 210
78 233.01 78024 31.96 15439 8632 4087 3206 2.02 1.40 1400 +74 256 ors 235 +28 223 19 +16 214 212 210 209
THICKNESS—H EQUALS 0,6250 |NCHES
LENGTH-B WIOTH-A
INCHES INCHES
6 8 10 12 146 16 18 20 22 24 26 28 30 32 34 36 38 40 42 a6 46 48
6 679026
8 476016 376435
10 388050 254253 154015
12 347022 198695 111615 TH34
14 320039 = 169269 88.79 56013 40013
16 309031 152404 76011 45075 31037 2352
18 300054 141409 67075 39030 26402 18689 14668
20 294039 133496 62628 35015 22052 15691 12406 9063
22 291620 129418 58.54 32015 20012 13.88 10.28 8.05 6658
24 287666 = 125492 55490 30403 18645 12043 9204 6695 5058 4065
26 287666 = 123465 54400 28649 17617 11042 8.13 6015 4686 3099 3037
28 267266 122407 52260 27033 16621 10661 7.45 5.55 4.33 3.51 2093 205)
30 287666 120696 51.58 26046 15048 9498 609% 5209 293 Bole 2.59 2020 1.90
32 288615 120618 50081 25479 14091 9450 6453 4676 3061 2086 2034 1696 1.68 1.47
34 287096 = 119663 $023 25.28 14047 Fol2 6420 4047 3436 2064 2013 1e77 1.51 1.31 1e15
36 287685 119425 49080 24.87 14.12 8682 5493 4023 3017 2046 1497 1663 1637 1.18 1.03 992
42 287671 1194025 490046 24e11 13043 8621 5440 3076 2.75 2009 1065 1033 1610 293 279 +69 261 255 250
48 287067 = 119425 48671 23074 13406 7287 5.09 3049 2051 1668 1045 1015 94 +78 +66 +56 249 +43 039 235 232 229
54 287067 = 119425 48671 23055 12686 1667 4e91 3033 2036 1.74 1633 1206 +86 269 257 249 242 +36 232 229 226 +23
60 287066 119425 48.71 23446 12675 7456 4280 3022 2027 1065 1625 297 77 262 +52 943 +37 232 +28 225 222 220
66 287066 = 1196025 4Be71 23446 12.69 7249 473 3016 2020 1.59 1019 092 272 258 248 #40 334 229 225 222 els «17
72 28766 119425 48671 23446 12469 7045 4069 3ell 2616 1.55 1el6 +88 +69 255 +45 237 pert #26 223 220 17 215
78 287066 = 119625 48671 23046 12669 7043 4066 3008 2013 1653 1013 086 267 053 243 235 229 025 221 18 216 214

6-158

LENGTH-8

TABLE 6-17.

FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH

25-27 OZ, WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED

THICKNESS- EQUALS 0,0625 |NCHES

PHYSICAL CONSTANTS:

Ex = 1.81x10® PSI
Ey = 1.54x10® PS|
Gxy = 0.45x108 PS!
Oxy = Oyx = 0.19

WIDTH-A

INCHES: rere
6 8 10 12 14 16 18 20 22 ray 26 28 30 32 34 36 38 40 42 44 46 “8
6 19
8 12 206
10 209 204 202
12 208 203 202 201
as 208 203 201 201
16 207 203 201 +01
18 207 202 201 201
20 207 202 201 201
22 207 202 201 201
24 207 202 201 201
26 207 202 201
28 207 202 201
30 207 202 201
32 207 202 201
34 207 202 201
36 207 202 201
42 207 202 00
48 207 202 001
34 207 202 001
60 207 002 201
66 007 202 201
72 207 202 201
78 207 202 201
THICKNESS-H EQUALS 0.1250 INCHES
LENGTH-8 WINCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 rs 46 48
6 3005
8 1085 296
10 1046 264 239
12 1029 251 228 219
14 1021 045 223 “14 #10
16 117 41 220 012 208 206
18 1616 239 218 210 207 205 204
20 1615 038 217 209 206 204 203 202
22 lel 037 216 209 205 204 203 202 202
24 1ele 037 016 +08 205 203 202 202 201 eo
26 1013 036 15 208 205 203 202 002 201 eo
28 1013 036 15 208 204 203 202 ool 201 ool
30 1013 236 15 207 208 203 202 ool 201 201
32 1el3 236 «15 207 004 203 202 201 201 201
34 1613 336 015 207 204 202 202 201 201 201
36 1013 236 215 207 204 202 202 ool 201 eo
42 1613 236 215 207 204 202 201 201 20 20
48 1013 236 015 207 204 202 201 201 201 201
54 1013 336 1s 207 204 202 201 201 201
60 1613 236 15 207 204 202 201 eo 202
66 1013 036 15 207 204 202 201 201 201
72 1013 036 015 207 204 202 201 201 201
78 1.16 236 215 207 204 202 201 201 ool

6-159

TABLE 6-17. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
25-27 OZ. WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.1875 INCHES

PAS hese “inoneS
6 8 10 12 14 16 18 20 22 26 26 28 30 32 34 36 38 40 ea “4 46 48
6 15042
8 9436 4.88
10 TA 3024 2.00
12 6055 2.58 1e41 396
14 6013 2026 Lele ml 252
16 5094 2207 299 359 240 #30
18 5.87 1.97 91 +51 033 +24 219
20 5.81 1690 $85 +46 229 +20 215 o12
22 5077 1287 81 43 026 +18 713 10 +09
28 5675 1086 79 +41 24 216 o12 209 +07 206
26 5073 1684 .77 239 023 «15 210 208 +06 205 204
28 5072 1683 276 38 022 14 210 207 206 204 204 203
30 Se71 1682 276 338 e2d +13 rr) 207 05 204 203 203 202
32 5.71 1682 +76 mag 2d 213 209 006 205 204 003 202 202 02
34 Se71 1681 +75 cen #20 +13 208 206 +04 203 +03 202 202 202 201
36 5671 1681 +75 +37 #20 012 208 +06 204 203 003 202 202 202 01 201
42 5e71 1681 74 +36 +20 o12 08 +05 104 203 202 202 01 201 +01 001
48 5071 1681 074 +36 020 o12 07 005 203 203 202 202 001 201 201 *01
56 5e71 1.81 74 236 a9 ell 07 +05 +03 02 202 +01 201 201 02 201
60 5071 1661 7% 336 219 ell 207 05 +03 202 202 201 +01 201 201 01
66 5670 1081 +76 336 +19 nw +07 205 +03 202 202 201 +01 201 +01 201
72 Se72 1681 Te 336 «19 ell 07 +05 203 002 202 201 01 01 01 201
78 5087 1681 07% +36 a9 eit 07 205 203 02 202 02 201 201 202
THICKNESS—H EQUALS 0,2500 |!NCHES
LENGTH-8 WIDTH-A
INCHES INCHES
6 8 10 i 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

6 48673
8 29060 15042
10 23041 10026 6432
12 20071 Bel6 4eA7 3405
146 19639 7013 3061 2626 1664
16 18.77 6055 3614 1685 1626 96
18 18654 6621 2486 1661 1605 +76 60
20 18436 6401 2468 1446 92 +64 49 239
22 18.24 5492 2057 1436 +83 +56 41 032 +27
24 18616 5087 2049 1629 +77 o51 237 +28 bas els
26 18612 5082 2044 1625 273 247 233 +25 20 216 ole
28 18,08 5679 2042 1621 +70 045 231 +23 a7 16 el2 210
30 18.06 5.76 2040 1619 +68 743 229 za a 213 +10 +09 +08
32 18405 5675 2039 1.17 066 041 oa7 220 15 ae 09 208 07 206
34 18405 5673 2038 1616 +65 240 +26 219 +14 ell +09 +07 206 205 +05
36 18404 5.72 2037 1616 64 239 +26 18 213 210 +08 207 +06 205 204 +04
42 18.04 5e71 2035 1614 +63 237 26 +16 ol2 +09 07 205 +04 204 +03 203 202 202 202
48 18.06 5671 2034 1.14 62 37 23 216 ell 208 206 205 204 03 03 202 202 202 002 eo 201 01
54 16.04 5071 2634 1613 61 236 223 +15 ell 208 +06 204 04 203 +02 202 02 201 ol 201 od 201
60 18.04 5e71 2034 isis 261 +36 23 15 +10 207 206 208 203 203 202 202 202 201 01 201 201 201
66 18403 5671 2034 1613 +61 +36 22 Bt) +10 207 +05 204 03 203 202 202 01 201 ool 01 201 01
12 18.08 5e71 2634 1.13 261 236 222 «15 +10 +07 +05 08 203 202 202 202 002 201 ol 201 01 201
78 18.56 5071 2434 1613 61 +36 022 215 10 207 205 204 +03 202 202 02 201 201 001 201 ol 01

6-160

TABLE 6-17, FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
25-27 OZ. WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.3125 | NCHES

tenors aioe
’ 6 8 10 12 14 16 16 20 22 Pry 26 28 30 32 34 36 38 40 42 “6 46 48
zx 118.98
: 8 72027 = 37065
10 57014 25401 15043
12 50057 19493 10091 Teh
14 4703317440 8.81 Se51 4202
16 45082 16400 7067 4652 3208 2035
18 45026 15617 6499 3098 2056 1286 1.47
20 464483 14.67 6055 3657 2024 1656 1019 +96
22 46653 14045 6027 3033 2003 1.37 1.02 +79 +66
24 44638 14.32 6408 3016 1689 1025 289 268 255 346
26 44022 14.22 5095 3404 1678 115 081 261 048 039 234
28 44014 14.13 5290 2096 171 1.09 275 055 043 234 029 225
30 44.09 14407 5087 2490 1665 14204 71 251 239 232 225 022 19
32 44.07 14.03 5083 2486 1661 1400 267 248 236 028 023 219 «17 015
34 46006 14400 5280 2484 1658 297 265 246 234 226 21 “7 15 13 12
36 44.05 13.98 5078 2483 1655 295 262 244 232 025 #20 216 213 e12 210 209
42 44406 13494 5074 2.79 1653 291 258 240 229 21 017 213 ell 209 +08 207 +06 205 205
48 44.04 13.94 5072 2077 1651 089 057 038 227 220 “el5 12 +09 208 207 206 205 204 204 203 203 203
54 44.06 13294 5e71 2676 1450 289 256 237 226 019 +14 ell 209 207 206 205 204 204 203 +03 203 202
60 44603 13.94 5e71 2676 1649 288 055 037 025 018 13 210 +08 206 205 204 204 203 203 202 202 202
66 44602 13496 5e71 2075 1649 088 055 036 225 018 013 elo 208 206 205 204 203 203 203 202 202 202
12 44013 13693 5671 2675 1249 287 255 036 225 218 13 210 +08 206 205 208 203 203 202 202 202 202
78 45031 13.93 5e71 2075 1649 287 255 236 225 218 013 10 207 206 205 204 203 203 202 202 202 201
é THICKNESS-H EQUALS 0.3750 INCHES
LENGTH-8 WIOTHA
INCHES 'NCHES.
6 8 10 12 14 16 18 20 22 24 26 268 30 32 34 36 38 40 42 4a 46 48
246672
149.85 78408
116049 = 51087 = 31099
106686 = 41433 22463 15.42
98014 = 36409 18628 11442 8633
95001 33618 15091 9037 6039 4088
93085 31046 14049 8616 5031 3085 3405
92095 30041 13459 7.40 4065 3024 2046 2000
92034 29496 13200 6490 He21 2085 2209 1064 1037
91495 29670 12060 6655 3091 2058 1085 1e41 els 296
91069 29448 12234 6631 3469 2039 1468 1626 299 282 #70
91653 29430 12024 6013 3054 2026 1.56 els +88 7 260 252
91044 = 29418 12016 6601 3442 2015 1646 1406 281 264 253 “45 239
91038 29209 12.09 5094 3033 2007 1.39 099 75 259 048 240 34 030
91036 29403 12203 5290 3027 2601 1034 +94 70 034 ry 036 231 027 224
91034 28498 11.98 5687 3022 1.97 1429 291 267 051 oa 033 +28 026 21 219
91633 28492 11689 5679 3017 1088 1.21 083 +60 08S 035 028 023 19 16 216 el2 eid 210
91633 28490 11.86 5475 3013 1686 lel7 079 356 4 231 024 220 16 14 012 10 209 +08 207 207 206
91033 2890 11484 5672 3ell 1084 1616 077 253 239 029 223 18 014 12 #10 209 207 207 206 205 205
91630 28490 11.84 5e71 3009 1682 1615 076 052 238 #28 21 217 213 ell 209 208 207 206 205 +04 204%
91627 28090 11484 5671 3409 1482 1el4 75 252 237 227 21 ole 13 210 209 207 206 205 Jo8 204 sae
91050 28490 11084 5e71 3208 1.81 114 e715 251 237 027 220 216 12 210 208 207 206 205 +04 204 203
93096 = 28.89 11684 Se71 3408 1681 1613 275 51 236 e27 220 015 12 210 208 206 205 205 +04 203 203

6-161

TABLE 6-17.

RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH

FIBERGLASS POLYESTER LAMINATES

25-27 OZ, WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.4375 |NCHES

WIOTH<A
LENGTH+-8 INCHES
INCHES : ; - a = 7 = x rs Te i or 30 32 36 36 38 40 a2 cry 46 48
6 423463
8 277062 144465
10 219053 96010-59027
12 194627 76057 = 41092-28457
14 181662 664686 «= 33086 021017 = 15043
16 176.03 61047 «29047 = 1703511084 9004
18 173088 © 58028 «= 26484 = 15013 9484 7013 5064
20 172021 56034 = 25018 13672 8e61 6200 4056 3070
22 171607 5505124008 12679 7280 5628 3088 3005 2053
24 170034 55002-23035 12014 7024 4678 3043 2062 2011 1079
26 169687 54462 22685 11469 6084 443 3ell 2033 1.83 1651 1030
28 169.57 54429-22067 = 11436 6055 4018 2088 2012 1464 1632 lel] +96
30 169.40 54.07 = 2205312013 6034 3299 2071 1.96 1649 1.19 298 283 +73
32 169030 53090 = 22e40- 11200 6018 3084 2058 1484 1.38 1.08 #88 274 264 57
34 169.25 53078 = 22029-10492 6406 3473 2048 1675 1.30 1.01 81 267 257 50 244
36 169623 53069 = 22020-10487 5096 3064 2040 1.68 1.23 295 75 262 252 45 239 235
42 169621 53.57 22203 10.72 5087 3448 20246 1.54 1.10 283 064 251 242 035 230 026 Bee o21 19
4a 169.21 53454 21496 10465 5480 3046 Zelz 1.46 1.03 cigs 258 045 36 #30 225 e21 e19 e16 o15 213 12 oy
54 169020 53054 = 21094 10.61 5076 3040 2015 1642 299 72 254 oh? 033 027 222 s19 16 14 12 ou 10 203
60 169615 53054 21493 10.59 5073 3038 2013 1641 297 270 052 240 pee 025 +20 o17 ole 12 ell 209 008 207
66 169.10 53054 = 2169310458 5072 34036 2011 1640 +96 69 250 238 230 024 ony, one me oll aie Boe 07 on
72 169053 53053-21093 10.58 5071 3036 2610 1.39 295 +68 250 037 029 023 218 i, oe 210 09 208 007 20g
78 176,08 = 53453 21493 10.58 5e71 3035 2010 1638 295 267 049 237 028 022 218 e14 12 210 008 207 206 005
THICKNESS—H EQUALS 0.5000 INCHES
LENGTH-B WIDTH-A
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 46 46 48
6 577660
e 373011 246476
10 31451 163693 101ell
12 279040 130063. 71e51 Ba 74
16 262032114607 57077 = 36011-26032
16 260.05 106486 = 50028 = 29060 = 20020 1502
18 257081 99442 45480 = 25080 = 164679 1201 T 9063
20 256071 9601242095 23041 14069 100 24 1077 6032
22 255062 94070 = 4100921081 13031 9001 6062 5020 4032
24 254054 93085 39484 = 2007] :12036 Bel6 5085 4047 3461 3005
26 253046 93017 = 38099-19494 11068 7057 5631 3097 3013 2058 2021
28 253046 92662, 38068 = 19439-11018 713 4092 3061 2.79 2026 1690 1665
30 253046 9262338044 = 18499 10082 6480 4662 3034 2655 2002 1667 1042 1625 ee
32 253066 91095 3842218677 10054 6655 4040 3014 2036 1685 1650 1626 1.09 196
34 253046 = 91674 = 38003 1806310033 6036 4623 2.99 2022 1072 1638 1014 297 285 76
36 253046 © 91060 = 37087 18454 10018 6021 4.09 2486 2610 1.61 1628 1.05 88 +76 267 60
42 253046 = 91639-37459 18429 10401 5494 3483 2062 1.88 1.41 1209 287 o7l #60 251 244 239 236 032
48 253046 = 9103437047 18016 9089 5087 3071 2049 1.76 1.29 299 o77 262 51 243 036 032 228 225 023 o21 +19
54 253046 = 9143337043 18409 9482 5480 3066 2043 1.69 1623 292 71 256 #46 38 932 027 024 21 +18 17 15
60 252040 = 91033-37041 18406 9478 5076 3663 2040 1.66 1.19 288 268 253 942 235 29 #24 21 018 216 14 13
66 252040 = 9103337041 18405 9676 5074 3460 2038 1.64 1617 #86 065 251 +40 233 027 023 219 216 214 013 ell
72 253046 91033-37041 :18404 9475 5072 3059 2037 1.63 1616 285 264 49 39 231 226 21 +18 15 +13 ell 10
78 257081 91031-37041 = 18404 9074 5e72 3058 2036 1.62 1615 986 263 48 38 #30 25 220 “17 214 212 ell 209

6-162

TABLE 6-17. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
25-27 OZ. WOVEN ROVING - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.5625 INCHES

LenaTice "INCHES
INCHES
6 8 10 12 16 16 16 20 22 24 26 28 30 32 36 36 38 40 a2 a a6 “8
6 684.18 ;
8 485022 387405 Z
10 389056 262059 = 161096 a
12 348.84 209625 114455 78408 7
14 Beee4 182671 92053. 570A 2017
16 329070 167696 804054 = 47041 32036 24070
18 327054 159626 73635 4163326090 194A «1S 4 AZ
20 323066 1534096 6 Be80 37449 = 23053 160 ; _ —— =
22 323666 151669 65481 34494 = 2103214043 6.92
26 321058 150034 63681-33418 19479 13408 5.78 4.88
26 321058 149025 6204531094 = 1807012012 5401 4013 3655
28 321058 148436 61696 = 31605 1729111 2 rer) 3661 3406 2064
30 319087 147674 614658 3004117432 ~——«:10490 4.08 3024 2068 2.28 2.00
32 319087 147628 61020 30006 += 16088 ~=—:10450 7.05 50033078 2696 2e41 2002 1674 1654
34319087 146495 60491 29485 16458 10019 6677 4.78 3655 2075 2e2l 1683 1056 1636 1621
36 319087 146072 60066 = 29270-16030 9495 6055 4658 3037 2658 2605 1068 1641 1622 1607 +96
42 319687 146040 60622 = 2943016403 9052 6013 4420 3002 2026 1675 1639 1el4 +96 82 e71 +63 +57 052
48 319087 146431 60002-29409 15084 9640 5694 3499 2082 2.07 1658 1424 99 382 269 #58 +51 “45 +40 236 33 230
54 319087 146430 © 59495 28498 15473 9030 5687 3489 2.71 1697 1048 1els 91 +73 +61 +51 14 38 233 +30 027 024
60 319087 146030 59493 2849315066 94023 5481 3085 2065 1.90 Leal 1.08 +85 +68 +56 246 239 233 229 25 023 #20
66 319087 146.30 5949228691 15063 9619 5.77 3081 2663 1687 1037 1604 +81 +65 252 043 236 231 26 023 #20 18
2 321058 146629 5949228490 15461 9617 5475 3079 2061 1486 1636 1402 +79 962 +50 4 34 +29 226 e221 18 16
ie 327054 146427 5909228901460 9016 S75 3077 2659 1684 1035 1201 77 +61 48 239 33 +27 023 220 17 15
THICKNESS-H EQUALS 0.6250 INCHES
LENGTH-B8 WIOTH-A
INCHES INCHES
6 8 10 12 14 16 18 20 22 26 26 28 30 32 34 36 38 40 42 rr 46 48
6 907041 a
8 585648 510681
10470077 358642 246485 7
12 453002 -291632-174659 119400
14 425043 256693141604 = 88415 a2 — — —_
16 406498 = 255062 122675 72027 49032370
18403470 241044 111680 6340040499 2907123051
20 403470 234647 104486 = 57414 «35486 25401-18498 15443
22 400047 = 228475 = 1004631 53425 32049 21099 16416 «212069 «210 SH
26 397029 227471 97025 50057 «30016 = :19093 14028 «210091 8.81 7046
26 397029 225066 = 95419 48468 = 2865118047 12096 909 7.64 6230 Se4l
28 397029224448 = 944 4703327030100 «212400 8.81 6-82 5651 4063 #002
30397629 224448 = 93486 46435 26040-16061 11029 8616 Ge22 4694 4.08 3048 3204
32397029 223068 = 93029-45082 25073 16000104 TH 7067 5076 e52 3067 3408 2666 2035
34393465 223048 = 9208345049 2502315053. 10032 7029 5641 4019 3037 2679 2037 2.07 1685
36393465 223048 «= 92045 45426 24084 «215017 9.99 6699 Se14 3694 3613 2656 2015 1686 1.64 1047
42393065 222048 91078 44066 24083-14049 9635 6640 4.60 3044 2066 2013 1.74 1.46 1625 1,09 096 +87 79
48 393465 222068 = 91049 bhe34 -2hale —-14e32 9605 6.08 4.30 3616 2041 1688 1651 1625 1405 +89 “77 368 +61 255 50 246
56393465 222048 = 91038 Hel 7 == 23697 «del 8694 5092 eel2 3600 2625 1674 1638 ier2 292 +78 966 58 251 45 40 237
60 393465 222048 = 91034 = 44409-2387 «214007 8.85 5087 4.04 2490 2016 1665 1629 1406 +85 +71 260 oH 344 +39 234 o3
66 393465 222448 = 9143344406 23082 «14D 8.80 3681 #01 2085 2409 1659 1ezs 298 +80 66 255 047 240 35 +31 027
12397429 222048 = 91033 4005-23079 «213498 8.76 3678 3697 2683 2007 1655 1620 95 +76 062 52 286 037 932 228 025
TB 403470222048 = 91033 44004 «= 2307813096 8673 3675 3695 2081 2008 1654 1017 292 +74 +60 #50 #42 235 30 026 23

6-163

TABLE 6-18. FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
10 OZ. CLOTH - ALL EDGES SIMPLY SUPPORTED

PHYSICAL CONSTANTS:
Ex = 1.96x10® PS]
Ey = 1.70x10® PSI

Gxy = 0.52x10® PSI
Oxy = Oyx = 0.20
THICKNESS-H EQUALS 0.0625 INCHES
WIOTH-A
LENGTH-B INCHES
INCHES 5 ; = a x 7 aa a a Ze 28 70 32 36 36 38 4o 42 44 46 48
6 18
8 012 206
10 209 204 002
12 208 203 002 201
14 008 203 Ol «Ol Ol
16 007 203 oul 001
18 007 202 201 201
20 207 202 201 201
22 207 002 001 201
26 207 202 201 201
26 007 202 Ol
28 207 202 201
30 007 202 201
32 207 002 201
34 007 202 201
36 207 202 001
42 207 202 ok
48 007 202 201
54 207 202 201
60 207 202 201
66 207 202 001
72 207 202 ool
78 007 202 201
THICKNESS-H EQUALS 0.1250 INCHES
LENGTH-8 WIOTHRA
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
6 2093
8 1687 293
10 1048 264 +38
12 1.31 052 028 018
14 1.22 045 023 «14 210
16 1el7 4 #20 12 208 +06
18 1015 039 18 219 007 005 204
20 1el4 238 017 209 206 204 203 002
22 1613 237 16 209 205 204 203 202 202
24 1013 336 16 08 005 203 002 002 201 eo
26 1e13 236 015 208 005 203 002 202 201 201 201
28 1012 236 015 08 +04 003 002 201 001 sol eol 201
30 1012 236 015 207 204 003 202 001 01 00 eo 001
32 1012 236 015 207 204 203 002 eol 201 ool 201
34 1612 036 15 207 204 203 202 201 201 20d eol
36 1el2 036 015 207 204 202 202 eo 201 201 2ol
42 1el2 036 015 +07 204 002 002 201 601 eo
48 1el2 236 015 207 204 202 Cl 201 201 20
54 1012 235 15 207 204 002 201 eo 201
60 1el2 035 015 207 004 202 201 ool 20l
66 1.12 035 015 +07 20% 202 001 201 201
72 1el2 035 015 207 004 002 001 eo) 201
76 1e15 035 015 207 404 202 001 202 201

6-164

TABLE 6-18.

FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED

ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
10 OZ, CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0,1875 INCHES

LENGTH-B PINCHES
Matealoe) a A ie 12 16 16 18 20 22 24 26 28 30 32 34 36 38 40 42 46 46 48
6 14685
8 9444 4670
10 7249 3626 1692
12 61 206) le 093
14 6017 2028 1615 71 050
16 5690 2.09 1.01 059 040 029
18 3083 1.98 29d 052 033 024 018
20 5078 deal 286 047 029 20 «15 12
22 5074 1666 082 ory 027 e168 «13 elo 208
24 5072 1285 079 aay D 025 016 rr 209 207 206
26 5070 1083 077 240 023 015 ell 008 206 005 +04
26 5069 1.82 076 339 022 14 10 007 206 204 204 003
30 5069 1082 076 238 022 els 009 207 205 204 203 003 002
32 5068 1661 275 237 e2l 13 209 +08 205 204 203 202 202 002
34 5068 1081 275 037 ogi «13 208 +06 +04 003 203 202 202 002 201
36 5068 1.80 275 036 20 12 208 206 +04 203 203 202 202 201 eo 201
42 5068 1680 a74 +36 #20 o12 206 205 +04 203 202 202 201 20l eol el
48 5068 1280 074 236 019 o12 007 005 20% 003 202 002 2OL 201 el 201
54 5068 1080 274 336 19 el 007 205 +03 202 202 201 01 202 ool 00
60 5068 1280 074 236 19 ell 007 005 203 002 002 001 201 ool ool 201
66 5067 1.80 274 36 019 ell 07 005 203 202 002 001 00) ool ool ool
72 566 1.80 +74 036 ely ell 007 205 +03 202 202 201 201 201 201 001
78 5080 1480 274 035 019 elt 207 005 203 202 202 201 201 201 201
THICKNESS-H EQUALS 0.2500 INCHES
LENGTH-8 WIDTHAA
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 368 40 42 44 46 48
6 46093 _
8 29085 14085 7
10 23068 10029 6408
12 20290 8.26 4e47 2093
14 19049 Te21 3065 2025 1058
16 18.65 6061 3018 1.87 1025 293
18 18644 6025 2089 1663 1406 075 058
20 18027 6003 2071 1048 093 064 048 038
22 18016 5088 2059 1.38 +84 057 41 032 026
24 18.08 5083 2050 1.31 278 052 “37 028 222 018
26 18.03 5079 2044 1625 276 248 034 025 220 26 +13
268 18200 5676 2040 1.22 270 045 reDy 023 +18 a4 12 210
30 17098 5074 2039 1.19 268 043 229 e2l 016 013 elo 209 207
32 17.97 5072 2038 1.17 066 4 028 220 015 12 209 208 207 206
34 17096 5071 2036 1.16 265 #40 027 ols 014 ell 209 207 206 205 205
36 17296 5070 2036 1.15 264 039 026 018 213 elo 208 207 206 205 206 204
42 17295 5268 2034 Leis 262 037 224 016 12 209 207 206 204 206 203 203
48 17295 5068 2033 1.13 261 036 023 216 ell 208 206 205 2046 203 203 202 202 202 202
54 17.95 5068 2033 1.13 ool +36 023 015 ell 208 #06 204% 204 003 202 002 202 201 201 201 eo 201
60 17094 5068 2033 Lel2 261 036 023 15 elo 207 206 204 203 203 202 202 202 ol sol 201 eo 201
66 17092 5068 2033 1.12 061 036 22 15 slo 207 205 206 203 203 002 002 20d eo 201 201 ol eo
72 17.90 5068 2033 lel2 061 036 022 015 elo 007 205 004 203 002 002 202 201 201 201 201 201 sol
78 18.33 5468 2033 1612 061 036 022 15 elo 007 205 004 203 202 202 002 201 20 201 201 eol eol

6-165

TABLE 6-18.
RECTANGULAR PLATES - LATERALLY LOADED

ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
10 OZ, CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.3125 INCHES

FIBERGLASS POLYESTER LAMINATES

LENGTHS motes
INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48
6 114056
8 72087 36025
10 57081 25012 14085
12 51201 20017 10091 To16
14 47458 17060 8490 5649 3087
16 45054 16014 7076 e586 3006 2e27
18 45402 15026 7006 3098 2058 1084 1042
20 46061 14072 6061 3061 2027 1057 1el7 093
22 44033 14035 6e31 3036 2005 1039 1.01 078 063
24 Abele 14025 Gell 3019 191 1026 290 068 054 045
26 44001 14014 5097 3006 1080 1017 082 061 048 039 032
28 434094 14607 5087 2097 1072 1el0 076 056 043 034 028 024
30 43089 14.01 5083 2691 1066 1.05 e71 052 039 31 025 21 018
32 43086 13496 5080 2085 1062 1601 268 249 236 028 223 19 016 ole
36 43085 13093 5077 2083 1058 298 265 046 034 026 e2l 17 015 013 ell
36 43084 13091 5075 2081 1056 095 063 044 032 025 #20 16 013 12 210 209
42 43083 13088 5e71 2078 1652 #90 059 240 229 022 17 13 ell 009 208 207 006 205 005
48 43083 13087 5069 2676 1.50 089 056 038 227 #20 015 12 «10 208 207 206 205 204 204 203 203 203
54 43083 13087 5068 2075 1049 288 056 037 026 «19 014 ell 209 207 206 205 204 204 203 203 203 202
60 43081 13087 5068 2674 1049 288 055 036 025 #18 ole 10 208 207 205 206 204 203 003 202 202 202
66 43074 13087 5068 2674 1048 087 055 036 025 #18 013 210 208 206 205 204 203 203 003 202 002 202
72 43670 13087 5068 2074 1048 087 054 036 225 018 013 10 208 206 205 004 003 203 002 202 202 202
78 46675 13086 5068 2074 1048 287 054 036 025 17 13 10 207 206 205 204 003 203 202 202 202 201
THICKNESS-H EQUALS 0.3750 |NCHES
LENGTH-B WIDTHAA
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 ae
6 237057
8 151011 75017
10 119088 52008 30079
12 105078 41082 22062 14086
14 98067 36050 18646 11639 8.02
16 94044 33067 16610 9645 6035 4e70
18 93036 31065 14064 8626 5034 3082 2093
20 92051 30053 13071 7049 4e70 3026 2043 1092
22 91092 29075 13009 6097 4026 2088 2010 1e62 1032
24 914052 29054 12066 6061 3095 2061 1087 lel 1ei2 093
26 91027 29433 12037 6035 3073 2042 1670 1026 299 #80 067
28 Mell 29017 12017 6017 3057 2028 1057 1015 +89 oT 259 250
30 91001 29405 12010 6403 3045 2017 1e48 1007 281 064 253 046 238
32 90096 28496 12003 5090 3035 2009 Leal 1001 276 059 048 240 234 029
34 90093 26489 11697 5087 3028 2003 1035 296 o71 055 044 036 230 026 23)
36 90091 28685 11693 5083 3023 1098 1631 092 067 052 41 033 228 024 eat 018
42 90290 26678 11084 5476 3015 1087 le22 084 260 045 035 028 023 29 216 016 12 ell 210
48 90089 28676 11680 Sete 3ell 1685 Tel? 079 356 41 o3l 025 220 216 214 12 210 209 208 207 206 206
54 90088 26076 11679 5070 3209 1683 1el5 076 054 039 029 023 018 <i5 el2 210 309 608 07 OG ae aan
60 90084 28676 11678 5069 3008 1082 lels 076 052 038 0268 022 017 14 en 209 208 007 206 os Son AS
66 90070 28676 11678 5068 3007 1081 1013 075 052 037 027 21 ay PTs 310 <09 07 an a8 vee ane apr
72 90061 28676 11678 5068 3007 1080 1013 075 251 036 027 020 «16 12 10 208 207 206 205 204 204 203
78 92081 28675 11678 5068 3007 1060 1013 274 251 036 026 220 215 el2 AY 208 208 05 as ay s 365

6-166

TABLE 6-18,

THICKNESS-H EQUALS 0.4975 INCHES

FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED
ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
10 OZ, CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

Lenore "incres
INCHES =
6 8 10 12 ty 16 18 20 22 24 26 28 30 32 34 36 36 40 42 46 46 ae
6 437072 == 7
8 279095 139027
10 222010 96049 57005
12 195097 77048 = 41091 27453
14 182080 «67462 = 3He21 «= 2124010 14 BS 7 <a ;
16 174096 = 62001-29482 174650110 76 8670
18 172997 58.65 27013 15031 9090 7007 Eras _ 7 - - 5 — Ja
20 171039 56057 = 25040 13488 8470 6003 4051 3057 : :
22 170029 55011 2402412092 7089 5033 3689-3001 2046
24 169056 54473 23046 12025 7032 4084 3046 2062 2408 1072
26 169008 = 54034 = 220921 TT 6091 4049 3015 2034 14683 1649 1625
28 168079 = 54405-22055 11043 6061 4023 2092 2014 1265 1032 1409 093
30 168661 = 534822204211 AT 6039 4603 2074 1698 1.51 1019 297 082 270
32 168651 = 53465 22028 = 10494 6021 3087 2061 1686 1.40 1009 288 074 263 254
34 168045 = 53053 22018 = 10688 6408 3076 2050 1677 1032 1002 +81 067 236 049 +43
36 168042 53045 = 22009-10081 5098 3066 2042 1670 1025 096 +76 062 252 244 +38 034
42 168040 = 5303221093 10468 5083 3046 20261055 lel 083 265 052 242 235 230 26 AE 220 018
48 168040 53629 «= 21086 = 10460 5077 3042 2016 1647 14604 o77 258 046 237 30 25 022 019 016 015 +13 12 ell
54 168638 = 53028 = 21084 10056 5673 3039 2014 1e42 +99 72 154 042 033 027 222 019 16 o16 012 212 210 +09
60 168029 = «53028 = 2108310854 5e7l 3036 2012 1640 +96 70 52 40 231 025 221 17 14 12 ell +09 208 +07
66 168004 53428 = 21682 10653 5069 3035 20101039 296 068 250 238 #30 26 “1g 16 013 ell 10 206 207 +07
72 167087 = 53028 21082 10653 5069 3034 2009 1038 +95 268 049 237 029 023 +18 015 13 ell 209 +08 207 +06
78 171094 = 53026 = 21082 10253 5068 3033 2409 1037 +94 067 049 237 «28 022 +18 o15 o12 210 209 207 206 +06
THICKNESS-H EQUALS 0.5000 | NCHES
LenaTite “INCHES
6 8 10 12 16 16 16 20 22 2 26 268 30 32 34 36 38 40 2 a 46 48
6 574081
8 383021 237459
10 322038 164061 97032
12 286006 132017 = 7105046496
16 267024 115035 = 58036 = 36400 250 3H
16 261650 105679 = 50088 = 29686 = 20007 145
18 260038 100608 = 46029 2611 16689 = 12006 9028
20 259028 = 96050 = 43033-23468 = 14485 10029 7069 6409
22 258018 = 9400241036 = 22404 13804 9009 6063 5013 4e16
24 257009 «93037 = 40003-20090 120 50 8626 5490 4047 3655 2093
26 256001 92071-3901 = 20008 =~ 11080 7266 5037 4400 3el2 2054 2013
28 256001 = 92020 38047 = 19449110 28 Te21 4098 3065 2081 2025 1686 1058
30 256001 91081 = 38024 = 19406 = 10089 6087 4068 3038 2057 2003 1466 1040 1020
32 256001 91052 38002 18466 = 10060 6061 4045 3018 2439 1086 1051 1025 1.07 +93
34 256001 «9103237084 = 18655 10 38 bea 4e27 3002 2026 1673 1639 1e14 +96 083 +73
36 254094 «= 91018 = 37069 = 18044 102d. 6025 4el3 2089 2013 1663 1629 1006 388 075 m6 158
42 254094 = «90097 37042 182d 9096 5091 3085 2064 1490 1042 1610 388 72 ae ari a aaa es =
48 254094 = 9009137030 = 1808 9484 5083 3469 2050 1677 1031 1600 78 +63 52 saa sat oF nl as 5 ns aa
56 254094 = «90690-37025 18401 9677 5078 3464 2042 1670 1623 093 672 37 i 38 Se Ty ee Si ars ee as
60 254094 = «90409037024 17098 9673 5074 3061 2039 1065 1019 +89 368 3 43 Ss B25) a an ie aie a as
66 254094 = 90489-37023 17496 9071 5071 3059 2037 1.63 1el6 #86 265 51 Bei 033 “27 a5 5G ae at Fr a
72 254094 «90088 = 3702317096 9070 5070 3057 2436 1662 1615 284 164 Ras ae ou =a ey FG is ae F AG
78 257009 = 90086 = 3702317096 9470 5069 3056 2035 1061 els 286 363 ah +38 ay “a5 = iy ary ae aT Fe

6-167

TABLE 6-18.

FIBERGLASS POLYESTER LAMINATES
RECTANGULAR PLATES - LATERALLY LOADED

ULTIMATE UNIFORM LOAD - POUNDS PER SQUARE INCH
10 OZ, CLOTH - ALL EDGES SIMPLY SUPPORTED (Cont'd)

THICKNESS-H EQUALS 0.5625 |NCHES

LENGTH-B: WIOTH-A
INCHES INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 468
6 686015
e 496098 380657
19 401038 263068 «= :155 089
12 356032 211471 114053 75022
14 351079 184077 93048 57066 40059
16 332022 169045 81049 47683 32015 23078
18 330007 160426 T4 els 41062 27006 19032 14086
20 326018 154057 69040 37094 23079 16048 12032 9075
22 326018 150061 66025 35031 21057 14057 10062 B22 6266
24 326018 149456 64011 33047 20602 13023 9045 7016 5069 4070
26 324044 148450 62065 32016 16089 12026 8.60 6040 5000 4006 Be41
28 324044 147669 61661 31022 16407 11055 7297 5084 4050 3060 2098 2054
3c 324044 1474006 61026 30.52 17045 11.01 7049 5e42 4el2 3025 2066 2024 1692
32 324044 146460 60089 29088 16098 10059 7el3 5009 3082 2099 2042 2001 1e71 1049
34 324044 146025 60060 29072 16063 10027 6084 4084 3059 2078 2022 1683 1054 1633 1.17
36 322438 146405 60038 29454 16035 10002 6061 4063 3041 2061 2007 1669 1e4) 1621 1405 093
42 322038 145071 59694 29017 15095 9046 6017 4023 3404 2028 1677 1e41 Lens 297 282 e71 263 056 250
48 322038 145462 59075 28496 15077 9035 5490 4eol 2084 2009 1059 1025 1.01 283 269 059 051 045 240 236 032 029
54 322638 145460 59067 28085 15066 9025 5083 3087 2072 1.98 1649 1el5 292 074 261 052 044 038 033 +30 226 024
60 322038 145460 59064 28480 15459 9019 5078 3083 2064 1.91 1042 1.09 086 +69 356 047 #40 034 029 226 023 220
66 322038 = 145659 59064 28477 15056 9015 5074 3080 2661 1686 1038 1005 282 265 053 044 036 o3l 027 023 020 218
72 322038 145.58 59064 28076" 15054 9el3 5072 3077 2659 1085 1035 12002 079 063 250 o4) 034 029 025 e2l 019 ol
73 326018 145654 59064 28.76 15053 9ell 5070 3076 2.58 1683 1034 1.00 e7T 61 049 240 033 227 023 #20 e17 215
THICKNESS—-H EQUALS 0.6250 | NCHES
LENGTH-B WIOTH-A
INCHES. INCHES
6 8 10 12 14 16 18 20 22 24 26 28 30 32 a4 36 38 40 42 44 46 48
6 885061
8 602008 502072
10 482081 363654 237060
12 464041 298097 = 174457 114664
14 431052 263054 = 142047 87489 61086
16 409048 = 258627 = 124020 72089 48099 36025
18 406020 244026 = 113000 63675 41024 29045 22065
20 406020 235060 =—:105678 57482 36025 25012 18677 14085
22 402098 229055 = 100498 53.61 32088 22020 16019 12052 10015
24 402098 227695 97072 51202 30051 20017 14040 10091 8666 7ol6
26 399028 226034 95048 49002 28080 18669 13611 9076 7263 6019 5020
268 399028 225610 93091 47658 27054 17060 12015 Be91 6486 5049 4055 3.87
30 399028 224014 93036 460546 26059 16077 11042 8626 6028 4096 4006 errs! 2693
32 399028 223045 92081 45056 25088 16014 10086 7076 5683 4055 3068 3006 2061 2027
34 399028 222095 92037 45429 25034 15065 10042 7037 5048 4023 3039 2079 2035 2003 1.78
36 399028 222061 92002 45203 24093 15026 10.08 7406 5020 3098 3016 2058 2015 1484 1660 1e42
42 399028 222409 91035 44046 24030 14043 9040 6045 464 3048 2069 2015 1676 1647 1.25 1009 095 085 076
43 399028 221495 91406 44ele 24003 14025 9600 6ell 4033 3019 2043 1691 1653 1026 1.06 290 078 068 #60 054 049 045
54 399628 221092 90495 43097 23086 14610 8089 5490 Gals 3001 2027 1676 1.39 113 294 079 267 056 251 245 240 236
60 399028 221492 90691 43089 23076 14601 Be81 5084 4002 2091 2017 1066 1631 1405 286 on 060 052 045 039 035 231
66 399028 221691 90090 43085 23071 13695 8676 5079 3099 2083 2010 12060 1625 099 +81 266 056 47 4) 035 o3l 027
72 396016 221689 90699 43084 23068 13091 Be72 5075 3095 2061 2006 1656 1e2l 295 277 263 052 044 038 032 028 025
78 399028 221682 90490 43083 23067 13089 8669 5073 3493 2079 2004 1053 1.18 093 374 cae 250 042 036 230 me 023

6-1

68

DESIGN OF LAMINATES 6-169

DESIGN EXAMPLE 6-24. UNIFORMLY LOADED SIMPLY SUPPORTED
CLOTH LAMINATE PANEL

A 24 in. wide by 48 in. long plate is to sustain a head of salt water of 2-1/2 ft, Fig.
6-48. If the plate is a simply supported 10 oz. cloth reinforced polyester laminate, find
the thickness required for a factor of safety of 2.

Fig. 6-48, Uniformly Loaded
Plate with Edges Simply Supported

The water load on the plate is:

26 Dek Ole lt f
pis ede pe

For a factor of safety of 2, the ultimate load
the plate must support is:

Pe ee eee ce eel psa:

From Table 6-18
For a 9/16 in. thick plate : Py = 2.09 psi
For a 5/8 in. thick plate : Py, = 3.19 psi

Therefore, the 5/8 in. thick plate is required.

DESIGN EXAMPLE 6-25. ULTIMATE UNIFORM LOAD FOR SIMPLY SUPPORTED
WOVEN ROVING LAMINATE PANEL

A laminate is 10 in. wide by 36 in. long by 3/8 in. thick and is made of woven roving
reinforced polyester resin.

What ultimate uniform load can the plate support if the edges are simply supported simi-
lar to Fig. 6-48?

From Table 6-17 the ultimate uniform load that this plate can support is equal to 11.98
psi or 1725 psf.

6-170 DESIGN OF LAMINATES

Case 2. Plates with Clamped Edges Under Uniform Loads

The deflection equation for plates with clamped edges under uniform loads is (18):

a

woe Ax ox (x - a)n (n-8 ) + al E a (n-P ) sinh LG eg

Hy

siné.n sinh 'y, (n-8 )| sin AX +
bm 5 Qs A . .
m Tay si Cm(x-a) sinh d,x + sin c,x sinh ag(ara) sin Onn Pp (6. 61)

where:

je)
(=
—
W
Soe)
|

=y, sind 8 + 6, sinh y, B

Kn(a) = dm Sin c, a+ Cy sinh dy,a

are 8a Bon d F,(9) 3
= -_ pe ee
" Bo? B fn (one f Bee i Yn)? - Lb On :

ee coe ae aay °mnGm( 2) ee
= 3 m
oS ahr 2 [mn ( cn? + Ane + a,2)? - le Ne

cos 5n8 + cosh ynB

F,( 8) (ete + sinh y,8
Oo

+
cos ca cosh qd

G = —————
n(a) (4) sin c,a + sinh da

0

Symbols not defined are as previously noted.

From this general deflection equation 6.61, the following basic plate moment equations
and the equation for the deflection at the center of the plate have been derived:

Y

Fig. 6-49. Uniformly Loaded
Plates with Clamped Edges

DESIGN OF LAMINATES 6-171

Referring to Fig. 6-9, for 3
X=0 i
2
2
2 :
My = o{ A E om + ae sino§ (cos ca + cosh 2a) | (6. 62)

_ B2 abea . 8
m, = -Dy) pA] - 3 + —K— sino 5 (cos ca + cosh da) (6. 63)

Deflection at center of plate:

2R2 6
ap A a As ee as d
we af 32° ~ q Sin- sin-3 sin-% - & sin > sinh = sin a (6. 64)

Referring to Fig. 6-9, then for:

D) :
eC 2y6a si
J -D) O46 af o— A = BYE ee 5B + one (6. 62a)
")
ec § inhaP
my = =D e- A Ee + yea sin'at (cos 58 + coshyé )| (6. 63a)
Uyp OTs (6. 63b)

From the above equations the ultimate uniform loads for laminates with clamped edges may
be determined. As previously stated, load tables for this condition have not been developed.

Since there are so many possible combinations of reinforcements that may be used in
laminates, equations with accompanying graphs and tables of necessary constants developed
for orthotropic materials and applied to plywood (5) and isotropic materials (19) are presented
to obtain the unit loads and bending moments for both simply supported and clamped edges.
Tables 6-19 and 6-20 have been developed for simply supported plates only.

Fiberglass reinforced laminates are assumed to behave similar to plywood panels and
the following equations apply (5):

Case 1. Simply Supported Plates Under Uniform Loads

For a uniformly loaded panel with all edges simply supported and for a small deflection,
the deflection at the center of the panel is:

w= 0.155 K, Pal (6. 64)

K, = a constant from Fig. 6-50a
a = the short side of the panel

Other symbols as previously defined.

6-172 DESIGN OF LAMINATES
and the unit load is:

= Ww Ey h3 ee
0.155 Ky al :

To obtain Kj from Fig. 6-50a the following constant must be determined:

1
b S| i (6. 66)
a Eo

The maximum bending moment at the center of the span is obtained from the graph,
Fig. 6-50b:

— = value from graph (6. 67)
pa

and m = pa@ (value from graph)
mn

To obtain the value of above from Fig. 6-50b the constant “ must be determined:

pae

E
pial ween (6. 68)

6V E\E9

ae
1.0 4 it 7A ——

O.
/ K4 — UNIFORM LOAD
/

/ EDGES SIMPLY
SUPPORTED

J + 4
Kp — UNIFORM LOAD
EDGES CLAMPED D

6 \E4E>

tt UNIFORM LOAD
i EDGES SIMPLY SUPPORTED
}

(0) 1 2 3 4 0 4 2

1/4
b &4 1/4
Sr lkes b| E41
e | * a | E2

‘ REFERENCE 5 al “2

@. CONSTANTS FOR DEFLECTION b. BENDING MOMENT AT CENTER OF PANEL

Fig. 6-50. Curves of Deflection and Bending Moment Constants for
Flat Rectangular Panels - Small Deflections

DESIGN OF LAMINATES 6-173
Case 2. Plates with Clamped Edges Under Uniform Loads

For a uniformly loaded panel with all edges clamped and for a small deflection, the de-
flection equation is:

h
= pa 5
W = (OR (O}BVIL Ky aes] ( . 69)
Eyh
where K, = a constant from Fig. 6-50a similar

to Kj, for simply supported plates.
and

_ WEyh? (6. 70)
0.031Kpall

To apply the method of analyzing laterally loaded rectangular plates of isotropic
materials (19) to fiberglass reinforced laminates, it was necessary to determine additional
constants which are given in Tables 6-19 and 6-20. Table 6-19 gives constants for isotropic
materials with Poisson's ratios of 0.20, 0.30 and 0.37. These ratio values correspond to
the ratio values of cloth and woven roving laminates, steel and mat laminates respectively.
For the orthotropic characteristics of cloth and woven roving laminates the constants in
Table 6-19 are not directly applicable and the correction factors presented in Table 6-20
must also be applied. In establishing Table 6-20, the warp direction of the reinforcement
has been assumed parallel to the short side of the panel. Correction factors for shear force
constants have not been determined.

The following equations and Tables 6-19 and 6-20 are applicable only to Case 1 and give
approximate values.

Case 1. Simply Supported Plates Under Uniform Loads

Deflection at the center of the panel:

Isotropic Orthotropic
h a pal
mene (6. 71) w=Ky Xx (6. 71a)
W TORT a T2EL
Unit load:
1L2wET 12wEI
= 6. 72 pr= 6. 72
=e ee Kaa (b.72a)
Maximum bending moments:
m, = @,pae (6. 73) m, = K,Bxpa (6. 73a)
My eh ge (6.74) my = KyBypa (6. 74a)

TABLE 6-19. DEFLECTION, BENDING MOMENT AND SHEAR FORCE
CONSTANTS FOR UNIFORMLY LOADED SIMPLY SUPPORTED FLAT
RECTANGULAR PANELS OF ISOTROPIC MATERIALS

Bending Moment Deflection at Center Shear Force at

_ of Plate Center of Side b
Max = 8 pa? .

6-174

TABLE 6-20. CORRECTION FACTORS FOR DEFLECTION AND BENDING
MOMENT CONSTANTS FOR UNIFORMLY LOADED SIMPLY SUPPORTED
FLAT RECTANGULAR PANELS OF ORTHOTROPIC MATERIALS

10 Oz. Cloth
E

b/a oar Wes) ae 520
Ey

Bending Moment

1.0 109m 0.955

. 966

6-175

25-27 Oz. Woven Roving

= eS o= 0.19
By

Deflection

Ka

MANY)

aly, ite

1.129

1. 064

1. 049

1. 036

1. 000

6-176 DESIGN OF LAMINATES

Shear force at center of side b:

Isotropic Orthotropic
Vinax * 5P@ (6. 75)
where
a = deflection constant (Table 6-19)

By and By = bending moment constants in X and Y directions (Table 6-19)
6 = shear force constant (Table 6-19)

K K, and Ky = correction factors for deflection and bending

a? : :
moments in orthotropic plates

Other symbols as previously defined.

DESIGN EXAMPLE 6-26. ULTIMATE UNIFORM LOAD FOR WOVEN ROVING
LAMINATE PANEL WITH SIMPLY SUPPORTED AND CLAMPED EDGES

Given a woven roving polyester laminate 12 in. wide by 24 in. long by 1/4 in. thick.
Find the ultimate unit load p, bending moment my and bending stress f, for the laminate
when simply supported and with clamped edges.

Case 1. Simply Supported Edges

a. Value obtained from Table 6-17
p = 1.29 psi
My = 22,00 in.-lbs. (not given in this text)
fy = 2070 psi

b. Using the orthotropic method (5) for the unit load, p:

Ey = Ey = 1.81 x 106
Eo = Ey = 1.54 x 106
he O25 : : : :
Weg eee Oe125 sane maximum allowable deflection
z, | 2 6|F
BE 2k) VOLO ie oe ol O08 (6. 66)
a =| TZ] 1.54 x 106

meee
From Fig. 6-50a, for a | Q value of 2,08 the value of K, is 1.02
a ee

0.155 x 1.02 x p x 124 _ 0.250

and w = Saar E yeaa A Sua = @ea25 in. (6. 64)
1.81 x 10° x 0,25 2
6 953

Fe Paleo roc aol lO aces 1220 pai (6. 65)

Os155 x. O2 12

DESIGN OF LAMINATES 6-177

For the bending moment, m,: (6. 68)
E 6
cg ee ee 0

6VE}E2 6 V¥ 1,81 x 106 x 1.5 x 106
From the graph of Fig. 6-50b:

m

ee = Oss
pa‘
My = 0.1255 x 1.10 x 122 = 19,88 in.-1bs. (6. 67)

For the bending stress:

Stress due to my:

m
fox = = (6.31)
bh? 0.252

L=—- = 1x = .010k in.3 for a lin. unit width (6,32)

9.88 ;
Po SoroT = 1912 psi

Gs Using the modified isotropic method for the unit load p:

Gx dy = Ong

E = Ex; E, and Ey as previously given

le Pk
Pipes ma

From Table 6-19 for o = 0.20:
m= Oley

From Table 6-20 for woven roving:

Beach ade
and p = 22% 06125 x 1.81 x 10S SGseO Ne Sena “ie ay
Tala se HO MANS fg Le
For the bending moment, m,
From Table 6-19 for o = 0.20, By = 0.100
From Table 6-20 for woven roving, K, = 1.121
and m, = 1,121 x 0.100 x 1.30 x 122 = 20.98 in.-lbs. (6. 73a)

For the bending stress:

Similar to the orthotropic method (5) above; fpx = 2017 psi

6-178 DESIGN OF LAMINATES

Summary of results:

Modified Isotropic

Load Table 6-17 Orthotropic Method (5) Method
Dee psi der et@ 1.30
my, in.-lbs. 22.00 19.88 20.98
fox, psi 2070 1912 2017

The above results are in good agreement and any of the methods of analysis discussed
is considered applicable.

Case 2. Clamped Edges

Using the orthotropic method (5):

ae

5 1/@ 2 2.08

From Fig. 6-50a, for a value of G Es = 2,08,
the value of Ky = 1.0. ;

and the unit load is:
6 3 70)
Oel25 oo 1 Gi 10x O25 , (6.
2 ——— = 5,30 psi

ORO Se lsOh sxe 12

Plates with Large Deflections: When the deflection of a laterally loaded plate equals
several times its thickness, the formulas developed for plates with small deflections cannot
be used. March (18,20) has developed expressions which can be used to give approximate
values for load, deflection, bending stress and direct stress. Only the conditions for a
uniformly loaded plate with simply supported and clamped edges are presented in this text.
Fig. 6-47 and the symbols previously defined are applicable to this discussion.

Case 1. Simply Supported Plates Under Uniform Loads

For a plate that is uniformly loaded and whose edges are simply supported, the follow-
ing formulas can be used to determine approximate values of the various factors of the plate:

Maximum bending stress:

dB, hw
t, & TEx (6. 76)
na
Mean direct stress:
pw cb nen? ep 2.572 Exw? (6. 77)
2 3X ae ee

Total maximum stress:

frotal = fp + fa

DESIGN OF LAMINATES 6-179

Uniform load:

Exh | 64EW 20.6 Baw?

i) als Eh epee (6. 78)
h3 20.6 Eqw2
aren | 6xueye + oe aes | (6. 78a)
where
meee es zm
nh = ° Hf, Fy hi (6, 79)
1 cosh n-l
v- ne cosh 7 (6. 80)
1 cosh “T7. .f cosh 7-1
ne nécosh
and

E, = modulus in tension parallel to the x-axis, Ey,
Ej; = modulus in bending parallel to the x-axis, kh,
The value of a@ can be chosen from Fig. 6-5la. 1
RY E
The above expressions are applicable when the ratio E =< ie Le WS
Case 2. Plates with Clamped Edges Under Uniform Load

For a plate with clamped edges and uniformly loaded the following formulas have
been derived:

Uniform load:

p= S E Eyw + 23 a | (6. 81)
Maximum bending stress:
fh = Ey B e Ww Gin E Exw + 2.98ExEaw3 | (6. 82)
A | a h ja EF}
Mean direct stress:
es ae £ né (6, 83)

Total maximum stress:

+ 5
Ea| i iL

6-180 DESIGN OF LAMINATES

coshn-l
coshn

7 ( coshn-1
yar ea

cosh n

(6. 85)

)

The value of a can be obtained from Fig. 6-51b.

The above expressions are applicable when the ratio of

In the solving of problems with the above equations it is suggested that the unit load, p,
be known or assumed for a specific laminate and the deflection, w, computed. Knowing w,
the values of ) anda can be established. Finally the bending and direct stresses can be

determined.
50

30

i

te)

n REFERENCE 20

@. SIMPLY SUPPORTED EDGES

)

b. CLAMPED EDGES

Fig. 6-51. Coefficient % as a Function of 7 for Uniformly Loaded Flat Rectangular Panels

SANDWICH CONSTRUCTION

A structural sandwich may be defined as a combination of strong, high density, thin
The obvious purpose of such an
arrangement is to increase the rigidity and strength of a thin plate with a minimum increase

facings with a relatively weak, low density thick core.

in weight.

The theoretical analysis of sandwich construction, particularly sandwich construction
with orthotropic materials is a lengthy process and the theory is far from complete. The
theoretical analysis which has been done has generally resulted in expressions which are very
cumbersome and tedious to evaluate. In addition, some of the necessaryelastic properties of the

DESIGN OF LAMINATES 6-181

different core materials which vary with density have not been completely established. For
these reasons, alternate conservative methods of analysis which sacrifice accuracy for speed
and ease in design are generally used and are recommended for most marine applications,

Sandwich construction is generally used for flat or curved panels subject to flexure and
edgewise compression.

Flexure

The flexural analysis of sandwich construction includes the determination of the stresses
in the facings and core materials and the deflection of the panel. When considering a one-
way panel the analysis is similar to the analysis for a one-way composite plate or beam as
previously discussed. The flexural properties of some of the core materials, such as foamed
plastics or honeycombs are quite low and may be ignored in the analysis. Some core ma-
terials such as balsa wood have appreciable flexural moduli of elasticity, particularly when
the grain of the wood is parallel to the plane of the panel and may be considered effective.

As an example, consider a 1 in, wide strip of a sandwich panel having a 1 in, thick core
of 4 1b. density balsa wood and 1/8 in. thick facings of 10 ounce cloth-polyester laminate.
Ignoring the effect of the core, the flexural rigidity of the sandwich from equation 6. 16 is,
EI = 0.1270 x 10° in. -lbs. Including the effect of the balsa core, the flexural rigidity be-
comes, EI = 0.1397 x 106, which is an increase of approximately 10 per cent. When the
core is considered effective, the allowable tensile or compressive stress should not be ex-
ceeded at the outermost fiber of the core.

Simple One-Way Panels: In the determination of the deflection of one-way sandwich
panels, the effect of the shear deformation of the low density core may be appreciable and
should be considered. Shear deformation effect has been previously discussed for lami-
nates and beam sections.

As an example of this effect, the approximate deflection of a simple cantilever sandwich
beam section with a concentrated load at the unsupported end, Fig. 6-52, has been investi-
gated (12,21) and the resulting expression in a simplified form is:

57 3 2
a= 5p [ + se | (6. 86)
ne
Ey 3 Ey 3 3
[2-9 (8)> (8) ] BC) -oe(eP ee (E)] wm
Rr
ap ag
he ae
where r oe (6. 88)

P, EI and G are as previously defined.

Other symbols as indicated in Fig. 6-52.

A comparison of the deflection obtained by this expression and that obtained by various
other approximate methods is presented in Design Example 6-27.

6-182 DESIGN OF LAMINATES

FACE
z S| t -
xu a CORE = c h 2 =-— —s Y
XN
t
xX FACE
N
L
na Seas b

Fig. 6-52. Cantilever Sandwich Beam

DESIGN EXAMPLE 6-27, DEFLECTION OF CANTILEVER SANDWICH BEAM

Consider a 1 in. wide strip of the cantilever sandwich beam as indicated in Fig. 6-52 to
have a length of 10 in. and to support a load of 10 lbs. at its free end. The beam is con-
structed of the materials indicated below. Determine the deflection at the free end.

FACINGS: CORE:
LO ounce cloth laminate Balsa wood - l| lb. density. Grain
1 direction placed parallel to span
Thickness t = 7 in. of beam,
ie = 1,50 x 106 psi (Table 5-10) Thickness, c = 1 in.
=O 6 .
Gp = 0.52 x 10° psi (Table 5-14) Exe = 0.152 x 10° psi (Reference 23)
G, = 0.008 x 106 psi (Reference 23)

1. Deflection with equations 6.86 through 6.88 previously discussed.

6
ie eee Oe ee eos (6. 88)
re era eee

Cae erie e— wl Opeititers 5 = 0.80

6
1.60 x 10 3
Roe ner RS (0.80 + 0.60 ) (6. 87)
0.52 x 10
6 3 3
, Dekee 210" | 3-5 10.53 ( 0.80) S103 (0.80) + »( 0.80)
0.008 x 10
e = 96.36
2
3 i
be , Dita - betac
EL -) 51) = Eo oe + Er Ox To eX ile ( 5 ) (6, 16)
= 0.1397 x 10°
2 3 2
pis ela ya Bes | 10 x 10 ee lees ES (6, 86)
3EI LL 3 x 0.1397 x 10° , x 10

= 0.0329 in.

DESIGN OF LAMINATES 6-183

2. Deflection due to bending of the facings only, ignoring shear deflection and the effect
of the core:

D)
ot3 piece \c
El ¢ = Ef E x Dn ae Kel x eS | (6, 16)
= 0.1270 x 10°
PL2 -
d = | ee 0.0262 in. This is considerably less than the more
ft accurate method above. (6. 89)

3. Deflection due to bending and shear of the facings, ignoring the effect of the core:
ae. 6
Erl p = 0.1270 x 10
GpAp = 0.52 x 100 x 2x1x Fels = (0p ale ys '< 10°

ge ee eh (6. 90)
= Os02628 +O, OOO. —=n0 502 On ine

4. Deflection due to bending and shear considering the facings and core acting together:

be3 ot3 t +c\*
BI =) 5414 = Exc OS" + Exp re ea (6. 16)
= 0.1397 x 10°
GA -) GyAq = Gy x be + Gp x 2bt = 0.138 x 106 (6.91)
3
d= ser + (6. 90)

20239 + 0,0007 = .02h6 in.

5. Deflection as the sum of the bending deflection of the facings only and the shear deflec-
tion of the core only:

bt3 t+ce\?
yeas E+ phi ole Dp ta? ox 1D. bax =a (6. 16)
GopAg = G,be
PL3 PL
d= ater LE Gane (6. 90)

0.0262 + 0125

= 0.0387 in.

Alternatively, since the flexural modulus of the balsa wood is large, the bending deflec-
tion above may be modified to include its effect. The resulting deflection is then:

d = 0.0239 + 0.0125 = 0.0364 in.

6-184 DESIGN OF LAMINATES

The results of the analysis used in Design Example 6-27 indicate that the simplified
analysis, No. 5, which includes the flexural deflection, with or without the core, and the
shear deflection of the core only, assuming uniform shear distribution, gives a conservative
deflection when compared with the more accurate analysis, No.1. The difference is ap-
proximately 10 per cent for the simplified analysis and is considered acceptable.

Although the comparative analysis has been made for a simple cantilever beam loaded
at the end, it is believed that similar comparative deflections will occur for other beam
loading and support conditions. Therefore it is recommended that the simplified analysis,
No. 5 be used in obtaining an approximate deflection for simple one-way panels. This
proposed method is presently used in tests to determine the shear moduli of core materials
(22). In this test the core material is combined with very thin faces to minimize their ef-
fect on the shear deflection.

The analysis of the flexural stresses in a one-way sandwich panel or beam is similar to
the analysis for a composite laminate previously discussed, Design Example 6-28 indicates
the procedure used computing the stresses in the various components of a sandwich section.

DESIGN EXAMPLE 6-28. STRESSES IN A CANTILEVER SANDWICH BEAM

For the sandwich beam given in Design Example 6-27, calculate the flexural and shear
stresses in the facings and core.

Bending Moment, M = PL = 100 in.-lbs,
Shear V = P = 10 lbs,
Bending stress at any point, y in the cross-section

ayy (6. 36)

where EI =) Bilt = Stiffness factor of the entire section (6. 16)

Tensile or compressive stress in the facings:
100 x 1.60 x 106 x .625

a a 0.1397 x 10

Tensile or compressive stress in the core:

= 716 psi

6
0.1397 x 10

The maximum shear stress is: f, = ~ (6. 37)

where V, EI, b and Q' are as previously defined.
Shear stress at the interface between the laminate ard the balsa core:

1.0) 1.60! x 10° xl xe 25x 5625
tO L138S. 7 xO

f =

"Oe osm

DESIGN OF LAMINATES 6-185

Shear stress at the neutral axis in the balsa core

10 x [ 1.60 x 100 x 1 x .125 x 5625 + 0.52 x10°x1x.5 x ead
a L
Te OES Oi ee LO

12s (la pSa.
As an alternative method, consider all the shear

stress carried by the core only, Then the maximum
shear stress at the center of the core is:

(6.33)

fea pe

eae

This approximate method gives a conservative estimate of the shear stress and is con-
sidered applicable.

Fig. 6-53 gives the section moduli and moments of inertia about the neutral axis for a
1 in. wide strip for two types of sandwich constructions. In both cases the core is regarded
as ineffective in determining the above properties. The section moduli values are corrected
to give stress values directly, similar to the values given for the single laminates. The
moment of inertia, I, for the Type A sandwich is based on cloth equivalence and may be
used with a modulus of elasticity of 1.95 x 106 psi. The moment of inertia, I, for the Type
B sandwich is based on woven roving equivalence, and may be used with a modulus of
elasticity of 2. 06 x 108 psi.

Flat Rectangular Panels: Methods of analysis of laterally loaded sandwich panels have
been developed (12, 24), but all conditions of loading and edge supports have not been fully
investigated for orthotropic sandwich panels. The behavior of a simply supported uniformly
loaded orthotropic sandwich panel (24) is presented since it is applicable to the sandwich
panels with cloth and woven roving fiberglass laminate facings presented in Fig. 6-53,

Referring to Fig. 6-47 for flat plates, the lengths of the edges of the panel are denoted
as a and b and are parallel to the directions of the x and y axes which are the warp and fill
directions of the laminates and core. The formulas given are applicable only to panels
with small deflections that do not introduce direct stresses to the panel.

For a uniformly loaded simply supported panel, the deflection at the center of the panel:

acbep

VDxDy *| Ke ocr

weit (6. 92)
Tt

.

BATJOOJJOU] PALTAPISUOD 210D - diag OpIM “Ul I B OJ] ‘et}A9UT Jo jUaUIO;! pUe

HOIMONWS @ AdAL °Q

S3HONI — SS3NMOIH1 3x09
v/ a/b v/L
=o Eee 2
L)
N
S
5
ISd gO X 90%2 = 3
BON3 TWA IND|
ONIAOY N3AOM
SIX¥ Twalnan inoay JT

SNIAOY N3AOM ZO L2—-S2 Add L
LVW ZO 2/L—-b Ald Lb

3409
LWW ZO 2/L-L Add L

H1019 ZO OL S3I1d 2

20°O

£€0°0O

¥0°0

so°o

90°O

Z ‘SNINpO| UOTJDeg - seoey ayeuTUIeT Jajsad[Oq-sSse[S1aqiy YIM UOTJONAsUOD YoImpueg ‘gc-9 “Sty

HOIMONWS VW 3dAl *e@
S3HONI — SS3NWOIHL 3Yx00

L v/e e/t v/t

yHON| — [ GNW ¢HON! — 7

ISd gOL X S6%F = 3
BZON3IWAINDS HLO19
SIX¥ TWvuiN3N Lnoay T

ZO OL Ald
e/t-b Add

34y09

peo

L
z2/t-bk Ald b
ZO OL Ald

yHON| — [T GN¥ HON! — 7

6-186

DESIGN OF LAMINATES

and the bending moments at the center of the panel for a 1 in. strip are:

ac a2 [ at |
16 5 By + (Boas) ba + WBs pe L (85-28) be - Ba
Mee eee 2 L

a a
Pee ee Boe

2
2 2 = |
aay [5.3 f (1-8 2 + 3BQB3~28 A b

: ) (6.93)

2 2
a 2\a a a
(y+ ¥, 5) [C8 ee (5, + 2Bo pa ach

16 2 5} lige? ree) its)
Mi ee
ed jell >
B 2B = na
+ +
i 2 pe Byb
ae
+ V. 3 B,-2B + Babe
ae 2 az ( ie alt
+ Vy + Vise 1-B,, b + BS By + 2 y2 * 5 oh
Where: 3 D)
Exe | 3 3Pxe° ( ty-t2 )
Oe ree || ae c3 - :
iz ey
Ne Sil <p Oya
Ag = 1 - ye %yxe
Py 1 Exes
Ex phe
ieahsvie Nga fe gas yaeeve eres)
y 12h i 1- y=
24 Eyo\t
i) Eye
Gyyt
pats cere:
Duy 12 ( h c )
U. = cG

XZ xyc

6-187

6-188 DESIGN OF LAMINATES

ya yxc

RF v. C VV
x 3 SOV E, 'y
al +) Po + 230, C), | 2 + 230, Yy + cl, 4

Values of Kp and Kn above are applicable for deflection when
n = 1 and the length to width ratio:

is within a range of 0.71 to lel.

Also when the core is considered effective, Kp = 0

v,. = we Vos,
at Ux,

Dx oyxt + 2Dxy
Bo i

B3

Ce ipa ere 5 Cy = 13 Ce be

where n = number of half-waves and equal to 1 in the
equations for Kp and K, above.

C
On se!
= -B CC + BC Bc + 2BC +
: Te ee 5° (Ae, 22 =)

These equations have been applied to a sandwich panel in order to compare the results
with those obtained by simpler methods. The panel was taken as 24 in. by 24 in., composed
of alin. thick core, and 1/8 in, thick facings. The facings were considered to be of 10 ounce
fiberglass cloth-polyester laminate. Two different core materials were evaluated; balsa wood
of 4lbs. percu. ft. density andan isotropic low modulus material similar to a foamed resin.
The material properties assumed are given below:

DESIGN OF LAMINATES 6-189

Facings - 10 Ounce cloth - polyester laminate

Eyp = 160 x 10° psi (Table 5-10)

Eye = 1.52 x 106 psi

Sxyf = 0420 (Average of Tables 5-8 and 5-12)

Cunt = 0.20

Guyp = 0652 x 10° psi (Table 5-14)
Core - lb. density balsa (Reference 23)

Eye © Oslb2x 10° psi

Eve = 90,0023 x 106 psi

oO xyc a 0) 88

Syxe = 0.009
Gaye = 02008 x 10° psi
Core - low modulus isotropic (Reference 23)
Exe * Eve = 0.005 x 106 psi
Sxye = Syxe = 0.20
Go = 0.002 x 10° psi

Two alternative methods of analysis have been evaluated; the first considering the fac-
ings only effective and using the usual panel formula corrected for orthotropicity of the fac-
ing, Tables 6-19 and 6-20, the second considering a 1 in. wide strip of the panel as a beam
in accordance with the simplified method of analysis (No. 5) previously discussed.

The results of the investigation of the deflection and the bending moments are summa-
rized below.

Summary of Panel Deflections

Method of Analysis Deflection

Balsa Core Foamed Plastic Core
Exact 0.0033 in. 0.0038 in.
Normal Panel Formulas 0.00102 in, 0.00102 in.

Simple Beam 0.0043 in. 0.0048 in,

6-190 DESIGN OF LAMINATES

Summary of Panel Bending Moments

Method of Analysis Bending Moment
Balsa Core Foamed Plastic Core
M,, My M, My
Exact 5.24 in.-lbs. 2.3lin.-lbs. 4.27in.-lbs. 4.06 in.-lbs.

Normal Panel Formulas 2. 76 in. =lbs. 25.62 in.=lbs;. 2.76 in.-lbs. 2.62)1n.—lbs.
Simple Beam (G20 ins lbs. 20 anes: te 20 in. bss 7.20 in. -lbs.

A study of the summary indicates that the use of normal plate panel formulas for sand-
wich panels results in non-conservative values for both deflection and bending moment. This
is due to the effect of the very low shear moduli of the core materials. It is interesting to
note the effect of core orthotropicity on the bending moment as evidenced by the balsa wood.
The use of the simplified method of analysis gives conservative results and can be used in
lieu of the exact method which is cumbersome and tedious to evaluate.

Edgewise Compression

Sandwich panels loaded in edgewise compression may fail in one of two ways; by in-
stability of the facings and by column instability of the entire sandwich as a unit. The critical
stress for a particular sandwich section is the lower of the two stresses.

The critical facing buckling stress, below which rippling of the facing willnot occur, may
be conservatively predicted from the formula (13, 25).

al
F = = 3y (6. 95)
[ong 2 EE cfycc

where? Ep is the flexural modulus of the facing material
in the direction of load.

Eze is the tensile or compressive modulus of the core
material in the direction perpendicular to the
plane of the sandwich.

G is the shear rigidity of the core material associated

pate with the direction of the load and the perpendicular
to the plane of the sandwich.

The critical facing buckling stress for buckling of the panel as a unit is given by (24, 26):

BT

a Hy

F =

yfcr Be K (6. 96)

Where the x axis is taken parallel to side a, the y axis parallel
to side b, and the load is wniformly distributed along side a.

K i Ses

DESIGN OF LAMINATES 6-191

Kp and Ko are obtained from the equations previcusly given.
= £E - EC
Hy yf [b c | + a

For the case of all edges simply supported the C values used
in evaluating kK, and Ke are:

2 Ce
C = C6 a 5 iG = ae (3 =
Fees eae

In using equation 6.96 it is necessary to use a minimum value for K. This is obtained
by substituting n= 1, 2, 3, etc. successively in the formulae for Kg and Km and determining
which value of n produces the minimum Kk.

6-192

(1)

(2)

(3)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

DESIGN OF LAMINATES
REFERENCES

Mooney, Rodney, D. and McGarry, Frederick, J. - ''Resin-
Glass Bond Study" 14th Annual Technical and Management
Conference, Reinforced Plastics Division, The Society of the
Plastics Industry - February 1959

Kinny, G.F., "Engineering Properties and Applications of
Plastics", John Wiley & Sons Inc., New York, 1957

Timoshenko, S., ''Strength of Materials, Part II", D. Van
Nostrand Co., Inc., New York

U.S. Department of Defense, Munitions Board Aircraft
Committee ANC-5a Bulletin, ''Strength of Metal Aircraft
Elements", May 1949

U.S. Department of Defense, Munitions Board Aircraft
Committee ANC-18 Bulletin, ''Design of Wood Aircraft
Structures", June 1951

Mantell, C.L., ''Engineering Materials Handbook", McGraw-
Hill Book Company, Inc., 1958

U.S. Department of Defense, Munitions Board Aircraft
Committee ANC-17 Bulletin, Plastics for Aircraft, Part I,
Reinforced Plastics, June 1955

Freas, A.D. and Werren, F., ''Mechanical Properties of
Cross Laminated and Composite Glass-Fabric Base Plastic
Laminates", Forest Products Laboratory Bulletin No. 1821,
Madison, Wisconsin

Werren, F. and Norris, C.B., ''Directional Properties of
Glass-Fabric Base Plastics Laminated Panels of Sizes That
Do Not Buckle", Forest Products Laboratory Bulletin No.
1803 and Supplement 1803-B

"Strengths of Orthotropic Materials Subjected to Combined
Stresses", Forest Products Laboratory Bulletin No. 1816,
Madison, Wisconsin

Sonnenborn, Ralph H., ''Fiberglass Reinforced Plastics",
First Edition, Reinhold Publishing Corporation

Dietz, A.G.H., ''Engineering Laminates", New York,
John Wiley and Sons, 1949

Timoshenko, S., ''Theory of Elastic Stability", McGraw-
Hill Book Company, Inc., New York

Parcel, J.A. and Maney, G.A., ''Statically Indeterminate
Stresses", John Wiley and Sons, Inc., New York

(15)

(16)

(17)

(18)

(19)

(20)

(22)

(23)

(24)

(25)

(26)

DESIGN OF LAMINATES
REFERENCES

March, H.W. and Smith, C.B., 'Buckling Loads of Flat
Sandwich Panels in Compression", Forest Products
Laboratory Report No. 1525, Madison, Wisconsin

March, H.W., ‘Buckling of Flat Plywood Plates in Compression,
Shear, or Combined Compression and Shear", Forest Products
Laboratory Report No. 1316, Madison, Wisconsin

Seydel, E., Zeitschrift fur Flugtechnik und Luftschiffahrt 24,
78-83, 1933

March, H.W., ''Flat Plates of Plywood Under Uniform or
Concentrated Loads", Forest Products Laboratory Report
No. 1312, Madison, Wisconsin

Timoshenko, S., ''Theory of Plates and Shells", McGraw-
Hill Publishing Corporation, New York City

March, H.W., 'Summary of Formulas for Flat Plates of
Plywood Under Uniform or Concentrated Loads", Forest
Products Laboratory Report No. 1300, January 1953,
Madison 5, Wisconsin

March, H.W. and Smith, C.B., ''Flexural Rigidity of a
Rectangular Strip of Sandwich Construction", Forest Products
Laboratory Report 1505, 1944, Madison, Wisconsin

Engel, H.C., Hemming, C.B. and Merriman, H.R.,
"Structural Plastics", McGraw Hill Book Company,
Inc., 1950

Miner, D, F. and Seastone, J.B., ''Handbook of Engineering
Materials", John Wiley and Sons, Inc., New York, 1955

U.S. Department of Defense, Munitions Board Aircraft
Committee, ''Sandwich Construction for Aircraft",
ANC-23, May 1951

Hoff, N.J. and Mautner, S.E., ''The Buckling of Sandwich
Type Panels", Journal of Aeronautical Science, Vol. 12,
No. 3, July 1945

Ericksen, W.S. and March, H.W., ''Compressive Buckling
of Sandwich Panels Having Facings of Unequal Thickness",
Forest Products Laboratory Report No. 1583B, November
1950, Madison 5, Wisconsin

6-193

APPENDIX A
TEST PROGRAM FIBERGLASS POLYESTER LAMINATES
TEST PROCEDURES

The following test procedures are modifications of existing procedures or were especially
devised for this test program, by the participating laboratories:

Shear Strength - Parallel

The test for shear strength parallel to the laminate was modified from
ASTM-D-732 or LP-406-b method 1041.

Strips of the laminate under test were cut to the same width as the laminate's
thickness. The samples were then tested in the Johnson Double Shear Jig with
the side edge of the laminate up at a position rotated 90 degrees from the test
position used for perpendicular shear.

Poisson's Ratio in Compression

The longitudinal and lateral deformation of the compression samples were
followed simultaneously by SR4-X extensometers developed by Plastics Research
Laboratory, Massachusetts Institute of Technology. The simultaneous data was
plotted automatically on an X-Y recorder.

Poisson's Ratio in Tension

The longitudinal deformation of the tensile specimen is recorded by a micro-
former type extensometer and automatically plotted on a load deflection recorder.

The lateral deformation was followed by an SR-4 extensometer provided by
Plastics Research Laboratory, Massachusetts Institute of Technology with the
data plotted automatically on a separate load deflection recorder.

Calculation of Compressive and Tensile Poisson's Ratios
The data for lateral deformation was plotted versus the simultaneous longitudinal

deformation on rectilinear graph paper. The slope of the plotted graph is equal
to Poisson's Ratio.

APPENDIX B

TEST PROGRAM - FIBERGLASS POLYESTER LAMINATES
STATISTICAL ANALYSIS OF TEST DATA

By Mr. C. Daniel
Consulting Engineering Statistician

This Appendix is presented for statisticians and gives an explanation of the procedures
used in obtaining the results, and a discussion of some of the problems encountered in
analyzing the test data.

The following types of laminates were evaluated:

M1 - Mat - 2 ounces per square foot

M2 - Woven Roving - 25-27 ounces per square yard

M3 - Cloth - 10 ounces per square yard

M4 - Mat with 1 ply of 10 ounce cloth on each face

M5 - Woven Roving with 1 ply of 10 ounce cloth on each face
Original Design and its Modifications

The plan first proposed was a Graeco-Latin Cube, sometimes also called a quarter
replicate of a 4* factorial experiment. The four factors were: Material, Fabricator,
Thickness and Testing Laboratory.

To this plan were later added:

Four thicknesses of material M1 to form a sequence of five thicknesses
for this material.

16 duplicate panels arranged in a Graeco-Latin square.
Duplicate specimens in every panel for every property.
Discussion of Original Design
The general plan used (quarter replicate of a 44) was well adapted to estimate differences
among materials, among fabricators, etc. It was not well adapted to measuring the differing

variabilities of the several materials.

The testing of duplicate panels was not properly randomized. Thus the use of the panel-
to-panel observed variability as a measure of error in the analysis of variance is excluded.

The use of duplicate specimens was largely unnecessary for the estimation of the smallest
component of variance. The interactions withangle(withina panel) generally check the speci-
men standard deviation quite closely with ample degrees of freedom. When the two do not
check, the angle interaction estimate is preferable.

IB APPENDIX B

Methods of Analysis

Inspection of the data indicated that, with a few obvious and correctible exceptions, the
differences among test laboratories were negligible. The balanced part of the data could then
be viewed as a full single replicate of a '43'' experiment, with four materials, four fabri-
cators and four thicknesses. But it was known beforehand that the several types of material
would not have the same random variation, nor would they respond in the same way to the
several factors.

The five materials used were grouped into three sets. M1 and M4, mat and cloth faced
mat were put in one group; M2 and M5, woven roving and cloth faced woven roving, were put
in another group; and finally M3, 10 ounce cloth, was put by itself in the third group. The
two pairs behaved sufficiently alike to justify this grouping.

Secondly, the largely isotropic M1 and M4 measurements for all three angles were
analyzed together. Although M2 and Md were by no means isotropic, it was possible to
analyze the 0 degrees and 90 degrees data together in all cases. For some properties the
45 degrees data could be included in the same analysis.

For M1 and M4, then, we have a split-plot analysis, with angle and its interactions as
sub-plot variables. Similarly for M2 and M5. A typical example is given below.

If the error distribution is normal, the cumulative distribution of the specimen ranges
should be the ‘half-normal ' distribution. The empirical cumulative distribution (called ecd
hereafter) should then fit a straight line on a half-normal grid. Sucha plot was made for
every set of duplicate specimen ranges. In some cases all ranges fell nicely on a straight
line. In most cases, however, a Small proportion of excessive values, not fitting the pattern
set by the rest, was found. The number of such coupon mavericks is shown in the columns
headed ''c'' and in lines ''e'', in the Table of Standard Deviations, Table B-1. These values
were excluded from later analysis. As an example the plot for M1 and M4 tensile strength
specimen ranges is shown in Fig. B-1.

A similar half-normal plot was made for the panel ranges in each grouping with similar
conclusions. But since there were so few duplicate comparable panels, it is not often possi-
ble to speak of the pattern set or of the assured reliability of the corresponding distribution.
The results are shown in the columns headed ''d"' in the Table of Standard Deviations, Table
B-1. Fig. B-2 is an example of such an ''ecd",

As a numerical example the analysis of tensile strengths for materials M1 and M4 for
all three angles is given below.

First a full MxFxTxA table, with two materials, four fabricators, four thicknesses,
three angles and with all subtotals and differences was made up.

From the table above, the analysis of variance, shown in Table B-2 was computed.
All computations were written down, and the FxT and MxF'xT discrepancies were
all computed for inspection. (For several other properties some bad values were
discovered from these discrepance tables).

There were clear material and fabricator differences and there was an MxA inter-
action. The latter was expected, being due to the anisotropy of the M4 cloth faced mat
compared to the isotropy of the M1 mat. The conclusions must reflect these differences.

APPENDIX B B-3

99.8 |——;_——— a 99.8 = a =
z 9966 — coe Z 9966 ae
5 99 | +— Of, fli 5 28 —S
= 98 ———_—_——_— = ot a 98 [ a=
% 96 t Scie — - 96 +— aE
z 90 | | ot = 90 7 + +
= | fe) | 5 lo
2 *° ) i zc mec
oO” 57.0) — Q- it ° 70 — — —
z 60 a 2 t = g 60 fi = ~
E 40 t =I =i = 40 fF ae t —+—
z 20 a — B29 99 =
b | ea | e
fe) 1 C 3 4 5 6 fe) 1 rs 3 4
COUPON RANGE IN 1000 PSI PANEL RANGE IN 1000 PSI
Fig. B-1. Tensile Strength, Bigs, B=2. “Lensile strength,
Coupon Range for Mat (M1) Panel Ranges for Mat (M1)
and Cloth Faced Mat (M4) and Cloth Faced Mat (M4)
Laminates - All Angles Included Laminates - All Angles Included

Thus in the body of this report, different values are shown for the two materials anda
different pattern is shown with angle for each material. Finally, the fabricators must
be distinguished from each other since one was able to produce material with a 3.6 ksi
consistently greater tensile strength than the other three fabricators,

The best estimate we can get of the error standard deviation among panels made at
different times will be obtained by pooling mean squares for MF, MT, FT and MFT
if these are all of comparable magnitude. Such is the case here. The combined Mean
Square, with 24 degrees of freedom, is 10.6. This Mean Square estimates %, + 5%

+ 6,/2. Wetake as an estimate of panel variance, then, 10.6/3 or 3,53, remembering
that this does include some within-panel variability (in the present case about 0.33
from 0.98/3), The corresponding standard deviation is 1.9.

Having checked on the near normality of the data (by the ecd plots of the specimens,
of the panels, and of the discrepancies computed in the analysis of variance) it
appeared safe to use published tolerance factors to estimate ranges below means;
(called L.T.R. for Lower Tolerance Ranges, in the tables of this report). These
values, subtracted from the averages estimated in each cell of the tables, give the
Lower Tolerance Limits (L.T.L.) shown. All tolerance limits are computed at
the 95 per cent level of confidence. They are also the limits that are expected to
be lower than 95 per cent of the population that corresponds, The multipliers used
were published by G. Lieberman, in the Journal of Industrial Quality Control for
April 1958. For the present example, at 95 per cent confidence, and for 95 per cent
coverage, with 24 degrees of freedom, the factor is found to be 2.30 and the lower
tolerance range is therefore 2.30 x 1.9 or 4.4.

Similar operations were carried through for fourteen properties and for three groups
of materials. With only a few exceptions, the data were readily interpretable. The
exceptions were in the data on compressive Poisson's ratio and in some of the per
cent water absorption figures, The irregularity of the data on these two properties,
at least for some of the materials, greatly diminishes the value of these sets.

TABLE B-1.

ESTIMATED STANDARD DEVIATIONS

MATERIALS |
M1 and M4 M2 and M5 M3
Property
0°, 45° & 90° 0° & 90° 45° o° & 90° 45°
c a d p fe a d p fe d Pp ic a d p d P

Tensile s 0.95 0.98 0.80 1.9 1 psig 2.5 1.9 0,82 Lei 1,0 1,0 2.7 1.0 2.2 | 0,7 1,25
Strength n| 148 48 23 24 72 24 8 21 36 4 32 60 9 8 f) 4 9

e 0 0 5 2 Hi 0 0 0 0 0 0 4 0 0 it) 0 0
Flexural s} 1,85 1,78 1,00 2,88] 1,85 2,98 2.50 4.42] 1,2 2,50 4,42] 2.0 1.8 0.6 2.0 | 0.6 2.0
Strength n 108 47 22 24 70 48 12 24 36 12 24 60 30 12 9 12 9

e le 0 0 4 0 | it) 0 0 0 0 0 i) 3 tt) 0 tt) i) i)
Compressive s 1.30 1.33 T7007 *3,54 | 1.2 1.40 1.9 4.36 | 0.4 0.4 2.33 | 0.91 1.78) “230
Strength n 170 48 24 24 12 24 8 24 36 4 24 60 18 9

iS 2 0 2 0 4 0 0 0 1 i) 0 4 0 0
Shear s 0.40 0.88 0.6 0.82 | 0,65 0.62 0.3 0.84 | 0.40 0,24 0.25 en5
Strength n 168 48 24 24 72 48 12 24 36 60 12 9
Perpendicular e 3 ) 0 0 1 0 2 tt) 2 0 0 0

0°, 45° & 90° 0°, 45° & 90°

Shear s 0,60 0,54 0,45 0.89] 0.55 0.59 0.35 0.86 0.45 0,71 0.45 0.88
Strength n 168 48 21 24 72 48 12 24 60 18 12 9
Parallel e 2 0 1 0 A 0 2 it) 1 0 2 0
Tensile s 0.13) 0.13 0.07 0.73 | 0.15 1 0.22 0.22 0.20 0,17 0,24
Modulus n 168 48 24 20 108 12 24 60 12 9

e 12 0 3 2 10 i} 4 4 2 0
Flexural s 0.045 0.065 0.07 0,12] 0,10 0.20 0.11 0.26 0,085 0,10 0.08 0,11
Modulus n 167 60 22 21 108 48 12 24 60 18 12 9

(3 7 0 0 i) 2 i) 1 0 1 0 2
Compressive s 8 9 8 26 8 14 12 26 6 10 12 9
Modulus n 132 34 15 12 19 34 9 ma 41 12 2 6
Per Cent (= 25 0 0 0 6 tt) tt) 0 6 (0) t iu
Tensile Ss 10.4 16 7 23 9 44 15 35 9 32 12 120
Poisson's Ratio n 168 34 24 24 101 48 12 12 55 30 12 9
Per Cent ie 8 0 2 0 6 0 0 0 4 0 i 0

+

Compressive s 12 18 4 18 14 8 56 46
Poisson's Ratio n 133 40 15 23 59 8 24 10
Per Cent e | <2 0 0 0 9 af 7 2
Specific s 0.006 .009 0,013 seal 0.013 0.012 0.016 0.05 0,055 0.035 =
Gravity n 108 48 25 20 108 62 12 23 60 12 15

e 3 0 2 2 2 0 0 1 1 2 0
Per Cent s 1.0 1,03 1.6 Zo Lek 0.92 1.0 2.8 0.045 0.46 0.4 0.69
Glass by n 168 62 24 21 108 62 12 18 60 30 12 9
Weight = 3 0 1 0 af oO 1 tt} 4 0 0 0
Per Cent s 0.6 0.64 Tao, 138 1d 0.59 1.3 2.7 0.4 1,02 0.4 0,78
Glass by n 168 48 24 24 108 48 12 21 60 18 12 9
Volume ee) 2 0 0 0 1 0 tt) 0 3 0 0 0

—

Per Cent Water s 6 a 1 21 15 38
Absorption n | 34 10 32 9
30 Days ie i) i} ) 0

s=

from duplicate panels

from duplicate coupons

estimated standard deviation

from angle-interactions, i.e. within panel

p - from panel-interactions, after removal of occasional, excessive values

n - number of degrees of freedom for each estimate

e - number of values judged excessive

TABLE B-2. SPECIMEN ANALYSIS OF VARIANCE FOR TENSILE STRENGTH OF MAT

(M1) AND CLOTH FACED MAT (M4) LAMINATES; ALL ANGLES INCLUDED

Source of Degrees of Sum of Mean Expected Values of

Variation Freedom Squares Squares Mean Squares

Materials (M)

Fabricator (F)

Thicknesses (T)

Angles (A)

Residual

Total

* All angles

B-6 APPENDIX B
Discussion of Method of Analysis

Omission of some valid data: Only the balanced data ignoring test laboratories was
included in the analyses variance. A more ambitious program might have tried to use
standard least-squares methods (multiple regression, including all two-factor interactions)
on the complete and unbalanced set of data. However the considerable number of bad values
turned up in the balanced analyses warns that mere insistence on including all data does not
in itself guarantee greater validity. Since the spotting of bad values is much more difficult
in unbalanced data, it is not considered likely that much information was lost by omitting
the panels that were added later to the balanced plan. (These were the four panels of M1
added to form a complete sequence of thicknesses, and the sixteen panels added for
"duplicates''), These omitted data were not entirely wasted, since the computed Lower
Tolerance Limits were compared with the lowest values in all the relevant data. In most
cases no values lay below the computed L.T,L. In some cases several values lay below,
usually coming from related panels, These values were judged bad, and therefore rejected.

Rejection of some duplicate data: Certain pieces of data were rejected on the grounds
that they did not fit the pattern clearly formed by the remaining pieces. This practice, while
it gave neater conclusions, is especially questionable since judgments on future variability
are to be made. Unless enough data is taken in future qualifying tests by fabricators, so
that similar rejection of out-of-pattern pieces can be made, then even wider limits of
tolerance will have to be used. Less than ten panels of each type and thickness of material
from a new and untried fabricator should not be considered. Schedules for producing such
test panels should be prepared with statistical caution.

Omission of test laboratories as a factor: Except for a mistake in one test laboratory's
measurements of specific gravity, no serious differences among laboratories were noted.
However a full analysis including test laboratories was not made. If there were any serious
laboratory differences, they would show in the analyses of variance made as MFT inter-
actions, Whenever MFT appeared larger than MF, MT or FT, a search was made to see if
the larger discrepancies were attributable to systematic laboratory differences. No such
attributions were made. There is of course always the chance that MFT was in fact inflated
by its confounding with the laboratories and that at the same time MF, MT and FT were
large for other reasons, If this unfortunate combination of circumstances was obtained in any
case, we would miss all four, and would report a gross over-estimate of the panel error.

Inappropriateness of Lieberman's Tolerance Limit Table: This table is exact when the
error distribution is normal, and when a simple mean value and its associated standard
deviation are to be used. This case is different since we usually have a mean value estab-
lished by a regression-equation, but with variance a known multiple of the error variance.
Professor Henry Scheffe has worked out the exact distribution required. It turns out to be
a case of the ''non-central t-distribution.'' Because of the spotty tabulation of this distribu-
tion in the literature, two checks of the exact distribution were made and compared with the
values corresponding from Liebermans' Table. The differences were negligible and so the
easier tabulation was used in all other cases,

Conclusions

One of the commonest conclusions from a large statistical study is that a great deal of
care must be used in planning future extensions, This conclusion holds here. Much has been
learned about the systematic differences among fabricators and among materials. Much
more needs to be learned about the cause and cure of the random variability of the materials,
especially among duplicate panels produced by the same fabricator,

APPENDIX B B-7

Considering the clear evidence presented by these data of systematic and important
differences between fabricators all of whom are experienced in handling these materials, it
will be important to develop qualifying tests for fabricators. If this is not done, the fabri-
cators with better panels will be discriminated against.

Accelerators, 4-13

Air bubbles, laminates, 5-9

Aircraft, passenger, 1-7
radome, 1-3

Appendage connections, 3-14
rudder, 3-14
shaft, 3-14

Applications, present, 1-2

Attachments, chain plate, 3-13
fittings, 3-12 to 3-14

Autoclave molding, 4-18, 4-19

Bag molding, 4-18
Ballast, attachment, strength criterion,
design loading, 2-25
keel, laminate connections to hull, 3-8
Behavior of laminates, 6-1 to 6-18
compressive and shear strains, design
example, 6-15 to 6-17
directional characteristics, 6-5 to 6-14
stress-strain relationship, 6-2 to 6-5
tensile physical properties, design ex-
ample, 6-14, 6-15
tensile stress, design example, 6-17,
6-18
Bending, composite laminate, design ex-
ample, 6-55 to 6-61
mat or isotropic laminate, design ex-
ample, 6-52 to 6-55
moments, summary, 6-190
stiffener and plate section, design ex-
ample, 6-75 to 6-79
stress, longitudinal, 2-11
Binders, 4-10
Bolted connections, 3-15, 3-16
edge and side distances and bolt spac-
ing (table), 3-16
fasteners, insert for, 3-21
laminate bearing strength (table),
3-16
Bolts, spacing, 3-15
table, 3-16
Bottom pressure, distribution factors,
2-17
maximum, for high speed planing
boats, 2-16
Bubbles, laminates, 5-9
Buckling, critical shear, cloth or ortho-
tropic panel, design example,
6-149, 6-150

Buckling, critical shear, mat or isotropic
panel, design example, 6-150, 6-
151
Buckling loads, critical, cloth laminates
(tables), all edges clamped, 6-
140 to 6-144
all edges simply supported, 6-125
to 6-129
loaded edges clamped, remaining
edges simply supported, 6-135
to 6-139
loaded edges simply supported,
remaining edges clamped, 6-
130 to 6-134
mat laminates (tables), all edges
clamped, 6-100 to 6-104
all edges simply supported, 6-85
to 6-89
loaded edges clamped, remaining
edges simply supported, 6-95
to 6-99
loaded edges simply supported,
remaining edges clamped, 6-
90 to 6-94
woven roving laminates (tables),
all edges clamped, 6-120 to
6-124
all edges simply supported, 6-
105 to 6-109
loaded edges clamped, remaining
edges simply supported, 6-115
to 6-119
loaded edges simply supported,
remaining edges clamped, 6-
110 to 6-114
Bulkhead, laminate connections to deck
or shell, 3-8, 3-9
strength criterion, design loading, 2-
De 295
Butt joints, 3-8

Cabin, laminate connections to deck, 3-9
Catalysts, 4-12
Chain plate attachments, 3-13
Chemical resistance, 5-37, 5-38
Cloth laminates, compressive and shear
strains in, design example, 6-15 to
6-17
compressive stress versus slenderness
ratio for, 6-39
critical buckling loads (tables), all
edges clamped, 6-140 to 6-144

Index

Cloth laminates, critical buckling loads
(tables), all edges simply sup-
ported, 6-125 to 6-129

loaded edges clamped, remaining
edges simply supported, 6-135 to
6-139
loaded edges simply supported, re-
maining edges clamped, 6-130
to 6-134
plates, laterally loaded (table), 6-164
to 6-168
slenderness ratios for (table), 6-42
under tensile load, design example,
6-22
Cloth reinforcements, 4-7 to 4-9
advantages, 4-8
disadvantages, 4-9
plain weave, 4-7
satin weaves, 4-7
unidirectional, 4-8
Coast Guard, U.S., regulations, 2-24
Column characteristics of laminates, 6-
34 to 6-48
critical buckling load, 6-36
design examples, 6-43 to 6-48
effective length, 6-35
slenderness ratio, 6-36
compressive stress versus, 6-37 to
6-39
tables, 6-40 to 6-42
Combination reinforcements, 4-9
Composite laminates, bending, design ex-
ample, 6-55 to 6-61
compressive load in, design example,
6-46 to 6-48
hull construction, 2-7, 2-8
orthotropic, tension, 6-22, 6-23
design examples, 6-23 to 6-33
Compression, 6-33 to 6-48
column characteristics, 6-34 to 6-43
design examples, 6-43 to 6-48
flat rectangular plates loaded in, 6-79
to 6-84
design example, 6-145 to 6-147
tables, 6-85 to 6-144
Poisson’s ratio in, test procedure, A-1
sandwich construction, 6-190, 6-191
short members, 6-33
design example, 6-33
woven roving laminate, design exam-

ple, 6-44 to 6-46

Compressive elastic constants, 6-9, 6-11,
6-13
Compressive load, critical, composite lam-
inate, design example, 6-46 to
6-48
mat laminate, design example, 6-
43, 6-44
Compressive modulus, 6-6
Compressive strain, design example, 6-15
to 6-17
Compressive strength, laminates, 5-14
modulus (table), 5-23
Poisson’s ratio (table), 5-23
table, 5-22
Compressive stress, 2-10, 6-8
slenderness ratio versus, cloth-polyester
laminates, 6-39
mat-polyester laminates, 6-37
woven roving-polyester laminates,
6-38
Connections, appendage, 3-14
rudder, 3-14
shaft, 3-14
bolted, laminate bearing strength
(table), 3-16
fasteners, mechanical, 3-15 to 3-21
bolted, 3-15, 3-16
threaded, 3-17 to 3-21
fitting, 3-10 to 3-14
loads, pulling, 3-12 to 3-14
pushing, 3-10 to 3-12
laminate, 3-2 to 3-9
bulkhead or frame to deck or shell,
3-8, 3-9
cabin trunk to deck, 3-9
deck to shell, 3-2 to 3-5
gunwale, 3-5
keel ballast to hull, 3-8
repair joint, 3-8
shell to keel, 3-5 to 3-8
outfit, 3-14, 3-15
Constants, compressive elastic, 6-9, 6-11,
6-13
physical, 6-8
tensile elastic, 6-9, 6-10, 6-12
Construction, hull, 2-2 to 2-8
composite, 2-7, 2-8
fiberglass, wood frame and plank,
2-2
sandwich, 2-6, 2-7, 6-180 to 6-191
single skin, with framing, 2-3 to 2-6
unstiffened, 2-2, 2-3
Contact molding, 4-17
Core materials, 2-7
low density (see Low density core
materials)
Crazing, shop practice, 5-34
Creep, laminates, 5-27 to 5-31
Crew boat, offshore, 1-6
Crossing, knife edge, 3-24, 3-25
Cruiser, cabin, hull design example,
2-59 to 2-67
design, 2-61 to 2-67
dimensions, 2-59

INDEX

Cruiser, cabin, scantlings, summary, 2-
59 to 2-61
Cures, heat, 4-17
room temperature, 4-17
shrinkage, shop practice, 5-35

Data presented, 1-7 to 1-9
Day cruiser, 1-4
Deborine hull, 2-4
Deck, laminate connections, to bulkhead
or frame, 3-8, 3-9
to cabin trunk, 3-9
to shell, 3-2 to 3-5
strength criterion, design loading, 2-
23, 2-24
Deflection, cantilever sandwich beam,
design example, 6-182 to 6-184
summary, 6-189
Delaminations, shop practice, 5-34
Design details, 3-1 to 3-25
connections, appendage, 3-14
fitting, 3-10 to 3-14
laminate, 3-2 to 3-11
outfit, 3-14, 3-15
fasteners, mechanical, 3-15 to 3-21
loads, application, 3-1, 3-2
trouble causing, 3-21 to 3-25
Die molding, matched, 4-19
Directional characteristics, 6-5 to 6-14
Directional properties of laminates, 5-1,
5-2

Elasticity, modulus, design example, 6-
29, 6-30
Elongation, composite laminate at angle
to warp, design example, 6-30 to
6-33
various ]aminates, design example, 6-
23 to 6-25
Engine bearers, fitting connections, 3-10
Engine mounts, fitting connections, 3-10
Engineering properties of laminates (see
Properties of laminates)
Environment factors affecting engineer-
ing properties, 5-35 to 5-38
chemical resistance, 5-37, 5-38
loading, long term, 5-38
water immersion, 5-35, 5-36
weathering, 5-36, 5-37
Epoxy resins, 4-12
Equivalent laminate, 6-57
Express carrier, 1-4

Factor of safety, 6-18, 6-19
Fairwater, submarine, 1-6
Fasteners, bolted, insert for, 3-21
mechanical, 3-15 to 3-21
bolted connections, 3-15, 3-16
threaded, 3-17 to 3-21
direction for, right and wrong,
3-17
holding forces (tables), 3-17, 3-
19, 3-20
insert for, 3-21

Fasteners, mechanical, threaded, loading
directions, 3-17
screws, 3-14, 3-15
tables for determining, 3-19, 3-
20
Fatigue, laminates, 5-26, 5-27
Fatigue strength, low density core mate-
rials, 5-40
Fillers, 4-13
Finishes, 4-10
Fitting connections, 3-10 to 3-14
pulling loads, 3-12 to 3-14
chain plate attachments, 3-13
pushing loads, 3-10 to 3-12
engine mounts, 3-10
mast steps, 3-10 to 3-12
Fittings, attachment, 3-12 to 3-14
Flagstaff fittings, connections, 3-14
Flexural modulus, 6-8
Flexural strength, 5-14
creep, 5-27, 5-29, 5-30
fatigue, 5-27
low density core materials, 5-39
modulus (table), 5-21
table, 5-20
Flexural stress, 6-8
Flexure, 6-48 to 6-79
plates, simple one-way, 6-48 to 6-61
design examples, 6-52 to 6-61
moment of inertia, 6-49 to 6-51
section moduli (graphs), 6-49 to
6-51
sandwich construction, 6-181, 6-182
design examples, 6-182 to 6-191
stiffener and plate construction, 6-61
to 6-79
Floor boards, connections, 3-14
Foam, plastic, stiffener and sandwich
cores, 4-13 to 4-15
Foreign inclusions in laminates, shop
practice, 5-35
Frame, laminate connections to deck or
shell, 3-8 to 3-9
Framing, hull, side, impact pressures,
2-19, 2-20
single skin with, 2-3 to 2-6
strength criterion, design loading,
2-13 to 2-20

Glass content of laminates, 5-9
table, 5-12
Gunwale, laminate connections, 3-5
strength criterion, design loading, 2-
24

Hard spots, 3-8, 3-22, 3-23

Heat cure, 4-17

Honeycomb, stiffener and sandwich

cores, 4-15

Hooke’s Law, 6-34, 6-36

House, large, 1-3

Hull design, 2-1 to 2-69
considerations, basic, 2-11, 2-12
construction, types, 2-2 to 2-8

Hull design, design loading, 2-12 to
2-25
ballast attachment, 2-25
bulkheads, 2-24, 2-25
decks, 2-23, 2-24
gunwale, 2-24
shell and framing, 2-13 to 2-20
transom, 2-21 to 2-23
examples, 2-26, 2-67
cabin cruiser, 2-59 to 2-67
rowboat, 2-26 to 2-29
runabout, 2-35 to 2-50
sailboat, cruising, 2-50 to 2-59
open, 2-29 to 2-35
laminate connections to keel ballast,
3-8
laminates, selection, 2-8 to 2-11

Impact pressure, 2-14 to 2-20
Impact strength, laminates, 5-14 to 5-16
Impact test equipment, 5-15
Impact values, 5-15, 5-16
Inertia (see Moment of inertia)
Isotropic laminates, bending, design ex-
ample, 6-52 to 6-55
tensile strength for, 6-6
tension, 6-19 to 6-21

Keel, laminate connections to shell, 3-5
to 3-8

Laminates, 6-1 to 6-191
bearing strength (table), 3-16
behavior, 6-1 to 6-18
composite (see Composite laminates)
compression, 6-33 to 6-48
directional characteristics, 6-5 to 6-14
equivalent, 6-57
flexure, 6-48 to 6-79
foreign inclusions in, 5-35
isotropic (see Isotropic laminates)
orthotropic (see Orthotropic lami-
nates)
plates (see Plates)
properties (see Properties of lami-
nates)
safety, factor of, 6-18, 6-19
selection, 2-8 to 2-11
stress-strain relationship, 6-2 to 6-5
tension, 6-19 to 6-33
type A, 2-8, 2-9
type B, 2-9
type C, 2-9
Landing craft, navy, 1-4
Lifeboat, 1-4, 2-1
Loadings, application of loads, 3-1, 3-2
buckling loads (see Buckling loads)
considerations, basic, 2-11, 2-12
design, 2-12 to 2-25
safety factors and (table), 2-25
strength criterion, 2-13 to 2-25
ballast attachment, 2-25
bulkheads, 2-24, 2-25
decks, 2-23, 2-24

INDEX

Loadings, design, strength criterion,
gunwale, 2-24
shell and framing, 2-13 to 2-20
transom, 2-21 to 2-23
vibration criterion, 2-12, 2-13
direction of, right and wrong, 3-1,
3-2
long term, 5-38
pulling, 3-12 to 3-14
chain plate attachments, 3-13
pushing, 3-10 to 3-12
engine mounts, 3-10
mast steps, 3-10 to 3-12
uniform (see Uniform load)
Low density core materials, properties,
5-38 to 5-41
flexural strength retention, 5-39
shear fatigue strength, 5-40
shear strength retention, 5-40
table, 5-41
tensile strength retention, 5-39

Mast steps, fitting connections, 3-10 to
3-12
Matched die molding, 4-19
Materials, 1-1, 4-1
core, 2-7
(See also Low density core materials)
Mat laminates, bending, design example,
6-52 to 6-55
compressive stress versus slenderness
ratio for, 6-37
critical buckling loads (tables), all
edges clamped, 6-100 to 6-104
all edges simply supported, 6-85 to
6-89
loaded edges clamped, remaining
edges simply supported, 6-95 to
6-99
loaded edges simply supported, re-
maining edges clamped, 6-90 to
6-94
critical compressive load, design ex-
ample, 6-43, 6-44
plates, laterally loaded (table), 6-154
to 6-158
reinforcement, 4-5, 4-6
slenderness ratios for (table), 6-40
tensile physical properties, design ex-
ample, 6-14, 6-15
under tensile load, design example,
6-20
Mechanical properties of laminates (see
Properties of laminates)
Modulus, compressive, 6-8
compressive strength (table), 5-23
elasticity, design example, 6-29, 6-30
flexural, 6-8
flexural strength (table), 5-21
rigidity, 6-8
shear, 6-8
tensile, 6-8
tensile strength (table), 5-18

Molding methods, 4-16 to 4-40
autoclave, 4-18, 4-19
bag, 4-18
contact, 4-17
cures, heat, 4-17
room temperature, 4-17
matched die, 4-19
reinforcements, properties and, rela-
tionship between, 5-3
table, 5-4
sprayed reinforcement and resin, 4-19,
4-20
Moment of inertia, flexure, one-way
plates, simple, 6-49 to 6-51, 6-58
stiffener and plate construction, 6-61
to 6-74
Motor support area, dimensions (table),
2-21

Orthotropic laminates, 6-7
characteristics, 6-6
composite, design examples, 6-23 to
6-33
tension, 6-22, 6-23
tensile strength for, 6-6
tension, 6-21, 6-22
design examples, 6-21, 6-22
Outboard Boating Club of America, 2-21
Outfit connections, 3-14, 3-15

Patrol boat, Coast Guard, 1-6
Physical properties of laminates (see
Properties of laminates)
Pigments, 4-13
Planing boats, bottom pressure for, maxi-
mum, 2-16
Plate construction, flexure, 6-61 to 6-79
moment of inertia, 6-61 to 6-74
section moduli, 6-61 to 6-74
Plates, flat rectangular, 6-79 to 6-180
loaded in edgewise compression,
6-79 to 6-84
design example, 6-145 to 6-147
tables, 6-85 to 6-144
loaded laterally, 6-151 to 6-153
cloth, 6-164 to 6-168
design examples, 6-169 to 6-180
mat (table), 6-154 to 6-158
tables, 6-154 to 6-168, 6-174,
6-175
woven roving, 6-159 to 6-163
loaded in uniform shear, 6-147 to
6-149
design examples, 6-149 to 6-151
simple one-way, flexure, 6-48 to 6-61
design example, 6-52 to 6-61
moment of inertia, 6-49 to 6-51
section moduli (graphs), 6-49 to
6-51
Poisson’s ratio, compressive strength, 5-14
table, 5-24
test procedure, A-1
tensile strength, 5-14
table, 5-19

Poisson’s ratio, tension, test procedure,
A-1
Polyester resins, 4-11, 4-12
accelerators, 4-13
air cured, 4-12
catalysts, 4-12
flexible, 4-11
isophthalic, 4-11
rigid, 4-11
self-extinguishing, 4-11, 4-12
semi-rigid, 4-11
stabilizers, 4-13
Pontoon camel float, 1-6
Preimpregs, 4-9
Pressure, bottom, distribution factors, 2-
17
maximum, high speed planing boats,
2-16
impact, 2-14 to 2-20
Propeller shaft, connection, 3-14
Properties of laminates, 5-1 to 5-41
core materials, low density, 5-38 to
5-41
table, 5-41
directional, 5-1, 5-2
factors affecting, 5-33 to 5-38
environment, 5-35 to 5-38
shop practice, 5-34, 5-35
mechanical, 5-14 to 5-31
compressive strength, 5-14
tables, 5-22 to 5-24
creep, 5-27 to 5-31
fatigue, 5-26, 5-27
flexural strength, 5-14
tables, 5-20, 5-21
impact strength, 5-14 to 5-16
rigidity, 5-31
shear strength, 5-14
table, 5-25
table, 5-32
tensile strength, 5-14
tables, 5-17 to 5-19
physical, 5-9 to 5-13
glass content, 5-9
table, 5-12
specific gravity, 5-9
table, 5-12
table, 5-32
thickness, 5-9
table, 5-10
void content, 5-9 to 5-13
table, 5-13
weight, 5-9
table, 5-11
reinforcements, and molding methods,
5-3
table, 5-4
test program, 5-3 to 5-9
data, statistical analysis, 5-6, 5-7,
5-33
fabrication method, 5-5, 5-31
laminates, types, 5-5, 5-31
main variables, results of investiga-
tion, 5-7, 5-8

INDEX

Properties of laminates, test program,
materials, 5-5, 5-31
procedures, 5-6, 5-33
purpose, 5-3 to 5-5, 5-31
supplementary, 5-31 to 5-33
tables, discussion of, 5-8, 5-9
Purpose of manual, 1-9

Radome, aircraft, 1-3
Re-entrant corner, 3-24
Reinforcements, 4-1 to 4-10
binders, 4-10
chopped strands, 4-6, 4-7
cloth, 4-7 to 4-9
advantages, 4-8
disadvantages, 4-9
plain weave, 4-7
satin weaves, 4-7
unidirectional, 4-8
combinations, 4-9
finishes, 4-10
mat, 4-5, 4-6
and molding methods, relationship be-
tween, 5-3
table, 5-4
preforms, 4-6
preimpregnated, 4-9
rovings, 4-2 to 4-5
spun, 4-4, 4-5
unidirectional, 4-2
woven, 4-2 to 4-4
sizes, 4-10
sprayed, 4-19, 4-20
table, 4-3
Resins, 4-10 to 4-13
accelerators, 4-13
catalysts, 4-12
dryness, shop practice, 5-34
epoxy, 4-12
polyesters (see Polyester resins)
richness, shop practice, 5-34
sprayed, 4-19, 4-20
stabilizers, 4-13
Rigidity, laminates, 5-31
modulus, 6-8
Rocket, Thor-Able, 1-7
Room temperature cure, 4-17
Rovings, 4-2 to 4-5
spun, 4-4, 4-5
unidirectional, 4-2
woven (see Woven roving)
Rowboat, hull design example, 2-26 to
2-29
design, 2-28, 2-29
dimensions, 2-26
scantlings, summary, 2-28
Rudder, connection, 3-14
Runabout, high speed, 1-4
hull design example, 2-35 to 2-50
design, 2-37 to 2-50
dimensions, 2-35
scantlings, summary, 2-37

Safety, design loads and factors of
(table), 2-25
factor of, 6-18, 6-19
Sailboat, cruising, bottom shell laminate
for, 2-20, 2-21
hull design example, 2-50 to 2-59
design, 2-52 to 2-59
dimensions, 2-50
scantlings, summary, 2-50 to 2-
52
open, hull design example, 2-29 to
2-35
design, 2-31 to 2-35
dimensions, 2-29
scantlings, summary, 2-31
Sandwich construction, 6-180 to 6-191
cantilever beam, deflection, design ex-
ample, 6-182 to 6-184
stresses in, design example, 6-184
to 6-189
compression, edgewise, 6-190, 6-191
flexure, 6-181, 6-182
design example, 6-182 to 6-191
hull construction, 2-6, 2-7
Sandwich cores, 4-13 to 4-16
foam, plastic, 4-14, 4-15
honeycomb, 4-15
spheres, plastic, 4-16
wood, 4-14
Screw fasteners, 3-14, 3-15
Section moduli, flexure, simple one-way
plates, 6-49 to 6-51
stiffener and plate construction, 6-61
to 6-74
Shaft, propeller, connection, 3-14
Shear, uniform, plates loaded in, 6-147
to 6-149
design examples, 6-149 to 6-151
Shear modulus, 6-8
Shear strain, design example, 6-15 to
6-17
Shear strength, core materials, low den-
sity, 5-40
laminates, 5-14
table, 5-25
test procedure, A-1
Shear stress, 2-6
Shell, laminated connections, to bulk-
head or frame, 3-8, 3-9
to deck, 3-2 to 3-5
to keel, 3-5 to 3-8
strength criterion, design loading, 2-
13 to 2-20
Shop practice, 5-34, 5-35
crazing, 5-34
delaminations, 5-34
foreign inclusions in laminates, 5-35
resin dryness, 5-34
resin richness, 5-34
shrinking, curing, 5-35
voids, 5-34
washing, 5-34
wrinkles, 5-34

Shrinkage, curing, 5-35
thermal, 5-35
Side framing, impact pressures, 2-19, 2-
20
Single skin hull construction, with fram-
ing, 2-3 to 2-6
unstiffened, 2-2, 2-3
Sizes, 4-10
Slenderness ratio, 6-36
compressive stress versus, 6-37 to 6-39
tables, 6-40 to 6-42
Sloop, Bounty II, 1-5
Specific gravity of laminates, 5-9
table, 5-12
Spheres, plastic, stiffener and sandwich
cores, 4-16
Spray gun, 4-19, 4-20
Spun roving, 4-4, 4-5
Stabilizers, 4-13
Stiffeners, 2-5, 4-13 to 4-16
bending, design example, 6-75 to 6-79
flexure, 6-61 to 6-79
moment of inertia, 6-61 to 6-74
section moduli, 6-61 to 6-74
woven roving, half-round, 6-69 to
6-74
hat, 2-5, 6-61 to 6-68
foam, plastic, 4-14, 4-15
half-round, 2-5, 6-69 to 6-74
honeycomb, 4-15
spheres, plastic, 4-16
wood, 4-14
Strain, compressive, design example, 6-
15 to 6-17
curves, 6-3 to 6-5
shear, design example, 6-15 to 6-17
stress relationship, 6-2 to 6-5
Strands, chopped, 4-6, 4-7
Strength, bearing (table), 3-16
compressive, 5-14
tables, 5-22 to 5-24
criterion, design loading, 2-13 to 2-25
ballast attachment, 2-25
bulkheads, 2-24, 2-25
decks, 2-23, 2-24
gunwale, 2-24
shell and framing, 2-13 to 2-20
transom, 2-21 to 2-23
fatigue, low density core materials,
5-40
flexural, 5-14
creep, 5-27, 5-29, 5-30
fatigue, 5-27
low density core material, 5-39
modulus (table), 5-21

table, 5-20
impact, 5-14 to 5-16
shear, 5-14
core material, 5-40
table, 5-25

test procedure, A-1
tensile (see Tensile strength)
Stress, cantilever sandwich beam, design

example, 6-184 to 6-191

INDEX

Stress, compressive, 2-10, 6-8
slenderness ratio versus, 6-37 to
6-39
concentrations, 3-23, 3-24
in bonded joints, 3-24
table, 3-25
curves, 6-3 to 6-5
flexural, 6-8
shear, 2-6
strain relationship, 6-2 to 6-5
tensile, 2-10, 6-8
design example, 6-17, 6-18
Submarine, Fairwater, 1-6

Sunlight, direct, 5-36

Technical status, 1-2
Tensile elastic constants, 6-9, 6-10, 6-12
Tensile load, ultimate, design examples,
6-25 to 6-29
Tensile modulus, 6-8
Tensile physical properties, design ex-
ample, 6-14, 6-15
Tensile strength, 3-1, 5-14
core materials, low density, 5-39
creep, 5-27 to 5-29
fatigue, 5-26
isotropic and orthotropic materials,
distribution, 6-6
modulus (table), 5-18
Poisson’s ratio (table), 5-19
table, 5-17
Tensile stress, 2-10, 6-8
design example, 6-17, 6-18
Tension, 6-19 to 6-33
isotropic laminates, 6-19 to 6-21
design examples, 6-20, 6-21
orthotropic laminates, 6-21, 6-22
composite, 6-21, 6-22
design examples, 6-21, 6-22
Poisson’s ratio in, test procedure, A-1
Test equipment, impact, 5-15
Test procedures, 5-6, 5-33, A-1!
Test program to obtain properties, 5-3 to
5-9, B-1 to B-7
data, statistical analysis, 5-6, 5-7, 5-33
fabrication method, 5-5, 5-31
laminates, types, 5-5, 5-31
main variables, results of investigation,
5-7, 5-8
materials, 5-5, 5-31
procedures, 5-6, 5-33
purpose, 5-3 to 5-5, 5-31
supplementary, 5-31 to 5-33
tables, discussion of, 5-8, 5-9
Thermal shrinkage, 5-35
Thickness of laminates, 5-9
table, 5-10
Thor-Able rocket, 1-7
Threaded fasteners, 3-17 to 3-21
direction for, right and wrong, 3-17
holding forces, 3-17
tables, 3-19, 3-20
insert for, 3-21

Threaded fasteners, loading directions,

3-17
tables for determining, 3-19, 3-20

use of, 3-18

Through bolting, 3-21

Transom, strength criterion, design load-
ing, 2-21 to 2-23

Treads, rubber, connections, 3-14

Truck cab, 1-3

Ultra-violet rays, weather deterioration,
5-36
Unidirectional roving, 4-2
Uniform load, cloth, design example, 6-
169
woven roving, design example, 6-169
to 6-180
Utility boat, 1-6

Vibration criterion, design loading, 2-
1252-13
Void content of laminates, 5-9 to 5-13
shop practice, 5-34
table, 5-13

Washing, shop practice, 5-34
Water immersion, 5-35, 5-36
Weathering, 5-36, 5-37
Weight of laminates, 5-9
table, 5-11
Wet strength retention, 5-35, 5-36
table, 5-37
Whale boat, navy, 1-4
Windshields, connections, 3-14
Wood stiffener and sandwich cores, 4-14
Woven roving, 4-2 to 4-4
compression in, design example, 6-44
to 6-46
without buckling, design example,
6-33, 6-34
compressive stress versus slenderness
ratio for, 6-38
critical buckling loads (tables), all
edges clamped, 6-120 to 6-124
all edges simply supported, 6-105
to 6-109
loaded edges clamped, remaining
edges simply supported, 6-115
to 6-119
loaded edges simply supported, re-
maining edges clamped, 6-110 to
6-114
half-round stiffeners, 6-69 to 6-74
hat stiffeners, flexure, 6-61 to 6-68
plates, laterally loaded (table), 6-159
to 6-163
slenderness ratios for (table), 6-41
tensile strength for, design example,

6-17, 6-18
under tensile load, design example,
6-21

Wrinkles, shop practice, 5-34

Yawl, 1-5