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TECHNICAL REPORT CIVIL ENGINEERING LABORATORY
Naval Construction Battalion Center, Port Hueneme, California 93043
DESIGN FOR IMPLOSION OF CONCRETE CYLINDER STRUCTURES UNDER HYDROSTATIC LOADING
By
Harvey H. Haynes
August 1979 a ed by i FACILITIES ENGINEERING COMMAND
NO,
‘or public release; distribution unlimited.
Ret
Unclassified
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REPORT DOCUMENTATION PAGE
T. REPORT NUMBER 2, GOVT ACCESSION NO| 3. RECIPIENT'S CATALOG NUMBER TR-874 DN04405 3 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED DESIGN FOR IMPLOSION OF CONCRETE CYLINDER Not final; Jul 78 - Mar 79 STRUCTURES UNDER HYDROSTATIC LOADING
6. PERFORMING ORG. REPORT NUMBER
7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)
Harvey H. Haynes
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK CIVIL ENGINEERING LABORATORY : Hee ae hae cami Naval Construction Battalion Center : 3.1610-1 Port Hueneme, California 93043
11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE Naval Facilities Engineering Command August 1979
Alexandria, Virginia 22332 aoe OlF PINSIES
14. MONITORING AGENCY NAME & ADDRESS/if different from Controlling Office) 15. SECURITY CLASS. (of this report)
Unclassified
1Sa. DECL ASSIFICATION/ DOWNGRADING SCHEDULE
16. DISTRIBUTION STATEMENT (of this Report)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)
18. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on reverse side if necessary and identify by block number)
Concrete structures, pressure-resistant structures, concrete cylinders, implosion, submerged
concrete structures, undersea structures, unreinforced concrete, hydrostatic loading, design guidelines, buckling.
20. ABSTRACT (Continue on reverse side if necessary and identify by block number)
This report presents updated design guides for both thick- and thin-walled concrete cylinder structures under hydrostatic loading. The design approach for thick-walled cylinders has been changed from that described in previous work to a semi-empirical basis; improve- ments in implosion strength on the order of 10% are found. A test ona thick-walled 10-ft-diam (3.05-m) structure loaded to failure in the ocean is reported. A major change in the guides is
continued
FORM ps DD , jan 73 1473 = EDITION OF 1 Nov 65 1S OBSOLETE Unclassified
Ww neu nA
0 0301 0
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20. Continued
for thin-walled cylinders, where new data on 15 relatively large-scale specimens are reported. Design guides for thin-walled cylinders show an increase in implosion strength ranging from 0% to 35%, depending on the structures’ t/Dg and L/D, ratios, from that reported previously.
Civil Engineering Laboratory
DESIGN FOR IMPLOSION OF CONCRETE CYLINDER STRUCTURES UNDER HYDROSTATIC LOADING,
by Harvey H. Haynes
TR-874 85 pp illus Aug 1979 Unclassified
1. Concrete cylinders 2. Hydrostatic loadings I. 3.1610-1
This report presents updated design guides for both thick- and thin-walled concrete cylinder structures under hydrostatic loading. The design approach for thick-walled cylinders has been changed from that described in previous work to a semi-empirical basis; improve- ments in implosion strength on the order of 10% are found. A test on a thick-walled 10-ft- diam (3.05-m) structure loaded to failure in the ocean is reported. A major change in the guides is for thin-walled cylinders, where new data on 15 relatively large-scale specimens are reported. Design guides for thin-walled cylinders show an increase in implosion strength rang- ing from 0% to 35%, depending on the structures’ t/D, and L/D, ratios, from that reported previously.
Unclassified SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)
INTRODUCTION .
Background O\SNCEDE 3 o o o a Description of Tests
DESIGN FOR IMPLOSION Thick-Walled Cylinders
Thin-Walled Cylinders Factor of Safety SUMMARY . CONCLUSIONS ACKNOWLEDGMENTS REFERENCES
APPENDICES
CONTENTS
A - Thick-Walled Cylinder Tests . B - Thin-Walled Cylinder Tests
LIST OF SYMBOLS
24
29 39
81
b
INTRODUCTION
Background
In the mid-1960's ocean engineering attracted considerable interest in research and development on providing man with the technology to work in the deep ocean. Research on undersea concrete structures was initiated at this time, and exploratory test results showed much promise (Ref 1) for concrete structures at depths to 3,000 feet (1,000 meters). The economic payoff of the research was that massive undersea concrete structures would cost about one-tenth that of metallic structures.
For the first several years, research was directed solely to con- crete spheres, but tests on cylinders started about 1970. The early cylinder models had an outside diameter of 16 inches (406 mm). Param- eters such as cylinder length, wall thickness, end closure conditions, and concrete compressive strength (Ref 2 to 4) were investigated and studied.
The North Sea oil boom occurred in the early 1970's, and the first offshore concrete platform, called Ekofisk, was built. With the success- ful installation of Ekofisk in a water depth of 270 feet (90 meters), industry ordered additional concrete structures for oil drilling and production. A dynamic development period ensued during which it became apparent that knowledge on the behavior of pressure-resistant concrete structures was substantially lacking.
In an attempt to make existing data known, Civil Engineering Laboratory (CEL) test results were distributed widely (Ref 5 to 8). However, the early work on cylinder structures was quite tentative
because of limited data on thin-walled cylinders.
A major oil company proposed a test program on large-scale, thin-walled concrete models. This proposal eventually led to a joint industry-Navy test program carried out at CEL.
During this period another important test was conducted at CEL on a large thick-walled concrete cylinder structure. The structure, called SEACON I, was part of an integrated seafloor engineering experiment to demonstrate capability in constructing operational facilities in the ocean (Ref 9). The structure was built in 1972, placed in the ocean at 600 feet (180 meters) for 10 months, and then retrieved. After being on "display" for several years, it was tested to failure in the ocean in 1976
to determine its implosion strength.
Objective
This report presents updated design guides for implosion of con- crete cylinders. The guides are based on the test results from the thick-walled, SEACON I, cylinder test (Appendix A) and from the thin-walled cylinder tests (Appendix B). The approach to design is similar to that already presented in Reference 8. However, the new data are superior to that presented previously, especially for the thin- walled models. The updated guides for thin-walled cylinders allow such structures to operate at considerably deeper depths than indicated in
the past guides.
Description of Tests
Thick-Walled Structures. The SEACON I structure was a rein- forced concrete cylindrical hull having hemispherical end closures. The overall structure length was 20 feet (6.1 meters); outside diameter, 10.1 feet (3.08 meters); and wall thickness, 9.5 inches (241 mm). Steel reinforcement of 0.7% by area was used in both the hoop and axial directions. At the time of the implosion test the concrete compressive
strength was 10,470 psi.
During the long-term loading test of the structure at 600 feet, results were obtained on the structure's response from initial loading and creep. Although the data are interesting, the pressure load was relatively low, only 14% of its ultimate strength. Of more significance was the implosicn test where the structure was lowered into the ocean until failure. Complications occurred during this test which precluded obtaining structural response data, but the implosion pressure was successfully obtained. This test with its results is presented in Appen- dix A.
Thin-Walled Structures. The thin-walled cylinder test program
encompassed 15 unreinforced concrete specimens, whose dimensions were: 134 inches (3.4 meters) length, 54 inches (1372 mm) OD, and 1.31, 1.97, or 3.39 inches (33, 50, or 86 mm, respectively) wall thick- ness. Two different boundary conditions were modeled, a free and a simple support, in order that cylinders of two effective lengths could be studied. The concrete compressive strength ranged between a nominal 7,000 to 8,000 psi (48 to 55 MPa).
Structural deformations were monitored by recording radial dis- placements around the circumference of the cylinder. Accurate initial and deflected cross-sectional shapes were obtained which showed the progressive development of out-of-roundness.
An analytical study using actual material properties and geometric conditions was conducted. A finite-element analysis with an advanced constitutive material model was used.
This test program on thin-walled cylinders is presented in Appen- dix B.
DESIGN FOR IMPLOSION
Thick-Walled Cylinders
The design approach for unreinforced, thick-walled cylinders is
based on an average stress distribution across the wall of the cylinder
at implosion. Near implosion, the inelastic behavior of concrete along with plasticity and creep impart a stress distribution across the wall that is more closely modeled by a uniform stress distribution than by an elastic (Lamé) stress distribution. A uniform stress at implosion is
expressed by
Zo)
Gill ee = (1)
where OF = wall stress at implosion Me implosion pressure Ro = outside radius t = average wall thickness
The wall stress at implosion, OF can be expressed as the ultimate
compressive strength of concrete multiplied by a strength factor. oO. = KO f° (2)
where kK. = strength factor for cylinder structures under hydrostatic loading
Be = uniaxial compressive strength of concrete
The term K, was determined empirically. Figure 1 shows kK, as a function of length-to-outside-diameter ratio, L/D); for cylinders of various wall-thickness-to-outside-diameter ratios, t/D,.
For cylinders under hydrostatic loading, the wall is stressed biaxially in compression on the inside surface and triaxially in compres- sion at all other locations. The two major stresses are in the hoop and axial direction where the hoop stress is about twice the magnitude of the axial stress. The third, and smallest, component of stress acts radially. If the concrete is considered biaxially loaded, then the hoop-
to-axial stress ratio of 2 is known to increase the compressive strength
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of concrete by a factor of about 1.25 I (Ref 10). Therefore, Kk, values for the cylinder test specimen of this program should show a value on the order of 1.25. As a minimum, kK, should be 1.0.
Figure 1 shows that short cylinders, those of L/D, <1, hada kK, around 1.25. However, longer cylinders showed a K, on the order of 1.0. The decrease in kK, was probably due to specimen imperfection. The short specimens were also imperfect, but end-closure effects restrained the cylinder wall. At L/D, of 2.0 the end-closure effects were diminished.
An average K, value of 0.89 was observed at L/D, = 4. It was speculated that some unknown fabrication or testing problem existed for the cylinders of this length in comparison to the other specimens.*
For design purposes, a K, = 1.0 was selected for cylinders of L/D, 22. The reader is reminded that this kK. includes the effect of out-of-roundness and experimental error. The reduction in K, from 1.25 to 1.0, a 20% change, is difficult to assign solely to out-of- roundness effect because thick-walled structures are usually insensitive to small geometric out-of-roundness. Hence, K, = 1.0 should be a
conservative strength factor for design purposes.
*Much attention was given to why k_ should be as low as 0.89. If out-of-roundness was the sole causé, then the specimens showed a decrease in strength of 29% due to out-of-roundness, which was too large an effect for thick-walled cylinders. There appeared to be no reason based on engineering mechanics to cause cylinders with L/D_ of 4 to fail at lower pressures than those at, say, L/D. of 8. It is be- lieved that some problem related to specimen fabrication or test was responsible for the low strengths. The author personally participated in the fabrication and testing of some of the specimens under consid- eration. He discussed this topic with others involved in the test pro- gram, and no procedure was singled out as suspicious. One procedure that was distinctly different for specimens of L/D_ of 4 and 8 from that of the shorter specimens related to the interior mold. The inter- ior mold was made in segments having a length of L/D. = 2. Cylinders longer than L/D, of 2 used multiple segments. During mold removal operations it was quite difficult to disassemble the multiple segments to extract the interior mold. If harm was done to the specimens during this operation, it was not recognized at the time.
Although the cylinders were fabricated in rigid steel molds (Ref 2), the mold segments sprang slightly after the first disassembly. After References 2 and 4 were already published, a short cylinder section was mounted in a lathe to determine out-of-roundness more accurately than had been done previously. The inside and outside radius and the wall thickness varied by +1/32 inch (1.6 mm). The out-of-roundness parameters are summarized in Table 1.
Substituting Equation 2 into Equation 1 and using R, = D,/2 gives
the expression to predict implosion pressure for thick-walled cylinders:
Pe — ke Ee (t/D,) (3)
where k_ = 1.25 - 0.12(L/D,) for L/D <7) aks 1.0 for L/D, 2D. Equation 3 is shown in Figure 2, which can be used as a design _. ‘4 Sit ae ee mae chart. = Al Oe A more general design chart = He approach is shown in Figure 3. & Seah ao The chart is entered with a cylin- 5 ei der L/D, and t/D, to obtain the E Ee i ratio. The implosion pres- : 0.3 | sure can then be calculated by Z | assuming a concrete compressive ra a) strength, fo = 01 C\D, | The effect of different types — | of end-closures on the implosion oe OORe! OGL MOTELOLOMNODe strength was judged to be small Wall Thickness/Outside Diameter, t/D, (Ref 3) so this parameter was not Figure 2. Relationship of Equation 3 for
included in the design equation. thick: walled cylinders:
Cylinder Length/Outside Diameter, L/Do
lo)
long cylinders Pim/f¢ = 0.02 0.04 | 0.06 0.08 0.10 0.12 0.14 moderately / 0.16 long cylinders if | 0.18 / i ras i, thick fe cylinders Ht | | u 10) 0.02 0.04 0.06 0.08 0.10 0.12
Wall Thickness/Outside Diameter, /Do
Figure 3. Design guide for predicting implosion of concrete cylinder structures.
Thin-Walled Cylinders Table 1. Out-of-Roundness Parameters for 16-Inch OD Cylinders (Ref 2,4)
Thin-walled cylinders are t/Do NE a I AR;/t divided into two categories: moder-
ately long cylinders and long cylin- oe ae ders. Moderately long cylinders es 0:08 0.03 0.03 are influenced by end-closures 0.02 0.02 which restrain the cylinder from Pe instability failure. Long cylinders Thin-walled cylinder. b : Border between thin- and thick-walled are not influenced by end-closures eyinder and behave as infinitely long cylin- Grpaferewalledieylinder
ders. In Reference 8, thin-walled
cylinders included another category called short cylinders, but in this report the thick-walled cylinder category encompasses short cylinders (Figure 3).
The same approach used in Reference 8 is used herein. Donnell's equation is applied to moderately long cylinders and Bresse's equation to long cylinders. An empirical plasticity reduction factor, n, is used in both equations to account for inelastic behavior of concrete and specimen out-of-roundness. The new data permit an n relationship to Oe. to be determined with far greater accuracy than previously.
Empirical n values were determined by calculating the elastic stress at buckling and dividing this stress into the experimental stress at implosion.
The elastic buckling stresses were calculated as follows:
Donnell's Equation
0.855 E. i
Cao = 3/4 (Ge
R == |i (4) (Cs v’) y
and
Bresse's Equation
18,0 2 2 i ie EO ie # |e) i ra
Using v = 0.20 and the approximation R = D,/2, Donnell's equation
becomes Pes) t 1.25 Be i foal Gen = L/D, (7) and Bresse's Equation fs 2 GC )en = 104 B, "(a-) (8)
The elastic condition exists when n = 1.
E; was not measured for each specimen so an empirical relationship was developed to calculate its value. Figure 4 shows the experimental initial elastic moduli data as a function of compressive strength. The American Concrete Institute (ACI) expression for elastic moduli is
shown for comparison along with the empirical expression:
ES = 530 Ene (9)
10
The empirical expression has the rational basis of being derived from
the parabolic relationship for tangent modulus as follows:
2 f bo = se LS u c where E. = tangent modulus Ey = ultimate strain (experimental average was 0.0025)
and the fitted condition of o = 0.56 f when E. = EL:
6.0
57,000,/F2
5.0
4.0
Initial Elastic Modulus, E;, x 10° (psi)
3.0
© 6x12-in. control cylinder
2.0 5,000 6,000 7,000 8,000 9,000 10,000 Compressive Strength, f{ (psi)
Figure 4. Relationship between E; and f¢.
11
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Values of n are shown in Table 2. Table 3 shows the calculation of n values for the data from Reference 4.* All the data are shown in Figures 5 through 7. The fitted inelastic buckling curves of Figures 5 and 6 were transferred to Figure 8. From this representation of data, a design n curve was selected, which is applicable to both moderately
long and long cylinders. The n expression is:
oO. oO. n = 1.65 - 1.25 (G2) On5 2) ee (10)
Gerard developed expressions to predict n for metallic structures (Ref 11), and these expressions, which can be applied to concrete, are shown graphically in Figure 9. The n curve from Reference 8 is also shown. Its empirical shape was defined by limited data where several specimens had low implosion pressures which are not in agreement with that of the new data. The new design n curve has a maximum increase of 35% over that of Reference 8. (For a structure of given geometry, comparative n values are obtained by a linear curve intersecting the
origin and the n curves.)
*The values will be different than those given in Reference 8 because an assumption has been changed. Previously, the 16-inch OD speci- mens with hemisphere end-closures were assumed to be simply sup- ported cylinders. This assumption was made at the time because the analysis of results would be conservative. Data were limited so con- servatism was warranted. In this report, the 16-inch OD specimens, which had an L/D_ = 4, were assumed to be freely supported or, in other words, long €ylinders.
13
Table 3. Plasticity Reduction Factors for 16-Inch OD Specimens (after Ref 4)
Compressive Long Cylinders
Strength Sane Initial Elastic Implosion Average Wall Oe ts Modulus,? Pressure, Stress,© dim Bresse’s oO. a 2 : . Re ed cov’ E;x 106 (psi) Pin (psi) (psi) Stress, (im)B
(psi)
t/Do = 0.031; Free End-Supported; L/D, = ©
1/2-10-N 4.50 376 6,020 0.56 4,570
1/2-10-G ANOS, 349 5,580 0.51 4,610 1.21 1/2-6-N 3.00 203 3,250 0.60 3,050 1.07 1/2-6-G 2.60 214 3,424 0.59 2,640 1.30
t/D, = 0.063; Free End-Supported; L/D, = ©
10,700 1.5 4.50 1,110 8,880 0.83 18,280 10,480 1.4 4.32 1,103 8,820 0.84 17,550
6,620 LO) 3.20 543 4,340 0.66 13,000 5,920 5.8 3.10 530 4,240 0.72 12,590
t/Do = 0.125; Free End-Supported; L/D, =
3.2 3.90 DOS 9,340 0.95 63,370 0.15 407 4.24 2,455 9,820 0.99 68,900 0.14 3.0 3.29 1,387 5,550 0.91 53,460 0.10 2.3 3.36 1,447 5,780 0.96 54,600 0.11
t/D, = 0.188; Free End-Supported; L/D, =
10,350 2.8 4.10 149,910 10,800 DP) 4.60 168,190 7,000 3.0 2.94 107,490 6,200 Dol 3.11 113,710 4COV = Coefficient of Variation é 0:5 Pim Sim «eRe D iccranell oeltn, Do 2 t 40g, Jp = 1.04 F(55) to)
14
= 54 in. (1372 mm) = 127 in. (3225 mm)
\ material failure
Simple Support End Condition
h eee — ip ' : WAST ON ale Le f¢ = 8,000 psi (55 MPa)
elastic \ buckling 2) \
\ N \
inelastic buckling (fitted curve)
10) 0.02 0.04 0.06 0.08 0.10
Figure 5. Implosion of moderately long cylinder specimens with D. = 54 in. (1372 mm). I> y tong cy P Oo
\ Free End Condition © 4 A a f{ = 8,000 psi (55 MPa) \ a material failure \
, when 6; = fe elastic
buckling
inelastic JA
buckling (fitted curve)
0 0.02 0.04 0.06 0.08 0.10 t/D,
Figure 6. Implosion of long cylinder specimens with D_ = 54 in. (1372 mm). g Pp g cy P 0
15
1.5
1.0
1 = Gim/Gim)B
Plasticity Reduction Factor,
oe
\ Near Free End Condition © \ @ £¢ = 6,000 psi (41.4 MPa) elastic \ \ ® £2 = 10,000 psi (69 MPa) buckling @) N \ \ N material failure
\ \& 10,000 psi N 6,000 psi eK
inelastic buckling (curves not fitted, from Figure 8 design 7 curve)
ite = 10,000 psi
6,000 psi
0.02 0.04 0.06 0.08 0.10
© 12 © 1 T a © 1.0 =| aN © moderately long NS cylinders, from S Figure 5
long cylinders, 0.8 QU from Figure 6
design n curve
Do, End fc, Ej, Symbol in. Condi- psi psix 106 (mm) tion (MPa) (GPa)
0.6
54 simple, 8,000 4.24
(1372) L/Dg= (55) (29.2)
\ 5 2.35 i] re) 54 free 8,000 4.24 & cf!
(1372 (55) (29.2) \\,
0 16 near 6,000 3.05 Oo o)
0.4 (406) free (41.4) + (21.0) |
16 near 10,000 4.25
(406) free — (69)_~— (29.3)
a 0.2 =| “Specimens had known defects. (0) — J 10) 0.2 0.4 0.6 0.8 1.0 1.2
Figure 8. Plasticity reduction factor as a function of stress level in cylinder wall at implosion.
16
Gerard’s Expressions:
3/4 i
Moderately Long Cylind ae =p ie (al Slee Moderately Long Cylinders a= | eee care
1-v2 E _E; 4 TES
2
il > p E. E Long Cylinders n= (4-3 =|
ee iB \Oy 2 is,
Gerard, concrete this report
Gerard, concrete for 16-in. OD cylinders (data from Ref 14)
Plasticity Reduction Factor, n
0.6
0.4
0.2
0.2
\ design
nm curve
a
Ref 8
0.4 0.6 0.8 1.0
Figure 9. Comparison of various 7 versus O5n/t¢ relationships.
17
Moderately Long Cylinders. The expressions to predict implosion
pressure for moderately long cylinders are developed as follows.
Equations 9 and 10 are substituted into Equation 7 to yield:
1.5 t Fn = (i) (1)
The stress level at implosion, o, /fe is calculated by knowing the geometry of the cylinder structure. The following conditions determine
the next step:
(a) If Ohl hs > 1.0, thick-wall analysis is used to predict
implosion, Equation 3
Ca) lie O.52 < Oo /to < 1.0, then n is calculated by Equa- tion 10
(c) If Gy S 0.52, then n = 1.0
If steps (b) or (c) control, the following expression, which was developed by substituting Equations 7 and 9 into Equation 1, predicts
the implosion pressure.
fs (A085) 1320 n fe Gy.
im L/D,
(12)
A design chart approach is given in Figure 3. Enter the chart with the structure's L/D, and t/D, ratio to determine the Fee ratio.
The structure is assumed to have a simple-support end condition.
18
For the case of fixed-support end condition, it has been shown analytically (Ref 12) that an increase in implosion strength on the order of 6% can be expected. The implosion pressure can be calculated for this case by using the equations presented herein and a reduced cylin- der length of 0.85L.
Long Cylinders. The expressions to predict implosion pressure for long cylinders were developed as follows.
Equations 9 and 10 are substituted into Equation 8 to yield:
(13)
Once the stress level at implosion is calculated, the same condi-
tions as for moderately long cylinders hold; that is:
(a) If Oto > 1.0, thick-wall analysis is used to predict
implosion, Equation 3
(b) If 0.52 < Op Pe < 1.0, then n is calculated by Equa- tion 10
(e)) lit Oe 0.52, then n = 1.0
If steps (b) or (c) control, the following expression, which was developed by substituting Equations 8 and 9 into Equation 1, predicts
the implosion pressure:
= 8 ey = nie Gy) ee (-) (14)
1m oO
19
A design chart approach is given in Figure 3. Enter the chart
with the structure's L/D, and t/D, ratio to determine the Bitte ratio.
Factor of Safety
Overall Factor of Safety. Up to this stage, the implosion pressure calculated by Equations 3, 12, and 14 (or from the design chart of Fig- ure 3) is a short-term strength without any factors of safety incorpor- ated. Different codes of practice have different approaches to assign- ing factors of safety. Without discussing the various methods, it can be stated that the overall factors of safety for concrete compression members range between 2.5 and 3.0.
This report recommends the same range. A structure whose intended purpose is to store liquid material might be designed with a 2.5 factor of safety; whereas, a structure for human occupancy should have a 3.0 factor of safety as a minimum.
The design approach in Reference 8 included a long-term loading factor, A. Codes of practice typically recognize the long-term loading effect in the overall factor of safety without itemizing the effect. This report follows that practice. Results have recently been published on concrete spheres subjected to long-term hydrostatic loading (Ref 13) that have shown behavior similar to the Known behavior of concrete in on-land compression members. This represents some assurance that
following existing on-land practice is appropriate for in-ocean concrete.
Concrete Compressive Strength. The implosion pressure is directly related to the compressive strength of concrete, fe at the time of
failure. From available data (Ref 13), it appears that the strength development of concrete in the ocean is different than that of the standard fog-cure condition.
The results from Reference 13 are summarized herein.
20
If saturation of concrete is assumed to occur, then the following interim guide can be used for strength gain with age. The initial 28-day fog-cured strength should be reduced by 10% to account for saturation effects. Subsequent increases of in-situ strength with time may depend on the depth at which the concrete is located. Depth is important because it can influence the degree of saturation. At pre- sent, data are available at depths of a few thousand feet. In such cases, the strength increase relative to the 28-day fog-cured strength appears to be nil at 1 year, 5% at 2 years, and 15% at 5 years. These values of strength-increase-with-age are different from those generally accepted (Ref 14) for on-land concrete of 20% at 6 months and 24% at 12 months.
For cases where the concrete is at a depth of a few hundred feet, it is hard to estimate the strength gain behavior. First, it is unknown how much of the wall thickness will become saturated. It could take months for several feet of thickness to become saturated. If the inter- ior of the structure were to be at a relative humidity of less than 100%, the concrete would. never become saturated. However, some of the concrete would be saturated near the outside wall, and that portion would exhibit a strength different from that not saturated. For the saturated concrete the compressive strength should be reduced by 10% to account for saturation effects; then it is probably reasonable to permit a strength increase relative to the 28-day fog-cured strength of nil at 6 months and 5% at 12 months.
Effect of Reinforcement. The experimental specimens were unrein- forced concrete, whereas any full-scale structure would be reinforced concrete. The reinforcement certainly contributes to stiffening of the wall during bending caused by out-of-roundness. However, under ultimate conditions the contribution of the reinforcement is not easily
assessed.
21
It is recommended that the procedures stated in various codes of practice be adapted. For compression members the effect of reinforce- ment is permitted to contribute to the ultimate capacity of the member as long as the reinforcement is tied against lateral movement as in a column. If the compression reinforcement is not tied, then the member
is designed as unreinforced concrete.
Out-of-Roundness. The design chart in Figure 3 is based on
empirical data and, therefore, contains an inherent out-of-roundness allowance. This allowance for thick-walled cylinders is given in Table 1. The thin-walled cylinder test specimens were studied in detail for out-of-roundness, and Table B-2 in Appendix B (pg 51) presents a digest of their out-of-roundness. A structure having geometric toler- ances equal to or less than the test specimens will be safely designed using Figure 3. Conventional construction practices should encounter few problems in matching the geometric tolerances of the test speci- mens.
It is recommended that, once a structure is sized-out by Figure 3 and meets its other design requirements, a detailed finite element anal- ysis be conducted. The analysis should assume a realistic out-of-round
geometry and model the inelastic behavior of concrete materials.
SUMMARY
The updated design guides represent some significant changes compared to the guides presented in Reference 8. The design approach for thick-walled cylinders was made comparable to that for thick-walled spheres by using an average wall stress equation with an empirical strength factor, K.. Thin-walled cylinders used the same design approach as described in Reference 8; however, new experimental results from 15 relatively large-scale specimens permitted a more accu-
rate development of an empirical plasticity reduction factor, n.
22
The effect of test specimen out-of-roundness is included in the empirically derived portions of the guides so use of the guides implicitly assumes out-of-roundness of similar magnitude for the new structure. This is a safe assumption because out-of-roundness criteria as given in Table 1 and Table B-2 are lenient for large structures (in other words, large structures should have better geometry control than the test specimens).
Figure 3 is a design chart to predict implosion for thick- and thin-walled concrete cylinder structures. A feature of the chart is its simplicity. By knowing the t/D, and L/D, ratio of the structure, the implosion strength in terms of Bibs can be determined. Implosion pressure, Bee is calculated by assigning an ie to the concrete. A factor of safety is not included in the predicted implosion pressure.
The design chart has application in sizing-out a structure for a given depth. Advanced design techniques must be used to complete a final design, but these techniques need to start from near-final dimen- sions. This report provides the design charts to quickly determine the
near-final dimensions.
CONCLUSIONS
1. Failure of concrete cylindrical structures under hydrostatic loading can be described by one of three equations: an average wall stress equation applies to thick-walled cylinders; Donnell's equation to moderately long, thin-walled cylinders; and Bresse's equation to long thin-walled cylinders. An empirical parameter was used in each equa- tion to obtain agreement between the experimental results and theoreti-
cal expression.
2. The finite element analysis method with a constitutive material
model predicted the implosion strength and structural displacement
23
behavior of the test specimens with good accuracy (Appendix B). Fig- ure 3, which is the design chart for implosion, is within 10% accuracy
of the finite element method predictions.
3. The design chart of Figure 3 can be applied for quickly deter- mining the implosion strength for a concrete cylinder structure of given
dimensions.
ACKNOWLEDGMENTS
EXXON Production Research Company is acknowledged for their co-sponsorship of the thin-walled cylinder test program.
At CEL, Roy S. Highberg and Philip C. Zubiate are recognized for conducting tests on both the thin- and thick-walled cylinder specimens. Other participants were Joseph F. Wadsworth, Joseph Graham, Gene McMahan, and Michael Hanks.
REFERENCES
1. Civil Engineering Laboratory. Technical Report R-517: Behavior of spherical concrete hulls under hydrostatic loading, Part I. Explora- tory Investigation, by J. D. Stachiw and K. O. Gray. Port Hueneme, Calif., Mar 1967. (AD 649290)
Zo ; Technical Report R-696: Influence of length-to- diameter ratio on the behavior of concrete cylindrical hulls under hydro- static loading, by H. H. Haynes and R. J. Ross. Port Hueneme, Calif., Sep 1970. (AD 713088)
Be . Technical Report R-740: Influence of end-closure stiffness on behavior of concrete cylindrical hulls subjected to hydro- static loading, by L. F. Kahn. Port Hueneme, Calif., Oct 1971. (AD 732363)
24
4. . Technical Report R-790: Influence of compressive strength and wall thickness on behavior of concrete cylindrical hulls under hydrostatic loading, by N. D. Albertsen. Port Hueneme, Calif., Jun 1973. (AD 764054)
5. H. H. Haynes. "Research and development of deep-submergence concrete," in Proceedings of Federation Internationale de la Precon- trainte (FIP) Symposium on Concrete Sea Structures. Tblisi, USSR, Sep 1972, pp 180-185.
6. H. H. Haynes and B. A. Nordby. "Concrete cylinder structures under hydrostatic loading," in Proceedings, American Concrete Insti- tute, vol 73, no. 2, Feb 1976, pp 87-96.
7. H. H. Haynes. "Implosion criteria and behavior considerations for concrete deep submergence vessels," in Proceedings of Conference on Concrete Ships and Floating Structures, University of California, Berkeley, Calif., Sep 1975, pp 77-92.
8. Civil Engineering Laboratory. Handbook for design of undersea, pressure-resistant concrete structures, by H. H. Haynes. Port Hue- neme, Calif., Sep 1976, p 35.
De . Technical Report R-817: Seafloor construction experi- ment, SEACON I - An integrated evaluation of seafloor construction equipment and techniques, by T. Kretschmer et al. Port Hueneme, @alif., Feb 1975.
10. H. Kupfer, H. K. Hilsdorf, and H. Rusch. "Behavior of Concrete Under Biaxial Stresses," in Proceedings, American Concrete Institute, vol 66, no. 8, Aug 1969, pp 656-666. , 11. G. Gerard. "Plastic stability theory of thin shells," Journal of the
Aeronautical Sciences, vol 24, no. 4, Apr 1957, pp 269-274.
25
12. O. Olsen. "Implosion analysis of concrete cylinders under hydro- static pressure," in Proceedings, American Concrete Institute, vol 75, no. 3, Mar 1978, pp 82-85.
13. Civil Engineering Laboratory. Technical Report R-869: Long-term deep-ocean test of concrete spherical structures - Results after 6
years, by H. H. Haynes. Port Hueneme, Calif., Jan 1979, p. 48.
14. A.M. Neville. Properties of concrete, 2nd Ed., New York, N.Y., Pitman Publishing, 1973, p. 259.
15. Civil Engineering Laboratory. Technical Report R-588: Behavior of spherical concrete hulls under hydrostatic loading, Part III - Rela- tionship between thickness-to-diameter ratio and critical pressures, strains, and water permeability rates," by J. O. Stachiw and K. Mack. Port Hueneme, Calif., Jun 1968 (AD 8354926).
16. . Technical Memorandum M-44-76-4: Results of concrete cylinder implosion test program, by Harvey H. Haynes and Roy S. Highberg. Port Hueneme, Calif., Apr 1976, p. 391.
ee . Technical Note N-1367: Adhesives for use under- water, by R. W. Drisko, J. B. Crilly, and R. M. Staples. Port Hue- neme, Calif., Dec 1974.
18. . Technical Note N-1173: Evaluation of eight epoxy adhesives for bonding concrete and microconcrete structural components exposed to room and hydrostatic pressure conditions, by T. Roe, A. F. Curry, and P. C. Zubiate. Port Hueneme, Calif., Jul 1971.
19. S. P. Timoshenko and J. M. Gere. Theory of elastic stability, 2nd Ed. New York, N.Y., McGraw-Hill, 1961, p. 295.
26
20. Purdue University. CE-STR-78-2: Analysis of concrete cylinder structures under hydrostatic loading, by W. F. Chen, H. Suzuki, and T. Y. Chang. West Lafayette, Ind., Apr 1978, pp 157.
Dale A. C. T. Chen and W. F. Chen. "Constitutive relations for concrete," Journal of the Engineering Mechanics Division, ASCE, vol 101, no. EM4, Aug 1975, pp 465-481.
22. W.F. Chen. Limit analysis and soil plasticity. Amsterdam, The Netherlands, Elsevier, 1975.
23. University of Akron, Department of Civil Engineering. Report No. SE 76-3: NFAP - A Nonlinear Finite Element Analysis Program, by T. Y. Chang, and S. Pinchaktan. Akron, Ohio, Oct 1976.
24. Energy Research and Development Agency. Report No. C00-2682- 7: Extended NONSAP Program for OTEC Structural Systems, by T.Y. Chang and W. F. Chen. Washington, D.C., 1976.
25. University of California, Department of Civil Engineering. SESM Report No. 73-3: NONSAP - A structural analysis program for static and dynamic response of nonlinear systems, by K. J. Bathe, E. L. Wilson, and R. H. Iding. Berkeley, Calif., 1974.
26. H. H. Haynes and L. F. Kahn. "Undersea Concrete Spherical
Structures," Proceedings, American Concrete Institute, vol 70, no. 5, May 1973, pp 337-340.
Zit
TE tion
CWrOREE dinitarind « ’ ‘. eri ' ! . ; ¥ nc ea z brs ee i he! yEN aS str ; t ie 7 T eae
Appendix A
THICK-WALLED CYLINDER TESTS
SPECIMEN DESCRIPTION
The SEACON I structure (Figures A-1 and A-2) was assembled from three precast, reinforced concrete sections. The straight cylinder section, 10.1-foot (3.08-m) OD by 10-foot (3.05-m) length by 9.5-inch (241-mm) wall thickness, was fabricated by United Concrete Pipe Cor- poration. The concrete hemisphere end-closures, 10.1-foot (3.08-m) OD by 9.5-inch (241-mm) wall thickness, were fabricated in-house. Toler- ances on the sections conformed to concrete pipe standards: ID not to exceed +0.75 in. (19 mm) or wall thickness not to exceed -0.5 in. (13 mm ).
Steel reinforcement of 0.70% by area was used in both the hoop and axial direction. Reinforcing bars of 0.50 inch (15 mm) diameter were employed throughout the structure. A double circular reinforce- ment cage was fabricated for each precast section; the concrete cover on the outside and inside reinforcing cage was 1 inch (25 mm). For the cylinder section, hoop rebars had a center-to-center spacing of 6 inches, and axial rebars had a spacing of 27.25 inches (692 mm) and 31.25 inches (794 mm) for the inside and outside cages, respectively.
The hemispherical end-closures were bonded to the cylinder section with an epoxy adhesive; no other attachment besides the epoxy bond was employed. The gap between the mating surfaces of the hemisphere and the cylinder was less than 0.13 in. (3 mm) for 75% of the contact area. Prior to epoxy bonding, the concrete surfaces were sandblasted
and washed with acetone.
29
Figure A-1. SEACON structure prepared for ocean test to implosion.
epoxy adhesive
2" clear
sil
1” cover
epoxy adhesive
a” 10-1
acrylic 1 window axial and hoop reinforcement
9 eee 0.7% by area
penetrator
axial bars spaced a at 30°
oS
1 1/2” @ bars ; 5-0" -|
20'-0" overall length
Figure A-2. Details of SEACON structure.
30
A large hull penetration, major diameter of 50.25 in. (1275 mm) and minor diameter of 42.4 in. (1075 mm), was located at the apex of each hemisphere. This penetration size was equivalent to 40% of the hemisphere diameter. The design philosophy for the penetrator was to make it stiffer than the concrete material it replaced so that the hemi- sphere was "unaware" of the large hole. The steel penetrator was epoxy-bonded to the concrete, using the surface preparation method described for the joint.
During the 10-month seafloor construction experiment, an acrylic window assembly was used in one penetrator and a hatch assembly in the other penetrator. The window and hatch were subsequently replaced with steel plates for the implosion test.
Six penetrations, major diameter of 6 inches (152 mm) and minor diameter of 5 inches (127 mm), were included in one of the hemi- spheres; these penetrations were part of a seal and gasket study.
Two smaller penetrations, major diameter of 4.5 inches (114 mm) and minor diameter of 4.0 inches (102 mm), were also included near the center of the cylinder section to accommodate pressure relief valves.
For the implosion test, three of the small hemisphere penetrators were modified for electrical feed-throughs and pressure ports. The two cylinder penetrations were sealed.
Additional irregularities in the concrete wall included five feed- through boxes for strain gages mounted on reinforcing bars. These boxes were located on the interior wall and measured 2.5 inches (64 mm) deep by 4 inches (102 mm) in diameter. In these areas the local wall thickness was reduced to 7 inches (178 mm).
Prior to the implosion test, fifteen 3.25-in. (83-mm) diameter cores were drilled from the wall at various locations around the cylinder. Steel plugs were epoxied in the core holes.
During original assembly, the exterior of the concrete structure was coated with a phenolic waterproofing system. After lightly sand-
blasting the concrete, a primer and topcoat (Phenoline no. 300) were
31
sprayed onto the concrete. Many air pocKets were not coated; approxi- mately one pinhole per 2 in.2 (1300 mm2) existed in the final water- proofing coating.
The concrete structure was instrumented with a total of 40 electri- cal resistance strain gages to monitor hull response under long-term loading. Half of the gages were placed diametrically opposed to each other on the structure. The data were stored on magnetic tape inside the structure and were recovered when the structure was retrieved after 10 months.
The concrete material for the cylinder portion of the structure consisted of portland cement type II, sand, and coarse aggregate in the proportions of 1.0:1.4:2.5 by weight, respectively. The water-to- cement ratio was 0.40 by weight, and a water-reducing admixture was used; the slump was 1.25 inch (32 mm). The average compressive strength at 28 days of the 6-inch (152-mm) diameter by 12-inch (305-mm) long control cylinders was 7,800 psi (53.8 MPa).
Mix designs of different proportions were used for the hemi- spheres: cement-to-sand-to-coarse-aggregate ratio of 1.0:1.95:2.3 by weight; water-to-cement ratio of 0.38 by weight; and a water-reducing admixture. Slump was again 1.25 inch (32 mm). The average compres- sive strength at 28 days was 8,170 psi (56.3 MPa).
Of the 15 cores taken from the cylinder wall just prior to the implosion test, 7 were subsequently cut into 3.25-in. (83-mm) diameter by 6-in. (152-mm) long cylinders, which were tested under uniaxial compression. Compressive strengths of the cores and from a number of 6x12-inch (152x305-mm) control cylinders at various ages are presented in Table A-1.
Three of the core specimens were instrumented with strain gages to obtain stress-strain data for the concrete. Curves of this relation- ship up to about 90% of the compressive strength are shown in Figure A-3. The secant modulus of elasticity to about 40% of ie was 4.4x10®
psi (30.4 GPa), and Poisson's ratio was 0.20.
32
Table A-1. Summary of Concrete Compressive Strengths for the Seacon Structure
Specimens
Age of Compressive . : Concrete Strength Size Curing : Type (in.) Conditions@ ey) (psi)
field
fog field
fog field
fog fog and ocean?
field and ocean® d
part of structure
“Curing of all cylinders for the first 28 days was 2 days steam, 7 days water tank, and 19 days field.
> after first 28 days, curing was 270 days fog room and 302 days on seafloor at 600 feet.
“After first 28 days, curing was 270 days field and 302 days on seafloor at 600 feet.
4Structure was field-cured on land for 298 days, on the seafloor for 302 days, and then field-cured on land for 1,528 days.
As shown in Figure A-1, the concrete cylinder structure was mounted in a steel framework and fitted with a ballast tank. The in-air weight of the cylinder was 85,000 pounds (38.5 Mg), and the concrete- steel structure weighed 102,000 pounds (46.3 Mg). The positive buoy- ancy of the concrete hull was 12,000 pounds (5.4 Mg), and when bal- lasted the concrete-steel structure weighed 6,800 pounds (3.1 Mg)
negative in water.
33
10,000
8,000 ~ 6,000 z a a & cS ip) : z n
4,000 n
2,000
-400 -800 -1,200 -1,600 -2,000 -2,400 STRAIN (yin./in.)
Figure A-3. Stress-strain curves from 3.25-in. diam x 6-in. long cores.
TEST RESULTS
Long-Term Test at 600 Feet
Strain Behavior. The initial strain response of the structure on being lowered to 600 feet (180 m) showed an average strain of 380 ywin./in. in the hoop direction and 170 win./in. in the axial direction (Ref 9). From previous work (Refs 2, 3 and 4), it was anticipated that this low level of loading should not have produced any detectable strain variation along the length of the cylinder section due to the discontinuity of the cylinder/end-closure joint. The actual strains
showed this to be true.
34
The concrete was under sustained stress of 1,700 psi in the hoop direction and 920 psi in the axial direction for 302 days. The average total creep strain in the hoop and axial direction was 130 and 80 uin./in., respectively; these values represent a 34% and 47% increase, respectively, over the short-term strain (mot unusual for concrete). The data gave no indication that the creep strain was nearing termina- tion.
The large penetration had little effect on the behavior of the hemisphere. Again, the low stress level in the concrete might not have been sufficient to produce a noticeable strain rise at the penetration. In any event, it was significant that the penetrator, equivalent to 40% of the structure's diameter, did not produce a harmful effect on the
structure.
Watertightness. Upon retrieval of the cylinder from the 600-foot (180-meter) depth after 10 months, the interior of the structure was free from water that permeated the concrete walis. There was no evidence of condensation, or even dampness, on the interior concrete walls .* .
Results from long-term loading of concrete spheres in the ocean (Ref 13) confirm this finding of watertightness. The 66-inch (1076-mm) OD spheres had a wall thickness of 4.12 inches (105 mm) and were located at depths that ranged from 2,000 to 5,000 feet (600 to 1500 meters). Some of the sphere exteriors were coated identical to the SEACON structure and showed no water on the interior after 6 years in
the ocean.
Implosion Test
Depth at Implosion. The depth of implosion for the structure was 4,700 feet (1430 m).
*Three quarts of water were found inside the structure due to a leak in a check valve in one of the small penetrators under investigation.
35
The means of determining the depth of implosion was not as straightforward as originally planned. Pressure transducers were installed on the hull, but these were inoperative at the time of implo- sion. During launching of the structure, which was off the stern of an offshore work vessel, a small hull penetration became damaged and resulted in a leak of about 25 gallons (95 liters) of seawater per min- ute. The weight of the structure increased until a safety link in the lowering line parted, which occurred at a depth of 2,900 feet (884 meters), as recorded by the pressure transducers. From this depth on, the structure free-fell through the water column until implosion occurred.
Data from acoustic depth-recording instrumentation were continu- ously being recorded on tape during this sequence of events. The noise generated by the implosion of the structure was also recorded. This signal had a rather long duration and showed that implosion could have occurred at a depth between 4,500 feet (1370 meters) and 4,700 feet (1430 meters). Seafloor depth was 4,700 feet (1430 meters).
It was known from data on tape that the time between the start of free-fall and implosion was 160 seconds. By analytically bracketing the free-fall velocity of the structure between 11.2 ft/sec (3.4 m/sec) and 12.5 ft/sec (8.8 m/sec), it was calculated that the structure free-feli between 1,790 feet (546 meters) and 2,000 feet (610 meters). Adding these numbers to 2,900 feet (884 meters) gave the total depth range as 4,690 feet (1430 meters) to 4,900 feet (1494 meters). Hence, it was apparent that the structure hit the seafloor at a depth of 4,700 feet (1430 meters) before imploding.
A manned submersible inspection by the Navy's Sea Cliff was conducted in 1978 to determine whether the structure imploded after impacting the seafloor. The tight grouping of fragments confirmed that the structure hit the seafloor first. If the structure had imploded during free-fall descent, the fragments would have been scattered.
The inspection also confirmed that the cylinder section imploded rather
36
than that one of the hemispheres or a penetrator failed. The cylinder section was heavily fragmented while the hemispheres were rather recognizable.
There were no means of estimating whether the structure imploded immediately upon hitting the bottom or remained on the bottom for a time before imploding. In any event, 4,700 feet (1430 meters) is a conservative (or minimum) implosion depth.
It should be mentioned that the structure was instrumented for strain readings during the implosion test. The damaged penetrator, however, was also the electrical feed-through for strain-gage wires;
therefore strain readings were not recorded during the test.
Discussion of Implosion Strength. The effect of hull stress rate,
due to free-fall velocity, was not considered a significant parameter on implosion strength when compared to previously tested cylinder models. For a free-fall velocity of 11.2 ft/sec (3.4 m/sec), the hoop stresses in the hull increased at a rate of 1,900 psi/min (13.1 MPa/min). Previous cylinder models with geometry equivalent to that of the SEACON struc- ture had hoop stress rates about 700 psi/min (9.8 MPa/min). This difference in stress rate would have an insignificant effect on implosion strength.
Pressure buildup inside the structure was minimal during the entire test. At the 2,900-foot (880-meter) depth it was known that 13,000 pounds (5.9 Mg) of seawater leaked to the interior. This filled about one-quarter of the interior volume. By the time implosion occurred, the interior pressure would not have exceeded 5 psi (34 KPa) over atmospheric. The exterior pressure at implosion was 2,100 psi (14.5 MPa).
The implosion strength of the SEACON hull was
“an 2,100 psi Bae 02 407epsi
= 0.200
37
The compressive strength, fe was obtained from 3.25x6-inch (83x152- mm) core specimens. The strength of the cores was assumed equal to that of 6x12-inch (152x305-mm) cast specimens. The smaller size of the core specimens would cause a higher strength relative to 6x12-inch cylinders; however, this strength increase would be offset by the effect of drilling which causes a strength decrease.
With the use of the average wall stress approach as expressed in
Equation 3, the material strength factor was calculated as:
hare ee On 200 ee e° 240) ~ 205i ~ ™
This factor is shown in Figure 1 for the SEACON hull which had an L/D, =llOp
The effect of steel reinforcement on the implosion strength of the structure could not be determined from this test. If the reinforcement was considered effective, then the total wall thickness from transformed sections would be 10.07 inches. This represents an increase of 6% over that of the actual wall thickness, which should cause an equivalent increase in the implosion pressure. This single test could not deter-
mine such a small percentage difference in strength.
FINDINGS
1. The implosion depth for the SEACON structure was 4,700 feet (1430 meters). Core specimens 3.25 inches (83 mm) in diameter by 6 inches (152 mm) long taken from the hull gave the uniaxial compressive strength of 10,470 psi (72.2 MPa).
2. With the use of the average wall stress equation, the material
strength factor, Ko> was 1.27; the wall stress at implosion was 13,300
psi.
38
Appendix B
THIN-WALLED CYLINDER TESTS
SCOPE
A total of 15 unreinforced concrete cylinder specimens were tested under hydrostatic loading. The dimensions of the specimens were a constant outside diameter, D> of 54 inches (1372 mm), overall length of 134 inches (3400 mm), and wall thicknesses, t, of 1.31, 1.97, or 3.39 inches (33, 50, or 86 mm). The wall-thickness-to-outside-diameter, t/D,; ratios were 0.024, 0.037, and 0.063, respectively. Two different types of boundary conditions were used: a simply supported and a free end-condition. Twelve of the specimens were tested under short- term hydrostatic loading where the pressure was increased until implo- sion; the remaining three specimens were subjected to long-term load- ing.
Structural behavior was recorded by measuring radial displace- ments around the entire circumference of the cylinder wall at various locations along the length. Deflected cross-sectional shapes were plot-
ted from which the following data could be determined:
(a) Initial deviations from circularity
(b) Radial displacements due to membrane shell action and
bending
39
(c) Location of the worst flat-spot and determination of
maximum radial displacement
(d) The number of buckle lobes at implosion
Attempts were made to obtain strain data but difficulties were encountered in applying gages to wet concrete.
Inspection of failed specimens and fragments of concrete from the failure zones yielded data on the deflected shape of the structure and size of the failure hole.
A detailed presentation of specimen geometry and test results is
given in Reference 16. This report summarizes portions of those data.
SPECIMEN FABRICATION
Casting
The specimens were cast monolithically in steel molds. The same outer mold was used for all specimens, but different inner molds were used to change the wall thickness. The inner molds were built to fold inward so that the diameter became smaller for removal from inside of the concrete cylinder. The inner and outer molds were spaced on the bottom by a ring and on the top by a spreader bar.
Concrete was placed in the molds by free falling from a dome distribution plate. When the form was vibrated, the concrete flowed to the edges of the dome and fell into the mold. By this technique, the concrete was evenly distributed around the circumference.
Approximately 20 hours after casting, the mold was removed from the concrete (Figure B-1). All specimens were wrapped in wet burlap and then in polyethylene film. They were subsequently moved to a
sheltered storage area where a water drip system kept the burlap wet.
40
Figure B-1. Cylinder specimen Figure B-2. Specimen partly being removed from mold. assembled inside polyethy- lene tent.
The specimens were moist-cured in this manner until assembled for test. During assembly (Figure B-2) a tent of polyethylene film was used to maintain a high relative humidity environment around the speci- men to minimize shrinkage cracking. Keeping the cylinder in the moist environment assured the test conductors that the concrete was in a
"wet" condition at the time of the implosion test.
Assembly
The procedure to assemble a specimen for test (Figure B-3) began by placing the cylinder on the bottom end-closure, which was a flat steel plate. The top end-closure was a steel ring. The top and bottom closures were held together by eight chains, post-tensioned to precom- press the concrete by 20 psi (0.14 MPa) when the structure was sub-
merged in water in the pressure vessel.
41
high-speed camera
TV camera
lights (2 locations)
top, end-closure ring
bearing for ie
center shaft 7 four-arm spider A p | | 1 “6 Ay ! | betedh p \ i ; 4 \ potentiometer - le 5 ' i 5 is . i ! ( / —- s : | = 4 arm ———+ ‘ { j A. A | ie, Lae center shaft 6 mM 9 \ . P F za| | \ concrete cylinder Pus J i Bea test specimen 1 uss, aN \ ' , oe b O ‘ \ \ “ 6 ' iG ! p = Jb H j oP a : ' , 9 | 4 T ge : 7 pressure vessel 6 & i} | 2b ' 1 b \ “( = b 4“ ee : 1 e 4 iA : \ \ \ | 6 i) ' \ ‘ bo) 1 } ' ou , ( A \ : : \ ; De = » ' ! bz = : _ post-tensioning ' “4 : eee chain (8 equally spaced) g J » -
stiffener
! ; if | / /
bottom end-closure
\—&«—— high-pressure
ral ‘ inlet and drain
Figure B-3. Cross section of specimen, showing test setup.
42
For the simply supported end-condition (Figure B-4) epoxy adhe- sive was placed between the concrete and steel ends to correct for unevenness at the mating faces. Later, steel stiffeners were placed in the interior at the top and bottom, and expansive-cement grout was packed between the stiffeners and the concrete wall. For the free support end-condition (Figure B-4), a 1/8-in. (3-mm) neoprene rubber gasket was placed between the steel and concrete. A thin layer of epoxy adhesive or quick-setting gypsum was used between the concrete and the neoprene gasket.
When the specimen was assembled to the stage where the center shaft was centered at the top and bottom, radius measurements were taken using the following procedure. An arm off the center shaft had a scribe marker mounted to it. A fixed position table was placed beneath the arm, so when the center shaft was rotated, a circle was scribed on the table. The radius of this circle, r', was measured after the table was removed from the specimen. At the circumferences of 0, 90, 180, and 270 degrees, the distance from the scribe to the wall, r", was measured using a steel rule accurate to 0.01l-inch (0.25-mm). By adding r' and r", the inside radius of the specimen was obtained at the circumference locations. Deviations in radius around the circumference were obtained from deflectometer data, so by using the deflectometer data and the measured radius data, average radius values for the
specimens were determined. Instrumentation
Instrumentation of the specimens consisted of mounting a deflec- tometer system to measure radial displacements, applying strain gages (to some specimens), installing a television camera, and installing a
high-speed motion picture camera. These systems are described below.
Deflectometer. The measuring device of the deflectometer system was a potentiometer (linear position transducer) which had a maximum
displacement of +0.650 in. (16.51 mm) and a measurement accuracy of
43
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+0.002 in. (0.05 mm). The potentiometers were mounted on arms that extended from a center shaft. The center shaft was motor-driven at a rate of one revolution per 90 seconds.
Radial displacement calibration was accomplished by mounting aluminum shims of 0.125-inch (3.18-mm) thickness on, the inside wall of the cylinder so that the steel ball passed over the shims to record Magnitude and direction of inward displacement. These calibration marks also determined a 360-degree rotation.
The deflectometer system was insensitive to the axial orientation or lack of straightness of the center shaft. The top and bottom on the center shaft were fixed in location, and the shaft was rotated. The arms were fixed to the center shaft; and, in plan view, the end of each arm scribed a perfect circle. The steel ball at the end of each arm moved in and out to conform to the shape of the concrete cylinder. This radial movement was recorded as changes from a perfect circle.
In reducing the analog deflectometer data, an analog-to-digital converter was used along with a timing system to control the number of samples taken and the time interval between samples. Over 900 samples of analog data were digitized for each 360-degree rotation. This equates to a radial displacement data point every 0.17 inch (4.3 mm)
around the inside circumference of the cylinder.
Strain Gages. Strain gaging of the specimens proved to be diffi- cult because the concrete was in a wet condition. Various approaches for applying gages to wet concrete were tried, but none were success- ful. The problem was in maintaining the bond throughout the entire test.
The procedure for strain gaging is described as follows: (1) Electrical-resistant strain gages (type FA-06-125,
three-element rosettes) were mounted either on brass shim stock 0.002-inch (0.05 mm) thick or on steel shim
45
(2)
(3)
stock 0.005-inch (0.13-mm) thick and waterproofed, using standard procedures. These procedures used normal preparation steps for applying gages to metal and then were waterproofed using General Electric Clear RTV 109. This waterproofing approach works successfully under hydrostatic pressure loadings equivalent to thousands of feet of head. A second type of electrical resistant gage used was a self-
encapsulated, waterproof, weldable gage.
The objective was to apply these waterproof gages to the wet concrete surface with an adhesive of sufficient bonding strength that strain in the parent material is transferred through the epoxy adhesive, through the shim stock material, to the gage. To check the accu- racy of these shim-stock mounted gages, a control test was conducted on an aluminum tube loaded in uniaxial compression. Seven pairs of gages were mounted on the aluminum cylinder; each gage in a pair was diamet- rically opposite the other gage. The test consisted of three pair of single wire gages mounted with Eastman 9-10, two pair of foil gages on brass shim stock mounted with EPY-150, one pair of foil gages on brass shim stock mounted with Eastman 9-10, and one pair of foil gages on brass shim stock mounted with Hysol EA 934. Eastman 9-10 is an excellent adhesive in a dry environment, so it was used in this test as a control. The results showed that gages mounted on brass shim stock registered accurate strains. The different glue
systems did not affect the results.
In the first method of mounting foil gages on brass shim stock to the wet-concrete specimens, an under-
water curing adhesive developed at CEL (Ref 17) was
46
used. This method did not bond the shim stock to concrete for the duration of the test. A second method used epoxy adhesive Hysol EA 934, which was known to maintain a high bond strength when dry- concrete became wet (Ref 18). The strain data still indicated that the brass shim stock was not adhering to the concrete at the higher pressure (or strain) levels. The third method used Hysol adhesive again, but this time extra attention was paid to roughening the brass surface, deeply roughening the concrete surface (by grinding with silicon carbide grit) and, when applying the gage, embedding the edges of the brass shim stock in a thick bead of epoxy around the periphery. These additional steps also did not solve the problem. The fourth method was to try steel shim stock, instead of brass, and to use the procedures mentioned previously. At the same time, weldable gages were tried. None of these systems was success- ful; attempts at strain gaging were terminated. The deflectometer data were excellent, and additional
potentiometers per test were used.
Television Camera. A closed-circuit television camera was installed at the top of each specimen. The video tape system recorded implo- sion. Although the frames per second rate did not permit detailed study of the failure zone, the circumferential location of failure could usually be defined and an interesting sequence of failure was recorded,
including the sound of implosion.
High-Speed Camera. A high-speed motion picture camera was installed at the top of the specimens. It was hoped that a failure sequence could be filmed. The camera speed was initially set at 200
frames/sec which permitted 40 seconds of film time. The speed could
47
have been increased to 1,000 frames/sec, if desired. However, after several tests and no coverage of failure, the film speed was reduced to 100 frames/sec to increase the film time to 80 seconds. The camera was installed in eight specimens but failure coverage was not obtained in any test. The techniques used to try to predict imminence of failure
are discussed in the Test Procedure section.
TEST PROCEDURE
The pressure vessel used in the tests had an inside diameter of 72 inches (1830 mm) and an operational pressure of 5,500 psi (37.9 MPa). The pressure load was created by pumping additional water into the vessel and thereby compressing the fluid. Freshwater was used in the tests.
The temperature of the water typically varied between 3° and 10°C for different tests; however, the temperature inside the specimens typically varied between 10° and 13°C. The higher temperature inside the specimens was due to warmer room temperature and lights for the television.
All specimens were placed in the pressure vessel on the evening before testing and allowed to soak in order that the degree of water saturation of the concrete for the different specimens would be the same. It was hoped that soaking overnight partially saturated the concrete to equal levels.
The rate of pressure application was 10 psi/min (0.069 MPa/min) between hold periods where data were recorded. Hold periods occurred at 25 psi (0.172 MPa) increments and typically lasted for 2.5 minutes. From the beginning to the end of the test, the overall pressurization rate was about 5 psi/min (0.034 MPa/min).
The television monitor was operated throughout the test. Its use was invaluable in operating the deflectometer system, detecting leaks,
and recording implosion on videotape.
48
Several specimens leaked during the test. Most of the leaks occurred between the concrete and steel end-closures. However, some of the specimens had cracks through the wall and water slowly leaked through these cracks until the pressure load exceeded approximately 200 psi (1.4 MPa). Leaks did not affect the test results.
For the long-term loading tests, a digital comparator was used to control the operation of an auxiliary pressure pump and maintain the pressure load at +2 psi (0.014 MPa).
Failure of the specimens was instantaneous, with literally a fraction of a second of advanced warning. High-speed motion picture film of failure was not obtained during eight attempts. In several of the eases, the film was exposed before implosion occurred. In the other cases, implosion occurred while the operator was waiting for an indica-
tion of failure. Methods used to indicate failure are described below.
(1) Radial Displacement - A real time signal from a poten- tiometer -was displayed on an oscilloscope. During pressurization periods, the potentiometer was placed on the worst flat-spot (probable failure zone), and the rate of inward radial displacement with pressure was monitored. It was believed that an increase in the rate of change of radial displacements would indicate implosion. This was the case, but warning time was not sufficient to trigger a toggle switch to operate the
camera.
(2) Acoustic Emissions - Acoustic emission transducers were placed on the pressure vessel head or on the top stiffener to record cracking activity of the concrete. It was hoped that the concrete would show consider- ably more cracking activity just before failure. This method was not successful because the acoustic emis-
sion activity of concrete is high and erratic in the
49
inelastic region. It was not possible to distinguish between spurts of activity and the activity just prior
to failure.
(3) Pressure - The technician, who pressurized the speci- men, closely watched pressure gages during the test. A pause in the rate of movement of a pressure gage needle would indicate imminent failure. For several of the tests there was no pause in needle movement; and for the tests with a pause, time was not sufficient to
relay a message.
Upon removal, the specimens from the pressure vessel were inspected, photographed, and sketched. Fragments of concrete from failure zone sections were salvaged and pieced together for closer inspection of the failure zone.
It was at this stage that wall thickness measurements were made. The specimen was broken up, and the thickness of the pieces was measured with a micrometer. In this manner, numerous and accurate
measurements of wall thicknesses were obtained.
SPECIMEN GEOMETRY
A summary of the specimen geometry is given in Table B-1. Data on maximum and minimum wall thicknesses are presented. Also, con- struction out-of-roundness data at the flat-spot locations are given. Typically, the minimum wall thickness coincided with the flat-spot location because this occurred at the outer mold seams. Table B-2 gives a digest of the out-of-roundness parameters. This presentation of data, however, is not truly descriptive of the out-of-round shape. Figure B-5 shows a cross-section at an elevation of 50 inches from the bottom, € = 0.4, of specimen 2-3. The initial out-of-round shape for
the outer and inner mold are shown, using an exaggerated displacement
50
Table B-1. Specimen Geometry
Construction Out-of-Roundness (Flat Spots) at or Near Failure Location
Pee b || Ate SE eh es ‘max’ | min mn Inside Wall Outside Wall No. (in.) (in.) t
1.439 1.201 0.08 1.462 1.178 0.08
241 0.037 oo 1.975 | 2.047 | 1.874] 0.05 2-2 = (2.48) | 1.960 | 2.092 | 1.832] 0.07 23
2-4
3-1 O.037 || 2.35 1.965 | 2.064 | 1.848] 0.06 3-2 2.065 | 1.823 | 0.06 3-3 = = 1.966 | 2.069 | 1.856 | 0.06 3-4
A 0.037 | 2.35
42
4-3
5-1 0.063 co 3.392 | 3.588 | 3.255] 0.04 5-2 = (2.48)°
“Between 100 and 250 readings. 2 nevensce value from 6-in.-sq fragmented area of imploded specimen.
© Actual specimen L/D.
Table B-2. Digest of Specimen scale. In the regions of O and 180
Out-of-Roundness
degress, it is observed that the wall is thinner than nominal and that the Out-of-Roundness
Parameters curvature is flatter than that of the membrane circle. The center of the membrane circle for the outer wall is offset from the center of the inner wall by about 0.02 inches.
Another cross-sectional view at
elevation € = 0.4 is shown in Figure “Radius deviations are for radii less B-6. The data are a compilation from
thanthe nominalradt several specimens of t/D, = 0.037.
51
Radius deviation scale: 0 0.2 in.
outer shape
outer membrane circle
center of inner wall
center of outer wall sale
om oS
inner membrane circle
inner shape
Figure B-5. Initial cross-section shape (superimposed to show relative changes in wall thickness and flat spots) for specimen 2-3, showing radius deviations of inner and outer wall surfaces at 0 psi and & = 0.4 (50 inches from bottom).
52
& Sc! Co) ot . “ a3 & wy % ee %0 s Som M oa x 3S eo = 0 . J » ss x e | or Z 90 fs ‘ 23 Gh Sos a ‘ Ew 9 ive) lon mn N avg R 270° t=2.02in.9 26.10 in. @ t=1.99 in. eee 6 » oS Sg So ° a L095 | se 4, x | 2 . A 10} 5 <a x & ‘2, y ips o- JL ee 2 iT | 180°
Figure B-6. Variation in wall thickness and mean radius at different locations on circumference at & = 0.4 (50 inches from bottom). Values are average of several specimens.
53
90°
Variations in wall thickness and mean radius, R, are shown around the circumference. The average R was 26.03 + 0.05 inches (661 + 1 mm). The magnitude of the standard deviation was mostly from the lack of
accuracy in measuring the radius with the steel rule.
CONCRETE MATERIALS
Mix Design
Concrete was batched and supplied by a transit mix company. Each delivery consisted of 2.0 yd? (1.5 m3) of concrete. The mix was designed for 6,000 psi (41 MPa) at 28 days. The proportions of cement to sand to aggregate were 1:1.96:2.22, respectively. The cement content was 676 lb/yd3? (401 kg/m3). Water-to-cement ratio averaged 0.55. Slump at the time of placement controlled the total water content, and the slumps averaged 3-3/4 + 1/4 inches (95 + 6 mm).
Portland, low alkali, type II cement was used along with a water- reducing admixture, Zeecon H, at a rate of 6 ounces (0.17 kg) per 100 pounds (45.4 kg) of cement. The sand and aggregate were from the Santa Clara River Basin. Maximum aggregate size was 3/8 inch (9.5 mm), and the aggregate underwent heavy media separation.
A summary of the concrete properties is given in Table B-3. The concrete compressive strengths were measured at 7 and 28 days and at the time of testing. Stress-strain curves were obtained from numerous specimens. Several modulus parameters are listed in Table B-3, along with the ultimate strain and Poisson's ratio. Figure B-7 shows repre- sentative stress-strain curves for 7,000 and 8,000 psi (48 and 55 MPa) concrete.
Expansive-cement grout, used as a packing material between the stiffeners and concrete wall, had mix proportions of one part portland cement type K, one part San Gabriel River sand between sieve sizes 4
and 16, one part San Gabriel River sand between sieve sizes 16 and 30.
54
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Figure B-7. Uniaxial compressive stress-strain relationship for concrete.
The water-to-cement ratio was 0.37 and a retardant admixture, E42 Master Builder, was used at 4.1 ounces (0.12 kg) per 100 pounds (45.4 kg) of cement. The compressive strength of this mix was 5,520 psi (38.1 MPa) at 7 days taken from three 3x6-inch (76x152-mm) control cylinders.
TEST RESULTS
Implosion
Test conditions and implosion results are presented in Table B-4. The implosion pressure, Bat and nondimensional ratio of implosion strength, a eS are given along with data on the failure hole size and boundary behavior.
A summary of the implosion results is given in Table B-5.
56
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Table B-5. Summary of Test Results
Coefficient Boundary | Type of tro Dp: i of Condition | Loading ee Variation (%)
Remarks
0.024 | 2.3 simple short b = 0.037 free short Specimen 2-4 excluded
0.037 : simple short g Specimen 3-4 excluded
0.037 3) simple long -
0.063 free short Specimen 5-2 excluded
Post-implosion views of several specimens are shown in Figures B-8 through B-16. For those specimens having a simple-support boundary condition, the failure holes occurred in the midlength region away from the ends (Figures B-8 and B-13). For those specimens having a free- support boundary condition, the failure hole typically occurred at the top end (Figures B-11 through B-15), but the failure hole occurred in the midlength region for specimen 2-1 (the strongest Group 2 specimen) (see Figure B-10).
The experimental test setup was probably the cause for the failure holes that occurred at the top. When the specimens were fabricated, the top cylinder edge was hand-troweled and therefore uneven. On specimen 5-1 the top end-closure ring was placed on the cylinder with- out the gasket material to observe unevenness. A rather large portion of the mating surface showed a gap of from 1/16 to 1/8 inch (2 to 3 mm). A filler material, such as gypsum used in specimens 2-1 and 5-1, filled the gap adequately. However, use of the gypsum was discontin- ued because the material is water soluble, so small leaks grew into major leaks. Epoxy was used as its replacement, but epoxy filler material did not appear to perform adequately. Epoxy has a modulus about one-tenth that of concrete and probably about one-fifth that of gypsum. It wasn't until after specimen 5-2 was tested (at the end of
the test program) that it became quite apparent that the epoxy filler
38
Figure B-9. Fragments of failure
ew of 0.024
8. Post-implosion vi
Figure B
il.
hole from specimen 1-
sim-
?
y=
1 (t/D
specimen 1 ple support).
te
NX
Bs "
SS a vena
Figure B-11. Post-implosion view of
Figure B-10. Post-implosion view of
free
’
specimen 2-2 (t/D, = 0.037
support).
specimen 2-1 (t/D,, = 0.037, free
support).
59
material was not a good substitu- tion. Figure B-16 shows that specimen 5-2 had a very local failure at the top edge which was a bearing-type failure.
Boundary behavior is quanti- fied in Table B-4. For conveni- ence, a nondimensional value, 90, was selected to express boundary behavior as the ratio of radial displacement at the end supports to the radial displacement at midlength of the specimen. A rigid support would be identified by »® = 0 and a free support by 6 = 1.
Observed boundary perfor- mances showed a small difference between actual and _ theoretical behavior. For free-support speci- mens the ideal » of 1.00 was closely approximated. Two specimens with t/D , = 0.037 showed free-support behavior where was 0.90 and 0.96. Specimen 2-3 showed unusual behavior where the bottom of the cylinder moved radially inward the least, » = 0.60, but the top moved inward) the, most.) 16) =) 17s6 sane. the top of the cylinder at the flat spot location moved inward more than the middle).
60
Figure B-12. Fragments of failure hole from specimen 2-2.
es
oes: SSS Sees Sr
oS ro tees
é S=
ra
rans ZS
Figure B-13. Post-implosion view of specimen 3-1 (t/D,, = 0.037, sim- ple support).
For simple-support specimens, thenenGdealiy on tol aezeromm wash not obtained. The radial deflection of the steel stiffener provided some compliance. The stiffener deflection was calculated to be about 0.01 inch (0.3 mm) at a pressure load of 500 psi 5 MRD, ce A o oF O.08,
Measured radial deflections showed
values about 0.02 inch (0.5 mm), a
Figure B-14. Fragments of failure hole from specimen 3-1.
134 Yl, y Hole y QI
120 -
1
100
80
60
20 F =|
Cylinder Length (in.)
0 360 330 300 270 240 210 180 150 120 90 60 30
Circumference (Deg)
Figure B-15. Post-implosion view of specimen 5-1 (t/D,, = 0.063, free support).
61
» of about 0.16, at a distance of 2 inches (50 mm) away from the stif- feners. The test specimens had a clear length between stiffeners of 127 inches (3220 mm). After accounting for the compliance of the stiffener, the "actual" length of the cylinder appeared to be about 130
inches (3300 mm); hence, the effect of stiffener compliance was small.
AY wt Wy XXX
Figure B-16. Local failure of specimen 5-2 (t/D,, = 0.063, free support).
To test for possible reduction in implosion strength due to sus- tained loading, the implosion resistance of Group 4 specimens was assumed to be equal to that of the average value of Group 3 specimens; i.e., Betas 0.079. Specimen 4-1 was subjected to 85% of this load. After 2.5 hours of load exposure the specimen imploded, which implied
a strength reduction of 15% for a relatively brief period of sustained
62
loading. Subsequently, the sustained pressure for specimen 4-2 was lowered to 80% of predicted short-term strength, while specimen 4-3 was subjected to 70%.
Specimen 4-2 was accidently imploded after 44 hours of load expo- sure during modification of the electronic pump control equipment; no record of the actual implosion pressure was obtained. The implosion value listed in Table B-4 was based on a calculated estimate of the pressure increase in the vessel for a known duration of pump opera- tion. Data were available on the exact time of operation of the pump before implosion occurred. The estimated implosion pressure is pro- bably within a 5% error limit.
Specimen 4-3 withstood a pressure load of 450 psi (3.1 MPa) for 168 hours without incident. The pressure was then reduced to zero where it remained for 16 hours before the specimen was subjected to 85% of short-term strength. The pressure level was sustained for 2.5 hours without any signs of major structural distress, then the pressure
level was raised to 95% where implosion occurred after 3 minutes.
Radial Displacement Behavior
Radial displacement terms are defined diagrammatically in Figure B-17. The deflectometer instrumentation method measured radial dis- placement from initial to deflected shape, w. Membrane radial displace- ments, wr were determined from the w data. The following method was used. The reader should picture radial displacement data being displayed on oscillograph paper as a potentiometer moves around the circumference of a cylinder. A straight line would mean a perfect circle. The specimens were not perfect; therefore, the lne moved upward (for inward displacement) and downward (for outward displace- ment). The wavy line on the oscillograph paper is a chart of out-of- roundness data. The wavy line can be digitized (i.e., each point along the line can be given a magnitude value). The average of these values is plotted as a straight line and represents the membrane curve. The
average defines the size or radius of the membrane circle.
63
initial shape
initial membrane circle
deflected shape
where: w= displacement from initial to deflected shape W,, = displacement from mem-
brane behavior Wp = displacement from bending wy = total displacement AR; = initial deviation in inside radius
deflected membrane circle
Figure B-17. Definition of displacement terms.
When a deflected shape was plotted the reference point was the location of the center shaft that held the potentiometer; however, this location was not the "true" center of the deflected shape. The opera- tion of finding the true center location was that of manually super- imposing the membrane curve on the deflected shape and using judg- ment to decide the location. Judgment was based on fitting the mem- brane curve (perfect circle) of known size to the deflected shape such that the area between the wavy line and the membrane curve was divided equally.
The initial and deflected cross-sectional shapes of a free and simply supported specimen with their corresponding membrane circles are shown in Figures B-18 and B-19, respectively. All specimens having a free support deflected into an elliptical shape where the num- ber of lobes, n, was 2. All specimens having a simple support
deflected into a shape with n = 3.
64
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The worst flat spot on each cylinder eventually became the failure location; this location consistently coincided with the wall sections that were thin and somewhat flat initially.
Radial displacement data, as shown in Figures B-18 and B-19, were plotted at various pressure levels for the test specimens. Data obtained from these plots were used in analyzing the _ structural behavior.
Pressure versus w and Wa relationships are shown in Figures B-20 through B-22.* The data for w are from the worst flat spot location. The wi, curves come from w data so the maximum pressure for the Wi curve (experimental perfect cylinder) cannot exceed oe of the experi- mental out-of-round specimen.
Radial displacement behavior along the length of the cylinder is shown in Figures B-23 through B-25. The influence of the boundary condition as it is affected by the simple-support and the free-support conditions is vividly seen.
Radial displacement data for specimens 5-1 and 5-2 were recorded, but meaningful data were not obtained because the end-closures shifted position as the pressure load was increased. The center of the shaft moved, which meant that a common reference point between various pressure levels was not available.
In Figure B-17, it is observed that the total radial displacement,
Wr» 1S equal to: w =i Wintan NRE (B-1) al i
and we = wh + Wh (B-2)
*The analytical curves will be discussed later.
66
Pressure, P (psi)
Pressure, P (psi)
T T t/Dg = 0.024
stress L/D9 = 2.35 GUD | comErol simple support failure 500 perfect \ cylinder, Case 1 gaa
Va 400 - »
A~ strain control
WA failure 300 + /_* (o)
200 - Case 2
—_O-—-__ experimental (one specimen) +
instability
out-of-round cylinder, failure
100 — — —_ analytical 0 ! “ifs (0) 0.05 0.10 0.15 0.20
Radial Displacements, w (in.)
Figure B-20. Radial displacement behavior at midlength of specimen 1-1 having
t/D,, = 0.024 and simple support.
Td u T Rg = 27 in. -——+ 700 Ale | WD» = 00387 ki L/D, = = 600 / | free support 500 ‘ t= 1.97 in pe perfect cylinder, Case 6 w 400 Le SESS 300 | out-of-round cylinder, Case 5 experimental range 200 ; of two specimens : ——O— experimental average ———-— analytical 100 oO stress control failure & strain control failure 0 | i 1 0) 0.10 0.20 0.30 0.40
Radial Displacements, w (in.)
Figure B-21. Radial displacement behavior at midlength of Group 2 cylinders having
t/D,, = 0.037 and free support.
67
0.50
700 +
I T
perfect cylinder, Case 3
600 Y w 500 out-of-round cylinder, Case 4 7 400 : & Ro = 27 in. Ou o 5 9 -+— yn A o 300 experimental | ie range of six | specimens ec ' 200 = | t/Do = 0.037 [| t= 1.97 in. ——_©——_ experimental average eee 8 L/D, = 2.35 FTAA Sa FCG le ae as = analytical : (c) stress control failure simple support a strain control failure 0 | L 0.05 0.10 0.15 0.20 Radial Displacements, w (in.) Figure B-22. Radial displacement behavior at midlength of Group 3 cylinders having t/D, = 0.037 and simple support. u TT ws Ur 7 1F- Vi T T T T SL| 4 8 \ \ \ ——©— experimental \ (one specimen) 4L —— — analytical me | | wat Ro = 27 in. an 3 ! ee hae coal I 5 = H TN [- We 8 | > N I | 1S) | @s | ~ ! = 3L H % 3 ! io SE ic s | 25 g qe eel t/Do = 0.037 | = / EK © Fy L/Dp = | > perfect 7 > — out-of-round is cylinder, / t=alestins oO free support N ttingter, / a | it Case 1 i = | Case 6 ce = = S | ; fi t/Dp = 0.024 Baul ce | y L/D = 2.35 28 | p= out-of-round simple support A cylinder, | L Case 2 perfect w 8 Al LE cylinder, \ = ———o©— experimental 8 Case 5 | (one specimen) —----- analytical | 4mm 6mm 2mm 4mm 0 1 i D 1 0 i | Ll it { = 0.15 0.20 0.25 10) 0.05 0.10 0.15 0.20 0.25
Radial Displacements, w (in.)
Figure B-23. Radial displacement behavior along
length of specimen 1-1 having t/D,, = 0.024 and
simple support at a pressure load of 0.89 P;_.
68
Radial Displacements, w (in.)
Figure B-24. Radial displacement behavior
along length of specimen 2-1 having t/D,, = 0.037 and free support at a pres-
sure load of 0.78 Pian
The Known terms are w, Wp and AR.. Hence, radial displacements due
to bending can be calculated as:
m = wy ob NRG (B-3)
An estimate of the magnitude of strain on the inside and outside
wall surfaces can be made because we and Wy are now Known. Mem-
brane strain is calculated from:
WwW : m on zm Ro = 27 in € Pav roe B-4 aL = pi m Ry Ce 8 n fe Males \\ eee \\ = | 3L 4 | | Sol e oye Us J and bending strain is calculated ¢ | Ny Dae Bl 1D = 0.037 | from an expression developed in {4% experiments et | aD ran f 1m r 3 3 | pentect eens Reference 19 as: | leylinder Case 3 Lb 4 8 | q out-of-round ———o—— experimental average | cylinder, —— — — analytical Case 4 | | “Db £ 2 0 LG L i et] E = —— im = i) (B-5) 0 0.05 0.10 OS OO b 2 RZ Radial Displacements, w (in.)
Figure B-25. Radial displacement behavior
Table B-6 summarizes _ the along length of Group 3 cylinders having t/D, = 0.037 and simple
support at a pressure load of 0.95P;
ultimate radial displacements and Fe
calculated strains. It is interesting to note that although Wy is typi- cally several times the magnitude of
Wit the calculated strains En and €, are nearly equal. At implosion
b the strains at the flat-spot location on the inside wall experienced slight tension while on the outside wall strains were on the order of 4,000
uin./in. compression.
69
Table B-6. Ultimate Radial Displacements and Calculated Strains
Strains at Flat Spot on —
1 No. of { i em Eb Specimen (win./in.) (win./in.)
Inside Wall, | Outside Wall,
€m_~ €b €m * €b (yin./in.) (win./in.)
Group
0.050 0.043 | 0.207 1,670 0.057 0.051 0.514 2,040
0.042 0.052 | 0.175 2,080
-40 Average = a #31880 tension compression
ANALYTICAL RESULTS AND DISCUSSION
Analysis Description
A structural analysis was performed on the experimental specimens using a finite element method called NONSAP-A that incorporated an advanced constitutive relation subroutine for the concrete. The analy- sis was conducted by Chen, Chang, and Suzuki (Ref 20) without the benefit of the test results. Information on specimen geometry (includ- ing the out-of-round geometry, boundary conditions, and material properties) was supplied. It was desired to computationally model the test specimens as realistically as possible and then determine the accu-
racy of the predictions.
Constitutive Model. The constitutive model was developed in three
parts - elastic, plastic and fracture - for concrete under general stress states.
For elastic concrete, it was assumed that, initially, concrete is an isotropic homogeneous linear elastic material and its stress-strain rela- tions are described completely by two elastic constants, Poisson's ratio, v, and Young's modulus, E. For the present analysis, v = 0.19 was used, and E = 3.66x10° sand) 4) 19x10® psi (25-2) vands28h9GPa) were
70
determined from Figure B-7. The elastic limit envelope in general stress space was obtained by scaling the fracture envelope down to a size where uniaxial yield point corresponded to about 43% of the uniaxial strength.
For plastic concrete, a strain-hardening plasticity model as pro- posed previously in Reference 21 was used to describe the nonlinear irreversible stress-strain response of concrete material. The plastic incremental stress-strain relationship based on the normality flow rule in the theory of plasticity are developed in detail in Reference 22.
For fracture, the concrete failed when the state of stress reached a certain critical value. Two different types of fracture mode are
defined here.
(1) "Cracking" Type - When the principal stresses are either in the _ tension-tension state or _ tension- compression state and their values exceed the limit
values.
(2) "Crushing" Type - When the principal stresses are in
the compression-compression state and their values exceed the limit values. When concrete cracks, the material is assumed to lose only its tensile strength normal to the crack direction but to retain its strength parallel to the crack direction. On the other hand, when concrete crushes, the material element loses its
strength completely.
In the present analysis, a dual representation of fracture criterion was expressed in terms of both stresses and strain and specifies the limit value under multiaxial state of stresses or strains in the following
forms:
Wl
(1) Stress Criterion
: La eae : H(i a) = a a A Ital, = us (B-6)
where (ae and u, are material constants and where a is equal to zero when the principal stresses are in the compression state and equal to -1/6 when in the tension-compression or tension-tension state. The
first invariant, I corresponds to the mean stress component of the
1?
stress state. The term Jo is the second invariant of deviatoric stresses.
(2) Strain Criterion
Bn en 2) 2 - = t esiloes paseo 1 = ee ae Baa) S dines (3 iq tn (=) a7) Cc c or Maximum of the Principal Strains = E, (B-8)
in which Yh corresponds to volumetric strain and Jo is the second invari- ant of deviatoric strains. The terms en and Et specify the maximum ductilities of concrete under uniaxial compressive and tensile loading conditions, respectively. Herein, the compressive cylinder strength was assumed as 7,000 and 8,000 psi (48 and 55 MPa); and maximum compressive strain, &,> was 3,500 pin./in. The tensile strength, fi was assumed to be 0.09 fs and maximum tensile strain, E,> was 800 uin./in. When the stress state in the concrete satisfied either the
stress criterion (Equation B-6) or the strain criteria (Equations B-7
72
and B-8), fracture of concrete was assumed to occur. If the fracture stress state lies in the tension-compression or tension-tension zone, a crack was assumed to occur in a plane normal to the direction of the
offending principal tensile stress or Strain.
Finite Element Program. In the present work all the analyses were performed using NFAP program (Ref 23) on computer system IBM model 370-158. NFAP is a modified and extended version of NONSAP-A pro- gram (Ref 24), which is a modified version of the NONSAP program originally developed by Bathe, Wilson, and Iding (Ref 25). The pre- sent concrete constitutive model has been incorporated as a subroutine in the NFAP program. The average computing time for the two- dimensional (plane strain or axisymmetric) problems was about 5 minutes for each case. The average computing time for each three-dimensional
analysis was about 62 minutes.
Geometry of Analysis. The eight cases as listed in Table B-7 were
analyzed using isoparametric shell elements.
(1) Cases 1 and 3 were modeled as axisymmetrical problems
with simple-support end-condition.
(2) Cases 5 and 7 were modeled as plane strain, axisym-
metrical problems.
(3) Cases 6 and 8 were modeled as plane strain, asymmet- rical problems. Out-of-roundness in the form of n = 2
(see Table 2) was included in the analysis.
(4) Cases 2 and 4 were treated as three-dimensional pro- blems with large displacement. Out-of-roundness in
the form of n = 3 was included in the analysis.
73
‘punoi-jo-no = YOO,
S-€ MGR L Worz 24/d g
“UIBIIS DAISSAIdUIOD JAIssadx9 Aq 1OU ‘sasRd [[R Ul UTPIIS [RIPeI JJISUDI %BO'O Aq Pauljap snyIeY ,,
. ‘ C = u [eloyeu Selo 096 0008 curems aueyd woo yeliaqeur SOLO 9S0'T 000‘8 ures aueyd yoayiod ie = [eoaeur 6700 Ive 0002 ‘ures oueyd woo jeli91ew i 7600 8tS 000‘Z uress sued ayiad [Pl1o7eur ae €Z0°0 80S 000°L ¢=u'd¢ bs (@X@) ajduits L€0'0 > jeuaiew | 060'0 | 920°0 000'L | WeuTUAsIxe qoajied ajduns | 2¢€0°0 ¢ — a Ayyrqeasut +£0'0 +200 000'8 € =u 'd-¢ ,1OO ajdurts +700 (4 [elaieul 090°0 0S0°0 dT aw AsIxe yajiad a[duuts dInjIey am ai siskyeuy KGET yioddns jo spow O(Uty) | 9g) jo Ala9uWI0d») 2 puq 1
synsay jeomdjeuy °2-g IqeL
74
Constant tavg
Varying Wall
Thickness Wall thickness = tavg -0.08 in.
Figure B-26. Idealized initial out-of-round shape for cylinders with n = 3.
AR, = 0.06 in.
ARj = 0.06 in.
450 | 459 % R. WA ‘ Xs 7 Jo S 4 nN Constant | tavg \ , AR; = -0.02 in.
Varying Wall
Thickness Wall Thickness = tayg -0.08 in.
Figure B-27. Idealized initial out-of-round shape for cylinders with n = 2.
15
Cross-sectional geometry Table B-8. Cross-Sectional Geometry for Cylinders for the cylinders, which
Numbers includes data on _ idealized of
Lobes, out-of-roundness, is shown in
Figures B-26 and B-27 with geometry values given in Table B-8.
26.345 26.345 26.015 26.015 26.015 26.015 25.305 25.305
Implosion Results. Table B-7 summarizes the results of
1 2 3 4 5 6 7 8
the analyses in terms. of hi
n=2 Rave = Ravggo + ARcos20 implosion pressures that were : ‘ tge OK @ < 45° controlled by strain failure , e o t o-tpo criteria, (P;)., and stress es an ELA) AD 2M < 902 failure criteria, (P._)_. The im’o fs be E : = n= 3 Rave = Rae AR cos 3 0 implosion strength is given by am 0 . . . te} < < oO the nondimensional ratio of io? OE Oe t Paw to ohne analyticalsimplo- GO =O a to + ap (0 - 30°) 30° < 0 < 60°
. . oO sion strength is compared to 30
bes ee , See Figure B-26. the experimental strength by
“See Figure B-27. the ratios shown in the last two columns of Table B-7.
The experimental specimens were out-of-round cylinders so a true comparison between analysis and experiment is only for out-of-round cylinder cases (Cases 2, 4, 6, and 8). The average ratio of strain- controlled implosion strength to experimental implosion strength was 0.89 and for stress-controlled implosion strength to experimental implo- sion strength was 0.93.
The stress criterion failure mode predicted implosion with better accuracy than the strain criterion method. Looking more closely at individual cases, Case 2 was an instability failure mode and analysis predicted implosion 15% lower than experimental. Cases 4, 6, and 8 were material failure modes, and analysis predicted implosion only 4%
lower than experimental.
76
Interestingly, the strain criteria that controlled in all cases, except Case 2, was a tensile strain limit of 800 win./in., and not a compressive strain limit. The limiting tensile strain occurred in the radial direction of the wall (increase in wall thickness) at midlength for the free-support specimens and at a distance of & = 0.4 from the end for the simple-support specimens. Tensile strain had an influence on failure because the wall thickness would laminate and facilitate a shear- compression type of material failure of the wall. Evidence of wall lamination has been observed in fragments of thick-walled spheres under hydrostatic loading (Ref 26) but was not observed in the frag- ments of cylinder specimens.
The effect of out-of-
roundness in reducing the
Table B-9. Reduction in Implosion Strength Due to Out-of-Roundness
implosion strength of a per- fectly circular cylinder is shown in Table B-9. Cylin-
der t/D , influenced the out-
Percent Reduction in Implosion Strength
31
Between Case Numbers@ —
3&4 5&6 Average a 8 9 (0)
>
Failure Criteria
of-roundness effect con-
Strain a
Control siderably. Cases 1 and 2 are
Stress
thinner specimens than Cases 3 and 4, but all have a
Control
ee ae simple-support end-condition; the thinner specimens showed a 44% reduction due to out- of-roundness, whereas the thicker specimens showed a 16% reduction. A similar observation is made between Cases 5 and 6 which are thinner than Cases 7 and 8, all having a free-support end-condition.
The influence of end-condition on out-of-round effect can be observed with Cases 3 and 4 and 5 and 6, all of which have t/D, of 0.037. Cases 3 and 4 are simply supported and showed a reduction of 16%; whereas, Cases 5 and 6 are freely supported and showed a reduc-
tion of 46%.
77
The effect of cylinder length can be observed from Cases 3 and 4 and 5 and 6, all of which have the same t/D , ratio of 0.037 but differ- ent effective lengths. Cases 3 and 4 had an L/D, ratio of 2.35, and Cases 5 and 6 had an L/D, ratio of infinity. For the out-of-round cylinders (Cases 4 and 6), the shorter cylinder had a _ predicted increase in implosion strength of 53% over that of the infinitely long
cylinder. Experimentally, the increase in strength was 41%.
Displacement Behavior
The predicted deflected shapes for free-support and _ simple- support specimens are shown in Figures B-18 and B-19. For the free- support cylinder (Figure B-18), the predicted shape is a fair approxi- mation of the experimental shape. It should be noted that the pressure level for the experimental shape is near implosion at 400 psi (2.8 MPa) where the analytical shape is at implosion at 346 psi (2.4 MPa). For the simple-support cylinder (Figure B-19), the comparison is good.
The predicted radial displacement behavior as a function of pres- sure is shown in Figures B-20 and B-22. Comparison of the experi- mental to analytical behavior is quite good. For the out-of-round cylinders, note that the predicted implosion pressures using the strain or stress criteria are approximately the same.
A large difference in ultimate radial displacement was observed between perfect and out-of-round specimens. For cylinders of t/D, = 0.037 (Figure B-21), the experimental out-of-round cylinder showed w = 0.508 inch (13 mm), while the perfect cylinder had w = 0.08 inch (2 mm) - a 6.4-fold increase. For specimens having the same t/D, ratio of 0.037 but different end-support conditions (Figures B-21 and B-22), the free-support cylinders showed an ultimate displacement of w = 0.508 inch (13 mm) compared to the simple-support cylinders of
w = 0.185 inch (5 mm) - a 2.7-fold increase.
78
Radial displacement behavior along the length of the cylinder is shown in Figures B-23 through B-25. The effect of the simple-support is vividly shown in Figures B-23 and B-25. The compliance of the actual ring stiffener in the experimental tests can be observed in Fig- ure B-25 where approximately 0.02 inch (0.5 mm) of radial movement occurred.
For the free-support cylinder (Figure B-24), the difference between experimental and analytical behavior appears great. However, this same difference is shown in Figure B-21, where the comparison appears better. Experimentally, the free-support end-condition using a
rubber gasket modeled the ideal free-support quite well.
FINDINGS
1. Analytically, using the finite element program NONSAP-A with an advanced constitutive material model, the behavior of the cylinder specimens was predicted with good accuracy. The implosion pressures were predicted 7% lower than actual when a stress criterion controlled failure. It was found experimentally that specimens of L/D, of 2.35 had an implosion strength 41% greater than specimens of infinite length (ong cylinders); analytically, the increase in strength was predicted as BSF
2. Out-of-roundness was an important parameter in implosion strength and radial displacement behavior. Analytically, the effect of out-of-roundness was to reduce the implosion strength of perfect cylin- ders by 16% to 46% depending on t/D, ratio and end-support condition. The ultimate radial displacement for the free-support experimental specimens of t/D, = 0.037 was 0.508 inch (13 mm), which was 6.4 times the displacement for a perfect cylinder. The need to model out-of-
roundness to obtain accurate analytical predictions was found important.
79
3. Radial displacement data for the specimens showed that the deflected shape for the free-support cylinders had two lobes (n = 2) and for the simple-support cylinders had three lobes (n = 3). The membrane and bending radial displacements were determined, and esti- mates of strain were calculated at the failure location. It appeared that at the worst flat spot the strain level at failure was slght tension on the inside wall and about 4,000 win./in. compression on the outside
wall.
80
LIST OF SYMBOLS
Outside diameter
Initial elastic modulus Secant elastic modulus Tangent elastic modulus
Uniaxial concrete com- pressive strength
Material strength factor for cylinder structures
Material strength factor for spherical structures
Cylinder length
Number of lobes
External pressure Implosion pressure Analytical implosion pres- sure controlled by strain criteria
Analytical implosion pres- sure controlled by stress criteria
Average radius
Outside radius
Average wall thickness
Minimum wall thickness
Radial displacement from initial to deflected shape
Bending radial displace- ments
Membrane radial displace- ments
81
Total radial displacement (see Figure B-17)
Deviation in radius
Inside deviation from average radius
Outside deviation from average radius
min Ultimate strain Bending strain Membrane strain
Empirical plasticity reduc- tion factor
Angular coordinate (see Figures B-26 and B-27)
Angular coordinates of failure zone
Angular coordinate of center of failure zone
Poisson's ratio
Nondimensional distance along cylinder length (see Figure B-4)
Wall stress Wall stress at implosion
Wall stress at implosion predicted by Bresse's equation (Equation 5)
Wall stress at implosion predicted by Donnell's equation (Equation 4)
Ratio of radial displace- ments between end and middle of cylinder
DISTRIBUTION LIST
ARMY CRREL Library, Hanover NH
ARMY ENG WATERWAYS EXP STA Library, Vicksburg MS
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83
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SEATTLE U Prof Schwaegler Seattle WA
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84
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LOCKHEED MISSILES & SPACE CO. INC. L. Trimble, Sunnyvale CA
MC CLELLAND ENGINEERS INC Houston TX (B. McClelland)
MEXICO R. Cardenas
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NORWAY E. Gjory. Trondheim; F. Manning, Stavanger: J. Creed, Ski; Norwegian Tech Univ (Brandtzaeg). Trondheim: P.S. Hafskjold, Oslo; R. Sletten, Oslo: S. Field, Oslo; Siv Ing Knut Hove. Oslo
OFFSHORE POWER SYS (S N Pagay) Jacksonville, FL
PACIFIC MARINE TECHNOLOGY Long Beach, CA (Wagner)
PORTLAND CEMENT ASSOC. (Dr. E. Hognestad) Skokie, IL: SKOKIE, IL (CORLEY; Skokie IL (Rsch & Dev Lab, Lib.)
PRESTRESSED CONCRETE INST C. Freyermuth, Chicago IL
SANDIA LABORATORIES (Dr. D.R. Anderson) Albuquerque, NM
SCHUPACK ASSOC SO. NORWALK, CT (SCHUPACK)
SHELL OIL CO. HOUSTON, TX (WARRINGTON); I. Boaz, Houston TX
SOUTH AMERICA B. Contarini, Rio de Janeiro, Brazil: N. Nouel. Valencia, Venezuela
SPAIN D. Alfredo Paez, Algorta
SWEDEN Cement & Concrete Research Inst., Stockholm; GeoTech Inst: K. Christenson, Stockholm; Kurt Eriksson, Stockholm :
THE NETHERLANDS Ir Van Loenen, Beverwijk: J. Slagter, Driebergen
TRW SYSTEMS REDONDO BEACH, CA (DAI)
UNITED KINGDOM (D. Faulkner) Glasgow, Scotland; (Dr. F.K. Garas), Middlesex; (Dr. P. Montague) Manchester, England: (H.W. Baker) Glasgow, Scotland; (M E W Jones) Glasgow, Scotland; (M J Collard), London; A. Denton, London; Cambridge U (Dr. C. Morley) Cabridge, GB: Cement & Concrete Assoc Wexham Springs, Slough Bucks: Cement & Concrete Assoc. (Lit. Ex), Bucks: Cement Marketing Co. Ltd. (Brittain) London; D. Lee, London: J. Derrington, London; Library, Bristol; P. Shaw, London; R. Browne, Southall, Middlesex; Sunderland Polytechnic (A.L. Marshall), Great Britain: T. Ridley, London; Taylor, Woodrow Constr (Stubbs), Southall, Middlesex; Univ. of Bristol (R. Morgan). Bristol: W. Crozier, Wexham Springs: Watford (Bldg Rsch Sta, F. Grimer)
WOODWARD-CLYDE CONSULTANTS PLYMOUTH MEETING PA (CROSS. III)
BROWN, ROBERT University. AL
DOBROWOLSKI. J.A. Altadena, CA
GERWICK, BEN C. JR San Francisco, CA
LAYTON Redmond, WA
NORWAY B. Nordby, Oslo
WATT BRIAN ASSOC INC. Houston, TX
WESTCOTT WM Miami, FL
WM TALBOT Orange CA
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