Report 1854 4 °: SHingtoN ne HYDROMECHANICS AERODYNAMICS oO STRUCTURAL MECHANICS O APPLIED MATHEMATICS oO ACOUSTICS AND TION , ICEL WRew=64 | /2¢ Soa) : : / oe August 1964 TESTS OF MACHINED HIGH-STRENGTH STEEL SPHERICAL SHELLS SUBJECTED TO EXTERNAL HYDROSTATIC PRESSURE by Albert E. Dadley STRUCTURAL MECHANICS LABORATORY RESEARCH AND DEVELOPMENT REPORT Report 1854 s ha9zeoo TOEO O WCQ 1OHM/198lN EMCO August 1964 TESTS OF MACHINED HIGH-STRENGTH STEEL SPHERICAL SHELLS SUBJECTED TO EXTERNAL HYDROSTATIC PRESSURE by Albert E. Dadley Report 1854 S-FO13 03 02 TABLE OF CONTENTS ABSTRACT COCCHOLHOHSGHHSSCHSCHSHSFEGHF2OHGSCHBHSHOSCHHLHFTLCHOFOCHOSCHLHOHFGHOHFFTFLCHOSSHHHFAHLCHH SEO INTRODUCTION ccoccccccccccccccccccccccccccce sere eves ec cnee cose sseceee DESCRIPTION OF MODELS = wcccccccccccccvvcccccccccccscecccsccccccccccees TEST PROCEDURE AND RESULTS) .occcccccccvecccccccccccecccveseccccsccees DISCUSSION (OF RESULTS), \5'55/5's\sieieiels ole ole e'e1s' e's oleic e\eleic oa c\0\s ow 0) ciceisieleleie eleieie CONCLUSIONS ccccccccvcesccccccccnccsccccc cece ccc ceeesseccesesescece ACKNOWLEDGMENTS = -cocccccecccsceccccvc ose cov vesevccc ec esesecoeeecesees REFERENCES =o ccocccccccccccc ccc c ccs coc ec seer cere eer eee eesen cols nses LIST OF FIGURES Figure 1 - Typical Compressive Stress-Strain Curves for Material (STS- Steel ) Used in Machined Steel ModelS ccoscccoeccccccvceccvcece Figure 2 - Representative Material CharacteriSticS .cccccccccccccccce Figure 3 - Details of the Cylinder-Spherical Boundary Intersections of the Models CHOOCHOHRGOHHSHOHLCHOHLHOHGH®HSLEHSHHSHHSHCHOHRHSCHOBSFHFOSLECHSCOH Figure 4 ent Collapsed Models aESio) Shale Siarclc Gia ietcve cuolata ace Siete ielorera Clete olazacain wince Figure 5 - Pressure versus Measured Change in Internal Volume for Model 7A eoe7 OOF Cee S2HSGH2H2SSFTHHOFFLCHFHFFCHHBLCHHR HO CHF HESHOFTHH8 O80 Figure 6 - Nondimensional Plot of Experimental Results for Machined Near-Perfect STS Hemispherical ShellS cescoccccceccccccence LIST OF TABLES Table ub a Model Dimensions CHOHSTHSCHSHOLCHOHHHOHOFSHFGOHHLGHOHHGOHHHSCT7HSSFCHXOCHKHSE Table 2 - Measured Wall Thicknesses and Initial Departures from Sphericity @coeaeeenvno@e@eeeoeeceaooeaeeeseoevoeseoevoeevneee2eeaeeee7e2 2082020802080 0808080 Table 3 - Pressures at Which Strains were Recorded ceccccccccccccccce Table 4 Table 5 - Comparison of Experimental Collapse Pressures with Theory for Near-Perfect Thin Spherical ShellS .cccccceccccce Measured Strain Sensitivity CoefficientS cecccccccccccccnce iat Page 10 10 1/ 12 13 14 Page A5 16 ayy | 18 19 ABSTRACT Six structural models, consisting of hemispherical Shells bounded by ring-stiffened cylinders designed to provide ideal boundary conditions, were hydrostatically pressure-tested to collapse. The models were accurately machined from high-strength steel (STS) and were designed to investigate both elastic and inelastic huckling modes of collapse. The resuits of the tests are compared with theory, and the collapse pressures agree within + 7 percent of those computed by the TMB empirical buckling equation. A nondimensional plot of experimental results is presented for the models tested. Based on the plot, a simple design method is given for similar accurately machined thin spherical shells. INTRODUCTION In the past decade, increasing emphasis has been placed on the use of spherical shells in pressure vessels. Their use encompasses a wide range of applications for confinement of internal pressure, and there is an accelerating trend for external pressure applications in the field of deep underwater research. Because most of the materials used in deep~Sea underwater vehicles exhibit strain-hardening properties, which may deviate widely from the perfectly plastic (plateau) stress-strain pattern, there is a great need for wider understanding of the nature of inelastic buckling. However, greater knowledge of elastic buckling must also be emphasized in view of the growing interest in new tough materials such as glass and ceramics which have such extremely high compressive strengths that practical struc- tural designs for pressure vessels prevent inception of yielding at even the greatest of ocean denehees A historical background of the elastic and inelastic theories which apply to spherical shells subjected to external pressure has been extensively summarized in Reference 2. To evaluate the validity of the hydrostatic collapse pressures predicted by the buckling formulas developed from the various spherical Re reranees are listed on Page 20. Shell theories, six small accurately machined high-yield steel models were fabricated. To facilitate fabrication and subsequent instrumentation and thereby save time and funds, the models were designed and machined as hemispherical heads bounded by externally ring-stiffened reinforced cyl- inders in lieu of the actual spheres. The cylinder of each separate model was so deSigned as to Simulate at the boundary the action of the remaining half of the sphere, i.e., membrane deflection and no rotation. The measured uniform strain-gage readings and collapse pressures are consistent with similar work being performed on spherical shells and suggest an adherence of the test results to the ideal boundary design. Five of the models were designed to fail after the inception of yielding (inelastic buckling), and the remaining model was designed to fail well below the yield point within the elastic range (elastic buckling). The test resullits of these six near-perfect machined models, all of which failed within their proper ranges of elasticity, are presented in this report and compared with theory. A nondimensional plot of experimental results is also presented and discussed. The plot is presented for the purpose of providing a simple method of structural design for similar accurately machined thin spherical shells with similar stress-Strain patterns. The results of a similar plot currently being developed at the Model Basin from work performed on larger Segmentally welded high-strength steel hemispherical shells are also dis- cussed. DESCRIPTION OF MODELS Six hemispherical models bounded by external ring-stiffened cylinders were machined from high-strength, special-treatment steel (STS). Models 6, 4A, 4A Revised, 1CR, and 1CR Revised are approximately 7 in. in diameter and possess respective measured spherical shell thickness to nominal radius ratios (h/R) of 0.007, 0.017, 0.018, 0.035, and 0.036. Model 7A is approximately 4 in. in diameter and possesses an h/R equal to 0.003. Structural dimensions including the average compressive yield strengths as individually measured from eight representative sample coupons taken from the stock material of each model are presented in Table 1 together with a generalized sketch of the models. Typical stress-strain curves for the STS plate used for the fabrication of each of the models are illustrated in Figure 1. Figure 2 shows the representative ratios of the square root of the multiplicand of the secant and tangent modulii to the elastic modulus as a function of uniaxial compressive stress for the curves of the inelastic models of Figure 1. These curves describe the plastic behavior of the material and were used in the calculations to obtain the Taylor Model Basin (TMB) inelastic buckling pressures PE presented indirectly later in this report. All the models, with the exception of Model 7A, were machined identically. First, the inside contour was machined using a form tool, then the outside contour was machined using a lathe and ball-turning attachment, and finally, the exterior ring-stiffened cylinder was machined. Model 7A, the last model fabricated, was machined more accurately using a method similar to that just mentioned but with the addition of a more recently developed system consisting of a support pot and mating mandrel.” All the models were designed for membrane deflection and no rotation at the intersections of the hemispheres and the cylinders. By maintaining lower stresses in the cylindrical than in the spherical portion of the model and thereby assuring failure in the area of interest, this design prevents the boundary with the cylinder from altering the stress pattern in the hemisphere from the pattern that would be created in a sphere of the same material, radius, and shell thickness. The inside diameters of the cyl- inders of Models 4A and 1CR were deSigned to be slightly smaller than those of the hemispheres for Model 1CR (Figure 3a). Because of machining error, the cylindrical portion of Model 4A was fabricated with a slight overcut; see Figure 3b. Although this resulted in a thinning of the cylindrical shell, thereby varying the ideal boundary condition somewhat, the spherical shell was machined correctly. Figure 3c illustrates the structural boundary configuration for Models 6 and 7A and also for the revised design of Models 4A and 1CR, all of which were fabricated with equal cylindrical and spherical radii. Model 6 was accidentally machined with a small gouge around the outer circumference of the third frame from the boundary juncture. AS a result, approximately 16 percent of the area of the frame was removed, having a possible adverse effect on the ideal design of membrane deflection and no rotation of the juncture. Table 2 lists the measured spherical wall thicknesses for the hemispheres of all the models. Table 2 also indicates the initial departures from sphericity for the hemispheres of Models 4A Revised, 1CR Revised, and 7A. Because the importance of sphericity measurements had not been established at the beginning of the tests, they were not taken on the three models tested earlier. All the thickness measurements were taken uSing a vidigage, and the initial sphericity departures were measured from a fixed point using a dial gage in a ieenose ae TEST PROCEDURE AND RESULTS Each model was instrumented with strain gages in both the meridio- nal and circumferential directions of the spherical portions with 1/8- and 1/16-in.-long foil-backed strain gages. The gages were placed in the configuration indicated in Table 2 to obtain strain distributions along the hemisphere toward the intersection with the cylinder. Strain gages could not be located at the boundary of the sphere and the cylinder because of the lack of clearance at the frame at this location. However, gages were located as close to this intersection as was physically possible. All models were tested using oil as an external pressure medium. The models were externally loaded in comparatively small pressure tanks to limit destruction after collapse. Model ICR Revised, however, which failed at a relatively high pressure, waS quite severely damaged. Pressure waS applied incrementally to each model as indicated in Table 3. Before the strains were read at each increment of load, pressure was maintained for 3 min to allow the stresses in the model to stabilize. The experimental strain-sensitivity coefficients, i.e., the slopes of the pressure-strain plots in inch per inch per pounds per square inch for each strain gage are presented in Table 4. Table 5 lists the collapse pressures of the six models. Photographs of collapsed Models 4A Revised, 1CR Revised, and 7A are shown in Figure 4. The pressure-Strain plots for Model 7A, the only model designed to fail within the elastic range, properly displayed no significant nonlinear Strain behavior for any of the loading cycles. Figure 5 is a plot of pressure versus change in internal volume for the final pressure loading of Model 7A; the insignificant variation from linearity of the curve indicates the elastic behavior of the model up to its collapse. DISCUSSION OF RESULTS Collapse pressures of the six models tested are compared with the previous work of Zoelly and Timoshenko, » Baiigandiec and Krenzke® in Table 5. The theoretical collapse pressures were computed using a Young's modu- lus of 30 x 10° psi, and a Poisson's ratio of 0.3 in the elastic range and 0.5 in the plastic range. The theoretical collapse pressures of those models designed to fail in the inelastic range are presented in Table 5. Experimental collapse pressures are within 7 percent Ppyp/P, = 0.93) of the pressures of the empirical inelastic collapse formula developed at the Model Basin.® As expected, these results are consistent with those obtained by Krenzke® for aluminum models fabricated in a Similar manner. The inelastic collapse pressures of Bijlaard also appear consistent with those inelastic values of Krenzke, indicating theoretical collapse pressures that are somewhat larger in every case than the respective theoretical collapse pressures calculated by the TMB empirical inelastic formula. Comparison of the membrane strain sensitivities for Models 4A Revised, 1CR Revised, and 7A obtained at the 2-deg longitudinal locations with those obtained at the remaining longitudinal locations reveals only small variations in membrane deflections. Comparison of the inside and the outside strain sensitivities in the longitudinal direction at the juncture of the hemisphere with the cylinder does indicate varying degrees of bending. As listed in Table 2, the smaller values of spherical thick- ness for each model obtained at the 2-deg locations as compared with the other locations suggest a reason for such bending. All sphericity deviations, also listed in Table 2, were very small, indicating insignifi- cant variations from nominal radii. In light of the satisfactory results obtained, the deflection and rotation at the boundary of the cylinder and the hemisphere appear to have been adequately considered. As indicated in Table 5, the maximum deviation between experimental collapse pressure and that computed from the TMB empirical inelastic equation was 7 percent (Model 6). It is possible that a premature failure occurred as a result of the machining error in the third frame of the model. The irregularity may have created a weakness in the hemisphere due to an increase in stress set up by a deviation in the desired boundary condition. The strain- sensitivity coefficients shown in Table 4 at the 2-deg longitudinal locations for Model 6 indicate greater membrane deflection than at any other location on the hemisphere. It is possible that analogous action resulted from the pressure loading of Model 4A due to the overcutting of the inside of the cylinder wall; a discrepancy in the desired boundary condition in this model may have effected a Similar decrease in its collapse pressure. The elastically designed Model 7A developed a collapse pressure of 290 psi. This is approximately 74 percent of the classical theoretical value of Zoelly and Timoshenko and 107 percent of the empirical elastic value of Krenzke. The theoretical values of pressures presented in this report were calculated using the nominal values of the radius and the thinnest measured values of the spherical thickness taken for each model. AS indicated by the ratios of experimental collapse pressure to the TMB empirical buckling collapse pressure P,, in Table 5, results for all the models showed reasonable agreement over a ae range of ratios of hemisphere thickness to radius. This consistency may be attributed to the high standard of precision main- tained in the machining process. Since the models were not stress relieved, residual machining stresses were present, but they are considered negligible in view of the very small sphericity departures indicated in Table 2. The good correlation of experimental to theoretical collapse value obtained for Model 7A (to which the most rigorous conditions were adhered in the machining process) tends to support the suggestion of Reference 4 that if machining standards could be maintained sufficiently high to satisfy the rigid assumptions of classical buckling theory, then the classical formula could be used for thin spherical shell design. However, even if such high quality control could be obtained, cost and time requirements would undoubtedly be prohibitive for prototype construction. The experimental results for the models pertaining to this report are plotted nondimensionally in Figure 6. The ordinate is the ratio of experimental collapse pressure to the equilibrium yield pressure Ey? as defined in Table 5, and was obtained by applying a 0.2=percent strain off- set as illustrated by the dotted lines in Figure 1. The abscissa is a ratio of the TMB empirical theoretical elastic buckling pressure P, to the same equilibrium yield pressure. The points display over a wide range of elastic stability, defined as the ratio of P, to a the proximity of the test results to an idealized plot of a perfectly plastic (plateau) stress- Strain curve indicated by the solid line in Figure 6. The value of the comparison is to indicate that for accurately machined spherical shells with similar stress-strain curves, the results define an empirical curve (dotted line in Figure 6) which departs from the elastic portion of the ideal curve at some arbitrary elastic stability ratio and rejoins the plateau of the ideal curve at some higher arbitrary elastic stability ratio. The purpose of obtaining such an empirical plot is to establish for any thin spherical shell design a practical design curve from which a single design formula can be selected. By knowing the design values of Shell radius, material compressive stress as determined from test coupons, and required collapse pressure, an approximate elastic stability ratio can be calculated. If the ratio were to fall on the elastic portion of the ideal curve, the shell would be designed using the TMB empirical elastic equation; if on the plateau of the ideal curve, the shell would be designed using the simple equilibrium yield pressure formula Wee and if the ratio were to fall on the empirical portion of the curve, then the shell could be designed by method of trial and error, using the reduced value of Pryp/P,, found on the ordinate of the empirical curve. By using any other selected empirical pressure formula, an empirical curve similar to that in Figure 6 could be derived to gain the same practical end. A Similar curve is currently being developed as a part of the Model Basin hemispherical head program for high-strength steel models.“ The models of Reference 7, however, are of a larger scale (approximately 3 to 5 1/2 ft in diameter) and are not machined but are fabricated by welding, resulting in a similar, yet individual curve to the one presented in this report. Each of the fabricated models of Reference 7 is constructed of pressed segmented sections, resulting in bending due to misalignment and sizeable residual stresses due to welding, undoubtedly affecting the collapse pressure and consequently nondimensional curve plots, to some degree. Also, due to the impracticability of constructing separate cylinders for each of the models of Reference 7, a Single cylinder is used for all. AS a result, none of the models is deSigned with the ideal bound- ary conditions of membrane deflection and no rotation, thereby further altering the stress pattern in the fabricated spherical shells. It should be emphasized that the plotted portion in Figure 6 should not be used for design purposes at this time because data are insufficient to verify its accuracy. Under no circumstances should the curve be used for design purposes unless the proposed spherical shell is to be designed and fabricated with the same accuracy as those models presented in this report; this precludes all but near-perfect machined models with ideal boundary conditions (where applicable). The curve may be used to design a spherical shell of any material provided it has the same shape stress-strain curve as those for inelastic failure design illustrated in Figure 1. CONCLUSIONS 1. The experimental collapse pressures agree within + 7 percent of the theoretical buckling pressures obtained from the inelastic empirical buckling formula for spherical shells developed at the Model Basin. 2. The experimental collapse pressures of Models 6 and 4A may be misleadingly low because of slight deviations from design due to errors in fabrication which occurred during the process of machining. 3. The design of ideal boundary (membrane deflection and no rotation) at the juncture of the hemisphere with the cylinder appears effective in preventing the cylinder from altering the stress pattern (and consequently the collapse pressure) in the hemisphere from the pattern that would be created in a sphere of the same material, radius, and shell thickness. 4, The empirical portion of the nondimensional plot of results for machined high-strength steel hemispherical shells (Figure 6) should not be used for design purposes pending verification of its accuracy. 5. Upon verification of the accuracy of the empirical portion of the curve of Figure 6, it may be used for deSign purposes only when the proposed spherical shell is fabricated with the same accuracy as the models of this report and provided the stress-strain curve of the material used has the same shape as those for inelastic failure design illustrated ine bisurce as. ACKNOWLEDGMENTS The author acknowledges the technical assistance of Messrs. Martin A. Krenzke and Robert F. Keefe and the contribution of Mr. Pendleton E. Humphries who conducted the hydrostatic tests. : Eealisel eae Cen a i) MODEL 6 (INELASTIC FAILURE DESIGN) MODEL 7A (ELASTIC FAILURE DESIGN) STRESS IN KSI > —) es (INELASTIC FAILURE DESIGN) MOUELS 4A, 4A REVISED, ee ICR, AND 1CR REVISED 0 0.002 0.004 0.006 0.008 0.010 0 0.002 0.004 0.006 0.008 0.010 0 0.002 0.004 0.006 0.008 0.010 STRAIN IN IN/IN Figure 1 - Typical Compressive Stress-Strain Curves for Material (STS-Steel) Used in Machined Steel. Models 90 2 z= B 80 Ww oc Be MODELS 4A, 4A REVISED, 70 MODEL 6 of ICR, AND ICR REVISED ieee ij me 60 1.0 0.8 0.6 0.4 0.2 1.0 0.8 0.6 0.4 0.2 0 (SECANT MODULUS x TANGENT MODULUS)!/2 YOUNGS MODULUS Figure 2 - Representative Material Characteristics 10 Figure 3a - Model 1CR Figure 3b - Model 4A Figure 3c - Models 6, 4A Revised, 1CR Revised, and 7A Figure 3 - Details of the Cylinder-Spherical Boundary Intersections of the Models all Figure 4b - Model 1CR Revised Figure 4c - Model “A Figure 4 = Collapsed Models aly 300 PRESSURE IN POUNDS PER SQUARE INCH 100 0 0.100 - 0.200 CHANGE IN INTERNAL VOLUME IN INCHES? Figure 5 - Pressure versus Measured Change in Internal Volume for Model 7A aS MODEL ICR REVISED ; MODEL 1CR MODEL 4A REVISED MO ae MODEL 4A exp = EXPERIMENTAL COLLAPSE PRESSURE MODEL 7A : = 0.8 E(h/Ry)? / (1- V2)1/2* 2 eae ie . ae ’ 2 Figure 6 - Nondimensional Plot of Experimental Results for Machined Near-Perfect STS Hemispherical Shells *P3 is empirical elastic buckling pressure for spherical shells developed from recent TMB tests and P. is equilibrium yield pressure where h is shell thickness, R is mean radius, Ry is outer radius, E is Young’s modulus, v is Poisson's ratio, and Py is average material yield stress. 14 TABLE 1 Model Dimensions Average Structural Dimensions in inches Compressive Yield Spherical Nominal Inside Cylinder Frame Frame Bay Cylinder Model Model g Wall Inside Cylinder Wall Thickness | Depth | Length Length Base Number Strength Thickness Spherical Diameter | Thickness l Flange it Radius ID t b d Le Thickness RG c in psi ins in. in. in. in. in. in. in. in. nl 6 92,000 0.0275 3.975 7.949 0.051 0.044 0.091 | 0.316 1.057 0.022 4A 90,770 0.064 3.812 7.646 0.107 0.138 0.299 | 0.516 1.892 0.069 4A Revised 90,770 0.071 3.825 7.652 0.118 0.131 0.264 | 0.480 1.769 0.066 1CR 90,770 0.113 3.190 6.312 0.200 0.226 0.420 | 0.619 2.423 0.111 1CR Revised 90,770 0.118 3.190 6.380 0.199 0.204 0.406 | 0.571 2.222 0.102 7A 96,120 0.0066 2.0065 4.013 0.0073 0.035 0.027 | 0.071 0.407 0.380 eee “Smallest measured value is listed for h. ath) *guoTIWOOT oFeF upws3e Quogorder yo3oys OTFJoId Topom uo (+) SOUT PessorD 2230N *amgsedop preauy soqeudysop (-) uite Sry £000" 0- | s000°0- | $000" 0- 000° O- AAC £000°0- | 6000°0- | 9000°0- $000°0- Z000° O- eee 6000°0- | 8000°0- $000°0- $000°0- 0 [Teno 0= [ sooo" [Zoo0"0= | [sonora | [too0ro= | “0 Bi E * 000° 0- 0 TT00* O- L100" 0- | z000* o- | 7000" 0+ $000" 0- 000° 0- 0 ol 9 6000" 0- TT00"O- 0 nasty posyaoy UOT O00" O+ 0100" 0- 8100" O- 0 0100" 0- 0100" 0- 4000" 0- 1000" 0- oo T100"0- $000°0- 0 © [rt00-0- 8000" 0- 2000" 0- 0 pee pecqaay Ve 100" 0- TT00"o- 000° 0- 0 FlaldlAal|Almlelala|rlefalalole] xseea] ie) sy ov of oz Sst aueydetweay JO eseg WoIs sOaIFeg UT UOTIBIUSTIQ TETIUSZIIFUMNIT) oueydstTmsy JO asug WOU sd0IF9qQ UT UOTIVIUSTIOQ TeTIUeTeFMMIITO WOTIBIUITIO 22UOUL UT SNTPEY 193NO TeUTWON woIy aunguedeq SayouT UT ssouyOTYL [TPM Teotseyds TeUwOTPT On ISCOUEEX AU NC ERE) NANO M NEU NOILVINGIAO TVILNAXAAWNNOAIO =| 2 v i Ayrotszsydg worgy sounjuedeag TeT}TU] pue sesseuyoTYL [TEM PeinsesW @ WIaVL 16 *paureaqo sdurpeas uresas ‘anTTey TepoK *uaye Zurpear ou ‘aimpres Tapow * a7. 0 x x x x a ae 0 2 * = 0908 OFT x sof * 062 oose oF x x x OOST ac x OL x Osze x x OOFT x re 09 x x x x oor x x x x 00Z7T = x 0s re OSLZ x x x x x x | o00t x x x Or x x 00SZ sc x 008 % ne x o¢ es al Dae x xe 0007 x x 009 x 50 SZ x x 00ST x x 00s x 0% x x ic x OO00T x x oor x x oT ale x x 005 x x 002 x 0 x x x x x 0 x x x x x x 0 x x € uy} zumy | tomy] z uny | Tt uny eumy | zug] tumy | ¢ uy | z uy | To umy zumy | Tum ted ee ted Pastaay red YOT WOT vr ve 9 aunssaig TepoK TOPoR sinssolg Topo T2Pon oungsotg T9POH ounssoig pepsoocay a19M SUTeIZg YOTYM 7e sainssorg € GTavi i Wve RA sit Wh i MO tas Ps yicerN meas) eh (ER z tea tye IU WLDpsN pris ais Waicrs Nie i wi Hy if il aly | ie 1 yy ati y Wes at i ali Y u : hil Wa Wi it hey i | HAV aie Hl tt Mi: iets Mi i ange th in me ett hea Sea He if eh i ty Wee ky Bian t4 OL aa Honaial hie foi i ma} Au mh! 7) IN Avy i A Ne BU va Ve Hg 1S t Hon arse! ney \ t an | Wo yi es Mi ave ah i a i Be fhe iby Vets RCE A ry uy ne nu hdr, Tis OY mea aaa Mesh m Peas AOLORG Rt pA i aa int heat ae 1 Nl Measured Strain Sensitivity Coefficients TABLE 4 Model 4A Model 6 i Model 1CR _——__—_—__— Meridional Orientation Location Ouraide, Inside Outside Inside Model 4A Revised Longitudinal Location on Hemisphere Outside Model 1CR Revised Outside 2 0.69 0.65 1.01 0.40 0.1 =a 0.68 “Values are listed in microinches per pounds per square inch with negative values representing compressive strain. Gage locations are represented on diagram of Table 2, “e, Represencs strain sensitivity measured in longitudinal direction, and *, Represents strain sensitivity measured in meridional direction. 18 oil i AW ‘i iW, We aH) i Mi ep) Ree AVON teal TABLE 5 Comparison of Experimental Collapse Pressures with Theory for Near-Perfect Thin Spherical Shells Experimental P Model: pomuenee 3 ressure P ea E EXP 6 925 0.73 1.20 4A 2700 0.91 2.45 44 Revised 3060 0.25 0.93 0.98 | 2.68 1CR 6160 0.14 ow |eueonl Macon paw? 1CR Revised 6600 O45) ocail aoa alos | eos" |: S209 mf aePo from ee a % All pressure values are in psi, ae (Classical elastic linear buckling pressure of Zoelly and Timoshenko”) = 1,21 E(h/R) t P; (Empirical elastic buckling pressure for machined spherical shells developed from recent Model Basin tests°) = 0.8 E(h/R,)? 2,1/2 orn TT Taeeene ‘ ?4 ie (Equilibrium yield pressure) = 2Rh o, /R, + re (Inelastic buckling pressure of Bijlaard’) = 1.154 (ELE. /(1 - 2 2 pI? (h/R) $# P_ (Empirical inelastic buckling pressure for machined spherical shells developed from recent Model Basin tests3) = 0.8 (E,E,/ (1 - wy /? (n/n? Tangent modulus Where h = Spherical shell thickness E. R = Mean spherical radius =i pedigs onitet ratiovanethe Roa Outer spherical radius elastic range = Poisson's ratio in the E = Young's modulus i) plastic range Secant modulus Average material yield Stress = (7) ll an ll 19 REFERENCES 1. Krenzke, M. A., "Exploratory Tests of Long Glass Cylinders under External Hydrostatic Pressure," David Taylor Model Basin Report 1641 (Aug 1962). 2. Krenzke, M. A. and Kiernan, T, J., "Tests of Stiffened and Unstiffened Machined Spherical Shells under External Hydrostatic Pressure," David Taylor Model Basin Report 1741 (Aug 1963). 3. Krenzke, M. A., “Tests of Machined Deep Spherical Shells under External Hydrostatic Pressure," David Taylor Model Basin Report 1601 (May 1962). 4. Krenzke, M. A., "The Elastic Buckling Strength of Near-Perfect Deep Spherical Shells with Ideal Boundaries," David Taylor Model Basin Report 1713 (Jul 1963). 5. Timoshenko, S., "Theory of Elastic Stability," McGraw-Hill Book Co., Inc., New York (1936). 6. Bijlaard, P. P., "Theory and Tests in the Plastic Stability of Plates and Shells," Journal of the Aeronautical Sciences, Vol. 16, No. 9 (Sep 1949). 7. Kiernan, T. 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