GENERAL DYNAMICS Convair Division GPL, PRICE $ CFSFI PRICE(S) $ A2136-1 (REV. 5-65_ I ff flS'_i J_ll_ f';5 REPORTNO. (;l;C-I)DG(;(;-O08 DATE:_I _pri ] l!)66 NO.OFPAGES 1(_2 . xxviii (;lllllilll) OINImAI., DYNAMICI i _ONAi.rw'Icm STUDY OF ST=k[]ILI£Y Of,' UNPRESSURIZED _HELL STRUCTURES UNDER STATIC LOADING FINAL REPGI_T VOLUME I Contract Number NASS-,IIIS1 Request Number DCN 1-5-53-01067 Prepared for the George C. Marshall Space Flight Center N_tional _eronautics and Space Administration ||dntsvi 1 le _ klabama PREPARED _. H. Hausrath S_U_A_. _t_Fe s Gr o u p '_n <inee r AU,PR0V[0eY VFrank .k. Dittoe o. Chief of _tructtir_tl _n,llv,_i,_ kdvanced Structures Group (Mail Zone 587-30) Research, Development and Engineerin_ Department General Dynamics Convair Diviaion Post Office Box 1128 San Diego, California 92112 REVISIONS DATE ' BY CHANG[ PAGESAFFECTED GDC- DDG66-O08 ACKNOWLEDGEMENTS This study was conducted at General Dynamics Convair Division by G. W. Smith and F. A. Dittoe under the technical direction of Dr. A. H. lLlusrath, Group _ngineer, Advanced Structures Group, _vho acted in the capacit_ of program leader. Programming for the digital computer wa_ accomplished by Mrs. L. S. Fossum and Mrs. N. L. Fraser of the Technical Programming Group, and J. R. Anderson of the Guidance and Trajectory Programming Group. Acknowledgement is made of the encouragement and advice furnished by E. E. McClure of the Advanced Structures Group. Appreciation is expressed to H. R. Coldwater and H. L. Billmayer of the Structures Division, Propulsion and Vehicle Engineering Lab- or,itory, Marshall Space Flight Center, for their support of the study. In the role of NASA Technical Representative, Hr. Billmayer provided valuable assistance in the definition and achievement of the study goals. The entire report was typed by Hrs. F. C. Jaeger of the Convair Advanced Structures Group. Gt,_NI.:R tl_ DfN./HICS ! Convair Division ii GDC-DDG66-O08 /© This final report covers the work performed by General Dynalnics Convair Division und_r NASA Contract NASS-11181, "_tudy of Stability of Unpress_rized Shell Structures Under ,Static Loading." The prim.ary intent of this study was to employ orthotropic shell theory to develop practical working tools for tt_e prediction of instabilJty in stiffened circular cylindrical shells subjected to axial compression. Empi_sis iz on approximate analysis techniques to be used in preliminary sizing, rouge checking, and the study of trends. Methods fop the more stringent requirements of final analysis are also discussed and a digital co,nputer program is provided for such applications. In addition to considering the overall buckling strerxth of the ,__tiffened shel', curves are also presented for predicting the buckling of curved isotropic skin panels such as tho_e found between stiffening elements. The report is divided into two distinct parts. Part I furnishes the theoretical and empirical foundations for the proposed _ethods while Part II gives concise pro- cedure:_ for the practical application of th:se methods° GgN ,R_L DYSVIILS Convair Division iii GDC- DDG66-O08 CONTENTS VOLURE I Section Title P._ass ACKNOWLEDGEMENTS ii ABSTRACT iii LIST OF FIGURES ix LIST OF TABLES xiv LIST OF SYMBOLS xvi GLOSSARY xxv 1 INTRODUCTION i 2 CONCLUSIONS 6 5 LIMITATIONS 15 4 iLECOMMEND AT I0 NS 15 PART I THEORETICAL AND EMPIRICAL FOUNDATIONS 5 BUCKLING OF ISOTROPIC SKIN PANELS SUBJECTED TO EDGE COMPRESSION 24 5.1 General 24 5.2 Buckling Criterion 26 5.3 Comparisons Against Test Data 32 COMPRESSIVE BUCKLING OF LONGITUDINALLY STIFFENED CIRCULAR CYLINDERS 42 6.1 General 42 6.2 Buckling Criteria 42 GENERAL DYNAMICS Convair DivisJ on iv GDC-DDG66-O08 CONTF_.,NTS (Cont'd) Section Title 6.2.1 Almroth Extension to Thielemann Solution 42 T 6.2.2 Stuhlman-DeLuzio-klmroth Solution 54 6.5 Fixity Factor for Longitudinally 3tiffened Sections Between Rings 75 6.4 Comp_risons Again:_t Test Data 78 6.4.1 Longitudinally _tiffened Circular Cyl i.nders 78 6.4.2 Longitudinally Stiffened Circular Cylinders with Frames, Panel Instability Mode 95 7 GEN!_RAL INSTABILITY OF ORTHOTROPICALLY STIFFENED CIRCULAR CYLINDRICkL SHELLS UNDER AXI _L CO_IPRESSION 98 7.] General 98 7.2 Buck]ing Criteria 100 7.2.1 Thielc,nann 3olution 100 7.2.2 Langley Solution llO 7.5 Comparisons Against 'rest Data 119 8 INTERACTION BEHAVIOR 127 8.1 General 127 8.2 Axial Col,pression and Pure Bending 129 8.5 Axial Compression and External Pressure 155 8.4 Axial Compression and Internal Pressure 140 8.5 Axial Compression and Shear 144 G_N,_R%L?r? DYN\_IICS Convair Division V GDC-DDG66-O08 CONTENTS (Cont'd) Section Title INITIAL IMPERFECTIONS 147 REFERENCES 159 VOLUME II ACK NOWLEDGEHENTS ii ABSTRACT iii LIST OF FIGURES ix LIST OF TABLES xiv I,IST OF SYMBOLS xvl PART II APPLICATION 10 G_NERAL 164 11 BUCKI,ING OF ISOTROPIC SKIN PANELS SUBJECTED TO ElSE CONPRES,ION 166 II.I Procedures 166 llo2 Design Curves 169 12 COMPRESSIVE BUCKLING OF LONGITUDINALLY STIFFENED CIRCUL_R CYLINDRICAL SHELLS 187 lfi. I Procedures 187 12._ Design Curves for Bare 7075-T6 Aluminum Alloy 206 (_N_RAL INSTABILITY OF ORTHOTROPICALLY STIFFENED CIRCULAR CYLINDRICAL SHELLS SUBJECTED TO AXIAL COMPR_SION 274 GENERAl. DYNAMICS Convair Divisi-n vi A _ ......... GDC-DDG66-O08 CONTENTS (Cont'd) Section _itle 15.1 Procedures 274 15.2 Design Curves 285 ].4 INTERACTION BEIIAVIOR 512 14.1 Procedures 312 . 14.1.I Axial Compression Plus Pure Bending 512 14.1.2 Axial Co,npression Pills External Pressure 514 14.1.3 A×ia! Compression Plus Internal Pressure 516 14.1.4 Axial Compression Plus 3hear 516 14.2 Design Curve 518 15 INITIAL IMPERFECTIONS 320 15.1 Procedures 5._0 15.2 Design Curves 320 16 BUCKLING OF MONOCOQUE CIRCULAR CYLINDERS 323 17 S_PLE PROBLEMS 350 18 DIGITAL CO,MPUTER PROGRkMS 334 18.1 Program for Buckling of Isotropic Skin Panels Subjected to Edge Compression 334 18.2 nrogram for the Compressive Buckling of Longitudinally Stiffened Circular Cylindrical Shells 354 18.3 Programs for General Instability of Orthotropically Stiffened Circular Cylindrical Shells Subjected to Axial Compression 570 GENERAL DYNAMICS Convair Division vii GDC-DDG66-O08 CONTENTS (Cont'd) Title P _asm 18.3.1 Thie lemann Solution 370 18.3.2 Langley Solution 590 18.3.3 CR Correction Factor 409 i_t.0V:C_ENCES 417 ..',|,_,t-n,l i x ,St}Pt't,t'_,HENTARY OPTIONS bX)R ANALYSIS OF l_lh:Kl ING OF' ISOTROPIC SKIN PANELS SUBJECTED 'l'o gO(IF.' COHI)RESSION A-1 A. ! ,.)I'i'ION '2 A-1 _.,I. I General A-1 ,1.2 Buckling Curves A-2 A-18 A. 2.1 General A- l 8 A.2.2 Buckling Curves A-18 ,:,)fix a i _" Divi:;i (,n viii GDC-DDC_6-008 LIST OF FI(IU;),,_S NO. Title Panel Inst..ability Vol. I, xx General Instaoility Vol. I, xxi Anticlastic Bending of Beams Vol. I, ×xiv Nondimensimal LogaritbJaic Plot of Buckling Criteria for Isotropic 3kin Panels 31 5 Buckling of Isotropic Skin Panels - Calc,11ated vs. Test (o R from OPTION 1) 59 6 Bucklin_ of Isotrooic 5kin Panels -Cnlculated vs. rest (o R from OPTIgN _')) 40 7 Buckling of Isotropic Skin Panels -Calculated vs. rest (c R from OPTION 3) 41 8 Equilibrium Paths for a Perfect Isotr,,pic Circ,ll,w Cylinder Subjected to 4xial Compression .9 Thielemann Notation 10 Interaction of Twistimr Moments in #all of Monocoque Cylinder 57 ll Semi-Logarithmic l_lot of N vs a with _, S as a Parameter 71 12 Buckling Curves for an Infinite Length Column Supported by _qually Spaced Deflectional and Rot,,tion_l Springs 74 15 Alternative Method for Evaluating Rotational Spring Constant 76 14 Semi-Lo_:_rithmic Plot of N vs. y 103 15 Alternative Rin,_ Loading Conditions 104 16 Semi-Logarithmic Flot of CR Correction Factor 106 GEN_,;R,,L !)YN U,IICS Conv-lir Oivision ix GDC-DDG66-O08 LI._;T OF FIGURES (Continued) Title I/ <<.t,:mt.-.t,ogarithmic Plot of Coulpressive Loading C.efficicnt for the General Instability of :>tiife_ed Circul,ir Cylinders 109 Example Interaction Curve 127 Itl Combined Axial and Bending Loading Interaction (:u_'ve for Orthotropic Cylinders 152 :.l.i) Stability Interaction Results for Combined Axial Compression and External Radial Pressure 159 '.lI $t<_bility Interaction Results for Combintd kxial Compression and Internal Radial Pressure 143 Interaction of Pure Bending and Torsion for Stil!ened Cylinders 146 _q ,.+,_ Selni--Logarithmic Plot of F vs., R/t for iJiisti ffened Isotropic Cylinders tinder Axial i:,nnp f'<: _ ':, i O n 148 J ) "i ,,.id-i)isplaeement Curve for Example Honocoque C_ I inder 153 _- .I .. ) l.,,ad--Displacement Curve for Example Orthotropic Cy 1 i ndt r 153 (ieomotvy of Isotropic Skin Panel 166 ,: 7 Buckling of Isotropic Panels 171-182 b R 183-186 I'} v'_'" _ for o R = 2Op lri,_ily Factor vs. Rotational Stiffness Parameter 192 50 ._linJmization Factor N vs. _ and the Parameter 193 S .) I Comprc._sive Buckling Stress for Longitudinally _.t ffenc,J 7075-T6 AI Alloy Circular Cylinders 210-225 C_,w,,_essive Buckling Stress for Longitudinally 5tttfcned 7(175-T6 A1 Alloy Circular Cylinders 226-241 _,b;\'i,i_,l, I)YNIMIC._ C,,nv lir" l) i vi:,i_,rl X GDC-DDG66-OO8 LIST OF FIGU,_d_S --_Continued) No, Title 55 Col:.,pressive Buckling :Stress for Longitudinally StiYfened 7075-T6 .tl Alloy Circular Cylinders 242-257 54 Comp;'essive Buckling Stress for Longitudinally Stiffened 7075-T6 A1A!loy Circular Cylinders 258-275 55 Design CL,rves for the Correction Factor CR 276 56 Critica:_ Compressive Loading Coefficient for the General Instability of Stiffened Circular 287-311 Cylinder_ 37 In-plane Punning Shear Load N 517 xy 38 Design Interaction Curve 319 39 Design Correlation (Knock-down) Factor for Pure Axial Load 521 4O Design Correlation (Knock-down) Factor for Pure Be nding 522 O cr R 41 T vs._ for Unpressurized Monoco_tue Circular Cylinders (Clamped Ends) Under Pure Axial Load; BEST FIT 324 cr R 42 vs._ for Unpressurized Monocoque Circular Cylinders (Clamped ,Znds) Under Pure kxial Load; PROB.kBILITY = 90%,CONFIDENCE0 = 95% 525 O cr R 45 vs._ for Unpr'essurized Monococtue Circular Cylinders (Clamped _nds),_'_ Under Pure _xial Load; _ROBABILI'r¥ = 99%,CI_NFIDENCE = 95% 526 o cr I{ 4,1 vs._- for Unpre_,_surized Monoco,lue Circular Cylinders {Clamped l_nds) Under Pure Bending Moment; BEgT FIT 327 O cr R 45 vs.