1、i i_L_-r_ CA$ F,COPYAm_ No. _AO_NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSIrl RTIMl RI: P()RTORIGINALLY ISSUEDMarch 1946 asAdve_ce Restricted Repart Tf:_05CHARTS FOR CRITICAL COMBINATIONS C_ LONGITD)INALAND TRANSVERSE DIRECT S_EqS FOR FLATRECTANGULAR PLATESBy Charles Libove and Manuel SteinLangley
2、Memorial Aeronautical LaboratoryLangley Field, Va.FILE COPYNOT REPRODUCIBLEWASHINGTONNACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution ofadvance research results to an authorized group requiring them for the war effort. They were pre-vlously held under a sec
3、urity status but are now unclassified. Some of these reports were not tech-nlcally edited. All have been reproduced without change in order to expedite general distribution.Reproduced byNATIONAL TECHNICALINFORMATION SERVICEU S Deportment of CommerceSprlngfied VA 22151L - 2Z4/Provided by IHSNot for R
4、esaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-., l_: ; T , _,r“ 7_,_(_i_;so.t,b,:_ skin cf :_n _:12:?,.,un.-_“r in r“ ;-:t is sub.-.-_:-.Fr:,! b ? Sqr , “ “ “ “ “ -, ,_n,_tz_
5、n,-, ,:,f s,tres:_, _tt_nLi n _._:s been4-/: V,%_ “; f“_-. “_,. _,.,_,.p._“ I p-“ r, i R.,k!:L_S ,:ii6ri :,C:Z_*“ ,;l_.tZ_:_: ,;tPeS.S :S :_C_S_:lt :,: lstresnes can be evalueted, the effect of the combinationshould be considered in investigating the stabilit F of theplate.The energy method is used
6、to derive 5ntersctionequations that define tl_e critical combfnations of lonzi otudinai and transverse direct stress for isotropic flatrectangular plates with the following four cases of edgeconditions:CO.S e(b)(o)(d)Long edsesSimply supportedSimply supportedClsmpedClampedShort edgesSimply supported
7、ClampedSimply supportedClampedCharts based upon the inter_ction equations are presentedfor these four cases.The solution obtained for case (a) is exact. Forthe other three cases the s_7utions obtained ere approxi-m_,te and, as is cheracteristc of the energy method,tmconservative. Comparisons with kn
8、own exact solutionsand lower-limit solutions indicate, however, tho t theerro_,_ in the present results are generally small.SY;4BOLSbtW7en_th of ol_tewidth of o!s_te (bt c !_hir-.: -_ t,:.,-iuti:zns t,_,_,_ v:hicb. _ tLe int, e_aet_ _Cl_tpt; _ are 1-_sc: i:e r.,“Vt; _ _lff. tDpcn_!x m:e ; f,_r_: , s
9、o !.:. _“ ,-,_-, :rz, i (a.:_,:;,s (_o)t,! !_ 1“(- r.j_ :)IL b_.t _“- . . ,_, . “ ._ _ i _ “ ., -(c), anJ (d) ,.r:. c -,:.+ ,r:._ ;1 .r;_ _ tO*u . .1., s ,I _ _ o .2,_ I uC_e SS_ ,_“_._,._. sr_ ,:irt “_. ?.-i s ,sT.r_c i krla/_ %o rcpp,Jsc_= aqt,.,;r i. _it _ _2 %);P -:aPe !llSEf “_,“ :. rSb-O t
10、 ecaus-, all- _ “_S =_u,-_l, s-._-_,lC(SIZ _i.L;P Lz S_:.I 0SS OOTIb_“ IiO-t, io: in *./.,.:,oh t!.:o tr:nzve: 3_- _.!z,.:lCb stne:.:s q, _ s one-Jt, “ _“ p, t%o :T:u:; .:.t ,z :.c!, - = := .s icun_ alorv: tKe,!- 7,?in.e ; - 2 in .:i .,_:,_ ! glue v:- iue :Tf :;: _ _:s p?int, 7 p.:_ t_c r,_Pres.O:C_
11、tz:_: t3is ._)-. The 7 t_,_:in,_ , ct s _“,_this :al:.:_.cf k: s g_ve:“, by c_,-,:.,_=_“-o,_ (5) as_“ _X rE= Z P g:.:G;0 psiIt. .s not:c( -_ _.t :._“ino thecr, itic_, co:,_bin.:A,:);is cf (.: “-._nc“ g7. _“_“_- cy?y,. ._ The p_“-_.Lnc_p:l_em_:ts of t:_J pPesent investigationare embodied in the inter
12、action okapis. T:ese charts canbe used t,:) cot _ ,._=t.:cu c: .,_ons_ :)._ longitudin_!NOT REPRODUCIBLEProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-and cra_Jr_,_e ,_Lr,_“_ct_t_“_so for _sotro_._c flat rectai_ularLan_!eT,- 7.-o_:_cP_il._.ero-;Ru:,
13、As;_lLaOcratoryNut_. ;:aal A, v!sory _3o_itCee for Aero_a_:tt,ss_,aK_inY P_-_l,f T._Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i0 NACA aru ._A PPY._ IX. ._ t,k.:_-plate, tl%i:_ e/lu_.litycan _ :_itten _- _hc, _,-I_,_ LnC _,- “ . . _ ,_fi_ V,i-ll
14、Oh is ada.% 0ecfr:m e:,qu_,t_on (21,3,) ,?f re.f_l.sultin.bckle p,_btuld ccinci,H :it;_h :,_rSions of ther_.9. sb_cd rtlP“s _:_e 3:tttTtA -R S!_:!_!I_ZeZ _ -i R_oe i_:_)_:,i _ .;- _._:.:e_ s:m_:lT :.u.ppJrted.-De,FL ;f) U; 12 z: ,7.“. _.;. , : 2_-,_ 3 :_:-; :l- /., !:):-:,j0I401 ftEPftOOtlotBLEProvi
15、ded by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-L+.KX . Ofor m -= l_ and n = . _i - 2:Lie f _e c t i s n _Lu n .s c n _,rI, _n- l)vxW a: A :_,S C%SL+ 2.$7 + I_c,)“5_2(L- k;f) (,LII)I -I + i c_s _t- L _fOP ?_ : i 2, z. an_ f “the :_o,s,:r_-_, r ,_.,._,._d:
16、 q-L.r_:, “;,_“_-_“Ore _“ Op “t . . _. _,_ i“ 0.? :_O _. ,; -.i“os .:,.I) i;_!i T p - _. ;_ _ / b-_3.8:- _ -I x “-_o 2 “ dl :- 6 5 4.5 42-Z TIill !l!_ ill,t,I iJLki Jlll lilll Ilitl il!J Llltl!fI 2 3 4 5D NATIONAt ADVISORYCO_INITTF F011 AEIIOI4AUTICS_: bT) _ = _kb_t/ #:m : number of Ionqifudinol
17、 bucklesn : r_inberof frcnsvcrscbucklesFigure 4.- Criftcot combinations of longiludlnol and frans,e.rse_.dl_“i_Ct - slrogS coefficients for flat rccf.qrig,atar pJatcs _+_Thion 9 edges clamped ond short edq_s 5imply :,upported.Provided by IHSNot for ResaleNo reproduction or networking permitted witho
18、ut license from IHS-,-,-NACA ARR No. L6AO5 Fig. 5kxttltl:H _1 ill i llrlrlrll rfillll liJJllliJll!llP ll*lliJJ Illlll r IIlll-_- r_,_, 1 , :_m=z ._ 4 _ 6 _ 7 8 ,_n=J/ _ ix i _ i t :_- ,_-_ . , . _:- rn=l _ -I_:! _“-_“-h-_ , _ _.-_.x“ _ “ : -“_. ,.“ _._ “, “_. ,-“_-_ 3 =-_.,o:2i n-I-, X “, !- 6 5 45
19、42 :-,9 _11_ilt_l_ll IlJlllJ _l_tJl_l IIII1_11 _l_lllllt lJltlll_ _l_l,l_l_ 1,1_1,1-_I Z .3 4- 5NATIONAL ADVISORY_IINITT_E FOIl AERONAUTICSm= number of longitudinal bucklesn:number of transverse bucklesF,qure 5.-Cnhcal combinations ol_ longitudinal and transversedlrcct-stress coefficients for flaf r
20、ectonqulor plates w_th_ll _:dqes clamped.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Fig. 6a-c0NACA ANN No. L6A05kx4,_Present solution_f A lower limitO I I L i i io Z 3ky(O) Long edges 5imply supportedshort edqes clamped.gkX(c)87 _ f Present solu
21、Hon-FA lower limit4“ 13I0 ,. i i i ii 13 4 5 60 I 214yAll edges clamped.76kx 5432I00I 1 j I II 2 3 4 5 6ky(b) Long edges clamped,_hort edgc_ 5imply supported.o_tiffa-ybZt, /Cry- k DYXbz f, )QNATIONAL ADVISORYCONI41TTEE FOIl AERONAUTICSFigure 6.- Comparisons of present 5oluhon5 wifhlower limits. #=4-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
