V^cAl-IIO 
 
 AEE No. L5F01 
 
 1 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 If 
 
 WARTIME REPORT 
 
 ORIGINALLY ISSUED 
 
 June I9U5 as 
 Advance Has trie ted Beport L5FOI 
 
 COLUMN AND PLATE COMPEESSIVE STRENGTHS 
 
 OF AIRCRAFT STRUCTURAL MATERIAI£ 
 
 2l^S-T ALUMINUM- ALLOY SHEET 
 
 By Eugene E. Lundquist, Evan H, Schuette, 
 George J. Heimerl, and J. Albert Ro/ 
 
 Langley Memorial Aeronautical Laboratory 
 Langley Field, Ya. 
 
 UNtVERSlTY OF FLOPiDA 
 
 DOCUMENTS DEPARTMENT 
 
 1 20 MARSTON SCIENCE LIBRARY k 
 
 P.O. BOX 117011 
 
 GAINESVILLE, FL 32611-7011 USA 
 
 WASHINGTON 
 
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 advance research results to an authorized group requiring them for the war effort. They were pre- 
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 \-x3 y^'? ^'^'^ •?sO*^7^ 1 
 
 NAG A A.^R No. L^FOl 
 
 NATIONAL ADVISORY COMMITTEE FOR /iERONAUTICS 
 
 ADVA^IGE RESTRICTED -JEPORT 
 
 COLUMI AND PLATE COMPRESSIVE STRENGTHS 
 OF AIRGR/iFT STRUG TUR..L MATERIALS 
 
 2I4.S-T ALUMINUM- ALLOY SHEET 
 
 By Eugene E. Lundquist, Evan H. Schuette 
 George J. Heimerl, and J. Albert Roy 
 
 SIJIViMARY 
 
 Column and plate compressive strengths of 2lj.S-T alu- 
 minum-alloy sheet were determined both within and beyond 
 the elastic r^nge from tests of thin-strip columns and 
 from local-instability tests of formtad 2- and channel- 
 section columns. These tests are the first of a series 
 in an extensive research investigation to provide data 
 on the structural strength of various aircraft m.aterials. 
 The results, which are pre>-ente5. in the form of curves 
 and charts that may be used in the design and analysis 
 of aircraft structures, supersede preliminary results 
 published previousl^f. 
 
 INTRODUCTION 
 
 Column and plate members in an aircraft structure are 
 the basic elements that fail by instability. If efficient 
 structures are to be designed, the strength of these ele- 
 ments must be known for the various aircraft materials. 
 Aji extensive research program has therefore been under- 
 taken at the Langley Memorial Aeronautical Laboratory to 
 ..establish the column and plate compressive strengths for 
 a number of the alloys available for use in aircraft 
 structures. Reliable and rapid pi-'ocedures for testing 
 such matei'isls have already been developed and are 
 described in referencjes 1 and 2. 
 
 The first m.aterlal tested during the present investi- 
 gation was 2[t.3-T aluminum- alloy sheot. The results for 
 this material, given herein, supersede those contained 
 In a preliminary report (reference 2). 
 
2 NAG A ARR No. L^FOl 
 
 SYMBOLS 
 
 L length of column 
 
 p rr^dius of gyrstion 
 
 c fixity coefficient used in Suler column formula 
 
 — p effective slenderne^s I'-atio of thin-stx-'io column 
 p^fc 
 
 b width of piste 
 
 brp width of flfinge of Z- or channel section (see fig. 1) 
 
 b™ width of web of Z- or channel section (see fig. 1) 
 
 r inside radius of bend of Z- or channel section 
 (see fig. 1) 
 
 t thickness of pl-^te 
 
 k nondimensional coeffj.cient used in plate-buckling 
 formula 
 
 k^ coefficient k used with bjy- pjid t in plate - 
 buckling formula (see fig. 2 and reference 3) 
 
 Sq modulus of elasticity in comoression, taken as 
 10,700 ksi for ^i+S-T aluminum alloy 
 
 T nondimensional coefficient for columns (The value of 
 T is so determined that when the effective 
 modulus TE(, is substituted for En in the 
 equation for elastic buckling of columns, the 
 computed critical stress agrees with the 
 experimentally observed value. The coefficient t 
 is equal to unity within the elastic range and 
 decreases with Increasing stress beyond the elastic 
 range. ) 
 
 r\ nondimensional coefficient for plates corresponding 
 
 to T for colu:nns 
 
 |j, Pois son's ratio, taken as O.3 for 2[|.S-T alumlniun alloy 
 
NAG A AR'R No. L5F01 
 
 ^ Q-p criticsl coiTiprsssive stress 
 
 <7^„„ sver^ee comoressiva stress at inaximurn load 
 
 o compressive yisld stress 
 
 ]\STHODS OP TESTING M3D ANALYSIS 
 
 All tests were irisde in hydraulic testing machines 
 accurate to within three-fourths of 1 percent. The ends 
 of the stress-strain specimens and the colunins were ground 
 flat end square. 
 
 Stress-stra in curves .- The compressive stress-strain 
 data, which identify the material for correlation v/ith 
 its column and plate compressive strengths, were obtained 
 from tests of single -thickness sceclinens in a compression 
 fixture of the Montgomery-Temp lin type shovm in figure 5' 
 This fixture v/as used only for flat compression specimens, 
 which represented the material before forming. Infor- 
 mation on the teclinique used in maklnn these tests is 
 presented in reference Ij.. For the bent material in the 
 corners of the formed Z- and channel sections, compression 
 specimens were cut from^ the corner portion and tested in 
 the special fixture shoivn in figure k. 
 
 Column strength. - The column strength and the asso- 
 ciated effective column modulus were obtained by testing 
 thin-strip columns of the m^aterial with the ends clamped 
 in fixtures of the type shown in figure 5. The use of 
 end fixtures of this type is discussed in detail in 
 reference 1. The fixtures used have been improved, and the 
 method of analysis has been modified since the publication 
 of reference 1. The method now used results in a columji 
 curve representative of nearly perfect column specimens. 
 In addition, the miethod now takes into account the fact 
 that columns of the dimensions tested are actually plates 
 with two free edges. 
 
 Plate compressi ve stre ngcii.- The plate compressive 
 strength of 'the material was obtained from compression 
 tests on Z- and channel-section columns so proportioned 
 as to develop local instability, that is, instability of 
 the plate elements of which they are comiprised. (See 
 fig. 6.) Inasmuch as the flanges and webs of such columns 
 are in reality plates with various ■ kinds of edge suoport. 
 
i| KAGA ARR No. L5?01 
 
 the problem cf Iccel instability of these colur.ms Is a 
 plete-buckllng pi'obleiii, aiicl tiie plate compressive strength 
 of the ..ripterlal wss evsluated frcm these tests. The 
 lengtlis of the colurniis were so chosen as to avoid colunxi 
 faiiui'e and still provide satlsf actoi^y local- Inatfbllity 
 data. These conslderptious ere discussed in reference 5» 
 
 The Z- and chaiinel-section cclanms were tested v/ith 
 the ends bearing directly agginst the testing-machine 
 heads, which were carefully alined to insure uniform 
 bearing on the colamia ends. A Z-section colioirji urider 
 test is shov.n in figure 7« Th'- relative displacemencs of 
 pointers, which 'vvera supported by extension arms attached 
 to the fl-snges of the specimens, were measiared by the 
 cpticfl -Tiicroirietyrs thet can bo seen in figure 7* Ttie 
 displacement was taken as a measure of the cross-sectional 
 distoi'tion, and the critical compressive stress was obtained 
 from stress-distortion curves of the type illustrated in 
 figure 3, The critical stress y»as determined as the 
 stress at the point near the top of the iaiee of the stress- 
 distortion curve at vjhich a marked increase in distortion 
 first occurred w3 th sm.all increase in stress. (See fig. 3.) 
 
 RESULTS AJTD DISCXjSSIOK 
 
 Because the compressive properties of aluminxxm-alloy 
 sheet may vary appreciabl;/ , the data and charts of the 
 present report should not be applied to the desifxi of 
 structures of 2IlS-T aluminum- allov sheet having compressive 
 properties appreciably different from those reported 
 herein unless a suitable method is devised for adjusting 
 test x'-esalts to account for variations in material 
 properties. 
 
 Compressive Stress-Strain Curves 
 
 Com.pressive stress-strain curves obtained for tne 
 flat sheet material used in marine; the colui:Xi3 are given 
 in figure Q for both directions of grain. The Z-, channel, 
 or thin-strip colutmis to which a particular stress-strain 
 curve applies are indicated in table 1, to^^ether with the 
 value of the coiiipressive yield stress CJ^^. for that stresS' 
 
 strain curve. These values average approximately i|Ij. ksi 
 for the flat sheet material in the v/ith-grrdn direction 
 
NAG A ARR No. L5F01 5 
 
 and Ij.9 Ksl in the cross -grain direction. The modulus of 
 elasticity in compression v/as taken as 10,700 ksi, the 
 accepted value for 2lj.S-T aluminum alloy. 
 
 When the flat sheet mrterial is bent to an inside 
 radius r of Jt to form a Z or channel, the cold vifork 
 done on the material evidently raises the compressive 
 yield stress for the curved corner portion above that for 
 the flat web or flange, about lei percent for the with- 
 grain and 10 percent for the cross-grain direction. (See 
 fig. 10. ) Because the curved corner specimens included 
 along their edges some flat material (about 1^.0 percent 
 of the total area) for which the yield stress is lower 
 than that for the curved portion, the actual increase in 
 the compressive yield stress for the corner portion may 
 be scir-ewhat greater than the Increase indicated in fig- 
 ure 10. The important result to note is that the com- 
 pressive properties of a formed section may not be uniform 
 over the cross section. 
 
 Col^ormi Stz-'ength 
 
 The results of the tests of the thin-strip columns 
 are given by the coluinn curves of figure 11 for the two 
 directions of grain. 
 
 At stresses beyond the elastic range, the experi- 
 mental values of a^^^ are lov/er than those computed by 
 the Euler column formula (see elastic-buckling curve, 
 fig. 11), because of the I'eduction in the effective 
 modulus of elasticity. The effective modulus to be 
 substituted for E^ in the Euler coluirm formula to bring 
 
 calculatsd and experimental values of o^^ into agreement 
 
 is givexi as tEc where t Is a coefficient that is equal 
 tc unity in the elastic range and decreases with Increasing 
 stress beyond the elastic range. In structural calculations 
 in vifhlch it is impossible to use directly values obtained 
 from the column curve (fig. 11), the value of t for a 
 given stress must be known. The variation of t with 
 stress for columns is therefore showi in figure 12 for 
 both directions of grain. 
 
D 
 
 NACA ARR Uo. LSFOl 
 
 Fl?fcF> ComnressT ve 3tren.2;th 
 
 The i-esults o'f ths local-instability tests of the 
 forined Z- rnd chaixne 3 -section col''aiiii"s , used to determine 
 the plate compressive strength, ar'e Piver. in tables 2 
 and 5. The important ralationcbips for corr.pressed platos 
 obtained from these testr are sho«vn on the curves ajid 
 design charts presented in the follov.'in^ paragraohs. 
 
 Plate-buck] ing c urve . - The plate-buckling curve, 
 which is analo.:ous to the colur::n .curve , is shovm in fig- 
 ure 15 for olstes loaded in the wlth-grain direction. 
 The abscissa Ir figure I3 is suggested by transposing the 
 plate-buckling equation 
 
 cr 
 
 krr^^t- 
 
 12(l-i..^)b' 
 
 (1) 
 
 to the form 
 
 a. 
 
 cr 
 
 TT^Hl, 
 
 ----|2 
 
 (2) 
 
 whore the subscript W is added to r.aice the terms b 
 and k of the equation correspond to the entries in 
 tables 2 smd 5« The siir.ilarity between the form of 
 equation (2) .and the follovv'lng form of the 3uler colur.xi 
 for.iuls 1? to be noted: 
 
 cr 
 
 ■J 
 
 C 
 
 Vp,v 
 
 (5) 
 
 At stresses bejor.d the elastic range, as in the case 
 cf colii/iins, the experimental values of Q for plates 
 
 are lovvex* than those given by equation (2) for clastic 
 buck]. ing (see elastic-bucicling curve, fig. 15), because 
 of the reduction in the effective modulus of elasticity. 
 The effective plate modulus corresoonding to tS_ for 
 
 columns is rlv-n as rS 
 
 c» 
 
 rnd the varlftion ol 
 
 c 
 r 
 
 th 
 
NACA ARR No. L5FOI ( 
 
 stress is given, togethex" with the variation of t, in 
 figure 12. The crossing of tne t_ and r:-curves shown 
 in figure 12 occurs because the formed columns apparently 
 had an appreciable degree of imperfection, which resulted 
 in the deviation of the r,- curve from unity at a lower 
 stress than that at which th3 T-curve, reoresentative 
 of nearly perfect columns, deviates from unity. 
 
 Relationshio of a to o_„/n for plates.- In 
 
 cr cr 
 
 problems concerned with the strength of plates, it is 
 sometimes desirable to insert the value of nS^ for E^ 
 
 in the plate-buckling formula, equation (1), and to write 
 the eqiistion in the transposed form 
 
 ('-^) 
 
 In this form the v?lue of "^cr/^^ ^-'^ given by the modulus 
 of elasticity, Poisson's ratio, the ji.eometric dimensions 
 of the elate, and the coefficient Ic, The value of a^^ 
 
 can then be obtplned by use of the curve of o^^ against 
 o^-p/v given in figure l!|. This curve m.ay be obtained by 
 plottinT the data directly or by plotting from the faired 
 curves of figure 15. 
 
 As in the case of equation (1), the subscripts W 
 may be added to k end b of equation (I).), and ^cr^''^' 
 m.ay be determined for a Z- or channel-section by the use 
 of the formula and curve of figure 2. 
 
 Maximum compressive strength of plate elements . - In 
 the case of a plate loaded in long i tud in a 1 c ompre s s i on , 
 the supported, or restrained and supported, side edges 
 remain essentially straight after buckling and ore capable 
 of carrying additional load. As a consequence, there is 
 a 'maximum strength for the plate that is greater than 
 the buckling strength. 
 
 Theoreticrl studies that appear in the literature 
 concerning the ultimate strength of plates and the asso- 
 ciated effective width of the plates after buckling 
 indicate that the average stress at miaxiraum load is 
 related to the critical stress. It is therefore reason- 
 able to assum.e that the average stress at maximmn loed 
 
8 FACA .Al^R No. L5FOI 
 
 a„, „^ for tli-^ co'.nbinatiori of "olgte elsL-'ents that ms-ke up 
 
 the 2- or chc'<rinel-sec tloii oolu.ia 11 slso related to tho 
 criticril str^ess for the ccmbinstlori . Accoriingly, tns 
 e.xeri:-.ner,t£l veluos obtcvinad era plotted in figure I5 
 as o^.^ sgap'nst the r.9t:*o ^cr/^r:irx5 ^nd from thi:; ^^S~ 
 ure a definite ralptior:ship ii s 3e:. to exist between 
 o^r, and '^r.iax ^-^ ^ given ve-lu3 of by;/t. 
 
 In corra c?S3F. , vcl.ies of "j.v.p;. r ether thsn ^cr 
 may be requi^-'ed in strength c£-lcalption:; . fj-.e values of 
 a.--^gy are therefore plotted against ^crA) ^^' ^'ifc^ii'"- 16. 
 The fe3sibility of making such a plot is indicated by the 
 rel.atlorshio bet'Ji/een o^v, aiid '^oxv'V shovVi'i in fii^ure 1I4. 
 and the I'elaticnship betv:een a.jia" ^^'^'^ "^cr sbo'Vn in 
 fiprure 15 . Figure 16 is i?articulsrlv useful because tne 
 qumitiby '^cr/''^ ^*-^ doterrninod by Imomi quantities 
 a-^cordlng to the fori!;ula fnd cur/-3 of figure 2. 
 
 The ressc-n for the diff^vrence in the curves of fig- 
 ures 15 and 16 for difTorent values of b.. /t is not 
 
 fiilly uTiderstocd. Tro s tress-str ■oa.n curves hi-ve indicated, 
 nowever^ that the bevidlng of the naterial in the for:r.ing 
 of the colunns raises the compressive yield stress for the 
 ma^'erial in tiie corners. ( 3ee fig. 10.) An exeunination 
 of the data Gliowed thct rs b'..-/t :s reduced for a given 
 thickness t and a given value of c^cr/hj the total cross- 
 sectional ax'^ea is also redj.ced; the fixed area of high- 
 strength tent matei'isl in the corners therefoi-e becoT.es a 
 higher rercentage of the total eres. This fact .may account 
 for the hi;Ther values of a^ax obtained at given values 
 of '^crAl '^''•*' "t-^'"^ Z- and cnannsl-section columns 'vith 
 lo'.ver values of b-j/t. (See fig, 16.) 
 
 Zf fee t of gr a i n d i ^0 c 1 1 on on plate s t r en .c t h . - The 
 data on plate strength '^rssen ted in figures IJ to lo were 
 obtained from columns loaded in the wibh-grain direction. 
 In order to deter^:ine_the effect of grain direction on the 
 values of o^r' f^'id ^v.ax» a ^'sw coliAjmas were constructed 
 pj.id tested with the grain of the sheet at right angles 
 to the axis of the col'jurji. These columns are herein 
 designated cross -gr fin columns. 
 
 In figurot. I7 and 1,,., th^ aata obtained from the 
 cross-grain columns are plotted as exoer-mental joints 
 
NACA AP.Vx Ho. L5F01 9 
 
 for comparison with curves taken from figures iL. snd l6 
 
 for the with-grain colioinns. Only at the higher stresses, 
 
 where the stress-strain curva i'or the cross-grain direction 
 
 differs noticeably from tne stress-strain curve for_the 
 
 with-srain direction, are the values of o and a „„,, 
 
 ' cr max 
 
 greater for the cross-grain columns than for the with-grain 
 
 columns. The average increase in the high-stress region 
 
 was about I4. percent for o and about 2 percent for '^rpax' 
 
 vifhereas the cross-grain compressive yield stress was approx- 
 imately 11 percent greater than the with-grain compressive 
 yield stress. 
 
 Ch. arts f o r loc a 1 in s t^ab i lity of Z- aj:;d channel-section 
 columns.- Th.e olaFe~compre"ssive strength of the materi al 
 was evplu^ted from tests of Z- and channel-section columns. 
 The results of these tests, which provided this information 
 regarding olates, may also be applied directly to formed 
 Z- and channel-section col'Jini:i3 that fail by local insta- 
 bility. These results can be conveniently sujuraarized in 
 the form of charts that give directly, in terins of the 
 dimension ratios bp/b;sr and b-,:/t, the critical stress 
 
 and the average stress at maximum load. Such charts, 
 based on the theoretical curve of figure 2 and the experi- 
 m^ental data, are given in figures I9 to 21. 
 
 COWGLUDING REMARK 
 
 The important conclusions of this report are em.bodied 
 in the test data of column and plate compressive strengths, 
 which are presented in the form of curves and charts that 
 may be used in the design 9nd analysis of aircraft 
 structures of 2l|S-T aluminum- alloy sheet. 
 
 Lsngley ]V-eraori?l Aaron ^^utical Lr.borat»ry 
 
 N-'tional Advisory Comi.iittcje iov Aoronautics 
 Langley Field, Va. 
 
13 NACA art; Y.o. I.5?01 
 
 Lundoui=:.t, R\x::er,B E., RossjT'Sn, Csrl A., nncl Houlolt, 
 JoVin G-: A Riethod. fo-' DsDei'ml/iinp- the Colurrm 
 Ci;rv3 frcin Tests of Columns vrith Equal Restraints 
 ai?iast Rotation cr. the Ends. iMCA Til No. ^OJ, 
 
 heliiiPrlj George J., and Roy, ■!. AlbO'rt: ih'-elitnlnsry 
 Report on Tests of 2l|.S-T Alurr.lniiiii- Alloy Coluii;ns of 
 Z-, Cnrnnel, ^nd E-Seotion That Develop Locrl 
 In£t?biJlty, IIA^^'A ?.3V.o. JJZ'?, lSl|5 • 
 
 •vrollj A. C. , risiiOi^, Gordon P., and Heiirnerl, George ^ 
 Charts for Cr'lcalrtion of the Critical Stress for 
 Locrl Instability cf GolUinns v,ith I-, Z-, Ghsnnel, 
 sna Rect£:n,!?:ui&r-Tub9 oectl-.)n. ,NACA ARR ?\^o. JKOIl, 
 
 ■9i 
 
 1 
 
 LL 
 
 iSiiJ. 
 
 Kotonchi':, Joseph lu , Woods, waiter, rnd Weinberger, 
 Robert A. : InvOBtigatlcn of r.-3thods of Supporting 
 S.lnj^le-lhiclcness Specimens m e. Fixture for DeterrrJ.' 
 nation of Corirpre3s;ive Stress-Str^^an Curves. KAGA 
 No. T,5E1S , 19': 5. 
 
 t31 
 
 Keimerl, George J., tnd Roy, J. Albert: Determinstion 
 of Desii'pble Lengths of Z- and Chf'imel-Section 
 Colunins for Locai-Instfjbility Tests. NAG A H3 
 No. lIilUO, IPL4. 
 
MCA .-iRR No. L5F01 11 
 
 TABLE 1.- CO!l'PRESSI"'''E PROPERTIES OF 2i|S-T ALUIvIBITOJ-ALLOY SHEET 
 
 [e^ = 10,700 ksi] 
 
 Co: 
 
 .umns to whic 
 
 h stress- strt.in 
 
 
 1 Compressive yield 
 
 
 curve E 
 
 apoly 
 
 Stress- 
 strain 
 
 ST^^aGSS^ f*lA 
 
 
 ■ 
 
 
 
 
 Type 
 
 Direotion 
 of 
 loading 
 
 Designation 
 ( See tables 2 and 3) 
 
 curve 
 (fig. 9) 
 
 iVith 
 
 grain 
 
 (ksi) 
 
 Cross 
 grain 
 (ksi) 
 
 Thin 
 
 "'ith grain 
 
 All 
 
 A 
 
 U2.9 
 
 U7.9 
 
 strip 
 
 and cross 
 grain 
 
 
 
 
 
 Z 
 
 '.'Vith grain 
 
 la to 6a, 6c, 7a, 10a, 
 10b, 11a to 19a, 26b, 
 27a, 27c, 28a, 29a, 
 31b to 32c 
 
 B 
 
 UU.o 
 
 U6.e 
 
 Z 
 
 Vvith grain 
 
 6b, 7t to 9, 10c, 19b 
 
 C 
 
 i+6.3 
 
 51.3 
 
 
 
 to 26a, 26c, 27b, 2et,| 
 
 
 
 
 
 280, 29b to 31a 
 
 
 
 
 Z 
 
 Cross 
 
 grain 
 
 la to Uc 
 
 D 
 
 U3.i+ 
 
 Ue.5 
 
 Channel 
 
 I'.ith grain 
 
 1 to 6a, 7a, 8a, 9a, 
 10a, 11a, 12a, 13a, 
 llj-a, 15a, l6a, 17a, 
 18a, 19a, 20a, 21a, 
 21b, 22a, 23a, 21+^, 
 25a, 27a to 28a, 2Qa, 
 30a to 31a, 32a, 33a, 
 5l4.a, 35a, 36a 
 
 E 
 
 U3.i4 
 
 i|6.9 
 
 Channel 
 
 'Vith grain 
 
 6b, 6c, 7b, 7c, 8b, 
 8c, 9b, 9c, 10b, 10c, 
 lib, lie, 12b, 12c, 
 13 b, 13 c, lUb, li4c, 
 15b, 15c, I6b, I6c, 
 17b, 17c, 18b, lec, 
 19b, 19c, 20b, 22b, 
 23 b, 23 c, 2l;b, 2i;c, 
 25b, 25c, 26a, 26b, 
 28b, 29b, 29c, 31b, 
 32b 
 
 F 
 
 Uh.3 
 
 UQ.7 
 
 Channel 
 
 Vi'ith grain 
 
 31c, 32c, 33b, 3^'C, 
 3Ub, 35b, 36b. 36c 
 
 G 
 
 U3.9 
 
 ii7.9 
 
 Channel 
 
 Cross 
 
 grain 
 
 la to L|.c 
 
 D 
 
 k3'U 
 
 1 
 
 US. 5 
 
NACA aRR No. L5F01 
 
 12 
 
 § 
 
 M 
 
 O 
 ^ 
 
 I 
 
 N 
 M H 
 
 a M 
 
 O M 
 
 ■< 
 
 PC EH 
 
 o m 
 
 t> o 
 
 OT O 
 «fj 
 E 
 
 HO 
 
 H > 
 
 M 
 
 QQ 
 
 §H 
 
 CO W 
 
 §^ 
 
 M m 
 OT g 
 
 SiJ 
 M O 
 
 Q O 
 I 
 
 
 IK 
 ID 
 
 K -H 
 Q 0} 
 
 o n 
 
 olfT a ^ 
 O \ M — 
 
 (\J 
 
 I 
 
 rH it 
 
 
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 ^ 
 
 ^ 
 
 ^ 
 
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 NATIONAL ADVISORY 
 COMMinEE FOR AERONAUTICS 
 
 Figure!.- Cross sections <^ Z-and channel 
 section columns. 
 
NACA ARR No. L5F01 
 
 Fig. 2 
 
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NACA ARR No. L5F01 
 
 Fig. 3a, b 
 
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NACA ARR No. L5F01 
 
 Fig. 4a, b 
 
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^ACA ARR No. L5F01 
 
 Fig. 5 
 
 NACA LMAL 
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NACA ARR No. L5F0] 
 
 Fig. 5 
 
 NATIONAL ADVISORY 
 COMMinEE rOR AERONAUTICS 
 
 Figure 6 ~ Typical cross -sectional distortion 
 of columns that develop local instability. 
 
NACA ARR No. L5F01 
 
 Fig. 7 
 
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 instability of plates. 
 
NACA ARR No. L5F01 
 
 Fig. 8 
 
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NACA ARR No. L5F01 
 
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 Figure 10.- Effect of forming on compressive 
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NACA ARR No. L5F01 
 
 Fig. 11 
 
 
 
 
 
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NACA ARR No. L5F01 
 
 Fig. 12 
 
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NACA ARR No. L5F01 
 
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 NATIONAL AOVrSOdY 
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NACa ARR No. L5F01 
 
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 NATIONAL ADVISORY 
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 Rgure 19. - Design chart for a^p ^o^ formed Z45-T 
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 develop local instabilittj loaded in the with -grain 
 
 direction 
 
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 = 44 ksi. 
 
NACA ARR No. L5F01 
 
 Fig. 20 
 
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 NATIONAL / 
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 Figure 20.- Design chart for CT>„ax for formed 24S-T 
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 instability loaded in the with- groin direction *, 0'j.ys44ksi 
 
NACA ARR No. L5F01 
 
 Fig. 21 
 
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 Figure Zl. - Design chart for o-j^qx for formed Z45-T 
 aluminum - alloy channel - section columns that develop 
 locol instability loaded in the with -grain direction j 
 
 <Tcy = 44 ksi 
 
I 
 
UNIVERSITY OF FLORIDA 
 
 3 1262 08106 493 2 
 
 UNIVERSITY OF FLORIDA 
 DOCUMENTS DEPARTMENT 
 120 MARSTON SCIENCE LIBRARY 
 RO. 30X117011 
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