ff Wf\6AL'lJ0 ^ KB No. LJ+HIO NATIONAL ADVISORy COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED October I9UI+ as Restricted Bulletin L^+HIO DETERMINATION OF DESIRABLE LENGTHS OF Z- AND CHANNEL-SECTION COLUMNS FOR LOCAL -INSTABILITY TESTS By George J. Helmerl and J. Albert Roy Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSIP.' OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 11 7011 GAINESVILLE, FL 32611-7011 USA W^ WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - 180 NAG A RB No. lL^HIO NATIONAL ADVISOP.Y COMMITTEE FOS ABiEONAUTICS RE S T';i C IE' D BIJ LL.a TI N EETr^^:.:i NATION or Dr;.:ihAELE leijotiis of Z- Ai^i) CfiANI^FL- SECTION COLUMS FOR L0C4L-INSTABILITY TESTS F^f Gecrgo J. Neimerl ani J, Albert Hoy EUMNAEY Local-irist3D:.lity tests of 2i|.,';^-T aluminum- alloy fonred Z- ar:.d chai'inel-section colurims lA'cre made in order to dw'.r3.nrij. le a length nf te^'.t speoi'r.en that v/ould avoid the mcroa.Bed strength associated vdth rhort lerif-Ttha anvi also perti^It the oocur.^ence of a convenient bueklxi.fei: p'lt^'vern. The effecc of ooluT.n length on the critica]. coi.iyT-essi ve stress, on the average stress at max.! ir.L,r. Icadj and on the nu.'nher of half-waves cf the biiollJnj, pattern 1? sho^/'Ti. A huckijng i..attei'-n of three half-waves is indicated as desirable for test purposes. A curve is presexited from which may be determined the lengths of Z- or chann^l-sectj on columiis that give a buckling pattern of three half-waves. "hen the strength for local instability is very high, a reduction in the length indicated by the curve may be necessary to prevent Golxiirin failure. In order to avoid the increased strength associated with short lengths, a ratio of length to web width above 5.5 should be used. INTRODNCTTON Tn local-instability tests of Z- and channel-section columns, suitable specimen lengths should be determined. As the flanges and webs of such columns may be considered plates with various kinds of edge suppoi'ts, the local instability of these columns becom.es a plate-buckling problem. ^^■raen a plate is long, the critical com/pressive stress tends to be independent of ].ength', whei-eas, if the plate is very short, the stress increases appreciab.ly . (See' fig. 6 of reference 1.) NACA RB No. liiHlO For an investigr.tion of columns that develop local instability, therefore, the aneciinen? should "be made long enough to avoir' an appreciable Incresse in stress and yet not long enough to result in column failure. In order to determine lengths of columns that n.eeb these requirements, tests were made of formed Z- and channel-cection coliiirnn of various len^^ths . This repor'* presents the test result? and a carve for determining desirable col^um lengths lor test piarposes. SYMBOLS bp width of flange, inches b„. width of web, inches L length, i n o ^le s t thickness of web or flange, inches E modulus of elasticity, ksi o critical 3omipr33.ri ve stress, ksi '^m.ay average stress at maxim'um load, ksi a cy compressive yield stress, ksi £PZCir/n:NS Formed Z- and chanre 1-section columns were made from 2)^S-T aluminum alloy with th^^ grain of the material parallel to the length of the column; .-jne sheet of material was used for each type of column, and 73 columns of each tj.'pe vjere tested. The ends of ''"he specimens were ground flat, parallel, and at right angles to the length of th3 column. Figure 1 shows the nominal dimensions of the three cross sections used for the Z- and channel- section colTimns. The mieasurcd dim.ensions of the columns and tne test results are given in table 1. For each cross section, the ratio of length to web width A'as varied from about 1 to about 10. NACA RB Ijo. Ll^HlO Stress-strain tests of the material were made with single-thickness specimens in a roller-tjpe compression fl:x-ture similar to that shomi in figure Z of reference 2, Compressive stress-strain curves are shov;n in figure 2. The values of the compressive yield stress, determined by the C.2-percent-of f set method, and of the modulus of elasticity are given in table 2. METHOD OF TESTING The colunin tests w'ere made in a J'^'CjOOO-pouiid- capaclty compression testing m.achine that is accurate • within three-quarters of 1 percent for the range of load used in the tests. A Z-sectlbn column under test is shown in figure 5. The disfilacement of pointers, supported by extension arm.s attached to the flanges of the columns, was measured by the optical micrometers that can be seen nn figure 3- The critical compressive stress was obtained from, stress- distortion curves in tie manner described and Illustrated In reference 3. In this method, the critical stress is determined as the point near the top of the knee of the stress-distortion curve v^here a miarked increase in distor- tion first occurs with small Increase in stress. RESULTS AND DISCUSSION The variation of o and o with L/b,„ for each of the different types of oolumji tested is presented I 'O'" 1 tip in figure a. Columns having —^ ~ 2ii and r'- =0.5 t ^ D,^, developed bending failure for r^ > 7' A definite rise In critical and m.aximum stresses when the columiis become very short is shov.Ti by these curves. For all except the very short columns, however, the curves are relatively level. The num.ber of half-waves of the buckling pattern that occurred in each case is also indicated in figure \\, It has been found desirable for test purposes to make the columin length such that an odd nam.ber of half- waves develops, because of the convenience in m.easuring i; KAGA P.B No. li|H10 cross-seotional distcrtlnn at the center of tlie coliimn. Econon.y of .rat^rial and the p'->G?lb'^ 13 ty of beading failure if the coluirn Is long le^^d to a choice of lengths such that the columns will develoD the lesLst number of half- waves aiid still avoid an pppreoiable in:jrease in sti-ess due to the effect of short len(;;th3. Thece considerations, together with the test results shown in fjgure k, Indicate thet a buckling' pattern of three half-waves is the one most desirable for i nves'^igations oi lo:;al instability of colui-^Jis. The length of the half-'vave developed when local instability occurs varies, for a given web width, with the crosE-ssotional latlo bp/b»-. The nuriber of half- waves then depends on the ratio of length to web v;idth Tj/b,„. By sho^ving the number of balf-'vaves that occur for given values of b-p/by^r and L/b,„ as i Illustrated in figure 5> curves na:/ be drawn thac sho-v the relationship betv/een bp/b^f: and L/t^- required to obtain any desired nior^ber of half-vaves. Tn order to give proper veight to the tost results shown in figure S, the number of tests for which each n-'urher of half -waves occurred is indicated. A recom:?,er:ded curx'^e is drav;n in figure 5 to indicate the propoi^tions of either a Z- or a channel-section coli.ijim reqi'dred to develop a buckling pattern of three half- v;aves, v.'r_lch is desirable for test rurposes. This cui^ve can be Tised directly for- selecting specimen lengths in many cases. ]n cases in which the strength for local instability is high (low values of t-^,/tj , however, specimen lengths s"lect'=d according to the recoirmended cui've may nor be short enough to prevent bending failure. It is therefore necessar7/ to checlr the column strength, of the spe clmens "selected and, in scire cases, to shorten the specimens. In any case, figure L. shows that, in order to avoid an increase in strength due to the effect of very short lengths, the value of L/b.^, usf^-d should be above 'J. 5- " CONCLUSIONS For local -instability tests of Z- and chiannel- section colurmis, the specimens should be just long enough to avoid th-c increased strength associated v/ith short l-ngths but of such length that a uvickling pattern convenient for test purposes occu.rs. A buckling pattern of three hali-v>.av3s meets these requlrem.ents ; the proper length for this condition may be obtained from a curve MCA RB No. LJ+EIO based on tests. Tnen the strength for local instabjlity is very high, a reduction in this length rray be necessary to prevent colurrin failure. In ordei' to avoid the increased strength associated with short lengths, a ratio of length to vi/eb width above ^.R should be used. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. , August 10, I9I+I4- REPERENCES J* J 1. Lundqulst, Eugene F., .^d Stovv-ell, Elbridge' Z* Critical Compressive Stress for Flat Rectangular Plates Supported along All Edges and Elastically Restrained against, dotation along the Unloaded Edges. NACA'^Hep. No. 735, 19l;2. 2. Paul, D. A., Howell, F. M. , arid Grleshaber, H. E. ^ Comparison of Stress-Strain Curves Obtained by Single-Thic'rcness and Pack Methods. NACA TN No. 8IQ, 19lil. Heimerl, George J., and Foy, J. Albert: Preliminary Report on Tests of SltS-T Aluminum-Alloy Columns of Z-, Channel, and H-Section That Develop Local Instability. NACA RB No. JJa?, I9L5 . NACA RB No. L4H10 TABLE I MEASURED mMEKSIONS OF FORMED SPEOIHENS AND TEST RESULTS Sp«cln«n t (In.) (In. ) (In.) L (In. ) i. b. ^ ^. "cr (ksl) ''maj; (ksl) Number of half- waves 2 -section column: section 1 1> 0.106 i.^h 1.30 2.79 1.10 21*. 00 51 1*7-4 46.0 50.2 1 16 .106 2.51. 1.50 2.79 1.10 21,. 00 51 It-^ 1 2« .105 2-55 1.30 5.55 2.12 2l*.05 51 1*4-2 1 2b .105 til 1.30 5.35 2.12 2k. 09 51 45-5 46.3 1 5« .106 1.30 7-92 3.11 21*. 00 51 41.9 1*4.3 2 5b .106 2.511 1.50 7.60 2.99 21*. 00 51 42.1 t2:5 2 11 .106 2.51* 1.50 7.82 5.07 I+.07 21*. 00 51 41.6 2 .106 1:1? 1.30 10.30 25.91 51 40.3 42.7 2 l*b .106 1.29 10.50 ^.05 25.98 2[,.00 51 4o.9 45.7 2 Itc .106 2.51. 1.50 10.30 l,.05 51 40.7 ?9.6 41.0 1*5-5 2 5« .106 2-55 2.51, 1.30 12.92 5.07 5.08 2l*.05 51 45-0 5 5t> .106 1.30 12.93 21,. 00 51 42.9 5 i: .106 2-55 2.5i 1.30 12.93 5.07 6.09 2l*.05 51 59.8 45-5 I .106 1.30 15.50 21*. 00 51 59.8 42-7 6b .106 2.51 1.30 15.51* 6.19 25.67 2l*.00 52 40 lo 41-9 4 6c .106 2-51* 1.30 m^ 6.11 51 43.2 4 7 .106 2.52 1.50 6.97 25.81 51 59.7 41.9 5 z -section solium; section £ 8> 0.105 2.51* 2.58 2.72 2.68 1.07 21*. 11* 1 02 54.0 38.7 40.0 8b .105 m 2.58 1.05 1.06 2l,.2l* 1 01 55.8 8o .105 2.<8 2.68 4.11, 1 02 52.2 41.0 <)• .105 2.51* 2.58 5.28 2.08 21*. 11* 1 02 21.0 30.9 9b .105 .106 2.51* -1 5.35 2.10 21*. 11, 1 02 22.8 51.2 10 « 2.51* 7.70 6.72 Ifi 21,. 00 1 02 15.6 Jl.O 10b .106 2.51. 2.60 21*. 02 1 02 15-5 1S.3 51.1 10 .106 2.51* 2.60 10.58 2.97 l,.o8 21*. 01 1 02 51.1 11« .106 2.5U 2.56 2.55 2.5l* 21*. 00 1 00 16.1 50.0 2 lib .105 .106 10.37 10.56 1,.06 2l*.2l* 1 00 15.2 29.8 2 llo 2-55 2.56 til l,.o6 2E.09 99 \l:l 30.2 2 12 « -.1^1 12.91* 5-07 99 29.5 29.6 2 12b 2-55 2.5U ii 12.95 5.07 99 16.9 2 120 .105 12.95 5. 10 2l*.19 1 00 16.2 29.3 2 15* .106 2.51* 15-55 6.11 21*. 11 1 00 14.9 29.2 5 13b .106 2.51. 2. 51* 15.55 6.11 2l*.00 1 00 15.6 29.4 2 HI .106 .106 2.51* 2-51* 2!5S \U', 6.11 7.10 21*. 00 1 25.95 1 2l*.09 1 25.98 1 00 01 H:'. 29.2 28.7 I lUb .106 2.51* 2.58 18.07 18.06 7.10 01 Zl 28.9 5 lUc .106 2. 51* 2.58 S.io 01 28.9 5 1^. .106 2-51* 2.58 20.60 25.95 I 25.96 1 01 14-4 lU 5 15b .106 2.5U 2.58 20.60 8.10 01 14.1 5 III .106 2.5I4 2.58 20.62 8.11 ij:?^ 1 01 III m I .106 2.51* 2.58 25.22 9.13 01 l6b .106 2. 51* 2.58 23.22 9-15 23.98 1 01 14.6 27-7 27-6 4 16c .106 2.51* 2.58 23.22 9.15 23.98 1 24.00 1 01 14.5 4 17« .106 2.5U 2.58 25.75 10.10 01 13-5 27.5 4 17b .106 2. 51. 2.58 10.08 2l*.00 1 01 m 27-3 26.9 4 17c .106 2.51* 2.58 10.11 21*. 00 1 01 4 - 2 -section column; e eotlon 3 le* 0.105 1.1*0 I-)*? 1.71 1-23 15.29 1 06 45-8 55.7 1 leu .105 i.to 1.1*8 1.71* til 15.29 1 06 45.9 44-9 55-5 1 19 .105 1.1*2 1.1,6 3-07 !*.57 15.52 1 05 pi. 2 ilia 1 20 a .105 1.1*1 1.1,8 3-11 13.58 1 u 45-2 1 20b .105 .106 l.liO 1.1,8 U.59 l*.!*o 5-15 13.29 1 42.0 1 20c i.Uo 1.1+6 III 13.22 1 04 m 46.4 1 21a .106 1.1*2 1.U5 5-95 15.50 1 13.43 1 02 45-7 2 21b .106 1.1*2 1.1*5 5.90 U.Ik 02 43.1 U5.5 45.6 2 21c .106 1.1,2 1.1*7 5.90 U.ll, 13-45 1 05 38.5 2 22a .106 l.l*i 1.1*5 7.55 til 13.43 1 02 45.8 44.2 2 22b .106 1.1,2 1.U5 7.52 15.45 1 02 59.6 41.9 41.2 5 22c 23a .106 .106 1:K \:^ m 5.11 6.07 13.55 1 15.58 1 01 00 44.6 2 5 25b .106 1.1*1* 1.1*1* 8.71, 6.07 15.58 1 00 42.2 5 Z .106 1.1,5 1.1*5 8.71* 6.10 \l:Vi ' 00 42.4 44.3 5 .106 \:d 1.1*2 10.05 10.08 6.91* 6.98 98 41.3 45-8 5 2ltb .106 1.1*2 15.62 98 40.6 t2:! 3 24c .106 i.U* 1.1,1 10.10 6.99 15.62 98 4i.o I ^5* .106 1.1*1* 1.1,1 11-51* 7.99 8.05 15.62 98 40.6 42.8 25b .106 J:K 1.1*2 11.52 15^62 11 40.1 45-6 4 25c 26a .106 1.1,1 11.51* 7.99 S.95 8.98 41.5 45.7 4 .106 1.1*1* 1.1*2 12.92 13.62 98 41.6 ilE:i * 26b .106 i.i*i* 1.1,2 12.92 13.58 99 42.8 * 26c .106 l:^ 1.1,1 12.98 8.93 15-72 97 41-7 40. i 1*5-9 * 27a .106 1.1,2 11*. 37 11*. 36 9.99 15.55 99 45-0 , 27b .106 l:^ l.lU 10.01 13.50 1 13-60 00 39.9 40.7 k2.J 42.4 4 27c .106 1.1,2 11*.56 9.95 98 4 NATIONAL ADVISORY coKyrmE for ASRoiiAnTics NACA RB No. L4H10 TABU 1 - (!onaluil*d MSASaREO DIlfEHSIOIS - ConsludMl Spaolnan t (In.) (In.) (In.) L (In.) (ktl) (kit) Riiab«r of baU- WBTVS Chaan^l-Sttotlon oolun; aaotlon 1 1« lb Is 2a 2b 2s 5« kb lis 5» 5» £b 6s 7« 7* 7o 1.26 1.26 1.27 1.26 1.26 1.26 1.28 1.27 1.26 1.27 1.26 1.27 1.26 1.26 1.26 1.26 1.27 1.27 1.27 t 1.05 2.10 I i; 0.L9 •U9 Wt-S a.u l2.1 a-7 ,5.6 lO.lt ►1.7 a.? 1^.6 59-9 Lo.9 UO.2 1(0.0 59-7 59.9 59-7 59-7 8* 8b 8s »• 9b 10 s 10b lOo lis lib lis 12s Ub Us 1J» 15b ifi Uib l4s 15s 15b ¥ 16b I6s 17s 17b 17o Cbsnnsl-asotloD oolvan; asstlor 2 2.58 2-55 !l t-^ 1.00 •99 1.00 1.00 1.00 .99 1.00 1.01 .99 liS 1.00 1.00 1.00 :|? 1.00 •99 1.00 .99 •99 1.00 1.00 .99 1.00 .99 1.01 .99 1.00 5-7 Ohsnnsl-ssotlon oolu iSStlOD 5 18 0.106 19 s .105 19b .105 .105 I9e 20s .105 20b .105 .106 21s 21b .106 21s .106 22s .106 22b .106 22c .106 25 s .106 25b .106 n: .106 .106 aUb .106 2^0 .106 25s .106 25b .106 25e 26s .106 .106 26b .106 i.Ui i.W. It 1.L5 m i.UJ» l.h2 l.Ul i.y, 1.I42 1.14. i.lio l.Uo 1.U5 I.U5 l.Uo 1.U2 1.U2 l.Ll l.Ul 1.U2 1.U2 l.k2 1.U7 1:^ l:i l.M \i\ l.tiD I.U5 l.h2 I.L5 1.U2 1.16 1.97 2.11 2.08 5.10 5.08 I1..06 U-U* 5.09 5.05 5.10 i-.a 7.07 8.07 8.12 8.25 8.98 9. 01* S5.6 U9.5 m U7.9 I U5-6 j*J-7 U5.6 kl.l U5.8 U2.5 U5.0 1,5.2 U5.0 U.l ltO.7 1*2.1 liTIOIAL AWisomr COIUITTn POK ACROIAHnCS NAGA RB No. liiTIlO 8 TABLE 2- CO?'!r'EESSIVE PF.OPSRTIES OF MATERIA] 1 j V;i tb t^^T'Gin j Cross £;rain Coupon (ksi) (krji) 1 (k3il (^csi) Z- sect! on Chsnrif-- 1 section 10,700 10 , 6co — — . , .. 10 , 6oo 10,600 lf^.7 1+0.2 NATIONAL ADVISORY C0JS1ITTEE FOR -ATFONAUTICS NACA RB No. L4H10 Fig. 1 r .3 -.102 T 2.50 -1.25- ! .3 .102 — -r 2.50- i-i ± Section 1 r ^^ -.102 "T 2.50 .i 250- i — "-r -2^0- T 2-50 ^Section 2 .3 J02 1.50 k rl, 3 .102 . k 1.50. Z- Section T 1.50 -L50*. 5ection 3 Channel secHon NATIONAL ADVISORY CGMMIHEE FOR AERONAUTICS Figure 1.— Column cross sections. NACA RB No. L4H10 Fig. 2 H— .00£— H Strain NATIONAL ADVISORY COMMintE FOR AERONAUTICS Figure E. -Compressive stress-strain curves. NACA RB No. L4H10 Fig. 3 c e ■-I O CJ C o o (U CO I tsi o 43 c CJ o ( to U 3 NACA RB No. L4H10 Fig, II c .O tj ^^ (S (3) A (3) 4 // \ (3) \9 V. "L ^(3) 2 (3) Number ot Number ha f- waves of fest5 1 1 1 J 1 . r- 1 1 (8) Location or rest . point5 1 J 1 _L b w 8 10 NATIONAL ADVISORY COMMinEE FOR AERONAUTICS Figure 5.- Number of half -waves in buckle pattern produced by various proportions of Z- and channel- secf ion columns of 24 5-T aluminum alloy. I UNIVERSITY OF FLORIDA 3 1262 08106 512 9 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY P.O. BOX 117011 GAINESVILLE, PL 32611-7011 USA