IVn^" fc- '/3 AER No. L5F08a NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY , ISSUED July I9U5 as Advance Restricted Report L5P08a COLUMN AND PLATE COMPRESSIVE STRENaTHS OF AIRCRAFT STRUCTURAL MATERIALS EXTRUDED 75S-T ALUMINUM ALLOY By George J. Heimerl and J. Albert Roy Langley Memorial Aeronautical Laboratory Langley Field, Va. UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY RO. BOX 117011 GAINESVILLE, FL 32611-7011 USA NACA 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 unclassiiied. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. L - 173 Digitized by tine Internet Arclnive in 2011 witln funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/columnplatecomlang p6 <^(ct HHl JtoTVf 2^ MCA AKR IJo. r.5P08a NA.TIONAI ADVISORY COMMITTEE FOR AERCaAUTICS ADVANCE FESTRICT"I;D Ri;pCRT COT-FM AED PLATE CC?''?PRESSIVE STR^NC-TFS C^ ^.IRCR"VT STRT'CTTJRAL Ivta.TERIAI^S FXTRTiDFD 75S-T AIUMTI^*ITM AILO"^'^ By George J. Heii^ierl and J. Albert Roy S'l'TTJT'.fARY ^cc o.^''}'''^' ^''"^ P^^"^^ cc>^DreEsive strergths of extruded C^b-^ aiu:^.inura alloy vere deterrrdned hoth mdtH'n Pnd :^^'^t^^,^^^^^^"^f^^^^ee from tests of thln-strip^olumns e.nd^xoca.L-.insr.al3ilit7 tests of H-, Z-, and channel- sec-cicn colmms. Those tosts are oart of an e-tens^-v° research investigation to provide data on the structural strength ol varirus aircraft m^tevlf^s. The results which are presented in the form of curves'ar^d cb^r^tq ' thc,-H are suitable for use in the design and a^aiysl' :^f ^i- cra o structures, supersede prell:in.lnary results -^ubVsh-d previously. ,. u.^j._bii,„u IN'^RCDYG'i^ICY _Colur^n_and plate members in an alrcreft structure ire _ the basic elenients that fall '^o-r j^nstabi li t-^^^ ' "por t^p ??^^?? "" lightweight, structurally efficient aircraft! the^strencth of these elements must be known -For t^-e IT^ll^ aircraft materials. An extensive res^arch^ program hao therefore oeen unaertaken at the Langley Memorial AeronauLical Laboratory to establish the colum.n'and elate compressive strengths of a number of the allovs svailaSle for use m aircraft structures. Parts of this investiga- tion already completed are given for ZJ+^-T and 17<3 r^' " " aliominum-alloy sheet in references 1 and 2, respectively. The results of tests to determine the column and place compressive strengths of extruded 75S-- aluminu- alloy, which supersede preliminary results Dubl-'shed in reference J, are oresented herein. ' ' 2 IT AC A ARR No. L5F08a SYMi=OT,S L length cf cclurnn p radi^Ts of gyration c fixity coefficient used in Fuler colunn formula ■ -^ ■_■•■ . cff3ctiv3 rlendernesc ratio of thin-strip column bi?, tp Vifidth and thickness, respectively, of flange of H-, Z-, or channel secticn (see fl^. 1} b,j, t,„ v:idth ard thickness, resprctivoljT-, of web cf H-, Z-, or channel section (see fig. 1) r corner radirs (see fl^. 1) k.,» nondinensi^nsl coefficfent used rith hy and t." m plate -buckling forniula (see figs. 2 and 5 and reference h.) E^ modulus of elasticity In ccrrpresslon, taken as 10, ^'CO ksi for extruded 75S-T aluininum alley T nondiiiiensional coefficient (The valae cf t is so deterjajned that, "l.en the effective modulus tE(2 is substituted for E^ in tho equation for elastic bu.cklint; cf cclunuis, the coinputed critical stress agrees ^'.'ith the experimentally observed value. The coefficient t is equal to unity within thw elastic r-ang-e and decreases wit?i increasing stress beyond the elastic range.) "P nondirnenslor.al coefficient for compressed plates correspcnoing to t for columns \i Poisson's i-rtio, taken as 0.5 for extruded 75S-T alup.inum alloy '^cr critical ccrapressive stress C'max average compressive stress at maximum load <^cy ccrapressive yield, stress 1I.A.CA i\HR No. I.5F03a METHODS C? T^STIHG ^HO ANAI^^SIS Al], tests were made In hydraulic testing ;T;achines sccurate within three-fourths of 1 percent. The methods of testing and analysis deve].oped for this research prcgram ere described in reference 1 and may be briefly supirnarized as follows: The compressive stress-strain curves, which identify the material for correlation Vvith its column snd plate coiripress] ve strengths, were obtained for the witla-graln direction from tests of sinrrle- thickness compression s'^eci- mens cut from the extruded H-sectlons, These tests were made in a com.pressicn fixture of the Montgomery-Tempi in type, which provides lateral support throu^^h closely spaced rollprs. The column strength and the r. ssociated effective cclu:;mL mcduliJS were obtained for the with-grain direction by thf'- use of the method presented in reference 5> i^'^ whlcn tlin-strio ccl'jLmns of the liiatsrial v;ere tested v/ith the ends clamped in fixtures that provide a high degree of end resoraint. The fixtures used have been improved and the method of anal;/ sis has been m.odified since publi- cation of reference S- I'^-G method, now used results in a column, curve that is representative of nearly perfect colu'tin specim.ens. In addition, the method now takes into accou?-it the fact that columns of the dim.ensicn3 tested are actually plates with two free edges. These colum.ns were cut from the flanges of the extruded H-section adjacent to the Junction of the web and flange. The plate ccm.pressiva strength of the material was obtained from com.pression tests c.f H-, Z~, and channel- section column.s so pronortioned as to develop local instability, that is, instability of the plate elements. (See fig. I4..) The extruded I>sect3,on3 v/sre obtained in three diffei-ent v/eb widths; the flange widths of each v/ere varied by milling off oarts of the flanges. The flanges cf some of the H-section extrusions were removed in such a way as to make both Z- and channel sections. The flange vuidths of the Z- and channel-section columns were varied in the same manner as the flange widths for the H-section column.s. The lengths of the columins v/ere selected in accordance v/ith the principles set forth in reference 6. The cclu.ims were tested with the ends ground flat and square and bearing directly against the tr sting -machine k- NAG A AKR No. L5PC8a heads. In these local-lnGtabillty tests measurements were taken of the cross-seotlonal distortion, and the critical stress was determined as the stress at the point near the top of the knee cf tlie stress-distortion curve at which a marked Increase in di^itortion first occurred with small increase in stress. A difference in the analysis presented herein from^ that employed in reference 1 is concerned with the measurement of bp . and b,., for use in evaluating a /x] by means of the equations and cu_rve3 of figures 2 and 5» In the theoretical derivation of the plate-buckling for- mula mathem.atically idealized sections were assumed, in which the effects of the thickness of the flange and web plate elements and the efff.ct of the corner condition - square, curved, or fillet - were nejlectsd in establishing the widths of the plate elements. Consequently, as the experim.ental investigation of the plate compressive strength of aircraft matei'ials progresses, some arbitrary dimensioning of the flange and web widths has been found necessary in order that the theoretical and experimental buckling stresses agree w' thin the elastic range. In the formed Z- and channel sections of references 1 and 2 with Inside bend radius of three times the sheet thickness, the widths of the flange and web were defined by center-line widths with sqiaare corners assumed. In the extruded sections v>fith small fillets reported herein, the widths of the flange and web wore defined by the inside face dimensions, as shown in figure 1. RESITLTS AI:D DISCUSSION Comipressive Stress-Strain Curves Compressive stress-strain curves for extruded 753-T alum^inuja allo^r, which were selected as typical or average curves for the colurin material, are given in figure 5* These curves were obtained from tests of ccmoression specim.ens cut from the i.-iiddle pai"'t of the flanges of the extrusions as shown in figure 5» In order to study th.e variation of the compressive prooerties over the cross section of an H-section extru- sion, surveys were made by tests of comoression soecimens cut from the web and flanges of the H-sections. The NACA ARR NO. LSFOSa variation of t-he compressive yield stress ccy over the cross section is shewn in figiare o. Valiaes ol'' Oq^t at the outer part of the flanges were 2:enerally higher than those for the inner pax^t of the flanges; the lowest value 'of Or^j was found in the web in all cases. The stress- strain curve? of figure 5j representative of the material in the middle part of the flanges, are therefore usually typical or avera^ie curves for the flange material and show values of Qq^ that are unconservative. in comparison with values of t:ie compressive yield stress for the material in the web. The thin-strip or K-, Z- , azid channel- section colum.ns to which a ^articular stress-strain curve applies eve Indicated in table 1 torether with the values of a_„ for that stress-strain curve ^ The values of Ocy have an average of about 7S" ksi for the with-grain direction. The modulus of elasticity in compression was taken as 10^500 ksl, the present accepted value for ertruded 75S-T aluminum allov. Golujrn and T^late Compressive Strengths Because the compressive properties of an extriided aluminum, alloy may vary considerably, the data and charts of this report should not be used for design purposes for extrusions of 75S-T alum.inum alloy that have appreciably different comipressive properties from those reported herein, unless a suitable m.ethod is devised for adjusting test results to accoi"'nt for variations in m.aterial properties. The resialts of the ccl-omn and local-instability tests of the extruded 753-T aluminum alloy are summaz^ized herelni . a. discussion of the basic 'relationships is given in reference 1. ■ • : Col umn stre ngth.- The colurnn curve of figure 7 ^hov/s the results of tests of thin-strip columjis loaded in the with-graln direction. The reduction of the effective modu].us of elasticity tIC^^ with the increase in column stress is indicated by the variation of t with stress shown, in figure B. ■ plate coinoressive str ength . - The results of the local- instability tests of the H-, Z-, and channel-section columjis used to determine the plate compressive strength NACA ARR No. L5F08a are given in tables 2, 5, and ij., respectively. The plate- buckling curves, analogous to the column curve of figure 7> are shown in figxire 9* The reduction of the effective modulus of elasticity tjEc with the increase in stress for plates is indicated bv the variation of r\ v^ith stress, which is shown together vi/lth the curve for t, in figure 8. In this figure, the T-curve does not cross the rj-curves as it did for 2I4.S-T alutuinum alloy. (See fig. 12 of refer- ence 1.} The extruded H-, Z-, and channel- section columns of 75S-T aluminum alloy apparently were more nearly perfect than the formed Z- and channel-section columns of 214.S-T aluminum alloy (reference 1), 30 that the rpcurves for the extruded 75S-T aluminum.-allcy columns diverge from unity at about the same point as the T-c\irve, which is repre- sentative of nearly perfect columns. The variation of the actual critical stress o^^ with the theoretica]. critical stress '^nx>/r, comiputed for elastic buckling by means of the formulas and curves of figures 2 and 3 is shown in figure 10. In order to illus- trate the difference betv;een the critical stress o^^^. and the average stress at m-axlmumi load 5"^^^^, the varia- tion of Ocp with Ocr/o^a.x ^^ shown in figure 11. Because values of Ojy^g^^ may be required in strength cal- culations, the variation of ^ma.x '^'ith ^cr/'H ^^ pre- sented in figure 12. Figures 9 to 12 show that the d£ta for H- sections described curves different from_ those Indicated for Z- and channel sections. One of the reasons why higher values of Oyj^g^y^ were obtained for the H-sections than for the Z- and channel sections for a given value of o^-p/r] (fig. 12) m.ay be the fact that the high-strength material in the flanges forms a higher percentage of the total cross-sectional area for the H-section than for the Z- or channel section. For the H-section, "Oraax ^'-^ increased over the valine for the Z- or channel section for the entire stress range covered in these tests (fig. 12); a^jo for the H-secticn, however, is increased only for stresses beyond the elastic range (fig. 10). For the variation of a^^, v.;lth ^cr/^raax (fig* H) and of o^ax with C!^_j.,/r (fig. 12), only a single curve is required for a given type of cross section regardless of the value of h-^j/t-^-i v/hereas, in the corresponding figures 15 and 16 of reference 1, separate curves were NAG A ARTi No. L5P0ea 7 necessary for different value? of this ratio. This dis- tirctlon is pi'cbably due to the fact that there is no increase in the conpressive yield, stress in the corners of the extruded sections cojaparaW.e with tho increase in the coriLers of forried specLnens caused by the cold work of forming the shapes from fist sheet. Reference 1 shows how the increased strength in the curved corners due to forming might produce a variation in the avei/age stress at m.axir-ium lead when 'b-^-t/t-rj is varied, L^ngley Memorial Aeronautic?! Laboratory National Advisory Committee for ^.eronautics hang ley Field, Va. REP:ifiSNC:3S 1. Liindquist, Eurene '^,. , Schuette, Even H., Heimerl, C-eorge J,, and Roy, J. Albert: Column and Plate Compressive Strengths of Aircraft Structural Materials. 2li.r'.-T A'^ umlnum- Alloy Sheet. NAG A ARH i;o . L3P01, ] 94-5 o 2. Heimerl, George J., and Roy, J. Albert: Column and Pl^/te Compressive Strengths of Aircraft Structu.ral Materials. 17S-T Alum Inu.m- Alloy Sheet. NAGA ARR No, L^FOS, 1 5:|5 , 5. Heimerl, George J., and Roy, J, Alberts Column and Plate Compressive Strength of Extruded XB753-T Aluminum Alloy. NACA R3 No. l[|-F26, 19I4.I:-, !(.. Froll, ".'. D. , Fisher, Gordon P., and Heimerl, George J. Charts for Calculation of the Critical Stress for local Instability of Columns with I~, Z-, Channel, and Rectangular-Tube Section. NACA ARR No. 3K0ij., I9U3 . 5. Lundquist, Eugene E», Rossman, Carl A., and Koubolt, John C: A Llethod for Determining the Gol-umn Curve from Tests of ColumrxS with Equal Restraints against Rotation on the Ends. Nh.CA TN No, 903, 19i+3.'^ 6. Eeimerl, George J., 'ind Roj , J, Albert: Determination of Desirable Lengths of Z- and Channel -Section Colum:ns for Local-Instability Tests. NACA RB NO. L4.HIO, 19hh.. 8 NAG A. ARR TO. L^FOSa TAT^^ 1 CORIPR^SSIVh: ^rop^tT^S CF ■^XTRUDED 75S-T AITiMINTTM ALLOY [Ec = 10,500 ksll 1 Cclu:"i.ns to v/hich stross-sorain 1 curves apply Stress- strain curve (fis. 5) Cor.roresc ive yield stress, a^y (ksi) ! Type Designation (tables 2 to k) Thin strip All A 77.5 H la to Jb, Sa to ^c , B 7a to 8b, 10 to ilc 78.6 H 1 15a to 170 i c 81.6 H 18a to 2?a D 79.3 H 23b, 25c 1 E 7G.I H h\.a to '4.C, 6a to 6c, j p 9a to 9c, 12a to 12c 78.1 Z la tc 3b G 79.1 z l[a, [|.b, 3 b H 78 J4 z 1 5a, 6a to 6c i I 78. 7 z 7a to 8b E 79.1 7 t-1 9a to 9c A 77.5 Channe 1 la to 3f^ G 79.1 Channel [|.a tc 5c H 78.14 Channel 6a to 6c I 78.7 Cbanrie 1 7a to 8c 79.1 Channel 9a, 9b 1 A r-}i-7 I- ; / -5 NATIONAL ADVISORY CCMITTEE FOR AERONAUTICS NA(?^ ARR No. L5F08a TAEtE 2.- DIMENSIONS AND TEST RESUI.TS FOR H-SECTIOH COHJMHS THAT DEVELOP LOCAt INSTABILITY Column *W *P L >> s a or (Tor ^IXAX "cr S •v L bw •V 42(1.^2, (In.) (in.) (in.) (In.) (In.) (fig. 2) (kil) (a) (kai) (kil) ^nz la 0.120 D.126 1.61 0.82 6.10 3.79 0.95 13.42 0.512 2.72 26.9 l!*J'' 79.5 82.5 82. J 0.961 lb .121 .126 1,61 .80 6.10 5.79 .96 lip .500 2.78 26.5 148.? Ui .955 le .120 .125 .126 1.62 .82 6.10 5.76 .96 .505 l:fe 26.9 28.8 14?. 85.1 .941 kt .120 1.61 .90 6.05 5.75 .96 11:^ •552 ■$5§ .608 125,0 78.7 80.1 .985 2b .120 .126 1.62 .90 6.07 5.75 5.76 .96 2.38 28.8 122.2 '7l:l 80. J 77.4 .975 5« .121 .126 i.62 .98 6.10 .96 13.43 2.02 31.3 106.3 .992 ^ .121 .126 1.62 .99 6.08 J. 75 .96 13.43 .610 2.02 31.3 106.3 77.0 ]U .995 .963 .120 .121 1.62 .99 8.75 5.40 .99 13.45 13.36 .615 1.92 32.0 100.7 101.6 75.1 76.3 74.4 76.0 kb .121 .121 1.62 .99 8.75 5.40 1.00 .612 1.91 32.0 ]U .985 kc .121 .121 1.62 .99 8.75 5.40 4.01 .99 .611 1.87 32.1 100.7 .967 .988 5» .121 .126 1.62 1.03 6.49 .96 .656 52.4 58-7 u 5b .120 .126 1.62 l.OJ 6!^6 4.02 .96 im .633 i.'s^ 52.4 98.5 75.5 76.5 5o .120 .126 1.62 1.05 5.99 .96 .636 Ui 77.3 .990 6a .121 .121 1.62 1.08 8.75 5.40 1.00 13 149 .671 .6^9 1.62 74.1 74.7 .992 6b .121 .122 1.62 1.09 8.76 5.41 1.00 1.6? 34.8 86.2 73.8 '7V7 M 6o .121 .121 1.62 1.08 8.76 4.28 1.00 15.36 15.41 .669 1.63 34.6 86.6 73.8 7a .121 .126 1.62 1.16 6.95 .96 .716 1.52 35.9 36.0 80.2 71.8 72.6 .989 7b .121 .126 1.62 l:ll 7.00 i;.?2 .96 13.43 .720 1.52 80.0 71.7 72.2 .99? 11 .121 .126 1.-62 7.01 4.55 .96 13.41 • 727 1.49 1.46 36.3 78.6 72.0 72.5 .99? .120 .126 1.61 1.16 7.82 1+.86 .96 13.36 15.42 .724 .72? 56.? 78.7 70.8 72.5 .977 .961 8b .121 .126 1.62 1.17 7.80 4.81 6.2? .95 I. jo ?6.2 79.0 71.1 72.5 9a .121 .121 1.62 1.17 10.10 .99 i?.4o .723 1.42 ?7.2 75.1 70.9 u .992 .989 9b .121 .121 1.62 1.17 10.10 6.25 1.00 15.39 15.45 ■Ml 1.42 37.1 75.2 74.5 69.0 9c .120 .121 1.62 1.17 10.10 6.23 .99 1.42 '7-5 40.7 40.6 68.5 f.l .966 10 .121 .126 1.62 1.25 7.82 8.72 4.83 .96 15.42 •1? 1.33 70.1 65.0 69.0 .991 11a .121 .127 1.61 1.5H- 5.42 .95 13.26 1.17 62.0 65.6 .945 lib .121 .127 1.61 I.5C 8.71 5.41 .95 1J.27 .834 1.16 63.1 61.6 65.2 64.1 .945 lie .121 .127 1.61 1.51+ 8.71 (,'M .95 15.51 .851 40.5 65.2 62.4 .975 12a .121 .122 1.62 i.5l 10.75 10. eo .99 13.41 .829 1.14 42.1 60.1 61.9 65.7 .972 12b .120 .121 1.62 I.5I+ 6.67 • 99 15.45 .850 i.ik k2.2 59.9 61.8 63.2 .978 12c .120 .122 1.62 1.51; 10.80 6.67 .99 15.45 .629 1.14 42.2 59.9 61.2 63.2 .968 13a .120 .125 2.25 1.26 11.62 5.21 .97 18,69 .562 2.29 40.8 62.2 59.5 61.5 .967 IJb .119 .12? 2.25 1.26 11.61 5.21 .97 l§-7? .$62 2.29 40.9 61.9 59.7 61.5 M z .119 .12J 2.25 2.24 1.26 11.60 5.20 .97 i§-74 •564 .608 2.26 41.2 61.0 59.9 61.6 .972 .119 .125 1.56 12.59 5.62 .97 18.76 2.00 1+5.9 55.8 54.1 55.2 57.8 .920 ll^b .119 .125 2.25 1.57 1.4 1.15 12.65 5.66 .97 18.7? ,611 .611 2.00 45.8 55-1 57.6 .922 ll+c .119 .125 2.25 2.2I; 12. 6 J 5.66 .97 18.71 2.00 45.7 5U.2 49.5 55.1 57.7 56.0 .920 .898 15a .119 .125 15.50 5.94 5.96 .97 18.78 .658 1.84 45.^ 50.5 15b .119 .125 2.25 1.U5 15.50 .97 1§'71 .658 1.84 45.6 49.9 51.0 56.1 .909 150 .119 .125 2.25 1.55 1.60 13.51 5.97 .97 18.74 .658 1.84 45.7 49.8 50.5 41.9 56.5 I6a .119 .125 2.25 15.82 6.20 .97 18.76 .718 1.51 50.5 40.7 55^8 !780 16b .119 .125 2.25 1.59 15.85 6.20 .97 18.75 .714 1.52 50.2 41.1 42.1 .783 I6e .119 .125 2.25 -1 15.81 14.70 6.19 .97 •9? 18.73 n 1.52 59-2 41.1 41.9 55.7 .780 .611 17a .119 .125 2.25 6.59 18.71 18.66 1.19 56.8 52.5 52.4 51.5 51.2 17b .120 .125 HI 1.8U 14.66 6.61 .96 .824 1.19 56.7 52.2 51-5 51.8 .625 17c .119 .125 I.8I4. 6.54 .95 18.75 .822 1.19 56.9 32.1 52.9 .655 18a .125 .121 i:a 1.16 11.49 k.l9 1.02 22.22 .425 5.19 41.1 61.3 61.8 62.9 .985 iSb .125 .121 1.1k 11.1+9 4.16 1.01 22.46 .kl2 5.37 40.5 62.3 61.2 63.6 .962 19a .122 .121 2.7U 1.2k 12 .98 4.74 1;.76 1.01 22.36 .454 2.95 43.1 56.0 kt 5^9 58.6 .950 19b .125 .121 2.75 I.2I+ 15.00 1.02 22.50 ■m .502 2.95 45.0 56.3 • 959 19c 20a .122 .122 .120 .119 2.75 2.7^ 1.22 1.57 15.01 i4.ko 4.77 5.26 1.01 1.02 22.55 22.47 5.00 2.50 42.7 47.0 57.0 47.0 46.9 58.5 47.6 m 20b .122 .120 2.7i^ i-'i 14.I4.1 5.26 1.02 22.50 22.46 .501 2.50 itl:^ 11:1 !878 .869 20e .122 .120 2.7^ 1.56 1I4..1+0 5.26 1.02 .608 l-M 47.0 21a .122 .119 2.7^ 1.67 15.21 5.55 5.54 1.02 22.48 54.9 34.? 34.4 m 51.8 .685 ! 21b .122 .120 2.7U 1.67 1.68 15.18 1.02 22.46 .608 i:l 54.8 51.1 .659 21c .122 .120 2.7U 15.19 5.54 1.02 22.50 22.42 .612 ki 34.4 Hi 51.3 !686 22a .122 .120 2.7^ 1.96 16.72 6.11 1.02 .718 1.57 ^5-2 25.8 49.1 .558 22b .122 .119 2.7U 1.96 16.70 17.80 6.09 1.02 22.45 .717 .817 1.37 65.3 70.6 26.0 49.0 .550 25a .122 .120 2.71I 2.2^ 6.50 6.49 1.02 22.1+6 1.10 20.6 20.2 47.0 i 2Jb .12? .12!| .122 2.71; 2. 21+ 17.79 17.81 1.02 22.25 .820 1.09 in 20.9 21.5 47.9 23c .122 2.71+ 2.2li 6.50 1.01 22.16 .818 1.10 21.3 21.9 47.9 .457 cr 1 12(l-(i2,b^ where Eg = 10,500 ksl and 1+ = 0.3. NATIONAT ADVISORY COMMITTEE FOR AERONAUTICS NACA ARR No. L5F08a 10 < Eh ^J o o a o M tH ( > w ^ N H 1- K l- f ) 0. fc < H CO r/; H » ^ M la ^ K c o t-i 1^ OT w 0-1 H o D Ei s > < K (-^ en 8 H C3 <: Hi ^ fvi S b"||b O 03 b ^ Pi .r4 *-^ O P 10 C8 J\o r— (\J rH ONCTsOCO ON ON ON c^ r— irvj- i/N C~-nO C^LfNO f\JOJ_d" C~-ff>C\JvO r-l WN CO O ON-d" ONCO CO LrNN£) O^ONLTNLrSLTN .H coc^cvj ^<^o ooo CO r-i rvj «H n^vo rH c~-_d-o Jod fr\ CVJ rOvKNrH rH OnO ^f^ KNCM l/NNO prvOJ rfN Lr^lr^^^\K^c\J (M rvj J--d--:iaD\0 rHt^rH jTVJ-d-irv>^NO rH O CO rH ONrHCVJ CM -d-ir^o o o rH o O O O ONOsONC^t-- iTNiTNNO C^LfNLTv VO-.0 J- J-rrNtrf\ _:tI3- iTNirwO NJ3 vO O O rH_d--d-(MNO J- O o o t^t~-t~-ro\rr\ rvlrH f-lvO ONf- _:j-_=tco ^-N^^<^ r<\ ITN C^ C-- ir\ LfN ON ONCO CO CO CM (M OJ C\J OJ C\J rH rH rH rH rH Oi C\J rH rH rH ,-1 (\i C^ <-{ r-t r-^ •-< r-^ 00 C^CM t-l u^v^onOO ITN ITNsD OJ rH OJ OJ CVJ vO nDnO C--t— t--COCD rHoj cy rvi_d-t~- COOO O O rH rH U-mTvC— c~-coco c\jno J-_d-0 O ^c^ ONO\J-_d-rH rH rH -d--ctNO NO cn CO CO r^ CO ITNCINONO rH C— NO J- J- J- irxj- j-j- J-rOlKNNO rCNrH C--C^C\J C~-C\J rH CO CTnQO t--t^rH •-* NO irNLfXj-C-C^O KN r O CJNO OsOSi-l CMCO O OJ CM rH rH J-LTN CM ojcoao3-I3-I3- t-lTNlTN ITMTNNO nONOnO LrNLCNa^LTNNONONO KN O rH rH CJnC^NMTN O O O C^ O O r-< ,-1,-tO ONONC^t— . CM OJCM CM CM CM OJ NO nOnoO nDnDnOnO ICNITVNO lTnC^nO CM CM OJ CM CM OJ NO NO NO NO CO CO oo < rH rH CM CM CM CVJ OJ OJ CU CM OJ OJ CM ai £> o t~-c^-aaco On ON ON KN O II Tl c 0) o o ONvO vO vOsO CM r-l so O iHvD lt>>0 t-JOiOMT^iH t-( rc> l/Xj-irNfOCO iTNfy .;t_d-c\iK>cMoo r-t- ooNcr^rvj cvjononos ir.so ONC^r~-_:4vo 0O_d-iH.dKD O f\J On ^l/Mr>O0 IfNOsO-livO C\J O t^lTNfrvKMC C*-C*-nO so sO sO vO NO O>C0 t^-sOsOsO l/MfNl/N ifMfN rcv fC\ rr\ CM C\J J-J-|C\CM0O OM*\^ tf\(\J K\j:J-rrM\) r-i i-t fU r-l O CM iH iH O t- ffSK\crvf- oococr^o^-^-^- vosovoj.iJ-J'Knkmcv irMr>rrc>cMCM C— t^r-(CO O O CVO a)OOaXDC000C~»O CSCsj-ICMCMaOCM I-* i-l^rcu^CQ CDOO KMC\K\fC\KN KN»rv»rv NOVO r< 1-1 i-t_:tNO t» 9sONC^ t^ t— K\ KM<\ CM irM/>CM CM CMsO irvo CM CM CM t-t— r^r*MC>lC\ rr\ K\r\ (-1 OSSO ITS CD 0 t— O CM O t^tOfl sOvO CM CM CM CM CM CJ vOvO t~- 1— C— 00 00 00 lor-t^-CO r-l O O-d-O »HOOO<-lr-'CMCMCM vOvOsO t^t--C-CO0OOO O CTNKNrH i-lCDCM O (JNSOVOSO Qr-1 U^_3vO SO sXXfi CO r-l rHC0_d-_:*O «r>ON ONCM rHsOCO CrsiH-dm HM/MTMrs irM/> CJnOO 00 CO o o LrMrs»Hir> CM K^_d•_d•^<^'^K^ KN ^f^ tfS fTv KMOv tC\ KN rHiHr-li-lr-trHi-ll-l CO 00 CO 00 CD CO 00 CO CO »-tr-li-lrH(H(-lr-li-lfH CM CM CM CM (\J CM CM CM CM CM CM CM CM CM SO ITvlf^esO ITSSO N^sO CTs ON CTs OS OS OS ^s OS t-C-C-r-OD t^^-^-^- C?s OS CTs OS OS OsCTs C7S CTs CM CM IH rH CM CM CM O O O O O OO iH iH 1-1 iH rH ^ rH COOSCMsO CM KNO O CTsirsirsO O CTSsOsOsO rrNKNffscM CM r-n/NLrsirs C^ ONCOOOCO ITMTS CM fMOOcocD irsirs icvrNj-_::t_;tirsirNirs irsi/si^vovososososo irMrsu^irsirssoso CM irsO iH O U>VfS d- i-lfMCMCMCMr-lOOO r-li-lO O O t~t^r- OsCJsOsOOOC300C~r-t— vOsO C-- 1~- C~-CO 00 CO O CJSO O O UMTS _d- KNr-1 r-l rH C3SC7S r-l rH r-l NM^SKVd-^-d- J--:JsOsOsO C^f- COOO C~-sO C^ lOv^trv O O iH rH r-l KSWSKN vOsO l/SCD OSC7SKN_:^fO\ KNKs roiirsirs iTxD ro CO so so CM r-l rH rvl KN KS fOvCOCOCO CM CM IrH rlr-lrHr-lrHr-lrHrHr-t rHrHr-lr-lrHCMCM CMCMCMr-ICMrHCMCM sD so N^ N^ so SO so so rH loo ol.ooai,oo J-J-_d-irsirMrvO sOsD t— C'-COCDCO OSOS o CO l-H CO o < O o 5 ta as M o KN O II zx. •o o o ITS O M_ •P iM O > .^ f rH .fe|p NACA ARR No. L5F08a Fig. 1 br >w t w t l:^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure I.- Cross sections of H-, Z-, and channel section columns. NACA ARR No. L5F08a Fig. 2 bf/bw Fiqure 2.- Values of k^^ for H-secfion columns. (From reference 4.) 'W ■ Tl I2(i-/j^)bw' NACA ARR No. L5F08a Fig. 3 7 r-i-r-r A£RONAOriCS bp/b^ Hqure 3.- Values of ky^ for Z-and channel- section columns. (Fronn reference 4.) O'er ^ ^w'^ LJ^tyy n iz(i-^^)bw^ NACA ARR No. L5F08a Fig. 4 Figure 4.- Local instability of an H-section column. I NACA ARR No. L5F08a Fig, \ tlons from h specimens ^t K.002H Strain \ P ^ B n- ^ 1, \^ 1 n D ^J 1 \ \ ^ ^ §|g" « E c \ \ ■^ 1—4^^^^ E o 1 ■ \ •-^ \^ ^ ^^ ■^ 1 \ ^ -T- ^ \ ^^ ^^ _L ■^ ^ V \ V (1 -^ V \ ^\ ^ "^ ^ X \ V N^ h ^ J3 \ ^ "\ ^ ^ ■^ strain curves itified in ta \ \ ^ ■-V h ^ \ \ "^ ^ ^ "^ ^ 1 \ ^ n ^ >ive stress - c. are ider V •v. \^ ^ ^ \ \ \^ ( ; ^ \ •-V ^\ ^ ^^ \ CO 0) E £D o , "^ s^ cf^ ^ \ ^\ ^^ ^ re 5. - C urves A i_ 3 o ^ Q ^ C <4l_: F ^ u (1) o r O n -«-=- _Q , O I^ 0) >> (_ o -J CJ» o NACA ARR No. L5F08a Fig. 8 { 1 "to oi ?-. ^1 z i K 3" - / o o> 10 a> o CD th str Hoy. o 1 ^ lO ^ E ■^ 3 o '(n S c ^ r £ -» 3 o to CO 'S o C) L. CO O I O CvJ 5 JO o re 6. - truded O «5 (O "^ Csl P" o ^^ NACA ARR No. L5F08a Fig. 9 60 60 O'er, ksi 40 20 \ V 1 Btic ckin H-^ ^ bu g 1 o\ '1% fe ' \ \ ^ W o \- A D _ ^> X \ — 1 NATIONAL ADVISORY COMMITTEE FOe AERONAUTICS 1 ' zo 40 60 60 bw /I2(l-/J") tw V kw Figure 9. - Plate -buckling curve for extruded 75S'T aluminum alloy obtained from tests of H-,Z-, and channel -section columns, acy = 79 ksi. NACA ARR No. L5F08a Fig. 10 80 ^ J§L- \ «o 70 o% k^ p^ ^l ^ f 1 60 i J A K i ti 50 f 40 30 ( Q r 20 ( / A -| 10 / □ 1 1 n 1 1 u 1 1 n a NATIONAL A WMFTTEE FM BVISOBV UKWU/TICS 20 40 60 ao 100 o? 'cr/n^Si 120 140 Figure 10.- Variation of Ocr with CTer/n for plates of extruded 755-T aluminum alloy obtained from tests of hi-, Z- and chonnel-section columns. acy = 79ksi NACA ARR No. L5F08a FiR. 11 arr. ksi Figure I!.- Variation of Ocr with Ocr/^mM for plates of extruded 75S-T aluminum qIIovj obtained from tests of H~, Z-, and channel- section columns. a^g=79ksi. r NACA ARR No. L5F08a Fig. 12 O'max.kSI 80 Qyr^ Jgo ft. ^ ^ < H 70 » ,^ ^ # c ^T _ or 1 1 60 ( r e if 50 ^ y| k 1' 40 u 30 20 o H A n_ 10 D 1 1 n COMM T10WW. ADVl .OfiV •junics 20 40 60 80 100 120 140 Figuns 12.- Variation of a^ax ^'"'''^ •^cc/'H ^°^ plates of extruded 755-T aluminum allov/ obtained from tests of H-, Z~, and channel- section columns. Ccy = 79 ksi. r UNIVERSITY OF FLORIDA 31262 08106 552 5 UNIVERSIP/ OF FLORIDA DOCUMENTS DEPARTMENT 1 20 MARSTON SCIENCE LIBRARY RO. BOX 117011 GAINESVILLE. FL 32611-7011 USA