NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS. ORIGINALLY ISSUED June 19^3 as Eestricted Bulletin 3F29

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1 KB N. 3F29 NTINL DVISRY CMMITTEE FR ERNUTICS If mll m XY ^ MM>M«äSL RIGINLLY ISSUED June 9^3 as Eestrcted Bulletn 3F29 TESTS F -INCH 24S-T LUMINUM-LLY SHER PNELS WITH l -INCH HLES 2 By Paul Kuhn and L. Rss Levn Langley Memral ernautcal Labratry Langley Feld, Va. hr~*m ^StS^SSB» B I WSHINGTN NC WRTIME REPRTS are reprnts f papers rgnally ssued t prvde rapd dstrbutn f advance research results t an authrzed grup requrng them fr the war effrt. They were prevusly held under a securty status but are nw unclassfed. Sme f these reprts were nt techncally edted. ll have been reprduced wthut change n rder t expedte general dstrbutn. I L " 5

2 a r NTINL DVISBY CMMITTEE TB ERNUTICS BESTBIGTED BULLETIN TESTS * -INCH 24S.-T LUMINUM-LLT SHEB PNELS I WITH lvg-inh HLES 3 By Paul Kuhn and L. Bss Levn SUMMRY Tests were made f a number f -nch ehear panels f 24S-T alumnum ally wth lv 3 -nch hles t determne the stress cncentratn at statc rupture and the defrmatn characterstcs. The average factr f stress cncentratn was fund t he abut.; renfrcements arund the edges f the hles dd nt ncrease the ultmate strengths. Permanent set began n specmens wthut hles at nmnal shear stresses f t 2 kps per square nch. In thn specmens wth hles, permanent set hegen at the bucklng stress. INTRDUCTIN In cnnectn wth a prevus nvestgatn f the strength f shear webs, sme tests had been made f 24S-T alumnum-ally tensn specmens nch wde wth 3 flnch hles (reference ). These tests ndcated a stresscncentratn factr f abut.8 fr statc rupture. The questn arse as t whether ths factr uld be appled t Bmewhat larger hles, such as thse used t permt the passage f cnduts, tubng, r cntrls thrugh a shear web, and as t hw much the stress cncentratn uld be reduced by renfrcng the edges f the hles. The results f a seres f tests undertaken t answer these questns are presented herewth. In the ' curse f the tests, nfrmatn was als btaned n the depth f the shear buckles bth under lad and after remval f lad.

3 SYMBLS a sde f sheer frame, nches d dameter f rvet hle, nches D dameter f hle, nches B Yung's mdulus f elastcty, kps per square nch P ultmate lad, kps t sheet thckness, nches * nrmal stress, kps per square nch a y<._ nrmal stress at yeld pnt, kps per square nch T nmnal shear stress, kps per square nch T Qr crtcal shear stress, kps per square nh TUST SPECIMENS ITD PRCEDURE Materal.- The materal used was 24S-T alumnum ally wth nmnal thcknesses f.3,.32, and.5 nh. The specmens fr each nmnal thckness were cut frm a sngle sheet. The stress-stran curves fr the three sheets are shwn n fgure. The shear panels fal essentally n dagnal tensn; the test cupns were therefre cut at an angle f 45 wth the gran. Specmens.- The specmens (fg. 2) cnssted f sheets 2 nches square and were "blted nt the squarepcture-frame Jg descrbed n reference. The dstance between the center lnes f the hnge pns f ths frame was nches; the clear wdth f specmen was 8 nches. The edges f the specmens were attached "by V 6 -nch hlts ptched nch.

4 edges were renfrced "by rvetng tw steel rngs Ve-nh thtök t- th-e- specmen*. The. sld specmens ether were plan r had steel bsses rveted t them (fg* 2).»+! lest prcedure.- Tw dfferent test prcedures were used. In predure, the lad was ncreased "by equal ncrements untl falure ccurred. t each lad, the depth f the man "buckle was measured wth a mcrmeter depth gage. In prcedure B, the lad was returned t near zer after each readng and the depth f the permanent "buckle at ths "zer lad" was measured. TEST EESUITS ultmate strengths f perfrated specmens.- Fr the spemens wth plan hles r flanged hles, the nmnal shear stresses T at falure were calculated "by the frmula.77p t(a - D) () where a = nches and D =.5 nches. t falure, the stress cndtn n the panels was farly clse t the cndtn f pure dagnal tensn; cnsequently, dagnal-tensn stresses * were calculated "by the frmula T.44P / Q \ a 2T a 7 r- KB) t(a - D) In the spemens wth rngs, the net sectn was reduced "by tw hles f dameter d fr the rvets used t' attach the rngs. Frmula (2) was therefre replaced "by a m 2T -«4» ' (2a) t(a - D - 2d)

5 Tle stresses calculated by frmula (2) r (2a) are gven In table. The stress-cncentratn factrs gven n table 2 were btan«! by dvdng the ultmate dagnaltensn stress gven by frmula (3) r (2a) nt the ultmate allwable stress determned frm the test cupns. Fgures 3(a) and 3(b) shw the factrs fr the specmens tested by prcedures and B, respectvely. The average factr s.9 fr the frtft grup and. fr the secnd grup. These values are nly slghtly hgher than the value f.8 fr rvet hles dscussed In the Intrductn. It n evdent frm an nspectn f fgure '3 that nether the flanges nr the steel rngs apprecably changed the ultmate strengths f the specmens. Ultmate strengths f elld specmens.- The ultmate strengths f all sld specmens - plan-r wth bss - were calculated by the frmula T = - 77P (3) at The stresses shwn n table ndcate that the presene * f a bss rveted t.2- r.32-nch sheet has lttle nfluence n the strength. The specmens wth bsses develped abut the same stresses as the plan specmens, and falure started smetmes frm the edge blts, smetmes frm the bss rvets. In the.5-nch specmens,, hwever, the presence f the bss dstnctly weakened the specmen, and bth specmens' tested faled ^thrugh the bss rvets. The stresses develped by the plan-sheet specmens are n gd agreement wth thse gven n reference f a rvet factr s ntrduced as descrbed n the reference. Crtcal stresses.- The rtcal shear stresses T cr f the plan-sheet spemens were cmputed by the standard frmula; the clear wdth f sheet was used, and the cmputatns were made n the assumptn f smply supprted edges as well as n the assumptn f clamped edges. Inspectn f fgure 4 ndcates that measurable buckles began t appear n the.5-nch sheet at a lad -between the tw calculated rtlal lads» n the tw thnner sheets, the appearance f measurable buckles cncdes mre nearly wth the rtcal lad alculated n the

6 ^ assumptn f clamped edges. ttempts were als made t determne-the- crtcal lad "by bservng the.r.efle.t-» f a rectangular grd n the specmen. n the,5- nch specmen the crtcal lad btaned by ths methd agreed very lsely wth the lad at vhh measurable buckles began, and the methd appeared t be very seas-3 -tlve. n the thnner sheets, the methd culd nt be used successfully because the sheets were nt ntally flat. Permanent set.- Inspectn f fgure 4 ndcates that the plan-sheet specmens began t shw permanent set at nmnal shear stresses f t 2 kps per square nch. tentatve curve f effectve shear mdulus was gven n reference 2, based n measurements f the change n length f the dagnal f the shear frame; ths curve ndcated a lmt f prprtnalty n shear f 2.5 kps per square nch. The fact that permanent Bet n the present tests ccurred at smewhat lwer stresses thab ths lmt f prprtnalty can prbably be explaned by stress cncentratn alng the man buckle. The exstence f such a cncentratn s ndcated by the greater depth f the man buckle as cmpared wth the ther buckles n the panel and als by sme slated stran measurements. The measurement f the lcal buckle depth an shw ths cncentratn better than the measurement f the length f the dagnal. In the perfrated.5-nch specmens, as well as n the specmen wth a steel bss, permanent set began at abut the same stress as n the plan-sheet specmen* In the.32-nch specmens wth hles r bsses, hwever, permanent set started at a much lwer stress and, n the.2-nch specmens wth hles r bsses, permanent set began as sn as the frst buckle appeared. The steel rngs dd nt defrm measurably ether wthn ther rgnal plane r nrmal t ther plane. The flanged hles elngated abut the same amunt as the crrespndng plan hles. Ths elngatn started at a farly lw stress (fg. 5) and was ampanled by flattenng f the flanges. The stffness f the flanges was nt suffcent t prevent the sheet frm bucklng acvess the flanged hles, Langley Memral ernautcal Labratry, Hatnal dvsry Cmmttee fr ernautcs, Langley Held, 7a.

7 REFERENCES. Kuhn, Paul: Ultmate Stresses Develped by 24S-T Sheet n Incmplete Dagnal Tensn. T.JT. N, 835, HC, Kuhn, Paul: Skn Stresses arund Inspectn Cut- uts. NC.R.R., Dec. 94.

8 TBLE ULTIMTE.DIGNL-TENSIN STRESSES [ll values n kps/sq. In.; n specmens, the lad was ncreased cntnuusly; n specmens B, the lad was reduced t zer after each ncrement] Perfrated specmens Sld s pemens Specmen Plan hle Flanged hle Hng ' Wth bss (a) Plan sheet (a) Cupns (b).3-nch sheet - -2 B d J nch sheet - -2 B , , c 59.2 d nch sheet B , d 56.2 d >68.9 a 3I allwance made fr redutn f area "by "Ve-nh hlt hles. ^verage f tw tests. c Talure at edge. Falure at hse.! Ill

9 8 TBLE 2 S TEE S S-C H C BUTE T I ff FCTRS!R PEEIETED SFB MENS [n spemens, Ehe lad was ncreased cntnuusly; n specmens B, the lad was reduced t zer after each ncrement] Specmen Plan hle Type f spe men flanged hle Eng - -2 B.2-nch, sheet nch sheet \ - -2 B nch sheet B ,. l,lfwp-l»:

10 L S =.33 x s kps/eg In. y.p. = *^.7 kps/sq a. B =.35 x Ö 3 kpe/bc n. y.p. = 45.3?=ps/3q s. =.5J x 3 klps/eq n. dj-.p kps/sq n. 6 4 CQ a h C Stran TgdTö.- Stress-stran curvja fr 24S-T altlamn ally 45 t drectn f rllng. >]

11 Fgure 2. - Typcal specmens after falure. > 9-

12 u p «H Ft H P t P g 8 Ü a a '3 h P.4 z..3.8 n! ü Flanged hle Ü Hng - Plan hl! l J_. < r\ D- <> y D (a) n.2.3 (a) Specmens v Thckness, n. >> /k. T ("b) Specmens- B ' P Fgar 3.- Stress-cncentratn factra. 4

13 , J a Plan hle. ( -a-q - 3 2, Ü / (, Flanged hle ± I» L I I I W C > s * 6 G 3 S^ C 3 * & j)2 n. Rng t =.32 n > t=.5 n 3 Bss 3 L Q Q " ' 4? G e * fl<?, 2 Q Plan sheet ^. - k 3 ÜP & 2 2 D 2 2 Nmnal shear stress, kps/sq n. -XVpmply supprted edges Depth f buckle under bad -'Zcr,clamped edges (lthck- /3z") Permanent set -n Fgure 4-Stress-defrmatn curves. -If. - - C D 7**

14 -yu +» 3 3 n u P. - l r!!!!! Lngtudnal Lngtudnal V! ' ; IV!,! X I \S \ \! '! < : """"^-«s! j \! I * Transvera ' ' Transverse j : (a) r! (b) r > N / (a) Plan hld StrjSB, kpb/eq In. 2 3 Cb) Tlanged hle ffgr 5.- Change n amtrs f hles. w

f TITLE: Tests f Inch 24S-T lumnum lly Shear Panels wth -/2 Inch Hles ÄTT- 78B ^ CfVtSIN (Nne) RIGINTING GENCY: Natnal dvsry Cmmttee fr ernautcs, Washngtn, D. C. PUBLISHED BY: (Same) D* June '43 BSTRCT: c an Unclass.

The average factr f stress cncentratn was fund t be abut.. Renfrcements arund the edges f the hles dd nt ncrease the ultmate strengths.

15 f TITLE: Tests f Inch 24S-T lumnum lly Shear Panels wth -/2 Inch Hles ÄTT- 78B ^ CfVtSIN (Nne) RIGINTING GENCY: Natnal dvsry Cmmttee fr ernautcs, Washngtn, D. C. PUBLISHED BY: (Same) D* June '43 BSTRCT: c an Unclass. CT'IMTCY U.S. IMU«Eng. r> 3 IUUST XIMS phts, tables, graphs tl. GENCY N. RB-3F29 ruushik CDKT H. These tests were run t determne the stress cncentratn at statc rupture and de- frmatn characterstcs. The average factr f stress cncentratn was fund t be abut.. Renfrcements arund the edges f the hles dd nt ncrease the ultmate strengths. Permanent set began n specmens wthut hles at nmnal shear stresses f t 2 kps per square Inch. In thn specmens wth hles, permanent set began at the bucklng stress. DISTRIBUTIN: Request cpes f ths reprt nly frm rgnatng gency DIVISIN: Stress nalyss and Structures (7) SUBJECT HEDINGS: Panels, Shear - Stresses (68747); SECTIN: Structural Thery and nalyss lumnum allys - Stresses (59) (Methds (2) TI SHEET N.: R ' Dcument«Dvsn, latttlgnc D«partmnl r Materal Cmmand IR TECHNICL INDEX Wr^ht-PMtrtn r Fre«Ban Daytn, h -J

CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California

CTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California Vlume Change fr a Unaxal Stress Istrpc lastcty n 3D Istrpc = same n all drectns The cmplete stress-stran relatns fr an strpc elastc Stresses actng n a dfferental vlume element sld n 3D: (.e., a generalzed