Investigation of Duralumin Channel Section Strut Under Compression Citation Parr, Warren Sherman and Beakley, Wallace Morris (1935) Investigation of Duralumin Channel Section Strut Under Compression. Master's thesis, California Institute of Technology. doi:10.7907/9VQN-K047. https://resolver.caltech.edu/CaltechETD:etd-12222005-115855 Abstract This investigation has clearly established the fact that, for sections built up of straight line elements, theoretical calculations can be made with a degree of accuracy sufficient for practical application and will be on the conservative side. Item Type: Thesis (Master's thesis) Subject Keywords: Aeronautical Engineering Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): von Kármán, Theodore (advisor) Sechler, Ernest Edwin (advisor) Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 1 January 1935 Record Number: CaltechETD:etd-12222005-115855 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-12222005-115855 DOI: 10.7907/9VQN-K047 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5122 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 22 Dec 2005 Last Modified: 03 Oct 2019 23:41 Thesis Files Preview PDF (Beackey + Parr) - Final Version See Usage Policy. 1MB Repository Staff Only: item control page

-* ,-, .a & l - ,-,r, 7- L q, 4 -- ",,,-<.* A 4 . * - L > . '3ec t ion - IT. '-c :10'11*?~i*< ! ~ f TII, SIZ~L.:--:~ ?f 9eslllts 13, @:;":: 7, ;it of ?robl$y:l- 1 : s ~ r r c t i c e l .Cul e u k t i n r s i Failme j & : e r (P) ?l3t@ F a i l u r e (c) Torsioxi !?nil_ur.e $ 1 &x--ssl~-:entcJI n v o s s i c s l t i n n VII. L ~ X U S U ~ Qof' A Lxpcsimntal R e s u l t s VIIT, Co ?c?l~~:si ons LC; o; : ~ . , z r ~ t a:!tits l 2c,'f'e:-.~nces 13 :LO?IP~ZZ~~":-:;Z:~S : The a ~ t l i o r sw i s h to tt.;a& D r , von ~ h hD ,i ~ e c t o r of the. Guggenheis ;:er~n:.zz.t i c a l L s b o m t o r y a t the Cal i f o r ~ i a I n s t i t t r e e of Tacf.nology f o r the o p p o r t u n i t y t o make tiiis resesreh an3 f o r h i s advice and a i d ir- xorlilng o u t t h e t h e w tic^' treetment: of t h e invostigntion, 1 ? ~ , ', ?, ' ??ley wish to tb&nk :chlar unclear rvhose d i r e c t i o n t h e research W E B c a r l i i c d o u t , f o ~ "Ids veilur,?lc ass3 s t a n c e during %ha reaenrch and h i s c a r e f u l :-cvlil;t: of the c o r q l e t a d manuscrlnt. a l s c due T I e L. haknowledgrnent is ' . K l c i n of the I n s t i t u t e a n d the Douglas Aircraf-t Coqwny, Inc,, f o r t h e c a r e f u l preparation of equip- nent an : e?ecfT-tens tasted. This i n v e s t i g a t i o n kas clearly %sLablish@athe f a c t t h a t , f o r s e c t i o n s b u i l t up of s t r a i g h t l i n e elements, t h e o r e t i c a l c a l c u l a t i o n s can. b e made d t h a degree of nocuracy suff i c i e n t f o r p r a c t i c a l a p p l i c a t i o n and w i l l b e on t h e conser-vative IT, STATS:%T fl? ~ R ~ S L D ; : Sec'clans b u i l t u;, of strtilbqlrt l i n e elements are ex- t e n s i v e l y used os s t i f f e n e r e i n aerm a u t i c a l c o n s t r v c t i o n an4 cgnsequently knovsledge of t h e i r strength under compressive l o a d i s of importsnee t o the i n d u s t r y , A 1 1 shapes of s t i f f e n e r s e c t i o n s mad@ u ~ of t h i n f l a t sheet o f refisonable l e q t h , are s u b j e c t t o tLhree e l a s s e e of f a i l u r e , namely: , 1) Local wrinkliq; or buckling of t h e s h e e t i n t h e component p a r t s , 2) Euler failure as l o n s slender uolwnne due t o t h e i r UBQ i n l e r ~ ~ t hwi.lich s are o r d i n a r i l y l a r g e compared t o t h e c r o s s t s s c t i o n , and 3) Torsion f a i l u r e due to t o r s i o n a l i n s t a b i l i t y . The q ~ e t ~ t l oant once a r i s e s as t o the p o i n t s of t r a n s i t i o n from one ty-pe o f f a i l u r e to another, 1.6. t h e llrnits within' which each type of f a i l u r c ,?ay be expected t o occur. T A t, is a : l ~ c r l ' ~ ~Tr*x G a m s i d e r a t i o n of t h e problem t h ~ t%-. s"6iff'ener s?iLT f r Z l at ,7hiohevsr c ~ i t i c a lvalue of the tlflecj t;l?en, of "aillxro h t h e rulnimwn for a qlven s i z e o f stiffa:1.>;., .'.nir1vasti::~t4on of oliqlc section stiffeners of equal I - R ~low.:.l;hs : hna previously been mde by A. B, V o s a e l l e r - i d C. C, ~ e r o r n e l ) ,consequently, as an sxtension, of t h e i r re- searc?.i, thc e x t e n s i v e l y u ~ e dchatinel section was chosen for this i n v s s l i g a t f on, I n order $ 0 present t h e resxilts of t h e invas-tlgation i n a c l e a r and concise manner i t , i s necessary t o exp$ess t h e f o r n u l a s for t h e t h r e e d i f f e r e n t Wves o f f a i l u r e in term of the sams ptlrmeters. I n a d d i t i o n , it i s d e s i m b l e t o have these para- meters dimensionleas. % o r i t i c a l s t ~ s s st o cause buokling o f r. flat p l a t e u n b r mnpreesion was s s l a a t e d as t h e Q p o equation. T h i s equation and t h e edge conditions affecting t h e c o n s t a n t , a r e s u m r i z e d i n o r e c e n t paper by ~ o n n e l $ ' ~i n which he gtvas the equation i n t h e form T h i s formula s a t i s f i e s the conditions o f dimsasionless p a r a m t o r s i n t h a t K is a dimensionless c o e f f i c i e n t dapeading upon t h e r a t i o of the l e n g t h t o t h e Bddth of the p l a t e and upon t h e edge conditions. The edge conditions i n t h e problem under i n v e s t i g a t i o n r e s u l t K becoming a function of b, w, 'L, t and where /" b = length of l e g ( d q l h of channel ) n = v i d t h of back L = l e n g t h of eh.?rtnel L = thiokne~s B /LL= P o i s s n s r ~ t i c(Taken ar; 3.; Tos "materid t s s . t r ~ 6 ) in Since t h e varfaSles which were t o be c o n s i d e r e d i n t h i s i n v e s t i g a t i o n were b, w cmd t , i t was thought a d v i a t ~ t l s t o o b t a i n K as a f i n c t l o n o f t h e dimensionless r a t i o b/w s i n c e by holdlrig b , t a n d p c o n s t a n t K can b e e x p r e ~ a e das a f u n c t i o n of ( b / w ) , E, ( Y o q ' s hbdulus),of course, i s a canatalrt f o r any given mnterrlal. - (a) E u l f ~ F r ailure: The t h e o r y f o r t h e f a i l u r e of s t r u t s as E u l o r columns i s well known ~ n dhas been checked. c l o s e l y by 3 , vor* ~ n m n ~ who! o r i c f i n a t e d t h e general mathod of ~ ~ l r y i n g%fie , end c o n d i t i o n s t o oounterac t i n i t i a l e c a e n t r i c i t i e s , which was used i n t h i n invootigation. The bhler long colurnri f01'1311119 f o r c r i t i c a l stress is emrrysse4 88 where: C = c o e f f i o i m t of end f i x i L y r = Imst radius of gyration of : : r o a s - ~ e c t i o n E = Young9$ Modeilu~ 2 = lengtli o f colvlmpl The end c o n d i t i o n s under which t h e e t i f l e n e r s were t e s t e c ! wese made a s n e a r l y p i n ended as mssf ble b y mnuntiny t h e eht~nncLsi n grooves on s t e e l q l a t e s which r e s t e d on a henispilere n f b:.n*dertafi s t e e l (Fig. I ) ,hence t h e ond A x i t y was ta':cn as \ i ~ l i t > r Cr>r611 calculstions, The effective lerqth o f the chaznel (L) to be t used in %?I@ k l e r wluxnn formula was deduced by Dr. ? von K a r r n a n The equalion f o r the bending of a benx is €1 4 --py dx - t h e s o l u t i o n of whhiqh is 9=A C O S ~ X FLEXIBLE (21 Boundary c o n d i t i o n s : I A 3 and 2D a m myposed t o be of infinite r i g i d i t y and hem e are s t r a i g h t lines, therefore w 0. =_($$Xs =d fox m a l l angles cot Qgj: = a 0% and equation 3 gl,ves the exact value of the Pmler for the case considered. For a = 0 we obtain c o t mIk :o z ton z I- & and an? @ornparl.ns e q u a t i a ? ~(6) w i t l a equation ( 4 ) f t i n s e ~ nt h a t t h e e f f e c t i ~ ol-np$h all? Fror: ( 5! I YL= "rnz so 3."' (II! me tnkr! 3iIffori:nt vnl.lres of '! 1 9 Can @ ? L m l-:bGe c o r m s - It may b e seen from the t a b l e that even i n such extreme cases where t h e ~ Q i dblook egcral8 27,5$ of" the l e n g t h of t h e beam proper, 9 0 ~ 7 %of the length of t h e rfgid portion, is t o be added t o t h e l e ~ t of h the bem a;o givg the e f f e c t i v e long column length. A s t a n d a r a channel length o f 22 inches was used i n this investigation, and t h e combine& depth of the two end blocks fpom the bottom of the grooves to the top of the hmisgheres ,aras aetarminsd as 2.3" giving an effective Eulss ool& length of' 24.3" t b be used i n the Uler formula. I n o r d e r t o determine the value of If f o r t h e Eulsr cblumn fo~mulgt, the Eulor sxlt;.Loal s t r e s s i s equated t o the c r i & ~ c astress l of tha Cype equation whioh give@ from whio h Considexin& that the channels are of t h i n she& and t h e area is approx2mately (i?b+w)t; @= 2btW ealculatf on of the C.G. give&? when t 2 terms e r e n e g l w t e d . (10) I~~omonfjsof' T i ~ t ? ~ ~:t i ~> :: I ~ Cl l l a t . i 0 ~about; ~~ 32 I + 2 . -e)'+ w t k and s i m i l a r l y f o r t h e I;hl.cr f t i i l ~ r ei n t h e athelcr d i r e @ l ; i o n , which i s outside tho region investigated since it aecurs only i n c h a r cls which k i v a v a r y nmrrnf buc'cs und o n l y t h e n provided t h o y ax-e iceat from t o r s i o n o r lni': d a t e f a i l u r e , (b) P l a t e Failure: - If t k o c i . f t i c ~ 1 .s t r e s s e s fa3* the f L r i t p l a t e f a i l u r e ol" t h e legs and back are c o n s i d e r e d s i j p a r a t e l : ~ t~h e f o n x u l n f o p t h e legs lis giam by -9;hs tjy:l: equation i n which b = l e q - b h of l e g and t h e c r i t i c a l . s t r e s s f o r f l a t p l a t e f a i l u r e of t h e back i s e x ~ r e s s e das where w = w i d t h of back, If .the l a g i s considered as having s i m ~ l e support aloil,; t h e edge where :9; joins t h e back, the v a l u e of D o n n e l l f s $1 f o r this eons t i o n is 3.4 an4 c o n s i d e r i n g t h o sams l edge concliti ans f o the ~ back , which would r e s u l t i n s i m p l e suppoleP; on a l l f o u r sldes, sdvers a H o f 3.6. Then t h e edge j o i n i n g t h e l e g and hack i s considered fixed, K becomes 1.2 f o r feg p l a t e f a i l u r e and 5 , 3 f o r back plzte f a i l u r e , (For t h e purpose o f comparison, t h e v a l u e of K usod by DonneU. i n Ref, 2 is r e l a t e d t o t h e K found i n ~imGshsnko4)and other books on e l a s t i c f t y by t h e equation K T n h e n p i s t a k e n a s 0.3). Itisapparentthat t h e exact v a l u e of IZ f o r t h e specimens t e s t e d i s somenliere between t h e s e two extremes of simpla sunport and f i x e d edge c o n d i t i o n s and must b e d s t e ~ i i n ~byd combinfrq t h e e f f e c t of t h e l e g s and back on each o t h e r , T l i ~railare 0.f" t h e l e g s as p l a t e s bucklin,; under compressive load 1 s e s s e n t i a l l y a p ~ * o b l e mof t h e e l a s t i c s u p p o r t given t h e legs by t h e back as t h e , v i d t h of the bac'c l r a r l e s , It i s , ~ O W ~ B O S s, t i l l a probl&x of p l a t e bu c'clin;; and may b s tnnalyzed i n one of two o r thee methodo a l l q u i t e compl-ox, Of t h e s e t h e Tn3rgy TY'lctlzod was ta'cen as t'no l e a s t involved, and t h e f o l l o ~ i nt h~e o r e t i c a l expressions were developed by LIT, V O K ~ &T;~I&~. The internal, enorgy s t a r e d up en t h e n l a t o durinr: de- formation i s f t r v t s e t un usfng n s i n e curve apvroxirmtion t o t h e t r u e d e f l e c t i o n curve in the 1enr:tI: d i ~ e c t i r ~ond i n t h e d i r e c t i o n of t h e width of the buck c o n s i d e r i n ? t h a t t h e elements of t h e leg l ~ n q t hb remain s t r a i & t The work dona by t h e e x t e n d . f a x % is then set UD i n toms of t h e d e f l e c t i o n , ,ad c o n s f d e r i n g t h ~ t h e encsrgy chrmge i s zerc, t h e wor:: done i s n u t equal t o t h e energy s t a r c d ug i n t ? l e d a t e , The c r i t i c a l va-lue of t h e c o ~ ? p r e s s i v ss t r e s a f o r b u c k l i n s i s s o dotermined an? t h e v a l u e of t h e c o e f f i c i e n t 'i f o r t h i s t y p e of f e i l u r e Sound i r ? terins o f t h e partmeters of t h e ch%mnel. Considering t h a t t h e channel I s made u:, of three t h i n p l a t e s simply s u p p o r t e d o r hinrged at t h c i r t o p a n d bottom e d ~ e s and are l e f o r m d by the sromnression l o a d , t h e enc3rGy of bondini: and t v i s t i n g for the deformad s h o t is: anti, if i-8 represent etd by assumed t h a t the deflection of t h e leg may be h'*Y , ,= AX,S,N L (23 and that t h e d e f l e c t i o n uf t h o back is %= B S , N % S I N qY( 2 1 t h e internal energy f o r both l e g s i s -- tho inte~nalenergy of tho back is f 2 . s ~ $ ' ) ' ( ~s/*.~@ ) ~ SIN~HEY d x dg L and the total interilal elastic mesgy i a : But i f the angle between the baclr md Leg is plneservsd, me hcive at t h e j o i n t : Thea A sin yr B $ C O $ + S ~ N ~ !he extern& mrk done &wing buokling i e given by: $hen for %he t a g lei$@P *=ct. [ / b V ( ~ ) b z y d i * and for the baok: and Bhe total external %ark dme is: subet-2tu%iagfor A: and ~ u t t f n gt h i s fa t h e form To f i n d t h e minimum B , N must t a k e a velue such that Let d b = O( 4 Simplifying It i s r e a l i z e d that t h e assumption made in a p proximal3 the deflected shape of the leg i e somawhat in error when I t i e asaumed t h a t t h e l e g element in the R d i r e c t i o n remains s t r a i g h t . To approach the a e t u a l c o n d i t i o n any c l o s e r , however, an a n a l y t i c a l expression must be chosen t o get the a e t u a l defamation, and t h e o a l c u f a t i on 5eeomss too 'involved t o be mersented hero. (c) ~ o ~ s i oqna i l & u : Tho theory for f a i l u r e of t h i s t y p e of s t i f f e n e r due t o torsional i n s t %bi l i t y has been t r e a t e d r e c e n t l y by 13, "irar?;nera d 7. T?wtschner5). This method was chosen by t h e a u t h o r s a s being most suitable for t h e i r use and expresses t h e value f o r the c r i t i c a l l o a d of a s e c t i o n under compression as where lsJp p o l a ~r a d i u s of gyration of t h e s e c t i o n w i t h r e s p e c t t o the s'noar p a i n t 01- e l a s t i c centsuru. G = Modulus of @ . U s t i c i t y in shear E = Young's lJhdulus of e l a s t t c i t y Ie = ~ f " e v $ i v emoment o f i n e r t f a f o r t h i n s h e e t open s e c t i o n s CBT = Constant deternnined by t h e bending r i g i d i t y of t h e nangss L This f o r n u l a is m d a up of two p a r t s wlsic'n will be t r e a t e d s e p a r a t e l y m d ooitibined later, Por "art T I n e a ~ 3Leg du and d d dLo --L+ dy dx SHEAR DlSTRlSVnON t h e n cLif resent fati in{; and wlb st Pt u t ln.g and i n4;; egra.tin;; f o r oach l e g Z= a t t h e e d p of e a c t lo: x=&, 7 - 0 then b:; s u S s t 6 t u t i o n and the nhcarl over each l a g is given by f.7 = .w-b(b-X) & 0 from which f S T = Qz 4'z Then the moment of shear force in b o t h legs &bout shear center This is b a l ~ a c e 0by t h e d i s o c t shear force in the back (Q) a c t i n g at distance a, Cd.cul.:: tkon o f 'L ~ S F = -. A1 . z LsP .SP f ~ o mwhich f o r Palat I sf T o r s i on Ponnu.la: e = hZ for Part II C C g y La where W i:, = t1wice t h e aroa swept through by a radius - v e c t o r f r o m t h e shear c e n t e r t o o u t l i n e of sectiola, For t h e b a c k W = warping w = Z F = g e s 2. For h a l f the back then kt 24 fa"cQ=t/5'e2d.= f p 2 w 3 0 - 19 - 0 a% l i n e of s r n z ~ e t r y . VI , EXP~TUlJlJm?& SF?%~TIG;LTTON: The determination of t h e C O ~ ~ ~ E ~s t Sr e Sn g~t hV of ~ chrmml sections i n v o l v e s three v w i a N e s , nomely thioklzesa of n ! s l t e r i s l , width of baok, ~ n dLaty;th o f leg, I n o r d e r t o d@d;@r:zz2nst h a s f t e c t o f each variable, it b e c o m a rmceaamy t o vary on&nna ?t 3 tixw and this was done by using t w o thicknesses of m t e r i a l , ,025" and .05lW, v a r i a t i o n of width a f back from 0.4' o f 1enfl;Ch of leg from 0.4" t o 2,5n, t o Z.Ow, and v a r i a t i o n The tests were mde w i t h equal l e n g t h channel section s t r u t s 22" l o n q which, w i t h the supporting bloclrs, e t e , , gave an affective len,qth o f 2%,3'' f o r &ler failure, Since ncousate knowledge o f t h e end ffx i t y i s e s s e n t i a l For t h e determination of colurm b u c i ~ l i m gl o a d s , s g r e a t deo3, of care wae taken t o apprcach as n e a r l y a e porsoiblo t h e h i n r a d ends c o n d i t i o n f o r t h e channels t e s t e d . p l a t e used is shown i n r'ig. 1.. A strstch of an en0 b l o c k ihmd Tha p l a t e A was m!chinod on t h e upper s i d e with T grooves and t h e s e grooves .received t h e f a d of the epectmtsa, whiah had bean f i l e d t o an angle of 60 degrees, as s h o r n i n slcetoh. I n f i l i n g the ends, gssut care paas talcen not t o f i l e away m y of t h e c e n t e r l i n e md t o keep t h e e n d s squat*@. The key an4 keyway connectllng h and R allow a morsamnnt of A , (and thus the a d of t h e spocimern) by m a n s of t h e set; s e m w s C , r e l a t i v a t o E { t h e p o i n t of' q p l i c a t i o n of t h e l o a d ) . The motion of A and B i s such t h a t E always moves slo*? t h e a x i s of symmetry o f the specimen, and i n t h i s manner t h e point of a p p l i c n t i o n could b e placed e x a c t l y on t h e c e n t e r of g ~ a v i t yof t h e s e c t i o n , In o r d e r t o obtain d e f i n i t e and conditions for Xbler buckling, a 5/0" hmdened steel b a l l inser2;ed in t h e opposite s i d e of t h e end blocks transmitted the compressive loaa f r o m t h e t e s t machine t o 'the end b l o c k , p l a t e s and channsle;, Tho s t r u t s t h u s had pure hinged ends and eould buckle in any d i r e c t i o n . 1% was found, however, t h a t a s l i g h t dent mde by t h e s t e e l ball i n t h e cage p l a t e by one o r two t e s t a in. t h e same spot would give e r r a t i c r e s u l t s f o r Euler f a i l u r e , due to the change i n f i d t y of the ends i f tho beill w a s placed i n ths don% f o r subssqusat t e s t a , To eliminate this source of error, hardened stsel disco were made f o r t h e b a l l to r e s t on and the discs s h i f t e d a f t e r each t e s t . It was a l s o found t h a t the sl.i@t support given a ohannel by the up the specimen would prevent h e s di a 1 gauge use& f o r 1 i n . P ~ Euler f a i l u r e at t h e t h e a r e t i c a l point and carry t h e load, i n many cases, far above the W e r value. For t h i s reason, a f t e r t h o c h m n e l was l i n e d up ( i n i t i a l e o c a n t r i c i t i e s removed), t h dial gauge was rmoved before continuing the t e s t , The t e s t s were nade on a Riehle Rros, t e s t i n g rzachine o f 3000 lbsb c a p a c i t y . The mathine was a t e n s i o n tyne but w 0 8 converted f o r cornpression t e s t s by means of t h e cage shown i n t h e i l l u s t r a t i o n s , Fip,, 2. The specimens t e s t e d were o f 17YT aluminum d l o y and e o n t e r l i n e dimensions were used f o r a l l c a l c u ~ a t r o n s . The specimens of .025" thic!tness were m d e i n an o r d i n a r y hand brake mith r a d i u s of c u r v a t u r e at t h e c o r n e r s of approximately 1/16", b u t t h e specimens o f .05lV thic:mess were manufactured by t h e Douglas A i r c r a f t Company o f Sant a Uonica, Cal i f o r n i a , s i n c e t h i s m a t e r i a l was t o o heavy t o band on a hand brake without cracking. &itrelo cart? was n e c e s s a r y i n squaxing t h e ends, due t o the tendency t o have t o r s i o n a l f a i l u r e fiom uneven s t r e s s d i s t r i b u t i o n i f the e n t i r e snd of the channel was n o t f l u s h i n t h e bottom of t h e grooves. T h i s was accomplished by m i l l i p q o f f approximately ,001" on each end a f t e r t h e ends hnd been chamfered. The channels were made w i t h t h e < r a i n ( i , u , of t h e material n a r a l l e l t o t h e anqles. d i r e c t i o n of r o l l i n ? ) This was done duo t o t h e masked d i f f e r e n c e i n .the s t r e s s s t r a i n curve taken normal o r p a r n l l e l t o t h e d i r e c t i o n of r o l l i n g found by tests o f the. 3uretlu of Standards f o r N.A.C.A. an duralumin s h e e t s b J and t h e common p r a c t i c e of m a n u f a c t u r i n ~s t i f fenexs with t h e g r a i n i n t h i s d i r e c t ion. I n order t o p r o p e r l y l i n e up t h e specimen i n t h e cage, wooden j i g s were c o n s t m e t e d which would place t h e two p o i n t s o f c o n t a c t ( E ) d i r e c t l y over one b l o c k s were f i t t e d i n t h e j i g s . when t h e end An Ames d i a l gauge was t h e n p l a c e d a t t h e c e n t e r of the spcscimen and t h e end p l a t e s a d j u s t e d equably, as load was a p p l i e d , u n t i l a l l the eccentricity of the channel was removed as i n d i c a t e d by a c o n s t a n t rending on t h e gauge f o r c o n s i d e r a b l e part o f t h e expected load, The removal of a l l i n i t i s l e c c e n t ~ i c f t ymust be very e x a c t i n g for s a t i s f a c t o r y r e s u l t s due t o i t s infl.uence both in E u l c r and torsion failure. The gauge was t h e n removed and t h e l o o d i n - creased by small increments u n t i l the spuofmen f a i l e d . TIT. UESL'USSIOR OF E ] B ) ~ I I ~ ~ ~RlWT,,TS: L'LL The first t e s t s m d e were of %ht s ,025" b s 0,4w channels v a r ~ i r mthe back from O.4*' .to %,Qf* Pop which q u i t e oonsistent W e r f a i l u r e s were obtained and which followed the Idulsr owva very cloeely (Fig. 3) ahmirig t h a t the end conditions were as aetsfrtqd (approximately w;ni%g), The next $st of a b n n e l a t e s t e d wasi t a .085" b = 0.6" whiehvgave t h r e e t o ~ e i o nfailuxee with the shoreer backs aad We remainder Euler f a i l u r e as may be seen OR F f g , q * It w i l l be noted that the torsion Sailures obtained duriw th6 invtaet;i$ation were eitL consi atsn.t;ly higher than t h e i r t h w r ~ t i o a l .wrsion cuz'veklo The tBeoreOfcal eurv'es W sbased on an assumpttsn 05' free mde, i,a, €lie 6 a d . 1 ~are allowe4 t o amp when the ohannel t w i ~ t s . This conditf on n~fOurally is w a o t i c a l h y i m ~ o s s i b l et o obtain and m s u l t e d is the channels resioting the torsional, manicgnts until, a higher load than Che t h e o r e t i c a l va2ue plraa obtained. Tba channel mu2d then f a i l i n t p r s i o n and i n failing would ciause a l o c a l bu&l%ng of One corner oiF a l e g indicatinR t h e Qendencf f ~ r the lega t o warp i n t o r s i o n failure. 'If, however, t h e stress reached the %ler value bePore t h i s oocured, Euler f a i l u r e would r e s u l t , as alearly shown by thin net failures. of points follawing the k l e r curve after th3"8%t o r s i o n a l It baing fiesirable La obtaf n p l a ~ ofailuse also, channels nope chosen t t = c325w b = 0.8'; t = .025" b s 1rO"i = .025" b = k,3**; . t = .05bw b = 2,5*; t o insure plate failure o f thd Legs. The t e g t values obtained for these ohmnels, aa aurvattwe of the ?nay be seen i n Fig+ 9, followed the &@nerd thd'oratfcal plate failure curve etxaept for t h w e point8 where . It I . suggested for design that the dotted curve faired thsough the ex@%rirnmtal. ~ o i n t ssham in t h i s figure be used, In $hie e"e@fan,eonsMsPable .stpatWr is apparent due t o fb tmdenc?? tovard. tors%onalPailpre, five o f which were dbf i n i t e l y so, Tt is felt that aeveral. sf the othtsr poiats m e probably a eombihation of torsion and plate faf lure, since a s m a l l addStional laad after plate fatlure in this region wowld result in a twisting of $he channel, but the initsial failure could not be d e f i n i t e l y designate8, as other than plate failure. For a l l the point8 @horn, aot marked aa t o r s i o n a l , i n t h i s group of channels plater $alZqse of the3 legs oocurred gisnilar t o Fig. 2. The law values ob$gln&&fw this se$ of.channels as oompared t o t h s theuretical p$a%e'iailuPe curve i s explainable by thq jlaot t h a t in th theoretiea3. m a l y a i s far this case, the assumption was made t h a t t h e energy 02 t h e deformad section could b e ob- t a i n e d by asstmini., t h a t t h e l e g s deform a s B. s t r a i g h t l i n e , This assumptian w i l l hold fop very laripe values of w, o r m a l l b/w r a t i o s , b u t as w becomes small, o r b l a r g e ( l a r g e b/w r a t i o s ) , t h e n ' the assumption of a s t r a i g h t line d e f l e c t i o n f o r t h e legs breaks dawn. This must be true s i n o e at t h e l i m i t (w 0, b/w + oo), t h e l e g s of t h e channel w i l l a c t as p l a t e s f i x e d along one s i d e , m d w i l l abvlously not k v e a s t r a i g h t l i k e d ~ f l e c t i o ncurve, Thus f o r large values of b/w t h e treatment p e v i o u s b y given l e a d s t o a higher value of K than would 178 expected f r o m experinental t e e t s . Probable d i s c r e p a n c i e s i n the? end conditions may also b e h c l d ' . n ~ r t i a l l ya e c o ~ i n t a b l ef o r t h e low value. VIIIo CONCLUSIONS: It i s f u l l y appreciated th8.t t h e method of securing a channel s t r u t i n a s t s u c t u r e w i l l vary from no support t o r i g i d support f o r the back, and $hat the degree of t h i s support w i l l g r e a t l y influence t h e mount of f i x i t y given t h e edge of t h e legs. It i s hoped, hovfavor, t h a t t h i s i n v e s t i g a t i o n w i l l a t l e a s t 74ve qome basis fay makin3 a f i r s t approximation of t h e s t r e n y t h of channel s e c t i o n s t r u t s . The autllors believe' t h a t t h i s i n v e s t i g a t i o n has demonstrated the - f e a s i b i l i t y of anal yzi-3 up of f l a t sheet elements such as a11 sections b u i l t n,I x, @*c , t h e o r e t i c a l l y w i t h some degree of accuracy, s i n c e findamentally t h e y a l l r e duce t o t h e same question of determination o f R at the corners. . It w i l l be noted t h a t the experimental points check the t h e o r e t i c a l values f o r t h e plate f a i l u r e curve q u i t e c l o s e l y i n t h e usual range of channel s e c t i o n s , i.e. 0.4 <T6 (0.7 and beyond t h i s range t h e t o r s i o n f a i l u r e r e ~ i o nis entered and f a i l u r e occurs i n t h i s manner. It is recommended t h a t f k r t h e r i n v e u t i g a t i o n of t h i s type'of channel be made $or d i f f e r e n t methods of securing i n a structure. Investigation of t h i n sheet s t i f f e n e r s e c t i o n s made up of curved s e c t f o n s would also bo of considorable value t o t h e aeronaut i c a l i n d u s t r y * - 2Rs- TEST DATA -- Channel Dimensions Thickness Back Leg Test Values Load Stress Test Values Channel Dimnsf ans Tli~.clcnsss Back Leg BP~ Load Stress 1) A, 5. VosseILer and C, C, Jerome "Investigation of ReLat Zoa getween % l e r and F l a t Plato Bucir1ir.1 oT VL* ~ n c e t i o n Stsuts", f i a n s , 4,S.1!. E. Apy)Iiec? ;Ges'~*~nice D l v i s ion, August 1'234, pp. 569-5'73. 2) L. If, LtoraeLl "The Problern of :Qastis S t a b i l i t y P ' , T T J ~ S ,;.3e18.5. Ver. 15133, Val. 5 , N C ~4, p. 4, 3 c u t s e Ing., B e r l i n 1909, 4) S . Tfmshenlco "Strenffth of l J a t s r i a l s n , Part 11, p. 605. 5) Pon E, Vagner anit Sf. P r e t s c h n e r "Verdrahung unci Thfckung von T r o f i l e n " , L u f t f a h r t f o ~ s c h u n g , Band 11, Nr. 6. Solwn~-i:lof Equtil A n g l e Section", N.A.C.A. Tacl!nic:-?t S i l t e