Investigation of Extended Bulb Angle Sections Under Compression: Part One. As Euler Columns ; Part Two. As Stiffeners Attached to Sheet Citation Smith, Joe Nelson and Murphy, Joseph Nathaniel (1937) Investigation of Extended Bulb Angle Sections Under Compression: Part One. As Euler Columns ; Part Two. As Stiffeners Attached to Sheet. Master's thesis, California Institute of Technology. doi:10.7907/R62Z-6P10. https://resolver.caltech.edu/CaltechETD:etd-04252008-093950 Abstract No abstract. 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): Sechler, Ernest Edwin Group: GALCIT Thesis Committee: None, None Defense Date: 1 January 1937 Record Number: CaltechETD:etd-04252008-093950 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-04252008-093950 DOI: 10.7907/R62Z-6P10 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1501 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 25 Apr 2008 Last Modified: 16 Feb 2023 19:32 Thesis Files Preview PDF - Final Version See Usage Policy. 12MB Repository Staff Only: item control page

Part One: As Euler ~~olw;ms Part Two: As Stiffeners attached to sheet Thesis by J. N. Smith and J. N. Murphy In partial fulfillment of the requirements for the Degree of Master of f3cience in ,:~eronautical California Institute of Technology Pas~dena, California 1937 Zngineerin3. I ' The authors wish to thank Dr. von Karman, Director of the Guggenheim Aeronautical Laboratory at the California Institute of Technology for the opportunity to make this research. They wish to thank Dr. 2. E. Sechler under whose direction the research was carried out, for his invaluable assistance during the research and his careful review of the completed manuscript. Acknowledgment is also due Dr. A. L. Klein of the Institute and the major Aircraft Manufacturers particularly the Douglas Aircraft Company, the Northrop Corporation and the Curtiss-Wright Company, for the care- ful preparation of the specimens tested. -3- A Study of the Properties of Various Extruded Sections Commonly Used as Stiffeners ill Aircraft Construction. by J. N. Smith a11d J. N. Murphy Califoruia Institute of Technology Fo1'eword This is a report 011 work performed duri11g the year 1936-7 in the structures laboratory of the CaliforHia Institute of Technology. The work for this past year has been somewhat exploratory ill nature iuasmuch as it was necessary to design apparatus and to determine best testing methods. These preliminary problems have. how- ever. largely been solved during this year. a11d it is felt that the continuation of the research in the coming year should make available to the designer much needed information regarding this very commonly used type oi structural element. Purpose .2f the Investigation Recent inveetigatious have developed methods of calculation the colum11 properties of stiffeuer sections made up of formed flat sheet, a.nd further research work is beiug carried out 011 this problem by a number of lab- oratories. (References l a11d 2). H 0 wever, one of the most important types of stiffener section used in modern airpla11e co11atructiou is the extruded shape, aud in particular, the bulb angle is used extensively by a large number of manufacturers. For this reason, this research program was started in a11 effort to obtain design data 011 extruded sections when used as stiffeners. 8lld the first problem was the investigation of the properties of (I) twelve representative bul'ra angles. In order to make a systematic study of a problem such as this, it is necessary to a.l ter the variables involved individually over the range of values which are of iutereat. This would mean. in the case of the bulb angle, the variation of probably the following more or i·ess independant variables A a Le11gth of leg containing bulb B a Le11gth of second leg Tl• Thick11ess of leg co11tai11ing bulb T~· Thickness of the seco11d leg R : Radius of the bulb However, the above method of attack 011 the problem would mean au elaborate set of extrusion dies in order that each variable might be chauged in sufficient steps iu order to obtain the optimum value. It was therefore de- 0 cided to chose from the lists of extruded bulb auglea I\ that were i11 common use at the beginning of the research, a number of representative sections covering as wide a range of the above variables as was posai ble. The twelve augles chosen are shown in Fig. lA Rlld the dimensions of these sections are giveu in Table I. The problem was divided into two major fields of study, namely, Part I--Au investigatiou of the above twelve bulb angles when used alone as pin ended columns uuder concentric compression load. Part II--An investigation of the action of the same bulb angles when attached to sheets of different thicknesses. (t) Part I .An investigation of twelve typical bulb angles when used as piu ended columns under concentric compression load. Description £f Specime11a The cross-sections teated are shown full size in Fig. lA, aud the properties of these sections are give11 i11 Table I. It should be noted that, si11ce these sectio11s are extruded. their dimensions may vary considerably from those given in the speci fi ca. ti 011s. It was therefore ne- cessary to check all dimensions and to recompute the section properties. From the above table it is seeu that the variation from the specifications is so large iu dome cases that a11 appreciable affect loads would be expected. 011 the allowable design It is also noted that the de- viation from the specifications is no11-co11servative in almost as many instances as it is conservative. All specimens were formed of ~4ST aluminum alloy. The le11gths to be tested were chosen ou the basis of two factors of i11terest to designers. First, they were chosen so as to cover the range of bulkhead spacings commonly used. Second, limits of leugtha chosen were such as to insure covering both the 1011g a11d short column range. For these reasons, lengths of 22, lot, 11, and 5t inches were selected for testing. Description of Apparatus In order to obtain a true hinged end conditiou of the columns under test, an end fitting was coustructed. A half inch ball was sunk iuto the base plate of this fitting and rested 011 a circular hardened plate which in (3) turn lay upon the base plates of the compression testing Ciige. The ends of the bulb nngle were clamped iHto the fittings in which adjustme11ts in two directions were provided, enabling the ceutroid of the bulb angle to be located directly over the center of the ball. The adjustments in the fittings enabled auy eccentricity present in the set-up to be removed. Two dial ga.uges were used to determine if any eccentricity was present. One gauge was mounted 011 a bracket attached to the cage, the other was held by a rigid bar mounted on flexible tabs which i11 turu were fixed between the circular eud plates and the ends of the compression cage. The dial gauge plungers rested 011 the sides of the bulb a11gle at the midpoillt of the column. Si11ce auy restraint of the column was moat undesirable, it was uecessary to remove the plunger main spriuga of the gauges, haviug only the hair springs acting. The photographs show clearly the construction of the end fittings and the method of setting-up the specimens. T9stins Procedure The bulb angle was mounted in the end fittings and placed in the compression cage. The circular beariug plates were then inserted between the balls a11d the base plates of the compression cage. A alight load was ap- plied to the column in order to hold it iu the machine aud then it was placed approximately vertical by meaua of a level. The dial gauges were the11 attached and the load increased, a change in the readi11gs of the gauges denoti11g tl'be preseuoe of initial ecce11tricity which was removed by the adjustments in the end fi ttiuga. (~) When the load cuuld be i11creased to abou~ a third of the au- tic ipa ted final load without a ·change in the di al gauge readi11gs, it was assumed that all initial eccentricity had been removed. The dial gauges were then removed and the load increased steadily uutil failure. were made 011 The tests two Riehle B1=os. testing machi11es, the long- er col um11s in a 3, 000 pound capacity unit a11d the sho ...·ter columns in a 30,000 pound capacity unit. The type of failure, failing load, and the description of the specimen during the loading aud at failure were recorded. Length Correction Due to the fa.ct that the end fittiug is a rigid structure, a correction 011 the length of the column must be made. Thia is done in the following manner, using a method suggested by Karman and given in detail in the original paper of .Parr a11d Beakley: tp The moment equation for the beam shown is: (1) the solution of which is (2) y : Ac o s --./ P/EI • x L AB and CD are of infinite rigidity and hence are straight lines, therefore, at x• L/2 tan -, y e1.. • . -dy/dx 8 ex. = a. d.. • -ady/dx or A cos n/EI L/2 = -a L-A iP/El sinlf P/El L/21 or cot f P/EI L/2 • a VP/EI (5) (3) wl1 i ch can be solved for the gu1 er buckl i , column for auy value of a. cot -, P/EI 1 oa.d of a For a : 0, we obtai11, L/2 : O or (4 ) Putting -.JP/EI L/2 • Z equation (3) may be rewritten as Z ta11Z a L/2a (5) and -{P/EI : 2Z/L or (6 ) and, comparing equatio11 (6) with equation (4) it is seeu that the effective length is giveu by Leff =ir L/2Z (?) therefore: a' • (Leff - L)/2 = L(1T"'/2z - 1)/2 or, substituting from equatio11 (5) a' : a ('ii/2 - Z) tan Z ( 8) a/L = l/?-Z tanz (9) aud co11seque11tly, if we take di f fer~n t values of Z we can calculate correspo11ding values of a' and a/L. z tanz a/L a'/a 71/2 00 0 1.000 Leff 24.24 1 ?'TT/36 11.43 0.029 0.999 18.73 5Tr/12 3.732 0.102 0.982 13.21 11'/3 1.732 0. 2.75 O.<JO? ?.62 since Leff - L + 2a(a'/a) ( b) Theoretical ~ ExEeri.menta~- Failure Values Knowing the column effective length, it ia now possible to proceed with a study of the theoretical curv ls of failure. For this type of section there are three types of failure which are possible. These are: a. Column failure b. Local failure c. Torsional failure Nearly all of the specimens teated fell into the first class, i.e. column failure. Only two specimens failed locally, and none failed in torsion. We will discuss first the column failure. Iu col um11 failure, there are two ra11ges of the length to radius of gyration ratio to consider. The first is the Euler or long column range and the equati ou fccr the critical stress in this range is given by C"TT 1 E (lC) where C a 1.0 The second, or short column range is usually conaidered to be given by one of two equations; either the Johnson parabolic formula or the "Straight Line" forThese are, respectively mula. <Tc:' ~ ~ where o; - oy t.(Lefffpf (ll) is taken as 43,000 lbs./sq.in., and °':: -48000 - .t.100 (Letf/p) (12) Equations 10. 11. a11d 12 are shown plotted iu Fig.2 and the experimental points are also shown on the same figure. It can be seen that the "Straight Line" equation (7) gives a more couservative value for the critical stress in the short column range and also agrees slightly better with the experime11tal results. For this reason, it is suggested that the "Straight Line" equatio11 be used for this type of column in the sho:rt column range. Aleo from Fig. 2 it can be seen that the short column range starts at au L/p ratio of about 78. Investigations by Howland a.t C.I.T. ha.ve placed the proportional limit of alumiuum alloy 24ST at 19000 lba./sq.in. our investigations offer au opportunity to check this value, since at this stress the experimental points should separate from the Euler curve. From Fig. 2 we can see that the point of separation is at an L/p of 78. Then, usiug equation 10 we get 1f'J.E <JP • 1 · = (Le+t /f / n'L x 10. s ,., ,oE> : = (78f q 0 so lbs. I Sft. in. which, considering the fact that the contours of the sections are not extremely accurate, a11d that the material has been extruded, gives a reasonable check on the value of 19000 1 be ./sq. in. obtait1ed on ?.4ST sheet stock. The second type of failure, local buckling of au outstanding leg, only occurred i11 specimens No. 8477 and 8478 which, as can be seen from Fig. lA have fairly long ' and thin outstanding members. Using the sta11dard express- ion for the buckliug of a plate uuder compressive stress (see Reference 3) we have, for the critical buckling value: (C)) where 1ow, for specimen 8477 "'tb ,/ ; 1." l. ""ITs :: <o.' t-:: i. l%:z. ~ h<o)-=0.018 il "t X I 0 ,S X I 0 & :a.. - - - - - - - x. .o 0 2. 12. )(. 93 = ~SBoo If we assume three aides simply supported and the fourth free, we get for k k : o.5 and ~r : 0.5 x 35800 a 17900 lbs./sq.in. If we assume two opposite aides simply supported, the third built in, and the fourth free, we get, k = 1.33 and a:;r : 1.33 x 35800 s 47600 lbs./sq.i11. Now, experimentally we find a O'Cr of 37400 lbs./sq.in. and therefore we see that we have neither simple support, nor rigid clamping at the side which is supported by the other leg, but as should be expected, something between tr1e two. If we use this value of ~r• we may find the experimental value of k for this case as k = 37400/35800 • i·.044 In a similar marn1er, considering specimen 8478, we have: lTe • 35700 lbs./sq. in. aud 0-cr (exp) = 34400 l be. /stt. in. Solving for k we obtain, k • 34400/35700 • 0.965 Giving, for the two cases, a mean value of kave ! 1.0 Unfortunately there were only two plate failures in this group of specimens. However, if we use the mean value of k determined above, we can check the other specimens (which failed as columns) to see if the plate failure stress is lower, thus checking the possibility of that stress being critical. In every case, the value of ct;;r from a plate failure ata11dpoi11t is found to be higher than the crcr from column failure consideration. Timoshe1~0 {Ref. 3) gives values of k for a con- dition when three sides are simply supported and the fourth free, aud for a condition whe11 two opposite sides are simply supported, the third side built in, a11d the fourth free. For a bulb angle section, neither condition describes the actual fixity of the side at the base of the augle because, since it is attached to the other leg, it cannot be couaidered hi11ged, 11or can it be considered fixed, since the latter would imply complete rigidity which is not the case. Appareutly then the conditiou that describes the support of the aide at the ease of the angle lies somewhere between these two limits. ( 10) The average value of k obtained above confirms this assumption. It is therefore suggested that when bulb angle sections are used a.lone a.a columns under oompressio11 that the value of k be taken as 1.0. Further work 011 other sections should be done to more closely establish the exact value of this co1wta11t. Couclusious from Part I The material with which this part of the research problem was performed was not entirely satisfactory, due to the fact that the investigators had 110 control over the parameters involved. The bulb angle section, being an extrusion, had to be taken as it could be obtained from the industry. While possibly not warranted, it -vould be desireable from a research point of view, to have a special series of dies, thus permitting a series of specimens in which one dimension could be varied holding the others constant. This would permit a more systematic study of the effect of changes iln the parameters and should enable a prediction of an optimum croas-sectiou. From the i11vestigation as carried out, the following conclusions may be listed l) Above a value of L/p followed closely. • 78, the Euler curve ie See Fig. 2. 2) Below this value of L/.f' the straight line formula (er: 48000 - 400 L/p .>appears to approximate the experimental points more closely than the Johnson parabolic formula. 3) The proportional limit for 24ST extrusions is approximately 17000 lbs./sq.iu. (I I) 4) When investigating extruded bulb a11gle aectioua used as columns for possible local plF1te failure, since the couditiou of support at the base of the angle is neither clamped nor simply supported, but an intermediate case, it is eug~ested that a value of k : 1.0 be used in the buckling equation for plate failure under compression. 5) It is seen from Table II that the allowable stresses for these sections is quite low, and that, in general, these sections would be rather inefficient when used as columns without being attached to sheet. The sheet attachment generally prevents the Euler failure of the stiffener in the direction of the least radius of gyration and will therefore tend to increase the allowables for the combi11atio11. (11) F /ll.T r· 'TIJ I_. ;._'i.:., ' TJ\.BLE I Jompe.rison of dimensions and areas of extruded bulb angle sections as actually measured and computed, vi th those talrnn frOtTi the blue prints of the manuf'..lcturer. As measured and computed Section (ti. 1c00. No.) A 8477 8476 8478 K-10266 10265 10282 3046 5436 12224 K- 4200 K-766 12678 .rl.s l3 .138 .087 .2774 .113 .109 .051 .055 .073 .095 .094 .067 • 082 .156 .059 .052 .047 .052 .104 .105 .078 .062 .044 .061 .065 .053 .042 .058 .1501 .167'i) 1.000 • t388 .875 .750 .500 .500 1.500 1.500 1.094 1.094 .568 .996 .625 .879 .4')9 .507 .445 .624 .500 .438 12:.:-.:24 K-4200 .125 .118 .095 .065 .079 .108 .084 .067 .044 .1220 .0931 .0647 .1252 .2470 .1709 .1334 .085G .0402 taken from the blueprints of the m::mufac turer 12678 3046 5436 A.re a "' .125 K-766 K-10266 10265 10282 T0 .687 1. 2fi0 .687 1.000 .687 8478 Tl 1.2EO 1.125 1.500 1.125 1.000 1.125 1.500 1.125 1.000 • 87E· .750 1.500 1.500 1.094 1.094 .875 8477 8476 :\ .500 .500 .5625 1.000 .625 .625 .500 .125 .109 .109 .094 .094 .0625 .075 .156 .125 .1094 .094 .0625 .125 .0626 .256 .051 .072 .0625 .051 .040 .050 .051 .OG2 • 06~~5 .051 .040 .144 .125 .1094 .0781 .0625 .040 .OF,., .094 .1094 .0781 .0625 .040 .168 .122 .090 .057 .1154 .32152 • 204 85 .15555 .10399 .04476 Data,-, Pa,rt r>11e - /able II Speci,,..,., IK.' A 101,s .00113 ,Of3J f' 1 .01a,11f '110 10212, .0008? .otA? .OJS"l3 1,,,ff (~)(~fl? F;,tu.J a-tft,ory p p Evie,. 2'1.Vf 210 Jff'#OO /f,73 110 /3,2.I 7,(,1, 1,L/.'Llf f' ·'"' --·-> ' ~ cr&cte1a.I l'l'I !'lh 2JZO ZIOS 2i'fOO 33'1- ,,,3 to1S 35"'10 1'll 0 3S'fS l'l-1/-00 ,,, 33S ,,,0 1.1800 2.0ZO IS"IO 21100 J'15So 20'1 "#3700 J.S3 /'+7 23'-o 'l'l?S 2,1.010 2Sfo 210 3~<oo 3ZSO 13000 SIS '+10 /.ISIO IS62 to'J.S t.3'10 Zl.fOOO 15810 '~ 110 /fJ. 73 '"''· 5 ,,,2, ,S',1 I/If /J,l,J 7'180 I'd SJ' ~ c+ '/.,It. Zif 2.12' lfSooo 28'1 2'1'f 2.ato 231.fS H I ..... 18.73 f(,'l 'J.1,'IOO "IS'f 1-3 P> /J.ZJ 11s.s 13350 3ihS 7770 3Zl/-O ...... ,,,3 I/OS' ShOO <D ?.t.Z '"·" 11'/-'fO iqao !'/Ifs*' Z,3£1-00 I II. 'J., 12.380 2070 l2.30 8390 qo30 /fl,73 85.'I 7370 3'+70 31/i.S 11107() l'llilO 13.ZI (,o.'1 3(,'10 (.'f 80 (,O'/O ;l.8300 7,1,,z 35 J 2.2.5' 21000 'lhOS \15000 Z'1'150 3gqoo 2.'l.'l"I ,, •• S' 2t7SO ,, 3 120 3SIS If Boo li.73 '131 102.8 /180 <,010 "qoo 2.0(,0 23ZO 12.0?0 135'10 '2.IO SS"lo 3'-35'0 31.fZOo 30'fft, ,OOlfA. .llSZ ,01310 ,11'13 l: Sll3'1 .01111 .'lll-70 • Oll7h .z.18 '),'/, 'J,'f --·--"-"' ---~ / '2, Z Vf ,0031f8 , 1101/ ,02,0'f , tl/3 - /?ISO qz.'f tsio ,,,z, l. s3.3 13.:U I # 2/l'IO ?00 Indica.tes a.. cofomn fa.i/1Jrt of the bulb a,/one P4ro.metv5 Q.t-e bo.se<L Of'/ a.c.tuta..I d,i,,.cnsions} not on tho'" li'sted b'f the mo.1?11fa.ct11rer. 1sszo• ' o' ..... H H Dato, - Po,,...f 1n• - Ta,b/e II. spc,.,.,,,,,, I.' A p'- p L.11 (:;J!) (4;!} L.~J 1'+17 .Olt-1.7 .L"'l?'f ,OSll. ,J,11-2, 1,&/.%'f 100. :z, /00"10 511 7S.7 S'130 3SI 5'1.7 icr9z ' 17'1. c. --. /f.?S ---"---"~-··~'<" 13.~I - ?. (,,2, ~--·- --<• 8~7' ,0033.5 , IS'o I .oiia. " a1.s SB Cf9Z.3 I'"" ---- , 2."I. Zl/- 11.Z..'l ZW'loo 588 ··--·Jf,?S 12.S.1 1.Sloo 3SI ··- . - -- - . -- - / 3. a,1 78•0 17'+.t8B.7 '] .(,2, SJ.I U,10 SB ~---· -~-· ' ,. 9'1?8 ,OOi'1? , /(,?'I .OS"ZJ ·22.8 = 11' "' .ooi•& .11a.o .02,lfO •./SS" . 2i"S" 2.703 't800 4-3/0 7JwS er o;,tu..1 1oa30 q??S 17300 ISS'J,O 3'-17SO 10'-' 800 4".SSO 371foo" +~.,., '""'o 2'foSO 10310 SB1 S'IO 3fl/JO 3q30 'f 82 S?S 'S"lo sg30 J't7S lfo?O 13170 S'f 'fO J.loZ.O 39SSO 11120 2.'1800 'f 1cro IS3SO 11 S8B 1s1.13 /'+qo 82.1 S?.'I f.1'10 35'/ 45"80 33SS' l?lf,ft, 6200 lZ7S 3875 33.'f Ill'/- IS,'10 S??o• q32.00 21+.2.lf . IS/,.3 . 2,'1'130 G'BB 18.?3 1z.o.1 l'f '100 351 Sl(o -- 13. 2.1 ~- ~ ' P.~r.J 111,0 V/.llf /8,'73 /3.ll 7.ft,'J,, 102.,, '"' Pcu/er ,'], 95'.2, 7.1.z ~ IJ.'I ./ S8 3100() 8870 135'1/-0 21'1-SO 31.p{oo* c+ H • I 1-i SI> O" ..... ~ 38'fS g,11- I./"" ??S Lf Z'+O 70'l0 ?15'0 171.f,(, /737 . JS'fS 1'1-ZSo / 2,(,10 2.LI IS l SS ; 52%3 2,i:,SO '1-Zlo O 21100 Po.ra.meter.s a,re ba.~ed on 11c,tua..I dimensions, not on those Ii$ tcd.. b '1 the ma.nu fc&.c.tuYtt'. ~ Ii "aso H ..... -... () 0 .... Da.t0- - Pa.rt On ~ .. Ta..ble JI Spcc1'rt1en z: A .0032.I. .133'f 'f'J,OO 1hft> ,0011t- p" .01'f'f .otsh ,013'1 f' L,11 ("f) ( '7f!f F;,,10- P.ctw.1 0-theory a;.,tua.I .IS'1 2'/,2,1/- JSS 'LJIOOO S7S &ZI '13fJS lfloSO /f,?3 120 /J,fl/-00 CJ(,3 'ISS 7210 71&0 /3.21 v~.s 12,00 /900 ll.f5()0 7.t-t l/-8.'I 234'0 /'133 5'820 1/-280 113,00 l'l-ZSO 32.060 ,,, '13'1,SO 201/31f Z z"o 2.3SS 3 fJ'IO 396 "1000 lf.SOO 13·'-' //3.3 IZ8S"O r.S.'f 'laBO 2001 2005" io.lfo 2.35'00 8 2.lfO ?.'11 "'' 7()$" 'J,J/ 'J,lf 233 ''#JOO 77 101 1qz3 /l,73 180 32.'+oo I 'J, 'f !SS 3220 ,,,1, J'1.? ZSB '''"'o '73.a S3'10 7?8 305" '"'so 7/0 t'llfSO .11'1S ""· Z,IJ. IB.13 --··-··· . ----· zog ZSCJSO 2.3'+SO I /1,78 .000'#3" .0'1113 ,0108 .toll I 13.ZI ,.... r ... i l I Pa,ram ett. YS a.,..~ ba.sed on a.c.tva..I d,.men~ions , not on those. I istt.ci b'f the· m4.n ufa.c.turtr. 'J.'615 3810 1'11S 1?750 I'd P> '1 c+ 1-1 I I 1-3 $1' o' I-' tt 1-1 H 0 0 ::.::! ;-u-R T ?-R A. 'l - r-' -. -- -·- I -~ ~··· T, t T, ·---- i If A I --i A _J __ ~-. -_fLb --~~-~- I i ' I [-..--8 . _. ....; A.'..COA .--1 i ( i II rT l 10282 ALCOA 8478 .4LCOA 3046 17~ ----, ___ L_ L J ____ . I. ,i.. __l I;T b--1 ALCO!l 12224 ALCOA K-4200 Fir;.. I A i -~ '.- ! I I 7 -r . j \__ ----- _J ·, _t_! -·--~- 0 z ,. (19) - ~ ·1 ' t " +· II - fl I . . .,, ,_o 1-: • •I + , ' . - :;; . .... -~ '!+ n '" i~ I ~ . tt I ·-- .L ·o t ..ii, -t , h • ... 0 3. :;.: .. I Her,_, ii ., ' . .. ; .... ·;;:t:t "' ' . lli t: i i:; .., ... II .,"" . u . lttttJ· . • M ,J,. · O ' :· 0 ..,3 '«1·: :t . i .. :f!trt+HH++u ml . .. Jiil:. ·a;. -: - ... ......•.. ·· ::t ~S: .. ·· .. '. . ~ .... ~-: I ,.. :l .:,~' ' ' i . er' .....O " · =. a · Part II--The us~ of bulb angles e.e stiffeners for sheet panels under compression. Statement .2f Problem Extrueious of various shapes riveted to sheet to give added stiffness and load carrying ability, are used extensively in aeronautical co11structio11. Bulb angles are oue of the most common types of extruded sections used and, therefore, it is of considerable importance that complete knowledge of these sections be made available to the designer. Part I of this i11vestigatio11 has covered the use of bulb angles as columns under compression, and this second part of the investigation will study the effect of attaching these angles to sheet, forming the usual stiffened sheet panel used widely in semimonocoque construction. The sections used will be those studied in Part I, and a variA.tio11 in sheet thickness will be added to the list of variable to be studied. Inasmuch as the material of the extrusions was 24ST alloy, it was decided to use the same alloy for the sheet stock. The following report is a summary of a partial investigation of one of the bulb a11gle sections tested in Part I. The method of testing hae been developed, a11d a number of experimental observations have beeu obtained. These, however, have uot been completely analysed, but an outliue of analysis methods aud of the future program to be followed is giveu. Description .2f Panels For the stiffener, bulb angle section Alcoa No. 10282, with a cross-sectional area of 0.0647 sq. i11. and a radius (Zo> of gyra.tion of 0.2? inches, was selected. For all panels, the stiffener spacing was t.akeu as 4 inches and the rivet spaciug as 0. 75 inches. This r4\ivet spaciug was so chosen that premature failure should not take place between the rivets for either the thick or thin sheet panel used. Two thicknesses of sheet were used, namely, 0.020 and 0.040 i11chee. Panels of two, three, and four stiffeners were made and teated, using the above spacings and thicknesses of sheet. I11 order to cover the current range of bulkhead spaci11gs and at the same time extend into bo ~h the Euler long and short column ranges, the lengths of the panels choseu for test purposes were 3, 5t, ll, l6t, 22, and 27t inches. In each panel the sheet extended 2 inches beyond each outboard stiffener, that is, the width of the panel with two stiffeners was 8 inches; 3 stiffeners, 12 inches; aud 4 stiffeners, 16 inches. Table I gives a complete description of the panels, their areas, and the load carried. Testing Procedure In teats of this kind it is imperative that the opposite ends of the pauel be parallel in order to have a.n even distribution of the load. With this in mind, the panels were fabricated with a plus allowance in each length, and then placed ill a milling machine and milled to the le11gths choae11 for teat purposes. Before the panel was put in the testing machine, two exteneometers were placed on the aide of the sheet opposite the side to which the stiffeners were attached, and near the point of attachment of the eud stiffeners of the panel. From the readings of these exteuaometers, {&I) the effective width of the shee-t acti11g with the stiffener can be computed, giving a check on other methods. The free edges of trie sheet were supported by being lightly clamped in a slotted chrome moly tube. The clamping waa just enough to allow the slot to keep the edge of the sheet straight, but 21ot tight enough so that the tube would carry load through shear transfer. Even though the panels were made eo that the euds were as nearly parallel as possible, it was found to be necessary, particularly i11 the wider panels, to shim the ends in order to obtain au even distribution of the load. When the panel was placed in.~the testing machiue a light load was applied and, if necessary, shims were inserted until the load was evenly distributed along the width of the panel. The load was then iucreaeed until the panel failed. In a.dditiou to the exteneomet•r read- ings and failure load, the general behavior of each panel was recorded, noting in particular the first appearance of waves in both sheet and stiffener and the passage of waves though the line of rivets. This latter affect was not pronouuoed or consistent and failed, in many cases, to leave a permanent set in the rivet line. Experimental Results Table I and Figs. l, 2, a11d 3 show the ultimate failing loads of the three aeries of panels tested. It is seen from these figures that column failure has not affected the ultimate load of the panels until the longest length had been reached. This was .evident from the type of failure observed, inasmuch as failure occurred in every case due to local failure of the outstaudiug leg of the stiffener. From the faired curves shown in (2%) Figs. 1, 2, and 3, it is possible to separate the load carried by the stiffener plus effective width of sheet acting with it from that carried by the nide portions of sheet supported by the slotted tubes. The method of making this separation is shown in the uext aectiou. The exper- imental load call then be compared to the theoretical load for such a combined section acting as an Euler column and from this comparison, a value of the effective e11d fixity call be determined. Theoretical Value .£.! ~ Carried & Stiffeuere plus Effective Width .2.f Sheet. From the work of Sechler (Reference 4) the curve of effective width as a function of stress has been replotted in Fig. 4. To cover the trauai tioll regio11, the two end points on the low stress and the failure curve have been taken at values of A correapondh1g to stresses of 20,000 lbs./sq. in. and 45,000 lba./sq. 111. respectively, and a straight liue drawn between these two values. Thie method has been suggested in the above reference. The value of the columu failure load for tbe stif ... fener plus effective sheet will be calculated for two values of end fixity, namely, C:. 2.0 aud C • 3.0. It is first necessary to calculate the Euler failing stress for the stiffener alone, and, for the case where the stiffener will be acting with the sheet, it is assumed that the failure takes place iu a directio11 perpendicular to the plane of the sheet material. The value of the radius of gyra.tiou of stiffener 110. 10282 about a11 axis parallel to the sheet is f'o = 0.2? (23) from which, the Euler failing stress ca11 be calculated aa OE = C n"- E ( L/p).._ which gives. for values of C • 2.0 and 3.0 the following failing stresses for the differe11t lengths of stiffener used a L L/p <TE (C a 2) OK (C : 3) 3.0 11.l 1,680,000 2,520,000 5.5 20.4 497,000 746,000 11.0 40.8 124,000 186.000 16.5 61.0 55.600 83,500 ?2.0 81,5 31,100 46,800 27.5 102.0 19,900 29,800 The theoretical load will be calculated for one combination to show the method that has beeu used throughout. The complete tabulation is shown in Table II. Con- sider the ~7.6 i11ch length with sheet thickness of 0.020 inches, and an eud fixity equal to 2.0. The Euler fail- iug stress as given above is c:r.E • 19,900 lbe./sq.in. and - .o~o "4 : o. 115 giving, from Fig. 4 we/b a 0.265 or, a total width of sheet e.ctiug with the stiffener of 2 we : 2 x 0.265 x 4 • 2.14 inches Thie new column, composed of the stiffeHer plus 2.14 iHches of sheet actiug with it, will have a new value of (2'1) the radius of gyration which is given by the equation [1 + ( 5/poYJ I ;- Y. (t-t ~ywhere A0 : area of stiffener aloue = rad. of gyr. of stiffener alone f • " " " " " plus attached sheet l • total width of attached sheet fo t • thickness of attached sheet S • dietauce from neutral axie of stiffeuer to the center line of the sheet This curve is plotted in Fig. 5 for convenient use. For the case under consideratiou, t/A 0 : 0.309 sip 0 : l .15 /, = 2 .14 and, entering Fig. 5 we fiud, (%,) 1.-: Ci/~ = o. 9Z or, the new Euler failing stress for this combined colunm is = 18, aoo lbs./sq. in. Thie new stress will change the effective width slightly, and consequently the values of 0-/ao may change, so the process is repeated until the equation converges. In the above case, the first approximation is sufficiantly accurate, and the values of 2 We = 2.12 inches and ~ : 18,300 lbs./sq. in. are takeu for aualyaie purposes. (v) It will be noticed that the sheet acting with the stiffener has been reduced from 2.14 to 2.12 inches by the change in stress, but this was insufficient to further reduce the Euler stress of the combination by an appreciable amount. A similar analysis has been carried out for all lengths o.f stiffener and :tOr the two thicknesses of sheet, aud the results are shown iu Table II. From the above it is possible to obtain the theoretical load for each length of stiffener plus sheet, and this is do11e in Table III, and the results plotted. in Figs. 6 and 7. These calculated values must now be checked with the values obtained experimentally. Experimental Values .2f ~ Carried In order to obtain the experimental values of the load carried by the combined column of sheet plus effective width, it is necessary to subtract from the total load carried by the panel the load carried by the two side portions supported in the slotted tpbee. If we con- sider the panels of one length and one sheet thickness haviug two, three, a.ud four stiffeners, we can write the following equations Pe -r 2P 8 : P1 P8 : P2 P 8 -t- 4P 8 : P3 1"' 3P 8 In which Pe a the load carried by both side portious of the panel P8 : the load carried by ea.ch of the combined columns made up of stiffeuer plus effective sheet. Pi' P2 , P , : total loads carried by the panels 3 with two, three, a.ud four stiffeners 1 respectively. we can solve the above for P 8 and P 8 since P1 , P , and 2 P 3 are know11 experimentally. Doing this for each length, aud for the two thicknesses of sheet, we obtain the fol+owing values: t - 0.040 L: 3.0 5.5 11.0 16.5 22.0 27.5 Ps : 4400 4350 4150 3850 3350 2800 t • 0.020 L • 3.0 5.5 11.0 .615 22.0 27.5 P8 2600 2550 2500 2400 2150 1850 a The above values are taken from the faired curves in Figs. l, 2, aud ~. and the values shown above a17e plotted in Figs. 6 aud 7. Discussion .2.! Experimental Results The behavior of the panel while under test was interesting. The formatiou of WRvea 1 while the same in both thicknesses of sheet, was much easier to see in the 0.020 iuch panels. Under a relatively low load, a slight wave was first noticed iu the sheet ltetween stiffeners. As the load was increased, the waves in the sheet became deeper, and extended closer to the stiffeners, while the outstauding leg of the stiffeners went into a wave form. Near failure, the waves iu the sheet passed through the rivet line of the stiffeners and the waves iu the outstanding leg became pronounced. ln every panel tested, failure resulted from a plate failure of the outsta11di11g leg of the stiffener. In the 27.5 inch panels, a. teu(2rJ dency was noted for the pa11el to fail as au Euler column, however, the critical condition was still a plate failure of the outsta11di11g stiffeuer leg. It may be noted, that in Figs. l, 2, a11d 3 the value of the load carried by the 11 inch panel falls below the faired curve i11 every case. This phenomenon hP.S not as yet been explained, and it is suggested that several more panels of this leugth be tested ill order to mor~ closely check these points. From the curves of total load vs. leugth for the columns made up of stiffener plus effective width of sheet (Figs. 6 and 7), it cau be seen that an end fixity of 2.0 would appear to be indicated. It is therefore felt that this method of flat end testing, at least for this stiffener, and over the ra11ge of thicknesses used, leads to au eud fixity of 2.0. The check of experimental aud theoretical values shown in Figs. 6 and 7 also confirms the observation made during the test that failure of the pauel was not as a column but was due to local buckling, i11 this case, buckling of the outstanding leg of the angle. The curves indicate that only at the 2?t iuch leugth should one expect to find auy indication of column failure, a.11d this was borne out by all of the experime11tal observationa. Conclusions It can be concluded from the above coneideratiou of the test work that, for panels made up of flat sheet attached tobulb angle stiffener No. 10282 and tested flat ended: l)Failure will take place by local buckli11g of the (2.$) outsta11di11g leg of the angle for all lengths shorter than approximately 28 inches. 2)Failure will take place as an Euler column for lengths longer than 28 inches, using the ti:::uler column curve with an end fixity of 2.0. 3)For any other end fixity, curves for the proper Euler failure load ca11 be drawu in on Fig1. 6 and 7 and the experimental curve will fair into them in the usual manner. 4)The scatter of some of the experimental points should be eliminated by further test work. 5)The method of calculating the point of departure from the Euler curves for various end fixities should be determined. Future work !E, .!?.!, Done fill !h!J! Project The following is a list of problems to be carrie1 out to complete the studies of extruded sections. As many as possible will be attempted during the coming year. l)Check several points on the experimental curves just discussed to eliminate scatter. 2)Derive a method for determining the point where "" the local buckling of the outsta11di11g leg causes a departure from the Euler columu curvea. Thia should be doue for end fixities of l, 2, 3, aud 4. Work has al- ready started 011 this problem. 3)Derive an equation of load vs. length to use in the local buckling range. Preliminary work has been ata.rted on this problem. 4)C~rry out a similar program for the other bulb angles teated 111 Part I. {2fJ 5)From the results obtained ou the 12 bulb angles under co21aideratio11, attempt to derive some geueral method of aualysis which will hold for all bulb a11gles. 6}Repea.t the program for other types of extrusions such as Z sections, T sections, etc. ?)If possible, obtain the cooperation of the Alum. Co. of America towards making some t31pe of adjustable extrusion die which would make possible iudepe11da11t changes in each variable, thus leading to a. determiuatio11 of some form of optimum section. (Canta.ct has already been ma.de with Alcoa and they seem willing to give at least some aid in investigating this last problem.) (Jo) References 1--F. J. Bridget, C. c. Jerome, aud A. B. Vosseller-- Some New Experime11ta 011 Buckling of Thill Wall Cou- struction--A. S.M.E., APM 56-6, August, 1934. 2--w. s. Parr and w. M. Beakley--Au i11vestigatio11 of Duralumi11 Channel S~ction S~ruta Under Compreasion-- Journ. of Aero. Sci., September, 1935. 3--s. Timoshenko--Strength of l~aterials, Vol. II, pg 606. 4--E. E. Sechler--Streas Distribution in stiffe11ed Panels Uuder Compreeaio11--Jouru. of Aero. Sci., June, 1937. Part II--Table I The folloVIing tabulation describes the were lJo.of ·t) () t:., 2 2 2 2 <) G •J r_, 2 2 2 2 3 3 3 3 :)he ct r~tl ff Panel Pnnel ~:iti ff. Sheet Totc.l .02 .02 4 4 3 • o·) f_, 4 •o~~ 4 11 162; 4 22 .02 .04 .04 .04 .04 .04 .04 09 O'),_, 0"' .02 4 27} 4 4 4 4 3 .. . ~ 4 4 4 .02 3 .04 3 .04 .04 .04 4 .04 .04 .02 4 4 4 4 4 4 4 4 4 4 .02 5·1 11 16~ 22 2712 3 5l2 4 3 3 3 3 3 c: 1 "J :;S • Ot~ 4 4 4 4 4 4 4 3 which te~·>ted: stiff. thlcl{. epec. len. .:.., p~~nels 4 11 1,..02·1 22 27~ 3 512 11 16;i 22 ?712 3 5J.-2 11 .02 4 4 ..0"O') .02 4 4 4 4 ~37·k .04 .04 .CJ4 4 4 3 4 11 '"'~ •~JG ,,_, ~ .. 22 16-~ 5~ 4 .J4 4 16~ 4 .04 4 4 .04 4 22 ,. 71 G t.f 'Tio t81 width area area area load 8 8 8 .1294 .1294 .1294 .J294 .2894 .2894 .2894 .2894 .2894 .2894 .4494 .4494 .4494 .4494 • 4li94 .4494 .4341 .4341 .4341 .4341 .4341 .4341 .6741 .6741 .G741 .6741 .6741 .6741 .5788 .5788 .5788 .5788 .5788 .5788 .8988 .8988 .8988 .8988 .8988 .8988 6250 G550 6 8 8 8 8 8 8 8 .16 .16 .16 .16 .16 .16 8 12 12 12 12 12 12 12 12 12 12 12 12 16 16 16 16 16 16 16 16 16 16 10 16 .1294 .1294 .1294 .32 .32 .32 .32 .1294 .1294 .1294 .1294 .1294 .1941 ~\:) •'-'~ .32 .24 .24 .1941 .1941 .1941 .1941 .1941 .1941 .1941 .1941 .1941 .1941 .1941 .2588 .2588 .2G88 .2588 .2588 .2588 .24 .24 I .24 .24 .48 .48 .48 .48 .48 .48 .32 .32 .32 .32 .32 .~2 .2588 .2588 .64 .64 .;~588 .64 .2588 .2588 .64 .2588 .G4 (J2) • ~)4 5310 6170 6160 5040 9460 11080 9150 10080 11150 9830 7860 9390 7675 8915 7602 6650 16170 12290 12870 14010 14938 12240 11855 11450 8720 11390 9985 8810 18200 20230 17120 18590 17938 148:~5 :"-verage stress 21600 22640 18350 21300 21300 17400 21050 24700 20360 22470 24800 21900 18100 21630 17680 20530 17500 15320 23970 18230 19090 20780 22160 18150 20500 19780 15060 19670 17260 15220 20250 22500 19050 20670 19960 16500 Ta.bl€ II. , Part Two k-. z t:: 0.020 k=3 a- 2we O"" 't,7.5 /'?>300 2.12 Z2.o 31100 Jb.5 1/.0 Ltn9th t: 0.020 k:: 2 t . . o.o4o K=3 2wf! (j Zwe (j 2we 2'1800 J.24 /7300 2.42. 25bOO 1.84 /.I~ .fb800 0.4-'lb 2~4-00 /.to 4-b800 0,88 ss,oo 0.4'73 i53SOO o.3S4 ~S6oo o.s.+ 83500 o.?o+ JZ4-,ooo 0,32 18'1,400 0,28 12,,400 o."o t'IZ, ooo o.+~8 t = 0.04'0 "d 5,S 44'1,ooo o. 1'7& 74fl,000 0.144- 511,000 o.32 16'1,000 3.0 '·"80,000 0,08 . 2,szo,000 o.o,4 I, 715, 000 0.1?8 Z,5'10,000 0,144 o.2h• ~ ~ c+ H H I I ~ C' ~ The hi9'1 stresses CoYrespond. ;,,~ to the s hort~t' lengths ha.vt 110 prttc.tiea.I mto..n in9 , be1'n9 points on the ste~p po,..tion of the Euler C.ut've. Pl o' ...., <I> H H Part II--Ta.ble III L er 2we Ash Ast Atot. 3.0 ?,5?0,000 0.144 0.0058 0.064? 0.0705 5.5 769,000 0.264 0.0155 0.0802 11.0 192,000 0.498 0.0199 " " 0.0846 16,24') 16.5 83,500 0.?04 0.0282 " 0.0929 7,760 22.0 46,800 0.880 0.0352 0.0999 4,6?0 27.5 25,600 1.840 0.0736 " " 0.1383 3,540 3.0 1,715,000 0.178 0.0071 0.0647 0.0718 5.5 511,000 0.320 0.01~8 ff 0.0775 11.0 126,400 0.600 0.0240 ff 0.0887 11,190 16.5 55,600 0.840 0.0336 " 0.0983 5,460 22.0 :26,400 l.80 0.0720 " 0.1367 3,610 27.6 l?,300 2.42 0.0968 ff 0.1615 2,790 3.0 ?,520,000 0.064 0.0013 0.0647 0.0660 5.5 ?46,000 0.144 0.0029 " 0.0676 ll.O 186,400 0. :?.80 0.0056 13,100 16.5 83,500 0.384 0.0077 " " 0.0703 0.0724 6,040 12.0 46,800 0.496 0.0099 II 0.0746 3,490 27.5 29,800 1.240 0.0248 " 0.0895 2,670 3.0 1,680,000 0.080 0.0016 0.0647 0.0663 5.5 497,000 0.176 0.0035 II 0.0682 11.0 124,000 0.3?.0 0.0064 " 0.0711 8,810 16.5 55,600 0.473 0.0095 " 0.0742 4,130 22.0 31,100 1.180 0.0236 " 0.0883 2,750 27.5 18,300 2 .·120 0.0424 II 0.1071 1,960 {)'I) p t = 0.040 c - 3.0 t -.. 0.040 c = 2.0 t - o.o~o c • 3.0 t -.. 0.020 c = 2.0 ·v ·s '() ·tr:.l 1 J ~· ' i ·1;L ~;;• 't'·If!~ f! ~ NI 0]1Nll:ld t ' ctt lf 1'!, J . l! t • ' .I , •r /.. .r . + ' L ·t l J " t t ,.r t J h l Hl 1~ • t t• i!J TJ l ,, -1 L tf ::tl t t· "0'.) 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