S0~l3 NET EXPERI~S ON BUCKLI NG OF

THilf JA.LL COUSTRUCTION1 }

by

7 . J. Bridget2 ), c. c. Jerome3 ) and A. B. Vosaeller4 )

ABSTRA.CT

The firs t section of this paper describes a series of t ests of the

strength ot thin wiled cylinders under a col:l.bination or torsion and axial

compression or tension . Curves are obtained showi " the stre~th of each ot

the several tY!)es or oy·linders tested, under all possible combi nations of these

loads. All the curves obtained s oen to have the sane general form, and the

results sugi,Sest the poss ibility of finding a si11ple law by n ea.ns or which

-----~---------

l)The tests described in this paper were t:~.ade at the Guggenheim Aoi'Onautical Laboratory of the California Institute or Technology. The authors have been assi · ed to the Institute by the NB.Ty' Department tor gradua te work in aero­no.utics , and this work represents part of the requirements tor the Master 's Degree. The first sect i on is by Lieut . Bridget and the second by Lieutenants 1erome and Vosseller. The authors wish to thank Dr. '1'h.. V'on K~n. director or the Guggenheim Laboratory or the Institute , tor the oppor tunity f o r ma'l(1ng t hese researches . The rosearches were suggested by and oarried out under the direction of Dr . L . S . Donnell . Aoknowledg!!lont is also due to L . &,eretan, who coo erated in the fi r fft rosenreh , and to Dr . A. L . Klein end E. E. Sechle r (all or t he staff or tho Institute) tor numerous helpful sug ~eetions .

2 )Lieutenant , U. s . Navy; was graduated tro::1 U. s . Naval Aoadaey in 1921 and serTed seven years on eea duty in the fieot tr1 th ~nnery duties . Completed tlieht training in 1929 nt ? eMaeola , Florida. Served in fi ;;hting s quadron attaohed to tho u.s .s . Lexinr,ton in 1929 and 1930. Inspection iuty of naval a1rorsft in 1931. Attended Post Graduate School .s . !iaval Aeademv in 1932 , and upon e o:npl -tion asai ~ned to du ty at Cali rornia Insti tut ·' o"f Technology for nost gradu..'\te work 1.n Aeronnuttcal ~~ineeri~ .

3)F1rst Lieutenant, U. 3 . !{ ina Corps; graduated frQ!'!l u.s. :naval Ac ademy in 1 922 . \71th various !•arine Infantry units 1922-1924. 0n avi a tion duty with Harine Av i a tion in United States , China, Phillip ines, Gua~ and llic aragua , 1924 -1932 . Assi~ed to duty at Californi a Institute or Technoloey for post· graduate work in Aeronautical ~ineerin.~ , 1933.

4)Lieutenant. u.s . lle.vy; was era,duated trom u.s. Naval Aoade:my in 1924 and sorTed in Tarious ahd.ps of the fleet and on the staffs of ColTmander Battles hips and Commander Destroyers , Battle Force until assignment to Avia tion duty in 1930. U!><)n compl etion or :f'li;;;ht training s erved i n ft~htin;:; s quadron attac hed to the U.s .s . Lexington. Attended ?ost Graduate School U.S. naval Academy in lli)32, and upon ooi:tpl etion assigned to dutj• at California Inst i tute of Technology for ~oat graduate work in Aeronautical Eng ineering .

I

SO_~ r;::;v EXPBRI ®l!'S ON BITCKLI!'IG OF

THIN :'!AI.L 00USTRl1CTIO~r1 )

by

F. J . Bridget2 >, c. c. Jeroma3 ) and A. B. Vosse11er4 >

ABSTR~CT

The first section of this paper describes a series ot tests of the

st:rength of thin uullod cylinders under a combination of torsion and axial

compression or tension. Curves are obtained showing the stre~th of each of

the several t7pes ot cylinders tested, under oll possible combinations ot these

loads . 1 1 the curves obtained se~~ to have the same general form, and tP-e

results sug~est the possibility of finding a ei le law by means of which

l)The tests described in this paper were ~ade at the Gug~enheim Ael~nau~icul ·Laboratory of the California !natitute of Technology. The authors have been assigned to the Institute by the Navy Department tor graduate work in aero­nautics , and this work represents part or the requirements for the ster ' s Degree. The first section is by Lieut . Bridget and the second by Lieatenants Jerono and Vosseller. The authors wish to thank Dr . Til. von K8rnin, director ot: the Guggenheim Laboratory or the Institute , for the opportunity for niJking these researches. The rosea..rchea were suggested by and carried out under the di:r-eotion of Dr. L. l!. Donnell . Acknowledgmnnt ia also due to L. &cretan. who coopel'Uted in the first research, and to Dr. }_. L. Klein and E. 3 . Sechler {all or the staff of the Institute) for numerous helpfUl a ~,eations .

2)Lieutenant, U.s. Navy; was graduated tro:n u.s. Naval Acade:my in 1921 and served seven ,cars on eea duty in the neet with sunnory duties . Co!!!.p1eted flisht training in 1929 at Pensacola, Florida. Served L~ fiGhtinB squadron attached to the u.s.s. texin3ton in 1929 and 1930. Inspection duty of naval aircraft in 1931. 1-ttended ost Graduate School u.s. Naval Academy in 1932, and upon co:rrplotion asai ned to duty at California Insti tut t of Technology for po2t graduate work in Aeronnutical n3ineering.

3 )First Lieutenant, U.s. ':8l"in-o Corps; graduated i'rom U.s. Naval Academy in 1922. ITith various Mar!ne Infantry units 1922-1924. On aviation duty w1 th Marine Aviation in United Stntes, China, Phillipin-s, Gurua and Uicarae-ua , 192~-1932 . Assicned to duty at California Institute of Technology tor pos~graduate nork in Aeronautical ineerinc, 1933.

4}Lieutenant, u.s. navy; was eraduated from u.s . Naval Acadony in 1924 and served in various sb4ps or the fleet and on the st~fs of Commander Battleships ruld Commander Dostroyors , Battle Force until assignmant to Aviation duty i n 1930. Upon co~pletion of flight training served in fiBhti~ squadron attached to the U .s .s . Lexington. Attended Post Graduate School u.s . liaval Academy in 1932, and upon co~pletion assigned to du~y at Colifo1~1a Institute of Technology for post graduate ork in Aeronautical Engineering .

a designer could determine the buckling strength or a structure Ul)de:r any com­

bination of shear and normal stress, lf he knows ita strength under pure sbear

and under pure compressive stress.

Tho second section detrcribes tests made to test the independence ot

different possible types ot buckling of a structure. A set of L-seetion struts,

identical except for the widths of the sides, were tested 1n compression. With

small Widths the struts buckle rut Euler columns, but with the wider widths

buckling of the aides, as plates hinged on three edges, occurs first. Great

care was taken to eliminate the effect ot initial eccentricities. The results

check the well.Jtnown theories for these two types ot buckling, and indicate

that, tor practical purposes, the two types can be considered independently ot

eaeh otmr. The results el.eo illustrate how enormously the strength ... weight

ratio of thin wall construction may be affected by details ot design.

The stresses produced by the loads in the skill of monoeoque eon-

struction are usually combinations of co:npression or tension in one direction,

with shear in the same and perpendicular directions. Mu.ch theoretical and

experimental information is available to the designer on the behavior or thin

sheets under compression or tension alone, or under shear alone~ but nothing

seems to be know about their behavior under combinations ot these stresses.

The general nature of the behavior ot thin sheet eonatruction under

such combination loading can be predicted by some very simple reasoning. Let

o an.d T be the normal and shear stresses pro weed 1n the wall, and ~ and Yo the values of these stresses when failure occurs under pure axial compression

or tension, and under nure torsion respectively. Then by plotting %.c against .-,',

~ a curve is obtained, passing through the points 0,1 and 1,0, and showing

how failure occurs under all possible combinations ot these two types of stresses.

This curve o~viously must be symmetrical about the ~ axis. as a change in the

sign of the shear (for a ay:a~netrical structure) can make no dit'terence. Hence

the curve must be perpendicular to the~ axis where it crosses it, as it is

certainly continuous at this point. On the other htmd the curve will not be X .

symnetrical about the ~ axis, but must erose it at some engle as shown in

Fig. l( a), as compression will obviously decrease o.nd tension increase the

shear which the structure can take before buckling. This immediately suggests

some ind ot parabolic or power relation in Fig . l(b}, with an equation:

J- /i ~(~)" ~a ~ {1)

where n is greater than 1 (of course n should be an even number to satisfy the

condition ot symmetry cbrut the £' axis, but this relation can be used as an

empirical formula with any value greater than 1 tor n , provided {f., is 81.-

ways considered sitive) . This reasoning is pertectly general , applying to

the stability of any type ot a~trical structure whatever .

To et so e experimental intor.mation on this subject, series ot

similar thin walled cylinders have be n tested to failure under various co -

bin tiona ot torsion and axial co~presaion or teneion. In the most caaplete

ot these series, bout forty cylinders, made 8.fl nearly i4ent1cal as possible,

were tested. Fig. 2 sho s the reauha tor this aeries, (Ser,ks C9) • The

6: 'J/ experimental values tor %" and /~., being -n otted against eaoh other ( i "t ob­

¢

vi us::· makes no difference whether ~J', ~ 1 1;, are defined as above, or it a rY

and J are taken to mean the total axial 12!! and torsional moment and o;, and

J; the values ot these loads when failure occurs under pure axial compression

or tension and under pure torsion respectively). It seemed to make no difterence

in what order the loads were applied, that is whether a tixed amount6tQrs1on was

applied tirst and the axial load increased until failure occurred, or vice versa .

The :t'ul.l line in Fig . 2 is a cubic parabola, that is the curve given

by equation (1) hen n = 3 . This curve se to fit the points about as well na

anything. :ore definite information as to the nature of the relation given by

6 'Y/ these ereriments is obtained by plotting / - "t; gainst /:fo on double logarithmic

paper, as has been done in Fig. 3 tor Series G. It will be seen that the ex-

•

perimental points lie close to a straight line, whioh proves the valid! ty of -./

eq_uation (1) as an empirical formula 1'or this case. 1'he slope of this straight

line gives the value ot n which, when substituted in (1), gives the best em-

pirioal relation to :t"it these eXp'lriments. A determination of this slope by

eye or the method of loast squares gives a value or about 3.5 tor n.

The lower pOrtion of the curve in 71g. 2, shown dotted. obviously

represents stress combinations tor which some portion of the cylinder has

reached the elastic limit. The lowest point on the curve represents a pure

tension test. Uost practical applications do not tall within this region and

no particular study has bean made or this portion o~ tho curve. Designers

will , or course, realize that the relation given by (1) can hold only vhen

the principal stresses as given by elementary mechanics are within the elastic

limit (or, aceording to the maximUm shear theory, when the algeb.raic difference

between these principal stresses is less than the elastic l1m1 t stress}.

Six other lese complete series of tests have been made, eaeh series

on a radically different type of cylinder. These tests were made with torsion

and axial compression only, ana 1ft th a much amall.or number of cylinders. The

results are shown in Fig. 4. Fig. 5{a-f) shows the results plotted on double

logarith:nic paper for these acn-ies A- F inclusive. These results are simUar 'o

those :t'ro".ll the group of tests described above. The Talue ot n appears to be

different tor each type of cylinder, the values obtalne~ ranging from ebout 1.0

to 4.25, apparently indicating that n is a function of the dimensions or material

ot the cylinder. SOOJ.e of the sets or results, when plotted on logarithmic pal)er,

do not see~ to give a straLsht line, apparently indicating that (1} is not exactly

suitable as an ~mpirienl relation for these cases. However, the nunber of points

is so few and the unavoidable experimental scatter eo great, that nothing definite

can be aaid on any ot these 'Jtf~.rl6~~&. The results do indicate, however, that the

general empirical relation (1} covers all these tests (and hence probably all

thin walled cylinders, and possibly- all thin walled structures of any kind) sur-

... 5 ... " q3 IV'qs c/,,E> tt> ;>lot/,~ lie """i/c",..veth f&.1,

tic1ently well tor practical purposes. It n is t~en as 3" the deTiation be-

tween the empirical law and the experimental results is not. large compared to

the general scatter ot the points , tor any or the types ot cylinders tested.

It thm-e.tore seems sate to say that designers eo.n use the relation (1) with

n = 3, .tor designing cylinders. with considerable confidenee, until better in-

formation is available.

ObTioualy this work is only a small part, ot the work which should be

done along this oe.ne line. It is planned to continue this wo.rk at the Cali.tornia

Institute or Teclm,ology, and it is hoped that this paper will stimulate other

· researeh organizations to do work in this tteld.. Some tests have already been

started here on long square tubes under axial load and torsion, ~ ving approxi­

mately the condition ot tlat hinged-edge panels under normal and shear stresses;

the initial results are similar to those described above. As stated be.tore,

there has hereto.tore been little investigation in th~s field, tm.d it is telt

that further work wUl .result 1n information' or great value to designora of

stross~d skin structures.

AU of the teats ware made on s1ll811 scale models, ot steel o.nd brass

nah1m stock". They were made by a technique and were tested on s~ial testing

mt<tchines developed by Dr. L. H. Donnell, and deser1bod by him in a previous

paper«>). The figures mentioned 1n the t'ollowing paragraph reter to figures in

this paper. As shown in this paper the results trom euch small scale teats

co!!lpare quite tavorably with testa on a larger scale, but it is necessary to

use great care in selecting stock and in making the specimens in order to re-

duce experimental scatter to a J::l.inimum. In spite or this care it ts impossible

to avoid considerable scatter, especially when the load is mainly compression;

much of this is probably due to the tact that it is impossible to obtain such

thin stock entirely without initial •waviness.

- 6--The thickness or the eet 1tas r1eo.stn"ed 1n the thickness tester

shown in Fig. 14.8.5). '!'he modulus o-r elasticity, R, was obtained with the

special teeth'@ lllloh1IWJ end tenaometer shown 1n .Fig. 15a5) . The proportional

limit stress 6f was found at the same time, tdr purposes ot record. The

sheets were rolled around rods ot the proper diameter to g1 ve theLl. the correct

curvature. They were then wrapped around a wooden roll, ot the di~ter ot

the finished cylinder, hich had previously been oiled to enable re oval ot

the cylinder after soldering. '!'he sheet was held ainst the roll with a metal

strap 1 while a special clamp as used to prevent the edges tro.'n warping under

the h&at ot solderint;• The eds s we~e soldered with about 1/8 inCh QTerlap .

(It has been tound that buckling waves seem to tortt across the joints as ~eely.

a8 elsewhere, 8o the of'teot ot the double thickness at the joint is probably

TerJ. s'llal.l) • Arter removal tho cylinders were soldered at each end to rings

which fitted inside them, and the cylinder and rins were soldered to heavy

base plates with h1oh they e-re mounted in the testing maoh!ne. Tho shortening

ot the ettee~ive length or the cylinders due to the rings is allo d tor in

the f'ollowin table. The cylinders were tested 1n the special testing tm.chine

shown in Fig . ~a5). This tosti mehttte is capable of' testing apeoimens in

any eo"1btn.at1on ot torsion, bending and axial. compression or tens1on.7P11ga. 6

to 1~ i~clusive show typical tailures under combined cam reesion nnd torsio~ ,

hile Fig. l l shows a typical tailtre under c bind tensior and tora1on with

+he tens1o~ ~ ,.,e attac~ed_V Frj If< .Y6ow.s !he cy/thc/ey:I of J'erte..g {l- q~fer

ferJf,~. G ble I shows tho ;ro»orttos or tlrf cylinde a tn each of' the series

tested. The values ivan tor n are the elopes ot the straight lines 1n the

lo arithrnic plots, Figs. 3 and 5(a-t},a previously discussed. ___ _.....__... _____________ __

5) N.A.O.A. Re ort No. 479.

- 7 -

1'ABLE I

ProEerties ot ozltndera in series tested

Series t . Length D18!ll. Thick. EX 10-6 6p X 10-3 n - -A steel 5 .3~5 1 .88 .00204 31.4 57. 7 1 . 992

B bras a 5.316 1.83 .0032 16.5 27.0 4.25 c at eel 5.315 3.75 .00295 30.& 48.6 2. 625

D steel 11.315 1.88 . 00204. 27.06 53.3 2.1~6

E steel 5 .316 1 .88 .0029~ 30.G 4te.G 1 . 0 steel 1.32 3.75 .00204 31.4 57.7 2.781

G teel 5.315 1.ea .00395 29.6 36.0 3.33

/ ......., Table II shows t he ultimate axial loads o • end torsion 1:10ments J •

tor eooh or the cylinders tested. The values used tor ~ and :(, in plotting

J'iga . 2 to 5, were the averoees ot the values ot 6 an4 Y tound in the ptre

compression and pu~ torsion "testa. The values chosen tor ~ and J;; have

considerabl intluence on the value :f'ound tor n, and ~t is .,..robable that p l!l"t

ot the variatic;m in the Talues or n, tound tor different types ot cylinders,

is due to the inaccuracy ot these values, In makin thla type ot research U

is 1~tant to mak~ nunerous ure oo resaion nnd pure torsion tests (es-

pecie.lly re CO::lJ!l"&ssion, because the eatter is much worse here than tor

tor ion), so as to get a good average value to'r ~ and J;, ; 1n tuture rese rch

it is plan ed to nake even more ot such tests than have been made.

TABLE II

JExperilnental :Results used 1n Plotting Curves

Se1' 1 es .A. 50 : .., ,

.._ "

~ 1 s. 0 20 40 60 60 100 uo 190 172 230 1 a 218 231

'f 1b.1n. .

55 52 49 47 40 39 36 30 20 10 0 0 0

. B .,..1 6

0 • J ;: o lba. 20 45 90 110 120 150 175 190 230 260

J lb.in. '10 64 fro M 48 60 5& 64 30 0 '

-8-

Series 0

~ - :t o 1be. 0 0 50 100 160 155 170 200 200 220 230 250 279 287 287

7 lb . in. 217 2.a 226 1'78 180 1'74 210 210 126 06 70 100 72 0 0

Series D c;;; -:: 1 .. ' ;(

o1be. 0 4rO 97 100 100 120 125 130 140 156' 151

71 .. 1n. 36 34 23 1.2 16 24 0 0 0 11 10

Series B

~ .. -r C>

o 1 s. 0 0 100 100 200 200 200 500 300 420 430 455 470 490 520

:1 1b . in. 108 uo 9& 100 ea 78 90 e4 68 20 10 10 10 0 a

Series

~ .. :;: ) • I

a- lba. 0 as 50 75 100 132 f 1b .1n. 1&0 170 128 130 95 0

Series G

~ = T- , . ~ " - .. . -o = tension

o 1bs. -9so ...aoo -soo -'100 -&oo • 300 -500 -Soo -400 -400 -300 -~oo -2oo -:oo -uo r:' J lb.in. 0 16& 200 220 24.8 224 220 234 215 218 222 210 204 210 20&

O' lbs. ...100 -100 0 0 0 0 100 l.CO 200 200 300 3d0 4:00 500 500 _...../

J .• :v.!n. 200 216 178 196 186 184 172 180 1 6 174 144. 150 1.24 0 75 \

~

o 1bs. 600 500 540 595 613 610 60 :f lo.in. 132 :140 100 10 0 0 0

\

0 ~~ .-------------------------~-

0

.o&

.8 I 00

z 0 I I I • -(/') 6 V> .l.LJ tr: a. 2 .4 0 u I I I I 1 ao

.2. I I I - -- -.---

---· I - - 1--- ·- I ~·~ - - I

.0 .2 .4 -~ .8 I. 1.21 1.4 cr SHEAR (TORSION) -c>o 7 ,. eo -.2

0

I I ,

0 I I I I I I

.4 I I I I I . I

.6

~- I - --~~-~~-~- -

z .a I I I I I I 0 10

0 BUCKLtNG OF CYLINDERS -\1)

UNDER COMBINED TORSION 0 I 0 ~ -l.O AND COMPRESStON OR TENS\ON.J t-

I

1.21 I I I I I g

I /

/) A I ••

1.41 I I I I 7 ~/ _,..,...,..

~• - -:.;.I~ _,..,. ~ 1.6!::-- _... I -

' I . I I. I

I Do ~ A E

1.0 i ~ ~ ~cl~~~ 0o 6

c. E

E A

I A(j . it\ G

' .8 c B

I

D 10 D · B C

fo.J ·. _ c ~~:\{ B-c----l-----lr-----.

1 I I E

8A~ a\~\ 6 I I I .4-l B cf (; G

A\ 0

'BUCKLING . OF CYLINDERS .2t- UNDER COMBINED TORSION f-~.X:,c 1 F

AND COMPRESSION OR TENSION 6

0 ~ ~~& ' ,c;. ,4 .6 · 8 . GACEQ.FE --'----.J r . 1.o 1.2

-To

.. FIQ.1 I .J .

I I I ~

I I rJ

F

/

/ HEMI5PHERICAL BALL

FIGURE 1

•

A

F

FIG. I

•

•

c

HEMISPHERICAL BALL