Lyse, I.

Stewart, D. M.

English

Lehigh University: Lehigh Preserve

Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1935
A photoelastic study of bending in welded seat
angle connections, Welding Journal, Vol. 14
(1935), Reprint No. 7 (35-2)
I. Lyse
D. M. Stewart
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Recommended Citation
Lyse, I. and Stewart, D. M., "A photoelastic study of bending in welded seat angle connections, Welding Journal, Vol. 14 (1935),
Reprint No. 7 (35-2)" (1935). Fritz Laboratory Reports. Paper 1162.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1162
~LfI~'~~Z~
. F~/93S-.
.' INTRODUCTION
A Photoelastic Study of Bend1ngin'Welded Seat Angle
.Connectiena
by I118e Lyse* and.J)ouglas·M~ Stewart*
fRITZ ENGli'1EERrNG LABORATORY
LEHII1Y UNIVERSity
I3ETHLELi:::1, ~SNNS'(LVANIA .
A ;photoelastic investigation of the properties'
.of welded seat angle connections was undertaken at the Fritz
Engineering Laboratory of Lehigh University in conjunction
with ac·tual seat angle t~sts being carried on. in cooperation'
with .the StructUral steel Cotdt.tee of the American Welding
. .' . ".
Soc"iety. The investigation was limited by the nature of
. . . -
the apparatus to two-dimensional problems under plane load- .
'.. ing.andconsequently .this study is confined to the lateral
. bending e.ffect of the angles themselves. ~hermore. ideal .
. .
welding conditions must be assUD1ed and, perfect continUity of
weldingmateriaJ. .and pa.rent metal. S.ince we note that.
. .
where sufficient·weld·metal is present to.prevent a shear
failure. the first symptoms of failure. inact1lll!Ll seat angle
tests are always a dispropo:rtionate.inerease in deflection
of the outstanding leg. followed by chipping of ecaleor
.whitewash on the fillet of the angle. this 'bending eff~ct
is of prime importance as regards failure of the connection.
Consequently a coz-relatiGu could be made between the resu1ts .'.
'of the photoelastic tests and the da.ta on tkef1;rst S~gns
of bendiIl8. failure· in .actual tests:•.and theresults of th1.s
' ..'.
are shown later in this· report•. In. addition, a photoelastie'
* Research Associate Profe,sso~ of Ene;lneer4Ii8 Ma.terials·· and
Researeh Fellow in Civil Engineering •. resJ'jeet1vely. Lehigh
University. Bethlehem. Pennsylvania•.
.'
mode~will show the distribution of stres~ in the· angles
at various loads and will permit the s~udy of oth~r factors
which might a.:f'fect the strength; in this case. the effect
of Incr~asing the size of the fillet in the angles as rolled
was investigated as being of importance in causlng bending
rigidity.
TEST SPECIMENS
Three models were made and tested, these being
ha1.f-scale.sectionsofa pair of 4 x 4 xi", 6 x 4 X 5/8".
and 8 x 4 X 1" seat angles mOunted onUff thick plates'ex-
a.ctly as in the actual welded steel specimens. . These models
\vere accurately machined from sheets of. t'l thick transparent
bakeJ.ite and carefully polished and annealed to remove i111tisl
stresses. . At the same time a calibration beam was cut from
the saine sheet of bakelite as each,model. and subJected to
the same" conditiona of annealing and storing. The models
were then loaded by means of dead weights through. rollers
placed at the desired distance from the ba.ck of the angles •
.in a manner identical with the tests on" the full-sized' steel
2. :
specimens. The two larger of these models were made with a
. .
1" fillet on the angles~ which was then cutdown success~vely
to iff and i U , the latterbelngthe standard size rolled.
PHOTOELASTIC DTHOD OF ANALYSIS
It is possible by passing plane 'polarized light
.through such a transparent model, to obtain a series, of a.B.rk
lines on an image of the model from \,hlch the. directions of
'.
the tWQ pr1ncipa~ stresses at any point, that is the stress
traje~tories, may ~e determined. Furthermore, each.trlD8e
. .
as shown. when the m()de~' is sub3ected to clrcu+arly.polarlzed
'light, represents a definite v~ue of the 'difference of the
two principal stresses,' (p-Q), a.t that point. Since the
maximumshea.r is likewise ~roportlonal to (P-Q), these fringes
are. also lines of constant maximum shear~ At the tree bound-
arie.s ofa model, where. the stresses have lngeneral their
critiaalvaJ.ues, one of the pr.incipal stresses vanishes, and
thus the fringe order. is a. direct, measure of the fiber stress'
along the boundaries.,. This latter faet was made· use 01' in
'., ,. . , .
. ..
this investigation and from' the ca.~ibre.tion beam under uni.-
form bending moment, the value of, the stress difference corres-
ponding to the'fringevalues of' each ,model was determiD.ed.
From the values of the extreme fiber stress iil the outstanding
.leg of the angles, moment 'curves were then plotted,: and a.
first integration of thesega.ve the slope at any point, while
a second integration gave the· deflection curve of the outstand-
ing leg.•
VARIABLES· STUDIED
The varia.bles stUdied were as follows:
1} With the load at· 2'1 from the back of aIJ8le, the 10ad
was varied.
2) With the load constant the lever.arm was· varied, the'
. ~ points selected being 1.2" ,2.0" ,2.5" and 3'.0" from
.the back of' angle.
4'..
3) From these resuJ.t8 a comparison was made o~ the three
fillet sizei3, a11 other variables remaining constant.
4) The effect of,the ~ength 'of the vertical leg was
studied by ,cutting down the 8 x 4 x 'lu model. ill sue... '
cessive steps.
$) The effect of the size of the angle 'on ,the stresses
produced'was determined from the precediiIg resuJ.ts. ,
DISCUSSION OF VARIABLES
'; Fig. 1, shows the ,effect of the varia.tion of load
upon 'the maximum stress on both the tension and compression
sides of the angle. As is to be expectetl,' the relation is
:linear" the stress increasing directly with the 1oad, and the
compressive values exceed the tensile ones, iildi-eatingthat
the compressive stress at the fillet limits' the strength 0'£
the angle.
In,Fig. 2 is shown the variation in end slope and
deflection under the load with varying loa.ds and a constant
lever arm. In this case the values lie ,more close~ on,· the'
theoretical straight li1'1e8,s1nce the process'of 'integratiQ11
by which they were obtained tends to '1ron out any'irresuJ.arities
in the data.
. :..
The constant load of 16 lb '. ,per angle w~s then
'applied to each of the four lever arms, and Fig. 3 shows ~ ~y­
pical set of resuJ.tsfor ,the 6' x 4 x 5/8" model with i" fillet'•
.
The _~im~ stress, both,in tension and. compression, ,is seen'
..
to vary linearly down to a .point where the influence of the
fillet 1s felt. The curve ~or the end slope 1sa parabola.
'5.
while that tor the defleetion under the loa.d is a cubic para-
bola, both modified at low values by the restraint 'caused by
, '.
, the fillet.
The quantitative ~ffeetof the size of the fillet
"in the angle as rolled is 'Shown..in.. Fi.gs. 4, 5 and 6 for the
three sizes tested. The first·two:f'igures showing the ~e~ ..
.
flection ~er the load and the .end slope at each of the ~oUr
lever arms, indicate clearly the added rigidity caused 'by the
larger fillets, ,and give as well a comparison of thestif:fness
, . . '
of a 6 x 4 x518".and an·a.x 4 x 1" angle. Fig. 6 shows, the
. . .
variationln m.ax1mum stress, both in tension and compression,
as the fillet size is increased; it shows pJ.ainly that' the
less rigid angle is strengthened more by the· addition of a
larger fillet than is the stiffer angle. The amoUnt of this,
stiffezung has been summarized in Table 1, in which the max-
imum stress is expressed as' a percentage of the maximum ·st,..,ess
with, a standard i "fillet.. In addition, the percentage in-
crease in weight of the standard angle caused by the increase .
in size of the f.illet, has.been tabulated. Since the com-
pressive stresses limit the strength of the angle in every
case,' tested, it 1s these values that· are of' the greatest sig-
ni:ficance,. and the reduction of stress caused by the addit.ion·
of only. a very small amount' of material is remarkable.
The vertical legs of' ·the 8 x 4x 1" model, \Crith .,
a io" fillet, were cut down by i t1 steps, correspond.1:ng to ll'
on the :f'ull-sised specimen, until they were' 1i n 10IJ€; and
then by insteps untilln lOll~h Photograplls taken of the
, ,
fringes around the base of, the angle ,show no incre,ase in
,the t~nsileor c.ompressive. stresses until a. lengthofltn
was obtained. corresponding to a 3" vertieaJ. leg. be'low '
which the compressive stresses were slightly increased and
redistributed. This is 10:wer tha.nused,on,any seat angles
in practice. since eonsiderabl~, length of weld is needed to
iJrovide against shear failure. a factor Which is not appar-
ent from photoeclastic reSults. '
The relative strength of tha three ~izes of
angles tested is shown in Fig., 7. Each angle has the st~­
ard i " fillet a:nd the strength,or 1Qadrequired to produce
the yield point stress ,in,each angle, haa been plotted as a
per cent of the, strength of the 8 x,4 X1" angle va the 'sec-
tion mod.ulus of a cross":,,section of 1iheoutstandingleg of the
angle. The points group themeelves alO!l8 a straight line.
vaJ.uea for the 4 x 4:it in:,angl.e being more in error because,
ofdifficuJ..ties in observing the large number of fringes' pre-
sent. Each point is the avel"age for the four lever arms
used. In addition, there is shown on this figure the rela-
tive strengths of actual. , full-sized welded stee~ specimens',
these values being the loads at which the load-deflection
curves for the outstanding legs had a slope 5~ greater than
the 1n1tial slope. ' .Each point her~ is the average for the
, three lever arms used in the tests. A similar plot based
:on the yield point as determined by chipping 'of the Whitewash
on 'thefi,11et' of the 'a.ngJ..e, shows a wicier spread 1:1'1 VaJ.ues,
This,figure
shews a fairly g09d eorrelation between photoel.astic tests
and the actual vleldee. spe'clme~se.nd indicates tkat the seetion
medulusG~ a'cress...aection'o:f' the outsta.:n~ing legshGuld'dic-
ta'tethe:seleetion'of thethicbess efa seat angle.
, ' STRE$,S >~!STRIBUTION'
~hedlstl'ibution ,01'; stress in the ,extreme fi-
,0': •
, .'
in Fig. 8 for the three tiiffer~nt' fillet sizes. This ~igure
, ,
an ows the load at 3" :f"rom'the back,of angJ.e., the other lever
....., " , " ,', ,
arms shOWing identical effects. On the tension side" we
m~note,that all the curvespractieally eoincitie'outside
of the f~llet. Ale,o, they reach a maximumvaluediree.tl~
above the point whe're tIle 'fillet (lO~e~Cea,'and thls'~iBl'Uli1
value inc:r:-easesas'the'filletsize deQreases; the e:f'+eetGf
a local eoncentrationof stress under tl;1e 10ad.'pG1rit 1s like- ,
',wise shown. On the 'compre,seion'slde, ordilaatasaround the
fille't have been plotted radially. Agaillwe n.otlj) that' the
eur:ves e,{ineide beyond. the fillet., a.r.ul: th~ttheyree.chzero
, va.l.lles' lUldaX' the ,le.ad.· The. ~8JKim1flIl ,compressi.ve stress ,
, .
occurs fi)n the fillet at an 8.1'J81e' of roughly 20° - 30° witil the "
vert:icaJ., and the values increase with decrease in fi11et·
size,. It· 'm:ightb,~ 'noted that chippi1l1g ,of the whitewash in
"full-sized: tests,where'shear :ffai.l~e·a~(e'~'not do.em-,eomnien-
cas at this, point 'on the filletae nearly as can be observed.
- .
'.
- ,I-
- -
~xtremetiber.stresS fa.J.l.s eff rapidlyand,the ~()wer tip of
the angle takes nestr'ess at aU. -
. . -
The d1reetionsof the tW0 priiteipaJ: stresses
ha:vebeen i:l.etermined'bY'mea:ns -0fpla.nepola.r1zed light f:.0r
. the ~ x 4x5/8,n' arid the e %4 x 1," models and are Shown on,
: . .
<theltight.b.a1,-es. 0:e·lrigs~. ',andlO. . These ,stress ,tre.~ec-
tOl::tel:;J eons1.a!; ,~f_~wosetsofmutually perpenale'Ular lines,
. ',' .' _.' " _ ." ..' '.. : -. . .
and. a.t all: free' bounaarie.a one s.et of lines is normal to the
It is seen that the fibers are in a.J.most .pure ten-
s:ton just above the fillet a.nd that pure eompress1onexists
at the fillet and in the_ main body-of the' m~d,el. The po1'-_
tions .of the outstanding leg outside the load point aJild ,the--
lower tip et the vertical ,leg are Ullde.r ~er·ost1"ess. Onthe
. . . . .' . .
left side of these figures are shown theaire'ctions otthe
mu1nmm slieari~ stres~e.s.. or shearingtra3eoto1"1es. wh11ch
. .
aPe two sets of m1i1.tually 'perpendicular li~es in~linedat.
45° to the, stress t1"aje~torle~'. ,A sUJgul~ point-just ove~\'
the f1~let•. shoWn 1:m.t1tles~ two :f,'1~e,s'j has b~en f,oundtobe
a;po1nt ofzerostres.s. which maibesa,icl tQcorl.'es:pond. te
A. s1mi.larstUtiy wa:s made "of each of the
. tnree :fillet'·sizes.. to d.etermine whether this va.riable affe,ct.ecll . ~
the stress dista:'1butlo:ta~eat1.y. ,- 'Slight variat1-oaas were
,note,d,b:u:t the distr1bllt10n efst1'esswas n0t ~rkedly alt~re·d.·
T)le vertical ·sli.ea.ri]lgst:resswas ~1:l:eli:')U:I.a.J.y2;ei!l:',
by '\lSe of :l:0J:U:':',S Stress 9~r61.e a.iollg sections A, B and. C' as
shewn on 'Fig..9 for ,the 6 x 4 x 518Jf angle and the re~ts
..
a:resh~wn in Fig. ,1,1", On sectiol1A we have 'the ·us:u.a.lpa.-
rabolled.l·stributial1- of' the vertical shear.. 'At :a,' .the stl"ess
··tra-j6'c,tories are :horlzentu' and ~vertical tor a short distance
downf'ri(!)mth.etePl hence .there1.S~ n(l) v$rtieal Shear .f'ara .'
.ts :fitc.!u.ri.~~ 'th:e'~e~t;ica1 sh~~r has "8, value at thiS' PO:i~t",
At' 0,; q1i,itea d1.f:fe:pe~t,;forIn$f: distrfbution. lsQibs·erved.•,&1!I."
'explanationo.f which .mq be seen J>y. refe:rring to Fi,g. 9'•. '
At~-..d9~~O ':~.~~.~~a,i~ ~~iE.t, the, ii.:ne'~:\~:f stress (in ~en-
.. . .
. -sion~ a:t"!! :PuJ.lllat up, on ther:tght .til·:bdeo;t·tbe seeti'0nil1$teai'
- . - .'. . ' . - ".-
o,f down as at A;' in other words,~ the sign 0:£ the sh-etn".:1srth-
. . .' -, .
ver$e;Q... . Below' this. P01nt ·tb;ee0mpressj:veforcesare'· ~itig·
• • 1· ~, - '. -' •
.. '
don. as stA, ani. the s.lg.n of the .vertical she'~r is '. :~a.in po-
sitive.
-
The worst section is at B" :whichi,et the ~ransi1;ion
']p-01nt b:etween diagram,s .. o'J:types A and C. Fig.• 12 .shows. the.
ilstri'butlQn o:f verti,eal shear en seetionsA, B and. cor
Fig. 10. In this ease". the, tra.:l!l:S:1tlan'section lies betwee~,
:B ami Cj a.n.t1l. we note agai,n the. revaJl"s:a1~1Ji ~i6l:l at '-the· :~e'ar .
and. alse theJREtXimum vuues are sh,ewn en these f~.~e$~· The
.. are~,'lUlderthese,cUrve,s, ,repre-sentl:m.g. the lntfi)rn.aJ, she~r.
has been :f'ounfl teehe·ek the external-shear with.inlo,ttfn
CONCLUSIONS
c.,,· .. '
. 0. . '_,,' '.' , "t,'. _,' ,,/ .'
Fr0lD.· the a.bove, resUlts,. the f~J.l(')Wi11g~'l'onelu-·
SiOllS have been drawn with res~eet to the be.n4ing ofaeat
angles below their elastic ,limtts.
. '-:,~ c/.,";:. '~..
"
:.,
, .
the tlJ.let.weJ.ls·t0 P!te:v-e1Q;t·shea.ringfa;il't.U!"~ttheJ.imiting
00nditi(!)n:f:orper~aJllent'seti21.,0:r;oii»a.ry welie,a seat,. angle
conn,6)ct ions· i,s det~rmi:medby,the be»;tU.l'l8·stre~h.0.:it' the :
,2)' The>'ma::si:imum eeIlll'resslve stress a.t ,the fl1.let .
, ,(!)£ ~l;J,.~. '.a.ng~e: .;··~fsa.p~@x~ma.telY,lio 't~e~the nm.:x:imum te:nS7i1t,;~'
. .' '.' ...._.., ., . .: - '.;- .
stre.s,sa10Dg the t0P sl,{f;'! 0£the an;gJ.e l a~:eQrdlD8ly the .'
:p~eSisives~ressexisting ,in the fillet of the angJ.e.
, '
3) ~he maximum stre~,s,;~lild 'slope 'and :a.ef;Leeti01ll
f01" a c9nstant' lev~r a.rDL,. vary lineariy with tJae loaa,.,
~) For a giyenload. 'the '.~mumstres,s var.:te,s
. ' ..
iimea.rly ~with the' l.everarm of the load.. amd theenaslope
an...m,.d.e;fle,ctielitmd;er the 'load V8:ry.as's'e~ond.and· thirEl.()I"der
.. 'para'S·ola;$re,speetlv¢).y. except near the 1'1]).et where the,se
C1lU"V~s. are ;8.11 med.itieo. ~(f)mewhat au.e' to J.o-gal ce>neentrat,1ons·,
of .s;tress:., '
Q) The addltt,ion 0tS. very slna.lll>er.a.entage'ef •
material in the 'f0rmat a:... larger :fl~l.et in the· a.ng1e.s, .g1;ves
m...,ark~d reduetiensin bioth teli$lle .udeomiPlI'essive atr~ss.4lS,
the effeet »~ing more marked G~ the weaker angl.e seetions.
e>,)The l:ength of'tl1e, ver:tieaJ. l.eg has lj:ttle
. -
01" ;no et:f'~et·'Qn, the stresses in the angle above a le:ngtl\J,
, . '
equal.t6 that ef the out,stand1'~·.l.egl.$U:f'~le1ent~~e~h1 Iiiu.st
be proviae{t., however.,toprevent fa:ll~e by-shearing ~f tn.-e
welas.·
"
. , 7} The strength -of the seat' a.:r:tgl.e, it'se.lfin
. ..' .
be:l1dilig is geve,rned. 'by the section mociulus Qf a ep;0·as-sec-
t'1(1)11 0f thepu$stanQ,1ng l.eg•
. ' 8)' Tp;e graates·t· :tensile ·stre,s.'S'1n·;bae angle
occ'tl.l;-s, il1:"eetly' &'bove' ,the PO,illt: where the .fillet 0'0mmen(3es,:"
WhU~v.'t~e~~e~pest j,¢OIn:~elS$iv~stre$;s ooevs Oll the' fillet
o· . '0' _ _ '.' .' - .
at an .·~leo:f',:f'r0.m 20 , .1;Q30 witl1 the vert.leaJ..,.
. ~, ", \:'~
g) The vertical sheari1:Jg :a"$tril>utlon' 1,$ not .
UJdf0rm' Oll .a.ny$$etlo1ii.gt t:he' ang:L~,. anflQllSeetiensneal!, "
,..' . ... .. ", "." .. -).,... , ....~ . ',~'. '.- " ," ': .
. , .. ,,-,. -
the back, of thea.n.gle ,Shews a revE'rrsal, of sign... T;b.e JllaX-,
lmum vertlea.1sh.earing~tress Jm3,N' 'pe as- high as f.1ve. times'
theav.;~~age stress over 'th~~ec:t1on,•.
. EspecfaL tll8.1ika is; dlleto :Mr. N•G. Schre'iner
'f0rassistanee in performing and eon-elatdng. these exper-
iment.s.
:. "
.,. . '
u., L,
TABLE 1. Maximum stress ~Xpressed as a Per Cent of
the stress with a _" Fillet.
Load per Angle 16 #
6 x 4 x 6/8" Seat Angle
Distanoe trom All Fillet 1" FilletBaok of Angle •
3.0" 84.7 63.0
Compression 2.5" 76.a 61.62.0" 69.0 62~1
1.2" 71.3 47.0
- -
Average 75.2 55.9
3.0" 89.3 80.6
Tension 2.6" 88.6 81.62.0" 84.5 77.5
1.2" 90.5 66.8
- -
Average 88.2 73.8
Per Cent Inorease in 1.2 2.'1Weight of Section
8 x 4 x 1" Seat Angle
3.0" 83.8 71.0
Oompression 2.6" 84.3 76.02.0" 87.1 76.8
1.2" 84.1 '18.6
- -
Average 84.8 75.3
3.0" 88.9 83.0
Tension 2.5" 86.3 '19.12.0" 86.0 75.0
1.2" . 92.8 88.6
-
Average 88.2 81.4·
Per Cent Inorease in
weight of Section
.I' 0.6 1.5
Titles of- Figures
Maximum Fiber Stress for two Sizes of Angle with
Variable Fillet Size •.
. .
.Deflection Unct"er the Load for two· sizes of Angle
with Variable Fille.t Size.
End Slope for two Sizes of Angl~with'Variable
Fillet Size.
·Fig. '1. Variation in Maximum Stress with Load.
Variation in End Slope and Deflectiqn Under. the
. Load with Load.
Variation in Stress, Slope and Deflection Under Load
with Distance from BacH: of Angle.'
- Fig. 2
-.
F.ig. 3
Fig~ 4
Fig. 5
Fig. 6
Fig.? Curve ShowingR.elative'Strength in Bending pf,
Different Sizes' of Seat Angles.
Fig. 8 Average Values of Fiber ,Stress' Alon'g Top and Under
Sides' of Seat. Angle.
Fig. 9 Stress and Shearing Traje.ctories, 6 x 4 x 5/8 Angle.
,
Fig. 10 Stress and Shearing. Trajectories, 8 x 4 x .:1 Angle.
'. Fig 11.Vertical Shearing Stress Distribution, 6 x 4 x 5/8
.Angle.
Fig:. 12 Vertical Shearing Stress Distribution" 8 x 4 x 1
Angle.
.,
I
I
I
I. . .








I &
Shearing Trqjectones
16"
S/ress Trajec/ories
6;4',j5eal Angle
-i".Fillet
Load 01' 16# al Z'lrom Boc,/; .
of' Angle
No. 20510
,! .
...--~~~~~-----'~ .,-~-----------'-----'--
t Ft/;.· 9 stress. and Shearing Trajectoriee. 6 " 4 " 5/8" Angle
Shearing Trajectories
.
....
o .32"
Stress Trajeclanes
8". 4"' I" Seal Am/Ie
·FF"lef
Load 01' 32- 01 2" (,om Ihdr
or Angle
No .38/0"
•\ I\lV ..-.....
.'.
...,
stress arid Sb,ear1ngTrajectorles, 8 x 4 X 1'" Angle


A photoelastic study of bending in welded seat angle connections, Welding Journal, Vol. 14 (1935), Reprint No. 7 (35-2)

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A photoelastic study of bending in welded seat angle connections, Welding Journal, Vol. 14 (1935), Reprint No. 7 (35-2)

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