Beedle, L. S.

Huber, A. W.

English

Lehigh University: Lehigh Preserve

Lehigh University
Lehigh Preserve
Fritz Laboratory Reports Civil and Environmental Engineering
1952
Further results on the influence of residual stress on
column strength
A. W. Huber
L. S. Beedle
Follow this and additional works at: http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-
reports
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Recommended Citation
Huber, A. W. and Beedle, L. S., "Further results on the influence of residual stress on column strength" (1952). Fritz Laboratory
Reports. Paper 42.
http://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/42

PROGRESS REPORT
of
December 30~ 1952
B~l? ~IPJ-:&l~:.,-ij~~l_Rlli§.§~ ~Q~T~,_ c01~illJII~r"2±B~llq~lL
(Not for PUblication)
by
Alfons Wo H~ber and Lynn So Beedle
Tllj,s wOI~lr has h8e,n carried Oll't as a
par~t~ of Bj11 :i:;:l'~ros·t:i ga tj.()ll sporlsorE~,d'
j ()In'tly lrj C;>.,jI11.iJill Resec1.1~ 011 C(YLIJ.1C,t.,~L lJ
the Pennsylvania Department of Hig~~
wa'ys _., ai.1d tJ:J.8 B111~eau oft :P1J..bl,:i.c Roa(:1s:;
Advl~ory assistance has been r~ceived
fl"lorn tl18 Lef.ligll Pricject SUbconnnit;tee~;i
Welding Research Ccuncil Q
Fritz Engineering Laboratory
Depa~tment of Civil Engineering & Mechanics
Lehigh University, Bethlehem, Penna.
",F
Report No o 2-20A .. 7
220A o 7 12/30/52
The p11rpose of this report is to present in summarized
form 'the results obtained IIp to this time in ~the pilot in~
vestigation of the j ..nfluence of residual stress on column .
(1)
strengtfi.' Progress made in each phase of the program has
been reported previously in the quarterly PROGRESS }{EP'OR~CS
of the Column Research Council. A progress repo~t prev-
iously distributed has described "weak-axis ft test results
in more detaif;)and the discussion included therein will
not be repeated here~
,All bu,t one of the col,unm tes·ts \v-ere ma.de as a part of
the program, tlWelded Continuous Fra111eS tll1.d T11eir Components tt
sponsored by the Welding Research Council and the Navy De~
partment~
The c1lrrent tests using anneale<l Inaterial (including
column tests).should furnish final evidence for this phase
of the study: do residual stresses (and not sometbing else)
cause the redl1c,tion in strength of as-qG,livoI'ed CC)]..umns
that. have been observed and reported.
The test results are now discussed in the seque~ce in
which the figures appear, For easy reference, Figure numbers
appear en the lower right-hand corner of each'sketcho
- ~ ....j. - - - ........ ~ -- *""" - - ..., -- - .... - - - -... .... - -- -- - - - ....... - .... -
(1) Proposal,' "TIle Influerlce of\ Resid.ual Stress on Colu11ll1
Strengthlt , -Fritz Ellgineering Laboratory, Lehigh~,
University, October 22, 1951.
(2) nExperiment~al Results of the Influence "r Residual Stress
en Column Strength" of August 20, 1952 'by AeW o Huber
and R.L~ Ketter.
12/30/52 ..2...
.li. Ii II §. 11 ~ ! §.
Figure 1 shows that the material for the stUdy came from
numerous pieces cut from two rollings (A and B) out of
a single ingot. A typical des~gnation, IA2, indica'tes
Heat 1, Rolling A, Piece No.2.
Figure 2' presents in tabl11ated forrl1 the rna terial proper..
ties of the 8WF31 shape. The terms used are defined
as follows~
E -
-
Modulus of Elasticity, determined by drawing a
straight line through the test points in the
-
-
....
...
elastic range.
Proportional limit, determined by eye from the
plotted curve. The sensitivity of the strain
measuring apparatus is about 15 microinch/inch.
6yu ~ Upper yield-point stress, an unstable condition
determined directly from the testing machine.
Lower yield stress level determined from the
average of the readings in the plastic range.
Although seveI'al comparisons may be made ,it will suffice
here to note the following (see ttcomparison", Fig. 2b):
1. The agreement between YOlmg's Modulus determined
from cross~section and coupons is excellen~.
2. The lower yield level is always less in the cross-
section test than as determined from average coupon
values a This reduction also appears in the 'case
of the annealed test.
220A.7 12/30/52
Typical,stress~straincurves are plotted in Fig, 6;
in, Figs. 3 and 6 of the August 20, 1952 Progress Reporf2 )
stress--stra.in curves for 'as-delivered and annealed material
were compared,
Figure 3 indicates the sectioning method used for meas-
uring residual strains with the aid of a lO.inch
Whittemore Strain Gage.
Figul"e 1+ shows the resicltlal stress dis~tributions for the
annealed (T-3) and the as-delivered specilnens (TO, Tl,
T2). The stresses were computed from the measured
strains by use of 30 x 106 psi as modulus of elasticity.
As will be seen later, the C011l11U1 curves indicClte tllat
the magnittlde, of tensj..le resid'ual s,tresses in the web
is of minoI' impoI·tance. The h,igllest· c0111pressive re...
sidual stress at the edges is 17,500'psi and'the ten..
sile stress in the web reaches, to, 15,000 psi,
Figure, 5 shows the set-up of a cross ...section specimen in
~che 800,000#: Riehle testing machine, SR~ (type A-II)
strain gages were used at the flange edges and at the
web and flange centers respectively. Four dial gages
were used to measure the total shortenining of the
spe~imens. The average. strain over a lOinch gage
length at the flange centers, was also mea'Sllred with a
special compr~ssometer; generally such measurements
were found to be in fair agreement- with' the strains in~
dicated by SR.4's at the ,flange and web centers. The
220A.7 12'/30/52
yield lines which appear in the photograph developed
at an average stress of 28,260 psi and an average'
strain over the lOinch gage length of 862 microinches/
inch,
Figure 6 presents some typical stress-strain curves of a
compression coupon and a cross~sect1on specimen (T~O).
Although the stress~strain curve for the average of
the four corner dial gage readings is plotted, it does'
not appear to be representative for the specimen.
Figure 7 shows the coIl-iron curves calctl.l.ated from a com...
pression coupon and a cross-section stress~strain curve
(T--O) ? using l"losul ts obt[til1ed froE1 \veb SR.-l+· gages.
T11e stI-ength of an axially loaded coll1nm containil'1g
residual stresses is determined by the ratio of moments of
inertia of the elastic part of the section and of the total
(3) .
section i.e. Ie/I • For lei! =1 the expression is the
Euler curve. The ratio Ie/r can be expressed in terms. of
the tangent and elastic moduJ..tlS. Ovling to t11e residl1al
stress distribution, yielding of the section COlnmences at
the flange edges and penetrates toward the flange center
while the. web remains elastic. Consequently, Ie changes at
a different rate depending on whether flexure occurs about
the "strong" or the lI ovTealctt axis of the specimen; this re-
sults in the two column curves.
---~~-----~-~---~~-~---~~~-~-~(3) Progress Report No. 5 Welded Continuous Frames and
Their Components. ltResidllal Stress a11d ·the· Yield
strength of Steel Beams tl by Ching lIuan Yclng, LjTnn S,. .
B.eedle and Bruce G. Johnston. Welcling Journal, April, 1952
.220A.? 12/30/52
I,~ Fig. 7 the tangent modulus curve i~ plotted for ·the
strong axis. This curve is an approximation since it rteglects
the influence of the web o Later a comparison will be made
with the more exact expression which takes it into aCCoID1t.
Tne, agreement ~ith tests of aJcially...loaded colllllms is good.,
Colu~inn· IB2. 5 had appreciable initia]~ curvature which ShOll1d
account for the fact that its obsGrvod strength did not reach
the value predicted on the basis of residual stress nleasure~
ments.
Figure 8 compares "t11e coltl11ll1 ctlrves obtained from the
cross-section test (solid lines) with the column curves
derive~ from the residual stress distribution. (To
'facilitate analytical treatment the residual stress
pattern has been idealized&) The agreement is close
except for law L/r values in which region the average
maxilntlm stress of t-;he cross-sec'cio11 is less t11an the
average coupon yield stress level~ Also shown is the
AlSO specific"ation C11rve modified to correspond to the
average coupon yield point of 39,950 psio
Figure 9 shows the di~ference between the tangent modulus
curve (dot~dashed line) for the strong axis and the
more exact expression (solid line)Q' The latter takes
into account t.he infJ.llence of ·the "veb o The terms tt d ...1t
and ll(.i ll a.rG necessary in order to express the ratio
I e/1 in term of the tangent modulus, Et , and the mod-
ulus of elasticity, E. The figure malces use of two·
220A.7 12/30/52
sets of data; web SR~4 gages were used on one curve
and dial gages on the other. The comparison suggests
that, for intermediate length columns (L/r - 80 to 100)
where reduction due to residual.stress are most pro-
nounced, the r~finement is not warranted. lfuwever,
for short colu,mns (L/r : 40 to 60) the web effect is
more important, since the reduction due to residual
stress is of smaller magnitude.
Figure 10 presents the results of five cross-section tests
of which one was made on -annealed material (T~3)a An
average, momllus of elasticity was used for the Euler
curve. For each test 6y is the maximum average str~ss
carried by the cross-section. (As S}10'tvTI in ,Fig. 2b,
this maximum stress varies from 9J. to 96 per cent of
the average coupon test results~) There is relatively
little spread in t11e C1.1rVeS, but there is prono11nced
difference in behavior betwoen the annealed and the
as~delivered cross-sections~
Figure 11 presents the results of the five cross~section
tests and the column tests on a completely non~dimen~
s ional lJas is (\
Figure 12 is a conlparison of the n·on~dinlensio11al curves
derived from idealized residual stress distributions.
The "mea.sllred residtlal stresses \~ere aI>pl'oxinlated by
straight lines except for T~2 where a closer approxim-
a tion was tLnde. T...O ana.. T..t~ gave almost id611tical
220A.7 . 12/30/52
theoretical curves and therefore one common set of
curves has been plotted (dashed lines).
DISCUSSION_ ..-:;1... _
1. Fre§.i3.lJ...9~~ o~~.990~i~E_!1t§""~streJ2ses: The as-
delivered specimens all gave similar patterns of
cooling residual stresses while the annealed spec-
imen~ was practically stress free (Fig. 4).
2. liegltqtjoP~M--92JjJ..mrLE!en£~11: The results ob...
tained from as-delivered column tests, from cross-
section tests, and from curves based on residual
stress measurements all clearly indicate a reduction
of sJcrengtll below values predicted from cot~pon tests
(which eliminate residual stresses) and from an annealed
cross-section test,
For equal L/r ratios,: bucltling abol1t the weak axis is
more critical than when bending occurs about the strong
axis.
3. ~~~e$~~s~res~~: The variation in
the magnitude and distribution of cooling residual
stress (Fig. 4) is much smaller in the flanges than
in the web and is apparently only of minor influence
on the column curves,
4. Lar:iJl.-:~ipll..9f_polunm cl1rves:' Owing to the sirnilar
distribution and magnitude of residual stresses in the
flanges, the spread of the coluM1 curves of the four
as-delivered cross~section specimens was small for
220A.? 12/30/52 ..8...
both weak and strong axis (Fig. 10). The variation
in the magnitude of the tensile residual stresses in
the web is of little influenc~.
5. prE?st:i~q__tJQn,S>j'~ co:l.~1Jl!ID~~..tIel}.lt£h: It was found that
column strength predicted from cross-section cl1ryes
and from curves obtained from residual stress measure~
ment agreed well with a number of actual column tests
using the same section (8WF3l~) and heat ( Figs. 11,12)
6. These results are in agreGment with the tests and
theory upon which the investigation was based, Con-
sequently with the completion of tests on annealed
material, studies of other cross~section shapes may
begin.
LOCATION OF TEST SPECI}mNS
I-Ieat I 8\'&31
Rolle
~ Ingot Bottom (B) ,/ Hot saw cut Ingot Top (If)
-_/
·~-IhI OA_2__'"---[}AI-A3-~ __I_B_l__.....-.[ IB,~2_--"'---~--1==::;.B'._I_1 -..-jl
Q~ .__.__..:=.1~80 t -.__~~__-_--~&-~.-..---480.!-..-.-, ..--.---....-..-~- ..._-:..~
""~..../,, first rolling second rolling
IAI
IB2
IB2.1 IB2.y.
T...18
IB2.3
T-4 T-4
IB2.5
T...15·
t - tension coupons
c - compression coupons
c-s - cross-section specimen
\21 .. residual < strain specimen
col'•. - column SpeCiJJlen
f~~Lt~ annealed
Fig. 1 1
J.
FIG, 2~ ~1F3]~~T~RI~L PROP]JRTIE9.
COI!!:Q!,ession Cou'O~ TAnsi..on Coupons
lvlat arial. Spec. E dp Oyu 6y E c5p c)yu dyNo.
r~l it 1 1 29,250 17.0 36.8 I q,l. 3 2 30,300 39.8. 37.9
2 30,750 36.0 37.4 37.4 3 30,200 45.6 39,2
3 29, rj' 50 34.0 38.5 37.8 9--.90, 20Q..-__.~__1=3. 0 1Q-!-~
6 29.800 ~32.0 37.3 37.3 ~ve.-l 30,230 42.8 39.1
7 27,500 ' 31 .. 0 37.7 37.7
L_..3.~Lg.90 _. 34_~~~7_0__37 .7 5 30,200 44.8 43.3
~ve~-l* 29,220 30.6 37.7 37.4
,~ve.-2 30,220 L13.3 40.2
4 32.000 36.0 43.1 43 .. 1
L~ 25,500 17.0 42.3 42.3 14.2.1 3 30,200 41.1
~ve.-l 28,750 26.5 42.7 42.7 6 29,400 40.9
~V8. -2* L.-29 ,800 1Q..!_729,100 29.6 39.0 38.8 ~ve.-l 29,800 40.9
I i!l. 3 1 32,800 40.0 39.5 5 30,500 47.5
7 30,500 38.9 38.3
~-_..2..Q.1§_QL_._ .._1Q~0 39 ._£. 4,ve • .,..2 30,010 42.5
4.vA.-l 31,270 39.6 3'9.2
I ~2. 2 1 30,400 38.0 38.5 37,,8
I~2.1 1 29,750 38.8 39.2 2 29,800 27.0 41.0 40.5
7 3C',400 39.7 39.6 3 29,500 32.0 36.1 35.8
8 32..t-~OO__,_-i.!~Q...40 ! 5 6 30,750 38.0 40.1 38.5
~ve.-l 30,120 39.8 39.8 7 29,250 34.0 37.0 3fj,8
L.13-.hOO~-!.9 36.3 36.Z
IB2.1 2 29,200 20.0 4.2. 2 42.2 4.\1'8,-1 30,100 32.0 38.2 37.4
3 28,800 29.0 40.0 40.0
? 28.200 24.0 38.8 38~8 4 28,000 21.0 34,0
L._~.8,75)0 _~-&-~~9. 0 .139!~ lL- 2~.,300 34.5 37.7 37 -..1..-
4.ve.-l 28,700 27.2 40.0 40.0 ~ve.-l 28,650 27.7 37.7 35.7
5 29,200 17.0 42.542.5 irve.-2 29,730 30.9 38.0 37.0
~vA.-2 28,780 24.7 40.6 40.6 1"82.1 1 29,700 45.2 41.9
2 30,200 41.4 38.1
IB2.3 1 29,750 ' 38.5 40.3 40.1 L 30 1 300 43.9 41.6
2 29,000 35.0 37.5 37.5 ~ve.-l 30,090 43.5 40.5
Q.ve.-l 29,370 36.7 38. 9 '38.8
5 30,200 46.6 44.2
5 30,800 43.0 44.8 44.2
~ve.-2 ~10, 100 44.2 41.4
~ve.-2 29,700 38.2 40.4 40.1
IB2a** 2 31 30,300 34.8 34.8 34'18,
2 31,000 33.5 34.3 34.9 4
8 31,700 35.2 35.5 3502 5
~ve.-l 31,000 34.5 34.9 35.0
5 30,400 39.0 39.9 38.9
4rve.-2 30,840 35.6 36.1 36.0 6 7 8
*~ve.-l ~verage valuA
*~ve.-2 WeightAd ~vArage in proportion of flange and Web areas.
** anneal~d material 20
FIG. 2b SUlvll\1~RY OF COlvlPRESSION COUPONS
(~vArage Values)
Material
IU Flallg~
Web ~*
,~v'e, -2
I~2 Flange
IB2 Flange
Web
4.vo ...2
E
29,900 (9)*
28,750 (2)
29.580 (11)
30,120 (3)
28.940 (6)
30,000 (2)
29,200 (8)
29,580 (22)
efn
30~6 .( 6 ')*
26.5 (2)
29.6 (8)
30.4 (6)
30.0 (2)
30.3 (8)
29.9 (16)
*38.4 .( 8 )
42.7 (2)
39.4 (10)
39.8 (3)
39.6 (6)
43. 6 (2)
40.6 (8)
40.0 ( 21)
6 y
38.0 (9) *
4~. 7 (2)
39.2 (11)
39.8 (3)
39.6 (6)
43,3 ( 2 )
40,5 (8)
39.8 (22)
S1.~MM~RY "TEl'fSION ,COUPONS
(Q.vArage Values)
I 4.1 Flange
Web
i!.ve.-~
I 4.2 Flange
Web
,~Vf) .-2
IB2 Flange
Web
~VA •..., 2
30,230 (3)
30,200 (1)
30,210 (4)
30,010 (g)
29,270 (3)
29.820 (12)
30.090 (3)
30.200 (1)
30,120 (4)
29,970 -( 20)
32.0 (6)
27 14 7 (2)
30. 9 (8)
42.8 (3)
44. 8 (1)
43.3 (4)
39.1 (9)
42 t 6 (2)
39.9 (11)
43.5 (3)
46.6 (1)
44.2 (4)
41.6 (19)
39.1 (3)
43.3 (1)
40,.1 (4 ')
37.4 (6)
35.7 (2)
37.0 (8)
40.5 (3)
44,2 (1)
41.4 ( 4 )
38.9 (16)
CROSS ~ SECTI0N TEST
lViatarial
IB2
Test
T -- 0
E
29,400
COIvlP ~RI SON
QQ~IPRE~SION COUPONS
E d p dye
29,200 30.3 40.5
I~2 T ~ 1 30,100 28.0 36.20' 30,120 39.8 .909
Iij.l
IB2
IB2a***
T - 2 29.600 25.2 37.77 29,580 29.6 39.2 .963
T - 4 2~.340 27.0 36.72 29.200 30.3 40.5 0.907
T - 3' f 29.760 24.0 33.35 30,840 35.6 36.0 0.927
*Number of specimens
**vVeighted average in proportion of flange and web areas
***~nealed material
2b
Of
SECTION A
Section A
gage holes for Whittemore
strai11 gage
I I !
.l.!' -~l !+1+ ,. I
---->\ i~- III
! 2
\ 0'\
\ '\
\ \
\ \
\ \
\ \
\ \
\ \
\ \
\ \
\ \
\ \
\
\ ()
---------'1--
t
~
\
\
\
\
\
\
\
\.
\
\
\
\
-I\ -__-\-4O:_~~ )I
I
FIG 41 3 REPRESENTATION OF HOW RES IDUAL STRAIT':r l:iEASURElvffiNTS ltJERE OBTA lNED
3
\"\.
\
,..,'
,/ ,.
• ' ..y'
'-'$. ~-'"
!
1
..10Ksi
I~ •
);,., :....:~, <1' l~o~ .... ·~·I~~
"\f?(~ .r'R/:
.(, ......., ,0/ "
\~ 0 -', . .".... /)
........ .~~ () .r( /',/ , .'
l__~_~_~:~~ :~~.~~~~ ~_
.. ,~:: '~t-J --:-;.;/' ""
()
, I
.:
,I
'1,
: .~
;' .
I r"
I \,
ry .~
I
(
~
I
\
\
\
\
'~'
;+lOI(si ;
I, Jr,;) - ,/(' I ''-, ,\\ t/ " ~)" \'. I/. f) / ,,0 ~
I .-/ ~";</ /' .. ..., ...\ ','" ~ III ,s/O ,"Q" .....,_., ,
I r-Y /',..... .~, '. !
' .,",,~ ~':~/ tj--...... ~_v.~~-__~. -- ~;~~~ ....."~:-.: '''o~:''£ _._~ ..,..~.,'~,
"'0 . '/ ~ "
'':>''''''';:'/ ~''''
...lOI(si
T-Q.-' __
T-? _
_~'.~l
_~~.L (arlYlealod)
C0111pI'eSS iOrl
-~ tellS i011
8WF31 f{ES IDU.l\L SlrRESS DISTRI}3trll.IONS
4
IFIG.l 5' . CROSS .. SECTION SPECIMEN T - 1
I
..--±-
t
7t,r~~:tl -~\1i;: ~
H~~B
~
~~ c:::=:!_~ I:~
'1___ - ,~
DIAL
GAGES
Observed
Yield
..-c-.-o---';-;Q= ~ - 37/ ~~o_o -c ~-..-co c - • 3 ks i
/
;;tJ / ,...,,,0 -
,.0;" / /t:J / ,_~.-- 0 -
/
0/ I/f) P"
- /' p ~. ~ /-//'~ 1 ~. /)' Cross-S r> •/ i V / ~e,- t1.0n ./~rl / /,0'w' /;I 0 /
/
1 l ,/ d .D ! -
, / ~ -/ / J'" . I· ~
/ ,-:> /0
1
/ I '. d / I/ / dEB / /1 . '
/ /. SR 4s /0
I/
l6
f f
/ ~ ~
: ! ~~ / /p
I J /j ~ I~ ! !~
p /
I
0 !
. / 9
c I /
/ /' !
/
OV 1/ /
I .. jd
u;.c
1""1/ ....
I
a
/
/0
o
I
..I
;~
c
I
-: /Coupon ' 0
/
I
o
I'
6
I
/~
;¢
/-
I
/
COLTFOI\I
40 I f 0;0."'- 39.95 ksidc--
9
t If>
! (] !
! t
I ~ . Predicted
Yield
30
20 .-
10
if
ksi
en
i il.r.0,01 ---~
€ in per in
STRESS - STRAIN CURVES T-O
Fig.- 6
. .6'
Ksi
30
20
Cross-section
Web SR--lts
L -r~'"~t\~~""-:'-Jl .r ~w'
10 ~.
-t- rl) r-f
• • •(\j (\j C\J C\J r-f
~ ~ t=l P:"l ~H
,I· I -]: "H'" -~·f-l ..,
40 80 120
L
r
Fig. 7
160
7
, '"
T--O
(from res ...
idual stres
measure-
ment)
Cross-Section
Test
flanges
~"''''''''''r;Z ~.~.:~.~.:.~ \ ~':7f1 EI~/f:'
..--- \--~ \ ~........ .,.._........ ~ ,v
'" ........ ........ ---=..~~ \
, ~..... , ~ \
........ '~ \~~, ~ ....,-~~. ~ LX
,-, ',~.'-~,..~'~\...30
40
(j
Ksi
20
10
(modif'ied)
Idealized resid. stress distribution
40 80 L
r
12~ 160
Fig. 8
8
40
30 -
20 -
10
Coupon
vJeb SR..4 t s:
T--O
40 80
L
r
Fig. 9
160
9
0.6
«(
rr~)'I
0.4
Et from cross~section tost
20 40 60 80 100 120 lirO 160 180
L
...
"t"
-!.o
T..O --,.- T..2
T..l -· .. -T...3 (a1111ealed)
T-4
COLmfIDT CURVES FROrlI CR03S ....SEC'rrOl'T T~8TS
Fig. 10
1[)
.(;'\i'
10.1+
0.2
0.2 0.4, 0.6 0.8 leO Ift 2 1.4
'I'
T-O T-l T~2 T--3 T..4
____ 1·..._"1 -----.. .-.._1...... _ .... 10· .. "1""'1IIIo"-" ..--.... ...... 111_ -.......,.............._-
IB2.2 Ili2 .. 2 IAI.l. I132a IB2.3(anneaJ_ed)
F IG. 12 COLUl\ll\f CUFrVI~S 11111 OlVI IDEj\r~ IZ1~D RES IDUAL STRESSF~S


Further results on the influence of residual stress on column strength

https://preserve.lehigh.edu/cgi/viewcontent.cgi?article=1041&amp;context=engr-civil-environmental-fritz-lab-reports

Further results on the influence of residual stress on column strength

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