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s. Beedle and A. W.
FRITZLABOENGINEERING
TORY LIBRA,flY
H,,}bel~
,!~
J.~i'j(I
" .
July'. 1957"
'I, ,
Revised November: 1957
by
Lynn S.' Beedle
.'/' I'
SUMMARY--,REPORT
Fritz Engineering ~aboratory .;' :-.Dep·artment of ,Civil ,Engineering'~'·'::
,Lehigh ,University,'-,:Bethlehem, Pen~sylvani.a '
_Fritz Laborato~y Report No. 220A.27
;',' , :. '" .',' ~
-.
,'-,
This 'work has ,been carried out as a ,part of an il1vestig'ation sponsored 'jointly by''', ,the Column Research Council" the Pennsy!vania,:: 'Departm~n~t 'of Higl1ways and Bu:reau o~ Public'::"'"
-,Roads) and the~ National Scie~ce -Founda'~ion•.
ON
RESIDUAL STRESS AND THE COMPRESSIV~PROPERTIES OFSTEEL:>··
",,"-
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'1.1:';'
\ { ~, ., -" ~
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- - -'- --_._--~_._._----------------
.' '
"
B. MECHANICAL PROPERTIES
. ~
,,'. r
22 ~;,
23 ':',',• j"'t •
on .Column .Strength ,';, ",., 12 ,:. ,:.', " " .13:
1415161818
'; ::'
10. ,General Influence of Residual.Stress11. Effect of Flexure Axis12•. Column ,Curve --'''Residual Stress" Method13. . Column .Cul.'Ve -- "Stub. Column/' Method140 . Colurrtrl ,Curve Approximations .:',,'15. Effect of .'Continuously Curving JStress~St~ain":Diagram!::'16•. Cold-Be~ding,Residual.Stresses" ,
19., .Residual .Stresses20. Column .Strength ,:',: ':~".,
1.· ,Formation .of Res idual .Stresses2. Magnitude and Distribution of 'Residual Stresses3. Variation ,of 'Residual Stresses4. Influence of 'Residual ,Str~ss on, ,the Apparent' ,
.Stress-Strain Relationship "5•. Cold-Bending ,Residual ,Stresses
,TABLE ·0 F_..~ - - - ---
17. '; Cold-Bending ,Residual ,Stresses"18., ,Cooling Residu~l Str.esses
D. ECCENTRIC ,COLillfNS
6. Proportion~l Limit7. ,Coupon ,Strength, Accept~ce Tests...· and,.Strain ·Rate "80 Yield ,Stress Level9. ,Stress-Strain CUl-ve ,
.c~· .CENTRAJ~ LOADED COLUMNS
220A.27
v.· TEST TECHNIQUES
ACI~Ot(LEDGEMENTS
I. INTRODUCTION
II. GENERAL ,STATEMENT 'OF 'RESULTS OBL\INED
,:REFERENCES
IV• BUILT 'UP MEMBERS
VI•. REPORTS COMP~ETED,.;' ,".'
III. ROLLED ,SHA..PESJ.... RES mUAL .STRESSES
"
., ' ~' ~.
L '.(
'...,. .-.
.....
, ,~ '. . . " )
1:1
......
the magnitude and d.istribution .0£ these" stresses, and (3) to develop
The project on ,the. "Influen,ce of Residual .Stress on ,Column ,StreI).gth'
and the Mechanical PIloperti'es 0,£ 'Rolled Sh~pes" at Lehig,h University
forms a part of the work of .'Research Conunittee A o~ :the Colu~ .Research."'·~ ~ . . , .
1. ,I N T RD Due ,T ION- '- - - - - - - - _.- -
The first pronouncement of the Council (ba'sed on, ,the recorrnnendation
The objectives of the investig~tionwere: (1) to determine .th~
behavior of C91u~s containing residual stresses, (2) to determine
220A..27
methods of predicting the influence ,of resi4ual stresses on cplumn
Council. This committee was assigned the task of ,dete~ining the
column strength ,0£ as ,much ,a.s 30% ,below th4t which ,would' be in£erre~:.
Early work clearly showed this to be true) and in later studies
completed prior to the time that this general investigation.was
it was shown that residual stress~s mightaccou~t £or'red~ctions in
This formula cannot be applied to steel .columns ,if the'stressMstrain'
from coupon tests.
relationship be ,determined from a small ,coupon ,cut from the section.
,strength. As a ne~essary parallel study, the program included a de-,
of Committee A) was its Technical Memorandum No~ .1 entitled ,"THE BASIC
.COLUMN ,FORMULAI1 .(l) This memorandum statas ~hat the ·critical
" relationship'· between material properties and t~e strength ,of colunms ~
, .a column is given ,by the equation
, ,
tel.--mina.tion of the basic yield s~ress level of the material of"which'
columns'would be fabricated.
" .'"
yield stress level.and of the magnitude and.distribution .0£ residual
-2
Applicabi.lity of th.e st.ub-column as a basis 'ofp:r:e,dicting column' strength. " ,Influel1ce of cold-straightening ,on ,column ,strength,. ,'" ,,'
. Columns with large d/w and bit ratios.Statistical collection ·of, data on yield stresslevel (cry) "Comparison of 'mill t'Etns1on ,ttits '"with basic 4
compr~ssive properties •.Column control tests.
This tangent-modulus may be determined by two methods) '.>"
It has shown that the strength :0£ centrally-loaded A7
The remainder of this repor~ .aims to present .the results
l?h.~.se 1:
Ph.ase 2:Pha.se 3:Phase .4:
Ph,ase 6:
The study was arranged in the following phases:
220A.27
A. gene.l~al ,statement of the results obtain'ed on this project is
Q.!
2.
It is the purpose of .this report to summa:cize the findings of
Other phases related to this study are: ,
Phase 7: Angle~ channel ,and I shapes.Phase 8': Low alloy steels.Phase 9: Working f~rmulas for practic~l design.
· Phase 10: Local buckling.Phase 11: B~ilt.-up.members.
the investigation to date and to discuss the' significance thereof.
con.tain the" detai~ed experimental and theoretical ,work.: -
Reference is ma.de) t~h':cougho'ut J to the various p.rogress ,reports
both of which rely upon ,the state of residual .stress in the member.
modulus~ Et~
as follows:
structural steel colum~s may be expressed in terms of the tangent-
The project has also provided information .on .average values of the
stressesc
, '
~ . \ ~ ,
(1) Format.i.on of Residual Stresses
Residual stresses are formed.in.a rolled .sha.pe as a ,result of
plastic deformations.(2) These deformations always occur durinB tha
'process of cooling from tIle rol.li.ng tempe.raturtf to air C,Onlpt.lrlltul::e;
,,' ....-
220A.27... ' ",' ~,
I ft -, .
, 3. R O' L L E 'D S HAP E. S------ ------,A. RESIDUAL ,STRESSES
(Fo"!'"Illation of residual stresses) magn"itudeand di.st'ribution, influence on ,stress-strain,relationship> cooling and cold-straightening"residual ,stresses) .
~ 4.. •, .. .. ,
shape cool much more rapidly than ,others (compare the tips of A ~r8
deformations ill the slower 'cooling portions.
As an illustration,) co~sider the wide flange shape shown in
.Fig l(a) .and assume that the flange is isolated from, the rest of the
member, sketch (b). As the material starts to cool fromth,e rolling
tamperatuI'e) the flange ·.edges first will shri~k more rapidly thaxi t:he '
flange center (see. solid lines in Fig ,lb). '. Since the ,material .at' ~.the·
cente.r ";Lags behin,d"· and provides restraint J the edges will be in.a'-1'
state of tension and the center will be in compJ;ession ..as. shown~ ,
Because the ,material in the compression zone at the ~center is at
high temperature) the c6rrespond~ng yield stress level will be
practically zero and co~sequentiy the center will flow plastically•
.}~y stresses at this stage will be of. low magnitude. Eve~tually the
edges will cool sufficiently so that their yield stress level increases.
The center of the plate) being at a considera~ly higher temperature than
,the edge, will att~mpt to shrink further'with the resulting deformation
, ~
·4
. ,
results in a compressive stress. at the flange tips and·· a t'ensile
shown di.a.gr,~~.t:ically in Fig lc ~ ~he final sta.te of stre.ss thU'8
stress a.t th,e plate' ,center.'
220A.27
the welding operation. (4)
Residual stresses also are formed as a result of fabricat~on
operation.s. The process of cold-:-bending ,tl1at' is required in the
Ist~a.1.gh.ten.i.ng operation and the process of cambering both ,introduce'
residual stresses. (3) ° Residual stresses are,also introduced
coolir.g pprti.oXl:s of the section finally, will be in.residual c.ompression"
(2) M,,,+gn.itude and .Distribution ,0£ 'Residual Stresses
Methods for determining cooling residual stresses in plates
and fo'/: obtaining a 'qualitative estimate of 'stresses in..WF shapes
have been p~ese~ted.(3) The magnitude and .distribution .of these
streases .depend on the shape .of cross-section, initial temperature,
coolin.g conditions~ and material properties •. Usually, the ,fastest
and the parts to cool last :will be in ,residual tension.
The measurement of residual stresses confirms the tre~ds pred~cted
theoretically. A considerable number ·0£ such measurements have been
made and they permit a good estimate to be made of the magnitude and
dist~ibution..of residual stresses. likely to be e~countered in hot
rolledWF members. (3)5) ,Shapes were se~ected to have widely differing
geometry '~or the purpose of ,~ing thes~ measurements. Figs 2a) 2b
an.d 2c present some of the measured results J showing th,e' magl1itude
ar~d distribution .0£ stresses· across the .flange and web•. While the
, variation is considerable.,· the general pattern' ,in .the .flange 'is simi,lar.
-5
G:(~"OUP 1 ~
G:coup 2:G:coup 3:.Group L}. ~
Gro'up 5 ~
~n Ref (2) was described a method for'est~ating .the residual
st~ess magnitude and distribution in ,the flanges from the results
of a stub-coluuul test.
Ta.ble 1 contains a listing of ,all shapes 'studied in ,the proje'ct.':
l.l~ o:::dl?r l~c· eompa1:e ,different p,ropertias nlSasured ,during the same. tests,
"g',coup numbe~s" have .been assig1"~ed as shovm in ,this tableo '.·These
numbe~s also serve to ide~tify t~e tests used in ,obtaini~g a gi~en,
avera,ge. Ot" cu~\re" 'The .following information .is .~cluded in .the
diffe~ent groups:
Cool:Lng re.sidual stresses (all columns d/b ~ 1.50)..Cooling residual stresses (all beams d/b> 1.50)R.e.si.dual stresses by s6.ctioning and by stub column. ,testYield .stress level~-all stub coluUll1sYield stress level--stub columns and mill tests
.G:t~o'up 6: "'yield .stress level--stub columns, mil.l tests) simulated' ','mill te.st's·
Group 7: Proportional limit frolu all stub column tests .. 'Group 8: Proportional limit for certain ,stub coiumn tests.GJ:'oup 9 ~ Col1.11JL.~ tests--weak axisGt~o'Up 10:. Column tests--strong axisG~ouF 11: . Column tests--built-up members
Table 2 presents the average value of the residual stress at
.different po.sit-ions in the -cross ..section ,and gives the variation. as..
wallu Insofar as column.acti~n i~ concerned) the most important of
the st:cesse.s are tho'sa at the flange tip,s (O'rc) and the .Average com"
pressive stress th~re is about 12.8 ksi .with "a .m~imum compression
.of 18 ~ 7 ksi ',and a miliimum. compression ·0£ 7" 7 ksi.
The magnitude of tne residual stress at the flange tips may also
be' dete:crrd.fl.ed i-p,dire.ctly from a stub column te'st) and is the difference
be.tween the ,yield s~r~Bs level and the proportional/limit. This
value has been found to be about 13. 0 ksi. (6) .
, , . t~-.'''''''77!TT1''....~;:-,-pr''·:''H':'':Ttt~"':l1t:~~~~~nmT:;.t~rr=r.:':!c::.:r::E'[=m~'Q:t'Izr\'?:;;!1r1I.~J.Jc·~...;~~~J:n~'72"~1::':l-J;; ..'t!j·"}~'l".tti,{.t~u.ir.?z·:i.t~~"-m~;£'-:J'tJi!<\'f.~~":~~01~<:L~lT.Jl.'U['i1]I:n'"mmg;l:t:;~,:;:J" 1
.,. ~ ~.. .. .• i ~. ~ .. I of ~ • I
22Q.A..27
In, addition to avera.ge values, Table 2 give's the maxi.mum and
minimt.Im values of measure.d resi.dual, stresses. ,Fig 3 gives the
. -6
f:r~·~querJ.cy d.i.stribu.tion .0£ flange-tip stress' as .det'ermined by, actual
sectioning (Fig 3a),(3) and as determined indire.ctly from the propor-
tJon.al limit: obta:ined £orthe SBJl1e group of ."stub-columnlf tests.
(Fig 3b)
1~e vaxi~ion of residual stress within.material from ope ingot
is rela.ti·\rely small:l but larger vari~iol""LS may exi'S't .between mat~rial~.
from different lots.(2)
F..ow do ',cesid'ual stresses vary along the le~gth .0£ a column.?
n~eo~etical stlidi.e.s 'show that cooling ,residual stresses are
c01tstant along the raember except for a distance approximately equal
to tb.e la.:rger cl~oss ..,aectional. dimeIl:sion .a.t the ·ends •. Measurements·
a.:.t·e in .a.greement wi.th the theory as shown .in Fig 4. (3) Fig 5 gives
a p:f.C.t:uR~e of "'\Tsxi.ation .of the compressive re'sidual stress at flange
tips (arc) as a. function ,of the geometry of cross-sectional shape..
.~1hile t:h'ere .seems to be a trend, no pre.,cis'e relationship is evident.
(4) In.fl~J-en.ce of R.esidual. Stress on the Apparent :Stress-Straill Relatiollship
How do these ,residual stresses affect ,the average stress-strain
.relati.oIl.sb.:Lp of au, .entire· member? Fig 6 is presented to show this
influe.n,c.e diagramatically. ,Sketch (a) shows a;' short length of a wide-
flange srll.Q,pe,\vith .a simplified linear 'distribution of residual .stresses.
The c'uttiT.l,g of a coupon from the flange of the member'vould ·relax the
residua.l st~esses and the stress strain relationship dete~ined from
t:h,ls co'upon ,would be as shown by the ,dashed line in sketch (b).. If now',
we consider' the load as being ,applied to the entire cross-section
,I
,I
if~ j
it
;1
,J
-7220A... 27
contai.ning its residual stresses it is evident that when .the appl:i'ed
stress equals the ,valu:e (cry - arc) ,then yie·l,.~i~g will commence at the
flange tips (see sketch ,c). ThUB).'
: I ."
•• q 0 • (2)
Thereafter,) the average stress and average strain .are no longer .
proportional. to one' anoth'er and a no~-linear' 'av~rage stre'ss-strain
relationship. for th'e s'ection .as a wnole re'sults. .Above the prop07'tional
limit the strain.is given by
€ := ~ (cry. crrxo> · . . · • • • • • (3) .
with crrxo defined i~.Fig6c.(2)* .The yield stress level is unaffected\
by the residual stresses.
,Thus, the .effect of residual 'stress on .th.e. stress-strain ,relatiol1.-
ship is to reduce the proportional limit and to cause t~e str~ss-
strain ,diagram to be 'non-linear above that ~poi~t. The proportional
limit may be computed ,from Eq~ (2). For a' typical .WFcolumn (Af/~ =3.0)
,with ay = -34 ksi ~d with O~C = -13 ksi ,the theoretical stress-strain
,curve is as shown in..Fig 7.
To obtain experimental correlation with the .above predictions, tests
and ,measurements of stub co:Lunm's have be'en ,made .as 'sho~ in ,Fig 8.
,Typ~cal r'es'ults are shown' ,in .Fig 9 which .a~so shows th.e' contrast'with
.the curve bas'e'd on coupon tests. In .Fig 10 is the stress'-strain .cu:rve'
of an annealed stub column; the ,comparison ~ith ,Fig 9 clearly veri~ies
the influence of residu'al stresses '011 ,the stress-strain curve.
* The curve in .sl<etch (b) of ,'Fig 6 assumes the s11ape to be made up oftwo rectang"les) ass'wnes' linear distribution ,of residual stress, with'qy,~ ,40 ksi) and ap = 20 ksi.
(5) fgld-Bending Residual Stresses
-8
Residual stresses due to cold bending ,can be predicted with
reasonable accuracy,(3) assuming certain initial cooling stresses
and the extent of .deformation•. Some measurements are shown in Fig 11.
In general) the maximum and minimum stresses are of 'the same order of.:
magnitude as the cooling residual stres~es•.While the influe~ce on
the stress-strain "curve might .be predicted) this has not been "done
as studies (to be describ'ed below) show it .to· be. unnecessary., ~.
, B. M:ECHAL~ICAL PROPERTIES(proportional ,limit) yield stress level) labo,ratorycoupons--accepta~ce tests--stub column te~ts; stressstrain relationship)
(6) -Proportional Limit
The general effect ,of residual str'esses on the stress-strain
relationship was .discussed in Section 4 above. The proportional
limit is reduced below that ,obtained in .coup~n tests) and either
'may be computed from Eq (2) or may be' measured in,a stub column.test.. .
Fig 9 cle~rly shows this effect, and further compariso~s were ,made
in',Ref 2,. The average va'lue of the proportional limi~ is 21.7 ksi
(as determined indirectly by 'residual 'Stress ,measurenlents and usi11:g
group 1 and group ,4 data); the average value determine~, by'" the offset,
.method from stub column tests is 20.17 ksi, and the frequel1cy distribution '-,
curve for thes'e ,40 ,specimens is shown in "Fig 12a. Since .the offset
.method was ,used to ,determine the proportional limit (Fig 12-b), the
actual value is even lowek than 20.7 ksi •. It is·to be expected that
the stub column proportional limit ,would be lower than the value
determined indirectly. In the first place) the ,residual stresses are
.~
Factors such as uppe.r 'yiel,d point) strain .rate) and ,web. strength
deviations from these averages which ,will be ref~ected in a lowe~ing' ·
on the four corne..rs· and on two sides J and of cours'e tllere will b'e
" :
. "
.", .; ....
·9
Small inacc~racies of' aligr.unex;t also,,-,
• .f .,*.t + ~I ~ ,
220.~.27
'.(7) .Coupon Strength, Acceptance Tests, arid Strain Rate
of the proportional limit.
influence the observed proportional limit.
• .j
probably greater than the measured value by a small amount., . Secondly·~
the flange-tip values of arc in Tabie 1 a~e averages of measurements
versus flange strength cause the yield stress level of a. full cross
th.e yield level still fu'rther becau'se the acce.ptance test is made
properties. between ,web and flange, of 'a ·rolled ,shape) and this lOvlers
from the web. Finally the stub column tested at "static" r~te> shows
.~ ... ..
the same material. Tests 11ave shown that .even' the livery slow"
stre.ss·-strain .. curves that .may be obtained .dep'ending upon the type
section (stub c~lunUi) tested in~he, laboratqry in co~pression, to be
of the uppe.r ,yield point effect. Also the mill'-,type test gives a '"
laboratory strain' rate used in testing coupons (an elastic strain
, .of test that is performed. The ASTM acceptanc~ ~ype ~est may show·'
a ,X2:;:.l'!....stress 'which i's higher than the: yiel..d stress level because.. ,
,ma1:1~edly less tha11 the tensile yield ,stress level detel:mined in tr4e ,"':,' ,.~;
routine AS111 acceptance test.(3) .Fig 13 illustrates the different
,yield stress 'that is higller· th~ ,the 'correspondin:g static value' for
the effect of residual, stress ~pon'"the.\ stress-strain' ,cu~i'e.. alld averages
:~t:·~'..~~i' 4·~,;f~.'£e,n~:eJ~, ,~.~,tween '/.w.eh, .("and flan.ge m,aterial.iIfIII"" ...
xate of :~ne ~icro-inch, per inch per second) can raise th~ apparent "
',yield stres~ level by as much as 5%. (7) 'There is a difference in
220A..27
Concerning strainrate,.a study recently completed(8)on twenty
specin~ns cut from a 4 by 1/2 in~h .flat bar resulted in typical
curves shown in Fig 14. The influe~ce of strain.rate is quite
evident. In Fig 15 is shown the strain rate effect for these
specimens. It plots the. .ratio of mea.sured yield ,stress to,ust:atic"
value as a .function of the plastic strain rate •. I~creases in the
yield stress level of as .much" .as 16 per cent were measured in the.se
tests) and other .data show in,creases as h~gh as ~8%. '" Such .increases .'
could be expected in routine accepta~ce te~ting.,
'..,
(8) .Yie.ld Stress Level
.What, then) is the yield stress level of material .rolled to AS~-A7'
specifications? The answer depends on how the yield stress level is
measured. It 'may be ,determined from the results of an ASTM~~ccept~ce>
test or it may be determi~ed from a laboratory coupon test or from
tIle results of a stub column test. The yield .str~ss level obtain'ed .
from a stub column te'st agre~s' well .with .te~ts of tension and com-,
pression.coupons if ~he results of the latter ar~ averaged and if
both .the .coupons and the .stub column .are tested at the, "static" .rate'. (7)",
.An important relati011-ship insofar as establishi:ng a value for
th'e yield stress to use in' .a basic column, formula is the. comparison
between .acceptance test ~esults and .stub~column tests. Because if
this relationship can be' established ,for a fairl,y large sample, then
.this same ratio could be applied with .some confide~ce to the larger
body of acceptance test data available in the mi14so Figs 16, 17) a~d
18 show the distribution of the yield stress as determined by s'
number of ~methods as follows:(2)6,7)
mill test results may be approximated ,within about 4% by a laboratory _.'
test timt si~lates mill test procedures. The 'average value of the
'Comparing Fig 18(a) with Fig 18(b) shpws that on the average the
L ' ~ .'
, '~,
..11
Fig l8c
Fig l8d
Fig lab
Fig 18a
Figs. 16 and 17-#0- ••• '
ASTM Acceptance Testing in the millASTI1 Accep'tance Tests for 1I group 6"materialSimulated ASTI1 Tests for "group 6"l.uaterialStub-column tests for .l1 group 6"ulaterialStub-column tests (all availabletests) (group' 4)
(1). (2)
(3)
(4)
(5)
220A.27 .
control group (Fig 18a) was 42.9 ksi. Fu~ther 'comparisions of this
type are shown in R~f 7.'. ~', I
'i, .'_.,
Fig ~8(c) pre~~nts the results of the stub column ,tests of
control group 6 (see Table 1). The average yield stress level for
this group is 34.0 ksi with variations from 24.6 ksi to 43.0 ksi•
. The ,average value of the yield .stress level for !1l,stub columns
. tested in ,the program was '34.5 ksi.. (F:lg lad).,: ,.
I I
i,, '
,Comparing ,Figs 18(a) and 18(c) the probabl~' ratio of the basic
':""'>',:.-:. compressive st:rer~gth to tne, "acceptance test" strength. was found .to ,
•• ' < be 0.79. In Fig 19 is plotted t~e distribution -of the individu~l
. " ." _ratios of stub column to mill test yield stress.· , The average is
0,,80 with a minimum of '0.62 and 'a maximum of 0.92. From ,this
information it would be concluded that the ptatic yield stress ,~" :
level of a wide flange column ,averages about 20% less than .thet~iI' ,
valu~ obtained in ,the As~-type acceptance test.
Applying this average ratio (0.80) to the average' ,value of',the
'mill tests shown ill ..Figs 16 and 17 (42.6 ksi) one obtains a probable
'compressive strength for this material .0£34.1 ksi. The average
-12
,~tu~ obtained from all stub colulnns tested to date is 34.5ksi sugge~ti~g
thAt th.e sample .was· fairly representat:Lve.
(9) Stress -3 train. Cu:t:\Je
, ": ~:I
.;~,
'l""'he average stress-strai.n CUl"'ve for ASTM .A-7 steel was given in ',Section
4 and the curve is ShOWIl in ,.Fig 7. ,In ,Fig .20 is shown ,the average
,stress-strain .curve detezmined from stub column tests of group 7 •
. Th'e ,curve of Fig 7 is indicated by th.e .dotted line,? showip.g excellent
@
correlation.
" Co CENTRALLY LOADED COLUM.NS(bucl<ling str,'ength .of ce.ntrally loaded columns;method based on ,residual stress measurements;met·hod based on ,stub column test; effect of continuously cu~"ing stress strain diagram; mambers with 'cold-bending residual stresses)
(10) .General Influe.nce of Residual Stress on.Column Stren.g.th
C,olumns of a material like structural steel .with .a definite
yield ,stress level will h.ave a: reducedbucl<.ling strength once the
total stress (residual plus applied' stress) reach'es the yield point.
The reductions below values that: otherwise ,would be predicted on
the basis of coupon tests are the largest when -the slenderne~ss
ratio is between, .70 aa.£.d 90.
In order to show the general influence of 'residua~ stre'sses
on column strength it will be assumed, for the moment, tha~ Eq (1)
is app 1icabIe 0 ~~,
Actually EqQ. (1) applies only' to a special idealized case of a membercontaining residual stresseso However) as will be seen later) themaximum strength may be expressed in terms 0'£ Et but in.a modifiedform of Eq. (1).
a stress -vs- Et curve ,may be d1rawn ,as ShO·v1D. ,:tn .Fig 21(b). ABSUlJi...:tng
t.he applicability of the tangent modulus fO:t:rWJ.lB.:I t.11le ~es'ulting col"uw,-'
cu.:.-ve of stress -vs- slenderJ.1.ess ratio is s'h.ovJ7J. in ,Fig 21(c);I and th.e
influence of residual stresses when bucl<.ling OCC'Jrs in. "the inelastic'
range is thus seen by comparing the, .solid line with the das~ed' line
obtained for an ,f1ide.al,coupo~tr 1\Tithout residual stXf~sses.
Froceeding now to a discussion of t4e pToblem of dete~~ing the'
strength of an actual! colmun~ the basic equ.atioll for the:cxitical
strength of a column .containing ,residual ,stresses was derived in. .Ref'
(9) and is give7l by
Pcr ::;ODOOO (4)
where Ie is the moment ,of inertia of that po~tion.of.tae cross-section
which .remains elastic. ,(See Fig 6(d):I for ex.:'"rJmP1e).' m te.rms of t.~e
average critical stress, Eqo (4) may be .written)
.·0 .00 (5)CJcr = 112 E Ie/I.(L/r}2
Eq (5) is the basic equation for a column,co~~~ axially symmetric'
cooling _residual stresseso ,S~ce the fl~es contribute.significantly
to the fle~roral resiStanc'e, EI, it is thus 'eviden..t t.hat residual
stresses in t.he flang'es are of more pronounced influet+Cs on c.olumn
,strength t.haJ.1. are residual stresses in .~e .we-b.
(11) Effect of Flexure ~~is
There is a pronuunced difference in the behavior 'of as-delive~ed
column.s that is dependent upon ,the axis ahO'iJ.t wM\~ 'the me:mher bends.
".,'-14
This follows from .Eq (5) and is evident by an ,examination of Fig' 6(d).
Columns of a given sle~derness 'ratio in t~e weak direction, allowed to
bend in that direction) 'will carry' less load than columns of the same'
slenderness ratio in th~ strong directio~) allowed 'to bend in that
direction.
This difference in behavior may be shown ,as followso' For a
rectangular section bent about the weak axis the quant~ty E·le in.Eq.(5)
may be obtained from
. '. ,~ ..
E Ie::: Et I, ••• '. • • (6)
and Eq (5) would reduce to Eq (1). Eq (6) is also very nearly tr.~e
only a small por~ion to the moment of inertia and thus the action is
similar to that b£ two rectangles. However) ~or the rectangular sectio,n,
bent: about its strong axis and for an H-section bent about·i.ts weak
axis, the term EIe .will be considerably less than,Et!•. Thus the
buckling strength will be iess than t~e value predicted by.Eq (1) and
would be computed ac~ording to Eq (5).
This difference was shown .in Ref (9) and Fig 22 illustrateq it'
for an idealized case (parabolic residual stress pattern, residual
stress at fla~ge edges e,qual to -20ksi) re'~1dual at/ress at flange
cent~rs equal to +lOksi) yiel'd point stress equal to 40 ksi, effec.t
of web neglected~) ,The low~r c~rve is for flexure abo~t t1'l:e weak
.axis of an,H-secti~n) while t~e upper curve is for flex~re about t~e
strong axis ..
(~?) Colum~ Curve I1Residual StressU method
There are two· methods for obtaining the solution ,to Eq (5) for
1',I,
~.
.:~iP:8fJ).~f:?>~T:;:~~T;;:~
, 1 , . l' .•
--_·_~~-~"--_T_---------=~~~_.-w~~~~~~~~TT-::-j-r:;3·17;~·<!
220A.27 -15I
.These were described in Ref 2, Chapter III. The ,t'residllal stress"
wide-flange shapes with axially syrnn1etric cooling residual stresses.'
methods'requires t~e measurement (or estimation) of residual stress .~.
The residual stress pattern is next,
I
magpitude and distrib~tion .and a knowledge of yield stress level
from ~oupon tests orotherwise.
approximated by an a~alytical ,expression. A .. solution to E,q (5) may
then be found by obtaining an.expression for ocr in ,terms of the yield
treated in Appe~dix III of ~ef 2 ,and in Chapter 3 of R~f 7. Both
condition,2Qd by o~taining an expression for Ie in terms of the geometry ,~
at the rield condition. ~e solu~ion .will obviously depend ..on tq.e',
. distrib~uion of res~dual stresses; a number of typical, cases were
,referen~es contain ~~merous exro~ples, ,Fig 22 is dr~wn ,using this
technique except th~t the effect of the web has been ~eglected•.. ':'
.',
(13) Column Curve t1Stub Column" Method
The second method for obtaining t~e column curve is based on
a determination of the ave~age stress.,-strain, curve for a "stub column"
which contains the copling stress~,. For flexure about ~he strong(x-x)i
and tl1e weak (y-y) axes the 'following approxima~e.eiquation.shave .been
derived(2)
E ~ex, '):~. -'.
E~Y :,
= AEt· - 2/3 AwE,Af .+ Aw/3
3
~;j
....... , ~ .., (7)"
\vhere Af = ar-ea of both flal1ges of a,.WF shape a~d A.w =. area of -web.
Since for most ·WF col.umns tl1e rat.io~_.Af/~w is about ,3) Eqs <?)
reduce to
E Iex~-x
,m
••• II •.• (8)
How well ~do the ;l1 r esidual stressll and tIle " s t'ub c·olumnlt methods' ,
A simplification to Eqs (7) or (8) mig~t be .desirable for use,· ..
Eqs (7) may be used .either until the web starts to yield or 'until
-16
(9)CI .......
_ Et't" -_
E
220.A.27
where ~ is given by
the two solid curves of Fig 23b could, .be- repl~ced by the following'· "
.simple relationships> the ,first of which 'is t~e' a·sme fo:rm as
suggest·ed by Bleich (}O)
(~4), ,Column Curve ..L\.pproximations
strain CU1:"Ve ) and then ,.determining the tang·ent at various stress levels.. .',
the fla~ges are completely yielded. Examples of the use of Eqs (7)
resulting column C\.1rve is' a's sho'W'n in ,Fig 23 for the strong ..;md the
approximately parabolic in shape and that for ~uckling in the weak
as a basis for 'arriving at ,design ,fo~ulas. It will be noted ,from
agree? In refs 2 and 7 they were .compar'ed· and found to be in .very
weak ,axis of be~di:Q.g.
co~relate well ,with them.
good agreement for A7 steel. ,Further" the results· of tests ~lso
were given in Ref 2. Using the.stress-strain ,curve of Fig 20 the
,Fig 23(b) that the .curve for buckling in ,the strong .direction.is
·dire.ction ,the curve may be approximated by· a straight line" Thus,
'~ne magnitude of Et is determined by conducting a .stub column test of
a WF shape containing residual stresses, plotting the·average stress-
" ,..r : I,.. . ~ . ,.~ ..
'. I~ .:~ .! '"
""11/'..: ..//"~ , ~
. ,.
..... (10)
.. - ~ .I.... oJ
. WilJ3re cry is the 'yield stress ,level .and <Sp is the proportional limit.
:1"'he '~latte1C :value could be determ.ined ,either from stub column. tests or":' '" ':'. '
·i:f~~'~~idu.aI.. stress measurements u.sing Eq(2) 0 'UsiIlg .val.ues for. these
.'
',' '." ·pj;,,~i')e].~ies that seem most appropriate as a resul~ of t.his inv-estigation1
:"'. (lJy.= 34.1 ~i.E =: ;)0.0 x 1031-1:81, O"p.'= 20 0 6 ksi), Eqs (10) may be
.".' ~",' w.ci~t~- ..for.A1L"·st:.ru;c~ steel (with. stresses in ksi.)i:a. th.e fo:ou". ~' .
' .... '
a~: = 3401 - 9.37 x 10-4 $2,
rJyy.· :=. 34,,1 - .113 (L/r)
O"~,... ..... 0:.. . "" ~Ll05~ -:tY·· (L/r)Z--
(L/r ~ 120)
(L/r ~ 120)
('L/':· :/ ,120)
I ~ • •
~ '. .... " .. In the above fol.."1ml1as the yield s t.r~a~ level l~as b~'€.n talc-en as 34.1 .. "~'
:.. ' .....". ltSi; t!US\ yalue is so elose to the 8pecifica.t~oD..minimumof 3300 ks1'... ' .. '"
.'..':<; tWJ,t: :;·the -'iittter .D:dght jus.t as well be used as the11average' value in ... :.........: ..• ......... t' ..-' .4 + ........
;'.' ·' ~iti~g fA :deSigri. foxmula for ASm A7 ste~1'8o 'l~ ,as mill' t.est~ .., .' .' .:." '.' . ~
-I- ..... '~,.:.'...... pr~~tice: remains as at p·resent. The f.i?tCtor of ··safety woul~ accou:a1:... f+ .:,
:, .' fo~:, 'aIry': deviation' frow. this. average.
.,'
. '
I : ~,. : ..• I· -.". ~ _
.' ',... • '" I.t
. J~s 'an ,altern.a.te des,ig:n.pro~edure·,.O'D.e. e.ctl4d ,set .up .s., table of t .• ,,' •
.~~ ... ~,
I" sp~ci.Iaens. The ·Zppxoximat:Lcrn. of Eq (11) i.s also. shovtn in .~c.h all .t ~ ,~ 'II '" • •
_._.~---~~---------------------~=~.~~~==~~~-~~~~~~;;;~~~;
.' '
...... ,.. ~ ...t • ~ \ ... •
• • t.. ~
': line.·, ~pp.r~j'~t4.0D. . (Eq, 10) using 4 average -values £err the ngx'oup 8 t1
..-.':. ,.as-' detemdne.d .by tb:e: 11 Bt"ub-colun:m.11 method and also the straight
.'. :.\.:c ,.'~. .'.: -=~.; 'Values for use in Eq' (5) •..... ...1 ..
Fig 24 ShOV1S column curves (group _8) for a mrmber of specimens'
.. fle~~axis is shown in. .FIg 23 (a) and is the information used to·., ... ...:. "'~~a.J ~1 iIII
, ,~ . ~
220A.27
of the data in Table 1 has been included. ,While the 8?~tter is
..18
.....
considerable) the straight-line approximat~on is ~~idently a,good ona.
Fig 25 shows the results of weak-axis' colu~.n test.s (group 9)
L"1. comparison ,with th'e same straight-line app:c,Oximatiori. ,arrived at ,'~
from corresponding s'tub columns (group 8). ,'The c:trcles show the"
.maximum' load the columns carried, not th'e poin.t of first 'bendil1g.';'
:!he results of annealed columns are also shown.th€!~e•~ - ,~
.Fig 26 shows the ,results ~f cQlumn tests (group 10) and the
IJ'arabolic approximation ,of Eq (10) u'sing the a.pprOl)~iate·~verage
'properties from the', c¢rre'Spondi~.s tub c,?l~s (gro'up 8) ~. }...g~n. ,
there is good correlation between theory and test.
(15) iE.i.feet of Continuously CU':r'ling .St..~ess-St~ir! .Diagra.:m
ColunI1.lS of a .material ,without a definite yield level) and
.witl1.a continuously cUl.-ving ,stress-strain diag;,aJ.U ,show an influe~ce
· of residual stress £01: th'e whole range of L/~'C. For such materials
·and .for certain .residual .str'ess distributions') a~1~,r " bu~kli.ng stl;ength
.~ be achieved than for zero Desiduals (Fig 27). (l~)
(~6) 'Cold-beAding 'K(esidual Stress'es
The study of the ~"ef£ect of cold-be~din.g.. residual 'stre'sses on
'axial column.st~ength indicates that for short a~d ,medium le~gth
·,c'oiumns > these str·ess.es are no more critical that a:r:e cooling
'·'stresses. (3,11) Th.is means that findings based on .members w:Lthcooling
·p.atte.n1.S Will be cou"seJ:Vative when' .applied to' straight ,members wl1ich "
~contai~ not only cooling but supe~imposed.co~d-bendingstresses."
· '!he 'experimental cOIlfirmation is shown in ,Fig 28. (~l)
• f
; ~
i .
220A.27 -19
D. EC:CE~TTRIC COIJ1MNS
(17) Cold-bending 1lesidu'al Stresses
,.~though.a study of >eccentrically~loaded.columns was'not"
an important part of this investig~tion) some.work was done on the
problem. The critical stresse's for c'olumns ,with .equal end eccentricities·
and for axially loaded columns with ,residual stresses of only one ~is
of symmetry were predicted ,and the results are s~mmarized in ,Fig 29.(11)
(18) ~Cooling Residual .Stresses
As part of another investigation) the problem ,of the eccentrically'-
loaded' column ,with,~cooling.residual stresses has been .ex~ensively
treated in Refs 12 ,and 13. The exact solution is somewhat cumbersome
and an approximate method was developed in.Ref 11 which permits a
rapid calculation of the column ,curve. This is also summarized ~n,
Fig 29 and comp~red in Fig 30 with .the ,t1 exact lt method 'of 'Ref. ~2."
,4. BUILT,'-- - -- UP M.E:M B E,R,S'--~----
~ pilot investigation ,into the influence of residual stresses
on the behavior of built-up columns was carried Qut. (4) Certai~ of
the findings are summarized in the paragrap~s~ tha~ follow.
(19) Residual Stresses
~elded column's will have high ,residual stresses; the tensile
pressive residual st~esses may also be high) (Fig 31) a~d as shown
. stresses'w~ll be ,particularly high. For H-shaped members the com-. f
j
: !i
,220h..27 -20
in"Fig 32 these may be higher than the typical stresses measured in
rolled ~embers because t~e u~iversal mill, plates used in the specimens'
"already contai~ed cobling residual stress~s prior to .welding. ,Residual
stresses qave been.measured in.universal plates and compressive stresses
in flange tips of 5 to 10 ksi have been .observed (Fig 32). (4)
Since the magnitude and distrib~tion ,of welding residual stresses
.members ,.with cross-sectional shapes ot~er than t~.e H~section.. In
fact, it has been .poi~te4 out that the use of welded H-shape columns' ,
" .' ,wou~d be .rather unusual. .·The· "box" section would be more common,
Riveted . bUilt~up columns have a considerable vari.a.ti.on in
.residual stresses that is a function ,of t~e geometry of t~e, compo~ent
,pa,r,ts ~ ~'ig,33 S~QWS some measur.ements that have been ,made.,,
,(20) ~",Column Stren8!h.
The axial column strength of built-up H-shaped colum~s can be
predicted ,with ,reasonable accura~y by t~e same techniques as were used,'
for "ro11ed shapes with .. symmetrical cooli~g residual stresses (see
··:Sectiol~S 12 a~d ~3 above). ,T~e res.ults" correlated with ~ctttal. column
~ tests (group 11) are shown .in Fig 34.
,General conclusions regarding the column stre~gth of built-up
members (particularly' tq~'welded ones) cannot be made until further
st~dies are completed. Even tho~gh tQe strength of the welded
columns was proportionately less than t~e riveted or as-rolled
columns) it is very importa~t not to draw the conclusion that welded
columns will be, n\Veaker" than cor~esponding rolled shapes. The effect
"I" .'Vl0~ld be q~ite d~fferent if tQ.e cross-section .were in ,box fom) and
this is a common form used for welded columns. Studies of t~e effect!
of cross-sectio~al form.are ~ece~sary a~d are underway ..
; ,
~ I { ....
~-~"··"''''''''-t.,.-r-.~~''-:-~~~;-:~::·-::-:r.'~-:.,-.7~~":,-o,:-.r"~,,:,,,"~~s:~.~:,",,:~.r.:;:~=-.~~·~·l?:::;'~~-~f!~·~::;::::;':';7 ..":'~r::'~;~~~~:.':::?T'r;~~7:"~~,:"~:'!""~f:~~r7':'~;'9~:-::rr:;:~':'.:·:''::~t:~r~~m:,':li11'
220A.27",
. .~8, a result of the project, numerous technique~ were.developed
·8.tld reports 'i:SS\led .describing them. The details 'tv-ill l1.ot be repeated
here J but', eli€:, ,type of lueasurement is indicated .and, the a.ppropriate .I ~. •• l • j I I
reference report noted ·as ;follows:
Coupon testing--Reference (14)',Stub-colunm test-~Referer+ce (15)Residual.Stresses--Refere~ces(3~.4) ~6)
,Column tests--~e£ere~ces (2) 17)
, I '. ~
. ,'". "
. '"i
6. C011PLETED.-. - ~. ~ -- -.- - .-. ,.-
In .addition .'to this. paper; the reports com~~'~ted on,'th~ 'project.
are' Refs. 2-8, 11) ~4-17 and Refs 18~24..
• . I , w ~~j: ~ ~, J I.'
; ,"
.,
"
. "l'
., .. - -==-r~",~··-;~,:=-~~:::~==::,=::::-:,·:::::C::·::::.::::::':'~:;~-:;';"-;':;;;;;;;'h.Ji~:'-;:;~;~;:;~~~·::;;;;·;;~';;~;1!~"~;r,;~!~.~~~WJj;;,~-;~~:?r~t<T;~~;(~.,r,(:~~R~:;~~~13~ /,:~~~~1~J~~:~r7rrri:h~mijlY'i~frnry:m~1~~7~~!'itt
, .,. ~ , j ~
., ,;- ~ ~ ~l ¥. ~
" ,
, ~ .9. ts li Q R1 §. ']? Q ~ ! li 1.,E-• + • ~
, I'. . -22
made du~ing the course of a research program on tne influence of' ....t,
.... '
.residual stress on .col~.,streng~,~ ca~ried out"at·,the'Fritz Engineering'" "• ••• t • • I." .#",
, .'Lsborstory) Lehigh ,~~iversity) Beth~ehem) Penna.~ of 'which ,Wi~liam
J. Eney is directo~~
• t' _ I
- . l ,~. II .t I
The PennsylV2.!i.ia .Depa:ctme:q.t of Highw~ys and .th~ ~Buieau,'of 'Public,'
, :s;.oa.ds» the National Scie~ce' Foundation) ~nd the ,Engineering ,1fo~ndation ,.. ~ 4 ~ .. • J • + • J • I
't:l~I:ough tl'le Co~unm .R~search Cou~cil 9Ponsored jointly the res'carch
Since this report is esse~tially a summary of progr~ss report~-•• "f
. prepared on ,the:· .. inves tigation ,par,ticdlar acknowle'dgement is due ,those.,. '.': '\ · . ,':
otl,er inves tigato~s at ,Fritz. Laborc;.tory to whoseworl~ refere~ce,is ',,"
,made throughout the report. The work of .~ira Nitta in making
'calculations and in preparing the tables and figures a~d that of .
'~irs. -.Grace .Checl, in ,typing the '.report is gratefully 'appreciated •....,'
• t ~. ..... ~ ,
.. '
, t
to ... t. ~
" .- .,J
.'." ,
,1,_
I .,' ~
Itt ....
~ ~ .. .'~ ..-- .. -........~ ................---~"7"flj-7;+-n.:~<otr--~ r'~""'r~...-r -:"-f";o~-;~~L~ ~7~-:-;I;·i"~_~-.J-~.~~:::~;t~~~~1'""77':\:'~~~;;~V:-: ..~t0~-;--:-;~~0:::~T~~.~~P;:~:~.~II~f·t fr~ ~""?7~ry~r~~, ~\~~"J!1\·~.tt:'~t7;-7i~t.~_::;~~:""a:nv:i1-;'I~~:;~~r~~~1~;"I~~1~ ~~~r~~~~~~; ~
I • I ~ t
~ ... ... .,:! ! i ! !!:li .9. !"§. .
I' .
~ .:- / .. ,
","" , -23
'1 "' .••' ~" ,
"
1,' Column Research "Council
'0 '
2. Huber) A.•. vr.·and Ee'edle) L •.. S.
3. Huber, A.,W.
,5. Fujita, ·Y.
'" '
6. Tall) L.
7ft .Gozum, A.T. a.nd Huber) ·A.W.
8. 1-1arshm3.l1) John
.. 't. ,
9." Ya~g) .C.H. ) Beedle, L.' S.Johnst:~n) B. G.
..
10. Bleich) Friedrich
11. Huber) A.W.
12. Ketter) ~.L.) Kaminsky, E.L.),Beedle~ ,L.S.
13.. Galambos,,' 'T.. V.) Ketter ... R. L.·
"
,"THE BASIe COL'D11N For<J.\f1.JI.J~") Co1u.mnRes eair:ch.. Co'nr5,iJ~ Tech.rJ.:ical M.e.morandum ,'"
· NOn 1, ~1ay 1952 0 • -: ~::< ..: ;"
,"RESIDUAL ,STRESS AND "TEE' COl-1P.RESSIv""E- ".:'. STR~ENGTIr .OF STEEL'J (Fi,p,l?l F..epo:ct onJ?ilot Fxog:r.'~m)'~ Jt!':1~~Lh!l~g~~Jt 33 (12) "po 589 6V s, Dec.embe.~~ 1954.
"RES ID11AL .STRESSES IN WIDE FLANGE BEAlwISAND COLUYiliS 11
, Leb.igh·1Jnivers:Lty, 'F'. L.Report }~o~ 2.20Ao25, J'uly 1956'e- '
"~UILT-UP~ COLljMN STItENGTHII) heb.i.g~
,,',,' Un-i".!ers:Lty ~ ~.. 0 La .. Repo1C t 249'02,lo.1lgUSt,19560
"THE MA.GNll~JDE AND DIS1"RIBU'rION OF "REST..D7JAL .S'l.1\.ESS If
) Lehi@:. ;JT.J.i.'Te.rs :tty,F 9 Lo Repo'1:t 22,Q,A.o 20, Ju,:nB 19550
11MATEJlIA,I\ p~OPBglrI~~S O'~l S'rRj'C'IfCTBAL', ,R',~EL.~~~~~/~$'% ,\tJ:!t~i1Y~x:.s~tJ;y),',')f ~t.t' 22iJA.o 28 "ap.ril , -58
1'MATER1~~ PR01")EH,TI.ES ~ RESID7JAL S'I'IillSSES, , AND COL1TJY.fN STREt:1'GT1P", l,e.bjJ~ll~ Dnj,ve".csity,·
Fo~o Repo~t 220Ao14~ r1ay 19550
l1THE INFLUENCE OF PLASTI,G .S,~AINBATEON THE '-ilEI~O SjrRE~iG1TI .OF 11ILD STEELu ,Leb:lgb. tJn1.vers i t~Y:t F" L 0 Report 220B 02 ;t
June 1956 0
"RESID1TAL STI{ESS J>JID TILE YIELD STRENGTH .,OF STEEL BE.AMSll , ,Welding JO?1,rnal, 31(4)po 205-5 > April, 1952 L_ Ok
.·,·· .. IB1JCKLING STR.ENGTH .OF :ME~ .SI1RJJCTOIillSI1 )
" ,McGra'\"N~llill B'ock. Co ~', New York 1952.
"TIlE INFLUEN'CE OF RESIDUAl, ,STRESS ONTHE INSTABILIIY OF COLUlVINS", Lehigh~niversity, Fo Lo Report 220A~22) May 1956.
."PLAS'frC DEFORMATION OF 1-1IDE-FLANGB B&\L'1'COL~S") Lehigr~ llr,l:lversity', F o'Lo ,'Repo:l:t205Ao12, October 19530
IIF1JRTL~lER STUDIES OF COL1.l1.1NS UNDER COl-mINEDBENDING AND TrtR1JSTII
, LeE~~gb. lrn,i"'veX'sit~)
F .. ·.L. Report ~-zo-.sAo-r9) '"J·Ul.y 1957.
220l.. 27 -24
14. Gozum, A. T. "COUPON TESTING'·, Leh,i.f2h 'Uni"ersit.X,,FoL. R.eport 220Af,lS, jJuly) 1954
15. Huber, A •. VI,.
16. Huber, A.~_W.
" "CROSS-SECTION TEST", ~Jl Un.iversity,F.L9 Report 220A316, Ju~e 1954
tlRESIDUAL STBA~~:N .MEASUREMENTI1) ~E?h
'"Universi.!:y, FoLlI, Report 2.20A.\7, ,Ju\?,e, , 195Lr·
,"FIXTURES FOR TESTING' PIN-ENDED COLmmSu ,'"Lehi8..h Univ~E.§.i~) F~Lp Report ,220A..24,,, :,'",;July, 19.56 1I ' '
',ADDITIONAL ,PROGRESS REPOR,TiS
18.' . Rubel;, .A •. t~ ~)Ke~ter) IR,. ~~
20. Beedle, L.S..
21. .Huber ~. A .."YJ.) Baed~e .. ~~ S,. '
. 1tEXPERIMENTAL RESlJLTS OF TH.E .INFLUENCEOF RESID'UAL STRESS ON .COLUMN ,STRENGTH" , "Lehi·gh U~y'~si.tL, F ~ Lo Report 22.0A. 6 ... ,August 20" 19.52.
tlF'URTHER RESULTS ON' TRE It~FLUE~CE OFRE:SI.D1JAL STRESS O'N COLmYIN' STRENGTH'I ,Lehigh. TJni'rersity) FilL .. Report. 220A.7) ,:December' .30, 19.52.
n INEL.ASTIC BUCKL.1ING OF CONCENTRICALLYLOADED COL'i.TM~SC1, ,Leh,i.gh. _1Jniversity,FoLo Report 22.QA,.8) Apri.l 2..3, 1953
"DETAILS OF PHASES OF GENERAL INVESTIGA.TIONn ,
Leh,igh. Uni"ersity, FoLo Report 220Ar.1O, May,' 53 .
.. , ~ • + ~
t ~ • ~
22.
24.
Huber) A., tJl.
Huber> "A;W.• ')' 'Beedle), ~.S.~;.,,',• • . '. I'.· ~..,:
,"SUMJ.V'AR,Y R,EPOR1r ON PILOT PR.OGRA.M", 1~high~
,.UDiversity, :F 0 L(\ R.eport 22.0Ap 11, January, t 54'
1IB.t\s+c COLUMN s~.rRENGTH,u, l,eh.i~~ lJni.~~i tl>YoLo Report 220Av12, May 15, 1954
Dis.cussio.n. of .11 EFFECTS .OF, RESJDUA.L',S'rRESSE;S", L.\l.vlE4DED STRlJCTURESII, by Go Mo Boyd
.Welding ,Jo11rn,al, 34(11) >, p. ~75~s) "NOV. 1955
.1
, :
• ~-!' -.......,. -- _ ... ""'" .": ~~~,~"";--:-~-;..~-;~ ~ f-:","l;"'~::':"".t"~.~ -=-'"'~_.!""'t .......~..t+:':". ~ •~. ~~~ ........;:.... ..:"",...... ~, ~~ ~ .......~.'.-.'~~ .... ~ .............."::1-o......--:'n~ ~ ~~,:':;,. _ ......~ .•".;,........ _ .,. .........;.........._"".~...~.-...=.,.,j. "'"~~.... ~ "'",:".<;10- ............... ~ ...... ~'~"' •• '~ ... .-. ~ ..... -. """1.-':. ~~. ~""'''''',' ~~T. ~. ~_ .. _ ..........;- . ~
t\.)r....,lge-I\)~\
TP~rn' 1 (~ TEST RESULTS- - ...
Prop~.. - . ... -
~
Yield stress Level (6y ) Lirrlit ,~ Colunm Test Group }To~
~ (6p ) Re·sia:~Test
9,Stress ~-'" -.
lio oShape
Sim~ Stub' Stub (6;'0) Residt,t Yield Level Column. Mill Coupon ..
Test }fill Test Column Colurrrn .-. - °cr/6y L/r Stl~ess Prop'o Limit TestTest Test - Test .i - - "
1 2 3 4 5 6 7 8 9 10 11
TeO 8vJF31 L~3!t3 L~J_ o it. 3703 25 0 6 0 1309 0 0 0 0 0 0
L£Q2Ar=>T18 81~lF31 0,,99 28(x') -. 0
205A~T]-5 81fF31 0905 L~2( X) 0.
T~l, 81~31 37 0 0 360
2 ' 28.~O t=)ll o~5 0 0 0 0
20t5Ac:)Tll 811tJ~31.--
0935 56(x)-
0
Tc=2 81,lF31 4303 40~2 37 Q_8 25~2 ~12G5 0 0 0 0 0
205A~T25 8vlF31 074 -82 (y) 0
T~39 81tlF31~6;- 16nOY j U ·:=I~~t) . ' - .. JT~u . 8WF31. 4301' 40$1""1" 36HfEO e:.- -.9.~ O· o81~ ~8 (y) 0 0 0 0 0 C
Tr=.5 - 8vlF31~;b 33091 ,--31o~1&-=~.....,.;x= ..........._. T~5 .?:. 8WF'ill" - '.--·_~_o9~5.}32 (Y~ to~~__l? 8\~JF3I~:: o.-2l3 S8{Yj ()
TCJ6 a~ 81tJF31 __ ~16o 1 0
T~6 b 8\t1F31, (A"lrer.J1::) 0
T~ c 81ftP31.<c:' () I -"J I,
g,Jd:e).. {)
~ T=7~8VJ}l~~.iJ- ~3C) 8!JiO 7 Uf -'-·e:)ll~o_g__ o 7~ ~®(y) 9 '-f {) 0 0 C 0 0
u3°0137eT-.2 _0 .L ~;' o~=j1-s_at '---S9e- ,
Tt=>8~ 8vrFt~ 7 ~31qL _~--2.9 t; 8 rJi \ Q 0 0 o 0 Dt= 0o I I ~2- .-")-='::-~.~____ ~2~ ':.~._ (> .1, ...,! 2l-Y)
TQl8 b 8\\!'F67 ~ 84)0 {) ofhF- IT~9 a , 121iFrJO 42&6 u~lL3 _37 ~6 --~--8~f~'--r-
b ~CL5. ' 0 ~ 0j~ 0 ' c:1J_~.J
1'],2t~JFlS()_.... _. ._.). ,
~81 EiDJ ~v) ~L 1- °1T co9 bT~lO ·.12\~~ltt5 39 0 7 JACJ 01: ~8~3 .~ 36 66 2~~oO ~1.8 tr ~I (J76 8:l.l'Y) ! 0 0 {) ~ {'\ () 0 0
~r5E~Dl.~----:.:-...--=~ ~-~~~q~~~
lO1tlF931 .L; tJ . q~. " ~····li .--t.~' H ._. ~:..-_-e..._~_~~~--=~._
~~~~.? ~---=-p,~ _C! . ...---:-r='". --=~--=.!~ ~
2..9~)E=D2 I 8J~TF21~ ~q ~ H ! 11.0 .~ 11 -3~1.(; 4--~. -LL1~l__._. {) Q 0--
20~~E~D~ ].01:·JF3g il ?ILi" 0 1S~6, ..~ c; &. q { ?" 0 D 0Ll-.- 0 ~ j. ~ \
20SEe1D4 J_21WSO 42 o b!h2 0 0 17 0 2 ~6o_LU.-10- 0 0 D
£~E~D5 8)'W.Jt) 1l0 0 0 IltCl~8 ~'-1 0 6 :S6 6 ~7 f ?,) 0 P Ii-'l.
o_~1205EC)D6 lO1rlF2:L 46 ~ q Lt8 & 1, LLl~c, 37 ~2 (1. ) 0..
"
if
11
11.:
i;lj
~l
~~~i
f1tl;'1)1r';. ~
rl~1p~;1§,~'i~it~
Ii~ji~\'
~,tf:J~1Mf~~~
fj;j~:l;'1or}-,.l:
f~fit~t~~1)
~1~~~t~~"l:j\""1
~~
f~fA.:!'rj;'~:;j
M~t1 "Jf~ ez=-c~)~ .n-====
T/1BLE 1 «::0 ~PEST RESUTJ~:S (Cant t (1.)
Nf\)
o».I\)-.,J
i~
Prop~
.. f Yi~ld Stress Level (oy) I Li!1'litTest; ,.1 Sh -, - (O:p)N '. ape --
0 10 ' ,I-----r---.-.-=:------.------{----
SilTI e Sttlb StubMil~ Mill Coup~n Coluwfl ColumnTes~ T t Tes~ T t m t·as es- les
R --'.,t., - Colunm Test Group l~o"e S:.LO~Q "Stress t. .'.__. . .~
(ore) _ Reside Colurrm~r/Q L/r - St:t"ess Te st
ilz b 10 III
I------t-~- ::.::~-¥--~-i---:i-...-~..............;--J--...--:...--I---· -+--~:---..-;---~==±-; :---lill I : \ I I Iii I
ooo
o
~8 I .,. -! "--:'::~'\.
- .~ . ,~ -- .- ..... ,
'\! }, . t
+- ~ Co~d."..St;r~ai.ghterled Mat;el~ial
T~15 a 14vWU3 ~lo6 I~~ ~ 0
T~l:; b luvlFli'_) tlln6 ~ '8~~ 0 Ir~=~6 ....l6WF.lt50 u,7 ~9 = lo a-8 0 >--1
~:~A-- 12 .~~_.: SO <>4. .' ':' ; ~ __ '" li o 1 . 0 , I . l
~'I~~ .~~' ~2021~?~-~1~~~t:--~~~--"-~~.~~- j ~~Ic-·22 lO~lF6b 46 0 6 38 ~ 8 32o~ .3J-p..?-:.- I. _ 2~_c(~Cl __~,- ~~_~.-..."..,...~_~~_~~e-Z~2 f-x ) 0 0 "~_~ .
T~23 lOrlF66 t'~"q ~.~. I c; S ~-1· --r-=---=-~.?~ Ll" "': '.... \. L""':m- I---=24 ~--~~~" =r; Wl- >- ~'-rJ:L-~,L__.~:dJ'-:-~=:'::=-"':'!~....:;::o:..~ -" - ~-- ---==-=--- - ~ TT=? t ?'WFJ 8 -J II Ci 0 i J ir7 ,,"1 ~ -'8:-i· -::.;..; --. I .. . , - . I 0 0 0 0 t
~T~-2~---14IlFiif-I~~O-;'9'~;'~'1~~~7) 3.1~1)-1 ?t;"S' =~'-=--~ ~I .•__,=- Too {) ('t J J-- 4":::> 0 ') oU ~)~- 0 L!)~_~ f ...~~" • • H-% -,I
C=:I? .. ·1 ... r·- ... ,. -J J .. r" -""I 1. ~'... () ..'~ 0 {) 0~L-6 a fllj.'WFlll ~t 43 a 8 3309 j??S lOni =lL!~oO o_L160CU-L - "__ I L__~?6 b 11i1jIFll.1 . - ,,' ,., r;s 95UX:LJ _ J _. >---L.. __~_ ---.I~:r~~ 7 __ 61VF.12,5-~ -~-:L2"-LJJ,.kLL43-;JLLJ9oJ - I I G~£C:.. __ _~~~2!L- _8YJF2~~~._J±~7 01+. 48 0 i) 37 Q 8 I ;g o4t l5-o 0 i ~~ 0 1_° 0 , rr 1
T:-?_9 8~JF3]· 44. o.bL L~8_~~,370'7 36 "l I~- 2(.1.-~ • o.j~t~]::...., I _\~30 8WF'i~ liBe3 tIiIl?7 _~U.5.-,,3 -rzO_pO i o_~~_
~!=31 8'i'[F67 I -~i~STJT.L"L 2£~1 26 ell-r rw C' 01 {)! 0 =JTgr.,32 lO-t~rF'13 52 ()0lIiJi~ 3LL 0 3 3204 j 2J-=.p3 I 0 0 j 0 0. - - ---~
Ii~\.
~
f11~
tf
Z
fl
~!~~
~;}
[~~'1
~~
i~'Il
~!i~
3:
~i~
;!~ij
Ic~
~,~
~~ I~,~ ---a'1 •.~-
f\.)tvo)J>•f\)-..J
9110111
Group NO Q
R.esid~IYield Levell ColumnS.tress Prop 0" Lirnit XC?st
L/r'~r/6Y
Colunm ~:S1J
oioiolo0101010
-H-H-t--=--
J -
°lo~ Io GI Q I o- r ,~oIDII-L-i I
-:-Q- ~ ! f
IC {) 0 0 I i I i
- , I II~I j {1 I?ErP ~ __~L~_
r--1 ~--'- I I I------~__LiL~I
"112 13 I 4 5 61718-
0 0 0
0 0 0 0~ --
0 0 0 0-
0 0 () 0~~-~ I J ... I -{---I I' !
0 0
0 0 0 0
PrOp~· .
ILimit- (6p)
Resid~
Stub' StressColUrili'1. (~c)
·TestI
I -:--~
TiillIE 1 cc..TEST RESULTS (Cont i do)
Stub"Simc Coupon ColumnMilll Mill Test TestTest Test
Yield Stress Level (Oy>
f.
Shape
, ~ I. ) ~~-=~~~~-}o-__~~--l----------, J t ! i I I • , , I I
-~--.~~~~::c--?'" = -- ~l I ~.
I • I I I ~ I I' ; i t-j-
~ : I l : 'f I : : r
~-----t---- 1 I -~-J--.--...~I , I----t-:
'----+--1--l 'I' I I ~1 ! ! I : j
I , ~ I : .
.I i \ -( i I I
I ~ I ~~-.J--~-r-,-
Tes1:JNO G
r
l Tea33T~3 . ! . I I ! f J J -L
T~3
T-=36T=37_--+---~ -<:.-+~~~~~~---,}-~~-.;r--~T=38 '
o
t\)f\)
o>
• 0
tv~
Gr01.1p No o
Yield Levell Column~~opo Limit Test
11213
ColUJ1IO . Te atResid o
Stress I /Q..j" L/r: I Resido(~c) ~r Y. Stress
TEST RESUL~rS (Concl fi do)
st;ub·GOIUjlill
Test
- P:POpeLimit- (6p)
Ti1J3LE 1
Yield Stress -Leyel (o~J
- -
Stu..bShape
• SimD Coupon Colulm.1.Mill Mill Test TestTest Test;
TestROe
, 4J 5 6 71~ 9110 III_ 1~ 21,,7 On86 180uiJ 0 01
" 36 0 71 37 Q 3 22 0 ~ t' 8 J_6Qix.L1 . 0 0 l 0 I0" - ' RQ]_L9-C~t.t~~1 U'-l
~It n 1 1 ~ OCt 7_ 1 h? I i4-(x) 1 ° 0 0 r~ 0
3? ~ 7 12 0 S ~~1 ~ 0 06.4 L5.. :; (y) 1 .. 0 °.1 ~ro31 0 71 I ¢50 '-98(y)~
• Total number of Tests for each gr~up _.-_~ -_ .-=.~ _H - - -__" -·Itl~j3 3~;:-I~_15l5j
l~O~g
o~ (Shape.) 17Annealed~ mate:t:;ial;" others ~ tia.8 del:i."qer'edH
-.XieJ~d Stl~eS8 Level (Cott!)Oll Test;) v8..1u_6 n18i:LUS tb.'9 ~k-l8ight;Bd 8.:verage V8~]~1J.e '01: Tensi(Jll COlll)011 TestReBul.ts.; exeept those nlBJ?ked nyn ~·hj,cb. mba of Oonrpressl.oIl Test RB~rQlt~~ ---.,Col.urf1Xl Test g 1t (x)n means buckl:Lng 8~bout st]!ong ftxis
n.(y)u raeans buckling about 1<Jeak 8J;.::l,8
-1•
fI -J
~I'~
-11~
~i:4a-:;~
;~4
;j
tl:1
1[1~;1
~'ltF_;.1
n~~!][lt~bo-
s'~"J~-i
f1
U~~~.:'-J~1
b171!J~1
{~
t~'Jti
~lt"J.lI''1
t~....V,~j
[1"....f~-i
y~
?~
~~~"J~JL~
~ ~f{{ •~~1;-,,4 ~,(~1 I '--'
~~,..-.::~:1~-'-i .
TABLE 2 CO> RESIDUAL STRESSES IN "IF SHAPES DUE TO COOLING
.- .. -
Flange Edge «() -) Flange Center -( q:~) -IWeb Center (G ") "]
rc r~w
1'1axo "f Av I> 1- Min 0 -J}fax() Av~ Miu o Max" Avo Min 0
- - ~ ..~
- Co1unms I .-d/b ~ 1 0 5 '=707 ~12Q8 el1807 i~16 05 . ~} 4: 7 -~401 ~rlac2 1~ 8 0 0 ~15c5
- ~Group 11 I .. ..
'.
Beams Ialb> 105 ''''4 01 ~ 705 ~lOo8 ~~2L~o2 ~~15o l +803 Ct. 8 0 8 ~2108 ~4100
(Group ?) -. _.
- -
.... .,. -~
.. ~
r:· ....
~fi~ ;:----~t.... ~:~t\) .... ~
-.J
~ ~ , l
.' .' " . ,J' :~. I :
~ , -~ ~ ~.(a) Wide rlange Shape,
:; , .., "
",
. "
-. ' , .
. ,~ .. ' .
"
\,
(b) Shrinkage of Flange Pla.te - "'and Stress Distribution'(in hot, conditioTJ.)'
<+> .(-) .
: IlIG. 1 FOmiA'nON ,0]' COOLING RESIDUAL STRESS (DIAGRAlvlA.TIC.)
, • i,
" I'
(0) Shrinkage of Flange Plateand Residual Stress Distribution(in the f:ip.al· state) .
I :. ~ •• ',
, ' . ~.' .
.~ .. ., '
.. ,. ' ,~ • l r ~ ~, • ~:
~ 'I .~ t
,~.~\ I 2:?{lA •25-16. ~ 22 CP.•27 tB2
"
,,~(J,' .
' .. , .
.l~\NGE P.L\.TTER~l WEB" rA'fJ::f;k~ ..
,: '1IDIt11lli'-, ·" 'I
, .. . .
'. .,:1".
~ , : .<J ~ :-. f' ""~ ~ t :z" ~ ~~ +t oil: 'j
..
,. :
-.,
o'*,' ...
, ...
· 10,e
10
. ,.. ,
~,' t
t ~ ',' ..
. "
. .'
.... ~ ..
t • "',~... '
~ ,
.." .~ '. ~.
. ' .. : , ,'''~,
" ,2.0,H~'''-~'''' T . :
10,10
.'
20~
.' 'c ""'{--------~~p -r-L.... I .. ~ t. ...1 . ~ .~.
~ . '.:'1;
'u········,1. '\. "
, ',' 'I': . . ,... fhl~~7.. ,. t,
, ~
I:: ',',
-.' .. f-
I""" : ..
..,'.. "f·
• t,
.'. ..
, .
10 ~ ... ~.. . ~ , • ,'"
: i'. IIII~· I .... •
..... ~ ~
".1 :.4 .....
.F1U:~~;2 .'(EJ.)6 '~~SIDUAL', SlUSS DIS~~BUTIONS, I~ .WF-s~FES• j j 4 .. I
. ".... ~
'..
'.' ..
... ...... : .
..k~~_~~~~~~~~~~~=~~~~~~~~~~~;~~~~~~~~~~w~~~~;
"
ISHAPf: I I.FLANGEPATl'Eim] ,
',l
.. ~2WF65
'"
,10
, . 0,
.... .:. .... ~ '.... .;., ,. ,
,' ...
14WF426
ksi
).
20 10 0 10 20C L,.,l__-I.__--'1__~1~_.....·• :T'
"
RESIDUAL sTREss DISTRIBUTIONS· IN 'W.F SHAPEj 11= t • • 11III • • , • .. ., .. ,~
. ,
: • :," , ';,~ •• ' to • ',.'
t,,. "
. .,. ... "
226/~.25-1622~.27"'2Z. t "
.'
IFLANGEiATTER~..-~
1/2 .
. ':,
, ,.1• '+- ~ ~
" .".:. :, ... :'
i, '. ' • .i
, ~.
'- ~ , ~4o • •
',"',
o
10.. "C.
T10
.,'
'14WF43
.', ,.
I • ~ I: ..". j t
"
... ~. - ... I
~_ I I I"
,1
. '
.-. "
, ., .....
2- ' ..... ,
,',
• ~ -#0.
; " ... ~ .' .~ .. I ~ '.. • ,I •
~ ... .~
..-, "
'" ".
.,.
"
""ksi
'36WF150
FIG. 2 (0) RESIDUAL ST.RRSS DISTRIBUTIONS IN WE SHA.~ .t- " .. 'I ..
. 20 10 0 10 20,I' It,C . L.__~I__..1.---""---- T, .
"
,t". .. lo
, . '. • t ~
\.-]:&:-.:_:_2::-:----~ ""'------S
. l' ·
L' ••.• 4
1 ~ , I, .: " .. ~ ..
, ". . ~ , .
~. ..I. : ~... h '.. ..
~_ ~., ~ ~ • r , fI' - ~ "i~~. ~ .. 4 ,~ ..
, r ... · ~ ~ ~ ••• , : ~. I
• ;. I
• I~ "
I
:- Average 8IJ 12.8 (ks.~.)1 " " . ", , '.
·1'II
1II1I11 :'1It
q ............--~n+-t-.l-d--~l ........-..........~~ ...r-- _
5 10 15 20 25, (ksi)
10
40 -', ",.
%50
(Compression)
; ·"·:t
• L " •
FIG. 3 (a) RESIDUAL STRESS AT FLANGE TIFS MEASlJRED'. .- IN' SPECD:9001S (GROUP .3) .',' .. " '. ,
\ ~ • " .L -' ..,. , • " • "
",
., .....
.'
" ,, ...
j ,r, ': ,,'
25 (ksi)
(Compre~sionv
l .t~ Average .= 12.0' (ksi)' .I ~: t ' "
III
5 10 15' 20
6 r (~ 6" y -. 5 p )
"(%) "" , ,
50
40
30~0~ 20 .,'(i.)
"
::s0'"(D
rt. J.O
0
'4J ,11 " ..FIG. :3 (b) RESmUlLL SmESS MEAS11RED BY ·S~ COLrrMN 'l"'ES'l'S'
. (GROUP ·3)· " . '.' , ' I :;
22~4.~25"'3~~.·220A.27-4, .. ".. '
fiIJ. ,
I'
'f'" \,"
·t.' •
lit ' t
• ~'~" I •• •
..... I .,
. "
... ~ ~ t. t t
, '" ,
at .Flange 'E;dge;s
.. Ij' "4:',
" -1IiII
""'". '", ,',;
.,.• ill ~ ..
1 :,
.,. f.. ~
.' .~ . .'" ~ .-
,',
T
c
,Region. IClontlQii1ingCold-b~n~, ,Y~eld' ·~,~jn~a•• I j l"~ I t
'~--_._---~-_._---~
Average Stressat. Flange ~Cent~rs
Saw. Cuts
~~;==.=-~;=, J~='1. ,I I IIII1 II, 'ltd I •
~~·H.c:::r~~IF~.~~;;;)
9 t~Ou'
.. ~ IIIi ,
\ .
t' , '
(a)ii L
, ., ,
, -I< ~' .II'
,." ,' ..
. ." ;. ~ , ,:,.','I·... t ~
:.- . ~
" ~:." • to I
~ .' , .:'1
;,\vera&e StressFlange .Cent.ers
Aver'age. '. Stres s''Fl~ge :Edges
"-1', '., .~~Sl'tj'B COL7J10r:,.·::--i--~--+--....y.-~T---' '~ · ( )'. . ", '. ·.LE'NGni, ft~
, , .' . ',. ,': ,. ' ...... :.. " .'
G}~E ;LENGTI{ .10. 1'
t 1 ~
\ <
'.
f .•·.' ••1 It. ,t.-
'"
(.b)
'.
.. FIG~ J4.J:" (a),V&~IAT'ION ,OF RESIDUAL. STRESS '(K$I)~·}~.QNG;· ,::,~ .. l
. • ~l.' 8vlF3~ .BEA14 ' '.. ~, ,I • "
(0)' THE VARIATION OF. RESIDUAL,', ST.RESS~~~(KsI), ,/!iir. ' _"SECTIO~.· i- j ...AS. A Flf.NCT~ON,:.OF' ~",LEN~TH"
• I • ~
~ I ~-. : • ~ t • .~.. ~.'
,-J '.-
.... ,:,.'- \.
~ • I .~ . .-. .~
• - ) ~ I
,-...."' ...• l
, " ' ..
";
. I
,. I.
,/
.. ~ ..
~", 'i
" '
,:' I
FIG•. S· COMPRESSIVE RESIDUAL STRESS AT FLANGE TIPS AS' FUNCnON OF
./
'0'.
0
.0
0
0 0
0
0
00 0
0,. 0
0"0
bit-alW
o
'0 I
o
o
o
bit-ww(Group 1··& 2)
oo
..10 ·
.". ".
. '.
~ .:: ~ ~ t ' ...
00002~.e,
(b).'
"
(a)
220A.27-6 ·
(t)l-_~u..f-'oo-~l""r'M""'i
,f
, .'. ,
',-
......r
, ,
Initial Stress, ,
i'
l-)lt
tG..,;.::.~.,\?,0" """IUI"';~" -f-, '
,I ....
"
~y
,J
" ,
f I
'i
I.' .,
,,'
Plastic' ,Portio.n '~.f .: ~, I
I ..
(0) ',(d) < '
, I
/', ,:
l?IG., P :;~. INFLUENCE OF RESIDUAL STRESS ON THE STRESS..STRA.IN CURVE
B.. • r
Z20A.27-7'(
3
,;:[ji
1 20
10
Sr- sa 21 ksi:................................ _-,
',t."
"
: ~ .
o. f
FIG. 7., STRESSlWSTRJUN CURVE FOR 'Afnt7' COL~rs BASED ON·,'"MEASURED RESJJJUAL S1'RESSES(Group 1,) , .
; ,
·v
7,,'
.'; ., .,I'
\ ,
FIG. 8 TYPICAL STUB COLUMN TES'"f
8
/
\':
FlGo 9 '. STUB COnnVIN S~RESS~.'. STRAm CURVE FOR
AS-DELIVERED Yl1l.TERIAL
f',
s~~rB OOL\.DY.t1>T s·:~:p~..ss~
STl1~R.:~1\Y f.TtQ;~·Ql~ FC5~
A.Nntl1~ I~~~m:~4.L
, .A:VlmACrECOUPONS
S'WB '. .1 (~.i.~COLO~S', I )
40
8002
10
30G·.!.20
2'2 OAo 25tJ:'33 ,39220A.27~9,lO,1l ,
-_.....:..----------~
(ksi) A.VERlI.GJ<,;CaJJ;ONS
I', 9~I 0"'"
COi'1PRESSION ~ ,
~~. .
-.~ ...
",:
t
. (
, '
L
M~~~~f~~GAGE LENGTH 8 ~o ~I
,,
FIG. 11 COLD-BENDING RESIDUAL STRESS IN &/1F31 Sffi~PE
I lLt'
. ~:. .~ .- -,.... ..... ~ - ............. - • ....- ........... ."..~ lot ................. ... .",.......... ":...-·_ .._r~·..-r·--...,...--~-...- .... """ .........·-V-1' ~~,.~'" .......,.n-..·~·..,.,~ ...r'f1:~ ... ;rT"'"......,....-¥f'I'-.,..,·.-.r '1" ~"-"'-"1''1'.,..,.. .... ~ ..... '_T".,... ... 7'''':"''"' ~,,~ rT.:O" ~ .....~f .._~~~ .,...":""!'i""~~~-:"::" .... ~~f":. "foIIoi;[.'~ fI';- r··"l:~ *',\"". ~ .... l,~.~ ....~ ....'"~J~ :~... ~'1:t"" ( \
j'i.. ,'
i2'
, ~ I , I' ' .,
f. ..~
" "
I'
.. ," ......
30, .
, ..
. ... ,
I'I~if""!r4--
t .
I1III1,1 .'
J .
J
1 "
.1
iIIIIII
(b)
. "
20
+t t"j .. ~ .. . .
",
10
,,'
~ 4 f .. t· I..
" '... ·;t, ~ .\'~ ,I,
.' "',. ~ ~
, .' .. ~ ..~ "
I I ~ ~"
~__ :P _
o
(%) l·3,0· .
~p'. ,
, .
-, ., ,:(~) FREQuENCY DIsTRIIDTION OF THE PROPORTIONAL LIMIT DETERMDJED .FROM S1UB COLUMN TEsTS (Group 7)
\.
~~' 20 miCJ;'o .in/in
',. j'"W • ,
~ .' .
,FIG. 12
• ~. '\;. , ~ 4. 4....
" .
• - -1 '. ~
22o.A..9-33220A.27..13
, "
, ~'. ., ~ .
.. ' ."• l1li ~ 1If' ~
+.'" t ," .•.' l t ~
I;'. I
, .
J.'
0,·,,4 ..,
j"\
, I·, \
I
(GCi:.lpon W:i [, Sttlb CoJ.:u.mrJ.)(
t" ..Compr0st~io:rl):' .
1
!1.
(flange coupo~.)
]'\~r,'(
"
, .' ',j:'
P. Mill Type Tensiorl Test (web matezoial)
Laboratory Test
, , 'I.",
" "
Laboratory Test (vleb coupon) ,1 __
1,-m _..'-irJp·p-er<[~~;u-~w:...... _~ ...... ..-... .................... ~..... ...... 1. ,-'" .~~ .~~ .~".- (Stn:"s,:Ul ,',""t"a'be ~t
.,' tl ... ". \1'" ~ f "
__ ~ - ~'L. -- (\veb ~ jf»-t..71ge)-/J r----rc-=.-,
, Stub Co~amn Test
h .
.....
S'IRAlN
'. .
.FIG. 1;3 Dri'mENCE OF SEVERAL VARIABLES ON THE YIELD STRESS LEVEL~ ~y
13
!; .
.~ .
• ..:. • '. 4 ~
I •• •
, .. i;.
" ",
",
"
, ': '. I • " ~".,
" .
" .'~ ~' l ~.- 1. . '
Q
t:: p ~ 594
o
'-r,"-I
6u l1li 5'"1.9 (ksi)
e ~ AVfIt' •. Plastic StJ....ain Ratep . ,. " "
tSy ,. Yield S-l'.ress Le'Val
Coupon Noo 12)
Average cr:yo" Cia 31,300 'psi '(20 Tests)
Static value
(Test Noo 7
o 10
.~ , .', .'
\ 'r
1.06
1.04
1.10
.. ..'. '~
J I
4 8 12 16 20. .
FIG. 14 ;STRESS-3TRA.IN CURVE SHO.wO INFWENCE OF S'lRA.IN "MT~
.',.. 'l·~·t ...'~ "". J '.,.,:i.ih'.:
·1··
.1·~·i "
FIGQ 15 nEW S~S RATIO AS FUNCTION OF S'!RAIN RATE IN PLASTIC REGI~\I'
.i.
,'<
31,090 psi f 57 ~360 psi,
;-
yield pointttl tilnatB
2
= 1.070
3
Ratto ultimate Imedian's-trength to-yield point media.n strength
,101'1
.., f - yieJ.. d point.l ul timate
noo of mill tests ~124 3127 f
I91:140 p~ilhigh ,~_.2?_o650 ps i
- - Ist.ID"..dJo1~""d deliat:ton 312 psiJ 4998 C: i l:
2109~si 13371 psiprobability error 505~' - 502%
5:~~~~ i0 of . 7 0 ~9% _J_ ~-l
.i~
average yield pt.strength ~ 39,360
psi
,NoD of tests per 5% -praclcet
yield pomt-~r---;-/Btrength
FREQUErICY DISTRIBUTION OF THE YlELD STRESS (}IILL TEST)FIG o ·16
2
40
10
50
30 -T-~inl I:speC~f'i .'13~~t-:=g~t...f--:J:...+-----+--+-t_-4"r-_~33 A bOlO ··1 '- ~l Y _ 8.verage lllt~ma~e
~j strength § 66,150 psi
669b~011l II l' 'i~ ~ ~.!-) I " ,,",Ji1 o. I "-1 .- ·- -t-_. -&_
o ,..---3'..--9 --. --·~i,,---,~'ll---."1----~---
_~15 ~lO ~5 0 5 10 15 20 _. 25. 30 35 40 45-'; percent deviation rrom rr1edi8~n strBn'gt:l1
14 ]~86 1360 61l 347 273 204 69 37 14 2,3 458 1103 876 443 66 43 51, 42 19 24
~ .....~... .a-~ --v--' '--v--' '-v--' ~.-" '--"V""- \-. .<,'to'-~ ~~ --...~--'~~
- 20
~r-fr-l(lj()
Q-no H
..-leD
.J.)fjcj~
...-t ~poCD't1
'U(J)res
roo:>Q) (j)
-PomK0(1)
...-I'UH~o
*rtru
~(!)Ori
r-{~r;$..p;J-nO""MO)on.n.b!)oj~por{o CDH..oPi(J) §hO=r-Jcd ret
..J..:>(j)~EQ)
oSHOQ) HPiCH
CD
~ .~J
1{
]~~:J.~
~,
-Jj.
-j,"jS:1::l
'~
1~1
;ij
J~~.
~'
,:I',1
l~;1
~~J-=4.:;'~;.:~,,~
:;j
~j
a'~~"~
220A.14-5220A.27-17
.'
·1· 7·
, .,
60·5040
I -.0) Total (3010 specimens)
® Oo3n<,c < ·loOJU . (:1699 specimens)
-G) t ~ Oo3 zt (1311 specimens)
".. (2)I ...... 'J..
/ "I ,~
I' .( \\GJI /" ,\(
\ I
I \\I ~ . \\
./ / \,~'1/" " ,.
/ '.~,"
Yield point in. l<:si
".1.
....
" '
'FIG~ 17"'" MILL TEST YIELD POINT FREQUENCY DISTRIIDTION CURVES
;
I6001:
500l
IlrrAverage 42 09 l(si
(Gr uup ,6) "
,(a) Mill Test
!I
III1I11,t0,-__
;\.27-18
20 30 40 50. 60 (ks:t)
40~A'Vera.ge 41.2 ksi .I
(b) Simulated Mill Test ·(Group 6).;'~'
o20· 30 40 50 ····60, (ksi)
40.(%)
h 30()
~Q)
;:S 20at<0H
. ~ 10
~ Average 34~O ksi
(0) Stub-,(}olumn Test(GrOllP ;', ¢,) >:
FIG. 18 mLD STRESS LEVEL .AS DETERMmED BY VARIOUS METHODS 18(ksi)
". (d) Stub~olunnl'Test(Group 4)..:·· .'. .
5040
()y
I~- Aver-age 34Q5 (ks'i);
II1IItIIII,II
30 tSy20
40
·t~
() 20~ .<D~eJi
~ 10fi.t
o
. (%)30
..
·20
19
xlo,,-:3
... .. -
,:", I
, "
,. ',1,'111'
1.0
J . '.,
l---Average = 001,9:9' "J •
0.5
by "" 34.2 ksi ,"
006 007 008 009 100
-£.y-i§,};B~":9~..:LfSy (Mill)
., FlOe 19 FREQUENCY DIS1RIBUTION OF RA.'~~IO. ,
FIG. 20 A"VE1?J1.GE 6 .. e CURVE FOR S~JB· COliJ1JlNS( . ,frccru.p '7·)
. 0.4 0.5
o
20
t.' f
;0r
20
10
o
II'
19,20
I "')'fJ.ency\ ;q
,'6 ,.(ksi)
·'1111.•••
I '
~
, ;, ,;
- '
'I
I
,'! \, "
I
1..
"',l '
, ,, -
, ,~ L/r'
, ~ ........ ,II
;" ::; ,~, "'~'\ :;,,', '. " ri,, ~ !
, fl' d .... , ' E:
, • ~ I :/ ~ 'I'
---- E',) t
.... - ~ - -. -. - '~'-~l .' ,.J "
j
III
~ .........--,---- Member Fre.e of Residual Stress'•• ',_ '.M,ember Containing 'Residual St-re,ss
Avel~age
Stress, ,(l<si) "
· ~A.A ~'
50
40
30
(vlea~ Axis)
, 10
Assumed Yield Point,~:
~.,-
..... L - ~.. .. '
~. 11·' ...
",,. ;
"
, '
"
O,-i----~---~-_-.lo----""-----I----~-
40 80 120 160 200 240 '
____tiji;JDp S:len~ern,ess Rati9 t/r
FIG. 22 · 'IDEALIZED lNFLUENCE OF RESIDUAL STRESS ON TIlli"COl1T.MN qURVEu 8 EFFECT OF FLEXURE .AXIS , 22
. FIG. 23 (a)' l{OI~T OF INERTIA REDUCTION FACTOR FOR WF COWiNS ".
220A27--23
o
Ie'1'"
..'., ,
Strong ~i&
'..
• j
':,.,
I', ',.",
,J
~ I
"
//Weak Axis
" 'f.,-
, -..
Strong '.Axis .. ,
I,t,'
• I
I
~
10 Exact Solution (us~Jg Eqo 7)
-- - - - Approxima~e '~olution (using ,Eq~ ll)
" ,
o 40.' 80
(i/r)
120 160 200
FIGo 2.3 (b) COWMN CURVE FOR -1iF COIUMN WITH COOLmG RESIDUAL STRESS
23
. , .
220Ja.. 27 ~;24
..
~l
~[m~;t{ ~ISJ 1 ~1.0 !
, "r,;...~
1h:
0.8 ~.-
.;
'I.!
" I",
0.6 '"
8\-JF31 /, \
i.!1_ 8'ilF240
4
.. ~ (Grc>up )!y 8WF67 70.4 12WP65 1~
~~
I .."
l
1.' ,
:l
L"0.2 l
~
t i. "
0Oll4, 008 102 1·06 200
ll~',.
b I
j( E' r:~~" ",
FIG.24 : ,. COIJJ}1N CnR\l~S. OBT.t.\n:F~ FR~ ST'JBcnCODJMN TESTS"WEAK AXIS-.c:a-:oD "" ...
i ,
24, t I,
",.. ...... V ..k, &.- ...,.'".",'/
'Z20A. 27'~..25
, I
. :
...... I
'.
I
'\
--..........---~, . '.
, .
. rt" ."t;;,.;.
, .
.;
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.._ I.1 a6 '~oo
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1, ~..~
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, .,
·-:::·":'(:;.~;aZ5,.j··: :;:',CULmiN TEST.~~ AND' ·STaAIGm:,,1I.NE cOLtID'iN .. CWWE :·/wi",it ~ms,,":·::: :~:. tit......... '~.'~
"
, ." \
',,' .',II. .. ,~, ~ ....
, .,
'.
• _- ........ ~-- ~ n'
~' 220lL •27..E&·~' :,. . ~ .
";"'';'/'.;...,,,::"~ ;
'.
. '-:,.
r
0.4o
I r '1.0 ~~'~-~-u--------\
., -, I \
, ~~~Q~,I \ "I .,'. ~ I \ ·I ',. ~ " \'f J'~ \ ·.. o.8' t :-7~~O \1-----1-1:-----...i,~~
. ! "~ \'. ,P,ARABOl,IC! . '\:~, \ ' I
(Group a) 1"\ ,I, ' o. 6 II \ -- I t=
I f{
f GroUr) j~) \'~ ~
I" - J (I
l I ,,' ", ,0 ,
~---~~--~--~~-~-~._:,-~-~0.4 0 I · ;j"" .' ,
column test ", '"
'! ! " "'I~ ~. -{. ~ .---1....--- -!
rt) ,J e. 'j!.r ll~~ ~<d" "'<',. II I I
..0.2 ,,-. r' .-'
~') "f)
~JJ.,.
~~ ;~
~ 00
.!Lcry
.< '.
l~~' L__.Y. _1( 'E 17
FIG. 2.6: - COLUMN TEST 'RESULTS A'ND PA.:~.A:BOLIC. ,COI}JM.N,,"C!JRVE '- ... SITR,ONG' AXIS, ' , ..---~-
26\ .
.; ..
l,
r' f
II)
i·
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t ~I' I
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., ~'* ,l olio
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f"••
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... :" ,t
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,': /":It ': " ~', -',', ...' ' : • :i"; .
60
LJJ
a(ksi}20
g, XI !..... 127 • 1 ...~..............".r.-r-IIl!""'f'I"'-~",",,- ~--............J80 ' , 1;20 160 . ,. 200
" 'L/'"C,(Q:) , \
r/ro~ ',27: ~WW mSWI~~' .. lAit~O:r.J:C 'STAUSS-STAADi C1J&W
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;
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t.."') • '
"...............~SJ,........-.....-------...l!~l ~J80 120'
.:
, '.. ....
fr1~ ,r{," FIO. '2,~!AY':':: ,COLUl'JiNCUlWES ~' TESTS FOR !>W18 l/2
-' ,
.~ 't:, "~
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: f:~ t,*.. ,j t 11 I '"
'-~,,:.....::' . "',28,.
, ~....~ ~ ~ ~
- ,H: ••••• Hr··~H~c,:,·~~:~~;c~~~I2=:::I2~i:IZ(:~;-;rJ7:~=r~:=::t::i::::r::~T~2':r21[Z;::;rZl::l:z~S~:::;:!~:~[;~~~~;~~Z!~ZC~-=~~~~' _.
." " . ~~~UJt, ;~c~t:> ' ., .. '.' ,',,229A,;, ~~7~29 ..... '-II"" ~ ~
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• to 't •
40 120
. ~:. .. . ' .
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:.200
, .
·:FIG.~ :. UIAL .}-'-~ ECCmmlC .OO1..ttMN ar.rtV1W - C0'L.U ~i~.G, 'REStooAL )6XltES8ES '. " "
·1'
. "j-,"- . ,
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.... ~ .. ,~ .. ..~ ,.'
..
: F:tG.~3eL;:: EC~Ic"coiUMN .arm.VEs(l2L C~ARISON w"1'l'a,. '- A?~ROX)J1AT:e; SO:LUX1:eN ' '
..........
.'
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, ".." G~6 r -----.;
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, .220A~27-31 .
:,~~, ,".-. ,Or ...
l~'J'
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:.>... , FrG.~.: 31, RESIDUAL STRESS PATTERN lNl'lELDED ME1'1BERS- .;. I 'r ' • I • ~ I •
... ,..~ .- ., .
, "
31. '. ' .
STRESS
ROLLED
.....
PRIOR TO lVELD
,
RESIDUAL
Tens.
PATTEIDfS
6·
Compo
6,'
\
, WEB
Compo
.4,·mw~~"::
~
..
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t \
. co13,'
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. ", ;
'. FIG.. 32
, .-
RFSmU.AL STRESS -PATTERNS IN 'ROLLEDMEMBER',9:m P~~".AND IN WELDED MEMBER '
.', .if· ~
32. .
..... --'-7 .-:-. ;' ~:-'-"'"':"~C~r""~'''7rr-'''~'0:''C::~~'?t'',,::~~!{;;:::Z'::::~~~r,~;:::;:::7;'i:tJ~;.~:IL:t~~~7:1'£~iJJ:I::'1:::::2EC7Sm~i;:IZSC:;.~~f"d;~~~I;_.
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Appr~ximate'Column
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