THE EFFECT OF RESIDUAL STRESS ON THE .COLUMN

.
THE EFFECT OF RESIDUAL STRESS
ON THE .COLUMN STRENGTH OF MEMBERS
OF
HIGH
STRENGTH
STEEL
by
George Chao-Chi Lee
A
Thesis
Presented to the Graduate Faculty
of
in
Lehigh University
Cand!d~cy
for
the Degree of
Master of Science
•
Leh~gh
1
University
9
57
CERTIFICATE OF APPROVAL
This Thesis is accepted
and approved
in partial rulrillment or the requirement ror
•
the Degree or Master or Science
Date
Proressor in Charge
Head or the
I
~
D~partment
""--...
CONTENTS
1
(1) Definition of Residual Stress
, .....
(2) Importance of Residual Stress
II o
...
DESCRIPTION OF TESTS
...
...
(1) Test Program -
.5
TEST RESULTS AND A COMPARISON
WITH THE A=7 STEEL TEST. SERIES
(1) Coupon Tests(2) Residual Stress Measurements
(3) Stub Column Tests
(4) Column Tests IV..,
CONCLUSIONS ...
V.,
R:I~~FEREN
VI.
NOMENCLATURE
;vrr
6
6
7
<=>
,9
8
...
~:,
""
<=>
...
11
11
12
13
15
16
...
...
.
ACKNOWLEDGMENTS
10
..t'.,j."
...
-'
CES ...
6
<=>
=
Residual St~¢f3sMea$preme~ts
Stub Column Test ';'..;;
(6) Column Tests "'" ...
III o
,2
5
=
(l.n
(5)
1
..
On Column Strength
Purpose
of t'llis Investigation
(3)
(4) Material Descriptions
(2) Tension Coupon ~ests
(J) Compression qoupon Tests
•
.~
18
19
.
o
TABLES .imd: FIGURES
PHOTOGRAPHS
'..
<=>
...
<=>
20
21
36
I
o
INTRODUCTION
(1) Definition of Residual Stress
Residual stresses of the type considered herein are
the initial or "locked=in fl . stresses which exist within a
structural member when there are no loads on the structure
0
Since equilibrium mus-t- at ''8.11 times be maintained, the resultant of internal forces and moments due to these stresses
..
will be equal to, zero"
Residual stresseslarise from a number of conditions o
The major ones of these are as
follows~
(a) Welding, .
(b) Plastic Deformation (Cold Bending) and
(c) DifferentialColling,After Hot Rolling.
In this work only the third one of these is considered
and
Fig e 1 shows an idealized residual stress distribution that
would be expected in-- a WF shape
0
Generally speaking, it can
be shown that in such members tnatpart of the crosa section
whicl1 cools slowest will rema1nin ._residualtens.1on (that is,
wher e the flange s and w.eb -j o,in)
0
The actual distribution
will depend primarily on the geometry of the various elements comprising the cross section o
Longitudinal residual strains superimpose with other
strains in exactly the same way and to the same degree as
str~ins
arising from"other sources superimpose within the
elastic range
,-
0
It can therefore be shown that residual
stress has a definite influence upon the
averag~
stress-
strain relation of a struQtural steel member as a whole
0
·
2
(2) Importance of Residual Stress on Column Strength
As early as 1888 residual st!1'esses ·flVere lnvesti.gatedo
It is interesting to note, however, that tho effect of these
stresses on column strength has only been considered in
cent years(l)o
re~
Figure 2 illustrated for a general stress=
strain relationship {one-which inoluded
the1nf~uence
of
residual stresses) the influence of residual stress on column
strength.
At Fritz Engineering La.bora.tory, Lehigh Universit"y,
"
investigations of residual stress and compressive propertiE,:S of ASTM A-7, mild structural grade steel have been
completedo
It was found, in that 1nvestigation, that for
sucn. "as-delivered ll steel columns, the maximum reduction in
column strength due to residual stress may amount to as
much as
35
per cent(4)o
In Reference 4, which deals with the behavior of
A-7 steel members, the equations of the column curves
in
terms of the tangent modulus were given as follows:
for bending in weak axis
3 2
'r jJ' E
O'er =
(L)2
r
( 1)
for bending in ,strong axis
6 er
l
'trr 2E
= (~L2 .
(2)
in each of these equations oorresponds to the ratio
of the tangent
in questiollo
modulu~
to YoungUs modulus for the stress
3
Referring to F'1.g o
3~
consider the equ1.1ibrium
oondition for an infinitesimal bent position of the
originally straight oolumn o
The di.fferential equation
would be
( 3)
with the oorresponding solution
rr 2 B
,
POI" :;
-r:;-e
(4)
(,5)
Be ::::: Ere
where Ie is the moment of inertia of the unyielded
(elastio) portion of the cross section
Defining Et as the tangent modulus
j
Et
l:=E
(6 )
If the total area is denoted as A g and the area of the
elast~c part as Ae , it can be shown that the tangent
modulus value will decrease at the same rate as the
effeotive area of the oross seotion o
Ae :::::
However
Et
E
A ::::: 1: A
That iS
j
( 7)
j
Ae ::::: Awo
whioh gives
Xo
1
+ 4t Xo
::: 4t (70 A - Aw)
(8 )
4
For bending in the weak direction (y=axis), considering
only the flanges,
2t(2x )3
o
= ---=-~12
Ie
SUbstituting equation (8) in this expression and neglect=
ing the influence of Aw
Ie := ~b3t'"f = Iyy?f
From equations (4), (5), and (9), the equation for the
eritical load would be
or in terms of critical stress
3
()c..'r
Ie
(weak axis)
( ~:Jt
th~
For bending in
2
't rr E
= "'-""'""""::--~
(10 )
,<
strong direction (x=axis)
= I xx
~ 2(~)2(b=2Xo;t
Neglecting Aw and SUbstituting
I xx =
(g,
2
oA
Ie (xx) ~ I XX 9 't
Substituting this value in Equation (4),
6
cr
lrr 2 E
= -"'"---
(strong axis)
(~)2
r xx
( 11)
In each of equations (10) and (II) it is assumed'
~.
that Et (and
column testo
thereby~)
A more detailed
ure is given in
j
.....-
will be determined from a stub
Refer~nce
40
descripti~n o~
this proced=
5
(3) Purpose of this Investigation
The theoretical rp.ethods mentioned above have been
verified by tests of mild structUral ·steel columns (4)
0
The purpose of this work is to further verify the theo=
retical methods by tests of high strength steel (ASTM
. Grade A-242 steel) and to correlate and compare the re=
suIts with those obtained from A=7 steelo
The 8WF31 shape of A=7 steel is one of the most
commonly used rolled sections for structural columns
and
for this reason it was completely investigated as part of
the earlier studyUj.L
To afford a "tie=in" with that work,
this same (8WF31) "shape was selected as the member size to
be considered in this investigation o
(4) Material Descriptions
All of the material of this study was from the
~ame.rolling
\..
.
.
and was produced at the Bethlehem Plant of
the Bethlehem Steel Campany
0
It is a
~igh
tensile ti=
tanum steel meeting ASTM A=242 Specification o
Table 1
gives the chemical properties as supplied by the manu=
facturero
The material was in 'all cases tested in the
as-rolled condition o
It was not rotarized, gaged
in anyway cold=straighte:p.edo
j
nor
The measured residual
stresses should therefore be due to cooling aloneo Fig=
ure
4
shows the specimens as related to their position
in the rollingo
6
\~
11
0
DESCRIPTION OF TESTS
(1) Test Program
In summary, the test program for this investigat,ion
was as follows:
(A) Nine tensIon eoupontests
(B) Two compression coupon tests
(C) One set ,:of residual
stl~essmeasurements
(D) One stub column test
(E) Two axial column tests where bending
was allowed in the weak direction
Column curves were derived from the foregoing, and
were compared against "each other
0
Two columns of length
12 ft o and 9 ft o (Ljr=72, and L/r=54) were tested as' a
check of the theoryo
Comparisons 'Were also made between
these results and those obtained from the A=7 studyo
(2) Tension Coupon Tests
Nine tension coupons were tested, using a 120 000
jI
electronically operated, screw type Tinius Olsen testing
machine
.
0
The coupons were cut from the flanges and the
web of the cross section, as shown in Figure 50
The di-
mensions of these coupons were according to ASTM Standard(5)
(fUll thiclmess of the material and 1=1/2 in o width over
an 8-in o gage length) 0 .
An 8-ino Moore extensometer connected to an auto=
matic recorder was used to record the strains, and the
rate of straining was in each case 3 micro in/in/seco
Some
7
of the specimens were strained into strain ha.rdening range ~
at which time the strain rate was changed to 30 micro in/
~sec&
The Modulus of Elasticity 'was determined directly
from the recorded load=strain diagramo
elongation was
computed~
The percentage of
based on the measurements of the
original and the broken specimen as prescribed by the ASTM
Standard(5)0
Table 3 summarizes the results of these nine
tension coupons 0
(3) Compression Coupon Tests
Two compression coupons were tested, us1.ng the same
Tinius Olsen Machine' that was used for the tension coupons&
The specimens were cut from the tip of one of the flanges
'.
and
th~
center of
theweb~
as shown in Figure 60 The dimen=
sions were: 0 06 fJ x 0 &433" x 10 8o n* and 0045" x 0 288" x 10 35 11 ~
0
respectivelyo
These dimensions followed the recommendations
of Research Committee A of the Column Research Gounciloo
b>t'
That is ~
L ~ 4,~5t
r:, ~
2b
b
g ... 2b
.c::::
+
g
where g is the gage length (1/2~ino was used for these
tests)o
Strains were measured by means of an averaging
compr~ssometerf, whose measuring element was SR=4 gageso
The straining
r,~tefor
these tests was 1 micro in/in/sec
in both the elastic and plastic ranges o
o,
Width x thickness x length
ASTM Bulletin No o 215, JUly 1956
See Reference 6
8
Coupons rested on a bearing block and were provided
with a spherical bearing on top of the specimen o Alignment
under load was carefully checked before the testo
preliminary tests a load less than
one~·thi.rd
In these
of the estimated
yield load was used o When necessary, thin aluminum folls
were inserted as shims
The alignment was considered satls=
0
factory when the maximum strai.ns va:eied no more than
the average strain value
±5% .from
The stress·"'strain curves far thea e
0
tests are shown in Figure 6"
(4) Residual Stress Measurement - By Sectioning Method
A direct measurement of the residual strains (ad~
thereby stresses) was obtained by considering the original
material and then measuring it :in the released stateo
These
readings were taken over a lO=1nch gage length wi th a 1/10,000
Whittemore strain gage on a series of previously laid out
holes"
The final strains were measured after the 11=1nch
1/2~inch
section had been sawed into strips of
strip containing a pair of gage holes
width i each
A standard lO=inch
0
mild steel bar was attached to the specimen for correction
--
of readings due to temperature changes
"
0
the layout used in the sectioning methodo
Figure 7 indicates
The specimen was
cut near the stub column test specimen (see Fig o 4)0
was carefully selected to be free from yield lines o
It
•
9
(5) Stub Column Test
......'- ..
The stub column test was carried out to obtain a
direct stress=strain curve which would take into account
II.
the effect of the residual stress distribution across
the whole section.
The length of the specimen was selected such that
it would be short eBough to prevent column buckling
long enough so that the cutting at the ends, which
and
some~
what releases the residual stresses, would not affect the
stresses in the "gage section".
30 inches.
The length selected was
The specimen was tested in compression in
800,000~lb. screw~type
Riehle testing machine.
~
The ends
of the specimen were milled flat and between the upper
end and the head of the testing machine
a spherical bear-
ing block and plates were used.
Strains were measured by both SR=4 gages of one
inch gage length (type A=ll) and a pair of 1/10,000 dial
gagel3 over a
10~inch
,gage length act ing against a "frame"
attached at the middle of the flanges.
the positions of the strain gages.
Figure 9 shows
(The installation of
the dial gages can be 'seen from Fig. 15).
t~ps
Near the four
of the flanges, the average shortening of the stub
column was also measured, using four 1/1000 dial gages
and thin rods between the top and bottom bearing plates.
These corner dial gages were used for alignment.
•
=
The alignment was considered satisfactory when the
maximum deviation of one corner gage from the average of
the four gages was within
was about
one~third
:t.5%0
The maximum alignment load
of the anticipated proportional limit o
The specimen was whitewashed with a solution of
hydrated lime
0
Thig afforded a means of observing the ,
yielding process during'the testo
(Figo 17, 18, 19, 20,
21,22)0
The load increments were determined from the load
strain curve plotted during the test
Above the propor=
0
tional limit, criterion measurements were made and final
readings were taken ,when both the load and strains had
stabilized o
Testing was",continued beyond the point at which
.
the yield level was ,reached, until the load dropped 10
per cent and the specimen was severely buckledo
At this
stage, two of the 1/10,000 dial gages could no longer be
attached to the specimeno'
(6) Column Test
The columns were tested in the same 800,000=lb o
screw-type machine as the stub columno
The axial load
was applied through a set of end fixtures (Figo 24)0
detai~ed
A
description of these fixtures and test setup
using them is given in Reference 70
ured by means of
SR~4
gages of type
Strains were
A~ll
meas~
(one inch gage
length) le>cated at the center section and at positions
10
= 11
near both ends of the columns (Figo 23)"';
The ali.gnment
was checked by these SR=4 gages o Every reasonable effort
was made to ensure as concentric a loading as possible o
Both columns were tested such that failure would
occur in the weak direction..
Initia.l crookedness was
measured before the tests and was found to be essenti8.1ly
of a "single curvature type I! ~ having maximum values equal
to 3/+6-in .. and 3/32-ino
we;e>Ocoi86 and 00093
The corresponding ec/r 2 values
respectivelyo
During the test, de~
flections were measured by means of a transit and three
1/100 inch scales clamped tightly to the flange of the
column at the center section
and near both endso
While testing, load-strain and load=center deflection curves were plottedo
..
The load increments were
selected from a cons-ideration of the load=center deflect..,
ion curve..
Criterion measurements 'were made when the load
approached the critical values
0
These specimens 'were also
whitewashed so that the yielding process could.be followed
during'the testa
III..
~..
.
TEST
WITH
The testing setup is as shown in Fig o230
RESULTS
THE A-7
AND A COMPARISON
STEEL TEST SERIES
,
'( 1) . Coupon Test
The results of the tension and compression coupons
are listed in Table 4 and Table
5,
respectivelyo ""The re=
suIts obtained for the A=7 steel members having the same
shape (8WF3l) are also given ..
... 12
The Young U s modulus' of the coupon tests was obtained from an enlarged stress-strain diagram by direct
measurement
0
The pr·oportional li.mit 'was fmmd f:r'ctrl thi.s
diagram as the point at whlch deviation from linearits'first occurredo
average
st~ess
The yield stress was determlned as the
in the plastic range o
Percentage of 6p/6y vms determined' for both the
50
A-7 and A-242 steels, as shown in Table 4 and Table
For the tension coupon tests, it should be po:lnted out
that the strain rate was I micro in/in/sec. for the A-7
steel and 3 micro in/in/sec. for the A-242 steel o
For
the compression coupons, however, both speeds were I
micro in/in/sec
0
Comparatively, the ratio of the proportional
limit to the yielding stress for the high strength steel
is greater than that of the A-7 serieso
Therefore, the
effaet$ of'. residual stress'eS on the ,olumn strength of
members of high strength steel should be less
th~
that
for A-7 steels.,
(2) Residual Stress Measurement
The residual stress distribution across a section
was computed by using E
..
,'
residual strains.,
= 30,000,000
psi and the
measl~ed
The maximum value at the flange edge
was found to be 14.,8 ksi in compression, and at center of
the flange was 11.,7 ksi, in tension o
pattern is as shown in Fig o 8ao
The residual stress
"" 13
•
In Figure Sb, both the results of the A=7 steel
and the high strength steel are plotted for the purpose
of cornparison o
It is seen that they have approximately
the same magnitude and distribution o
Assuming that this
result is indicative of the general trend 9 the conclusion
can be made that the effect of residual stress on members
of high strength steel is relatively less than for members of the same size of A-7 steel o
Note that in Figure 8a the variation of residual
stress is very close to the idealized linear cooling residual stress pattern as indicated in Figure 1
0
(3) Stub Column Test
The flanges of the stub column specimen
inches length
buckled as indicated in Figure 9
of 30
before
the full yield stress level could be reached o The stressstrain diagram therefore dropped
a relatively constant yield level o
instead of maintaining
In general 9 it has
been found that this phenomena will occur if the flange
width to thickness ratio is greater than 17'(10)0
For
the S WF31 shape 9 the value of b/tF is iS050
From the stub-column tests, it was found that the
Ya~gts
limit
Modulus
6p
E = 31,200,000 psi and the proportional
= 39 02 ksio
The yield stress was
5604
ksi o The
first yield line, as determined by flaking of the whitewash, occurred at the flange edge at 51 ksl o
In the web,
the first yield line appeared at a stress equal to
ksi (about one kip before the'yie1d stress)o
5505
•
The stress-strain curves obtained from the lO=inch
gage length dial gages and the SR=4 strain gages are plot..,
ted in Figure 90
The compression coupon test result is
also plotted for comparison o
Since the SR=4 gage has only
a one-inch gage length, the strain readings eould be seriously affected by the yield condition within its length o
The column curve was therefore determined from the lO-inch
gage stress-strain curveo
The stress-tangent modulus diagram (Fig o 10) 'was
obtained by measuring the slope of the stress=strain curve
for the 10-inch gage at certain stress values
0
From Fi.g=
ure· 10 and Figure 11 the column curve was constructed as
shown in Figure 11, with the assumption that the residual
stress pattern has a linear variation
(~Io(2)
the influence of the web could be neglectedo
and that
The maximum
reduction in column strength (for bending in the weak di=
rection) was about 22 per cent less than the idealized
column strength
neglecting residual stress, and would
occur at a slenderness ratio of 740
As pointed out
earll~'
er, for members of A=7 s·teel the maximum reduct ion in some
cases has been as high as
35
per cent for bending in the
weak direction o
Table 6 gives the comparison of the values obtained from the compression coupons and the stub column testo
As will be noted, the E values did not agree very well o
This was possibly due to the inaccuracy of the
ga~e
fac-
tor of the compressometer used in the compressi.on coupons o
- 15
The value of the gage factor was taken as the average
•
value of the results from three
which was slightly
different~
calibrations~
Since the values obtained
from both tension coupons and stub
the· value E
= 31
.. "
.' I
200 ksi was
each of
colu~s
are
identical~
conside~ed reliable~
(4) Column Tests
The axially.loaded columns of 12 ft. and 9 ft o
(L/r = (72) and (54)
respectively) were tested, and the:;"
results were plotted on Figure
ll~
The load versus cen-
ter deflection curves were obtained during the tests
(Pig. 12, Fig.
l3)~
It is known that at the point of
bifurcation in the weak direction, the flange tips are
':"yielded due to'r'esidual stress and the stress due to the
':'ex~E?r.nall'Y applied;:~xial
,the,j:~olumn
load.
The effective st iffnes sof
is therefore reduced.
Once the column starts
buckling, it will continue to deflect at a relatively
fast"rate ~ti.i equilibrium can again be restored.
r~sult,
As a
it is extremely difficult to obtain any data with-
in this range for a column with a slenderness ratio in the
neighborhood where the Euler curve and the yield stress
meet.
Column C-l in Figure 12 is an indication of this
phenomenon.
The center deflection changed suddenly from
0.07-inch to 2.5 inches
0
For shorter members, however,
this condition is not so pronounced and unloadmg points
can be obtained.
column C-2.
These are shown in Figure 13 for test
"" 16
During the tests, deflections from the 8traight
configuration were observed before the theoretical tan=
gent modulus load was reached o
This no doubt 'was due to
the imperfection of the alignment and the initial c:rook=
edness of the columns o
C-l was 40003 kips
The critical load obtained for
and that for C... 2 was 4210.5 kips9 while
the predicted values from stub column test results were
398 kips and 429 kipsj respectivelyo
The dimensionless column curves (plotting -.Q. vs
6Y
.
a ~unction of L/r) for both A-7 steel and A=242 steel
for the same shape 8WF31 are shown in Figure
140
The
parameters are determined from the relationship
(5
cr
:.:::
n2 E
(L)2
-
r
C5
or
J..
6c.r
1
:=
-n
2
6y
0
F~
L
(_)2
r
and
CONCLUSIONS
1.
Residual stresses are present in high strength
steels and they do affect the carrying capacity of com=
pression memberso
2.
For the one section studied (F'ig o 8 ... 8WF31) j
the magnitUde and distribution of residual stresses are
comparable to those of the A-'7 series o
~
3&
17
Since the residual stresses in the A=242 study
and in the A=7 investigation were about
and sinee
equal~
their yleld points are quite di..fferent, the r'elative :l.n=
fluenee of residual stress on the compressive strengths
of members of high strength material is less pronouncedo
4&
Because the yield points are materially different,
however, the maximum deviation due to residual str'ess would
occur in relatively shorter members for the high strength
material (maximum deviation at L/r = 75) than for the A=7
(maximum deviation at L/r
= 90)0
For the weak axis con=
dition, the maximum reduction due to residual
stress~
as
compared to the full yield value, Py ' would be 22 per cent
and
5.
35
per
cent~t-
respect ivelyo
As mentioned. in the beginning of this report, the
materials tested were from the same ingot o ' Therefore the
conclusions apply in the strictest sense to only this one
situation o
It is considered, however, that they are in-
dicative of the general trend to be expected o
If more
conclusive results are required, further investigations
on various shapes and rollings should be made o
Reference
4,
page 19
"" 18
V"
1,.
REFERENCES
Fujita 9 Yo .
BUILT=UP GOLUl'1N STRENG~1fl
Dissertation for Ph"D,,:> Lehigh Unlvers::Lty
19,56
Shanley, FoR"
APPLIED COLUMN THEORY
:Trans" ASeE l.t5 9 698:>
3..
Bleich, F.
THE BUCKLJNG STREI:iJGTH OF METAL STRUCTURES
McGraw=Hi11 Book Coo, 1st Edo
1952
40
Huber, A. W. ·and Beedle, L. S.
RESIDUAL STRESS AND COMPRESSIVE STREI:iJGTH
OF STEEL
Weld~gJ9urnal, pp" 589S = 614S
December 1954
AS TM STANDARDS
E 8-46, po 1233,
6..
•
1950
1949
HUber, A.W.
COMPRESSIVE PROPERTIES OF ROLLED
STRUCTURAL STEEL
Fritz Laboratory Repa~t No o 220A,,1
Lehigh Universi.ty
1951
(
... 19
VIo NOMENCLATURE
A
Cross-sectional area
AF
Area of both flanges of WF shape
Area of the web of WF shape
.
b
Flange width
Be
Effective 'bending stiffness
d
Depth of Section
E
Youngis Modulus
Et
Tangent Modulus
I
Moment of Inertia
Ie
Moment of inertia of the elastic portion
of a partially yielded cross section
L
Length of column
L/r
Slendernes's -ratio
P
Axial loaGin column
P cr
Critical load on column
Pp
Proportional load
Pt
~angent
Py
Load at yield ,level
r
Radius of -gyration
t
Flange thickness
w
Web thickness
modulus load
E:Unit stram--'
6
Average stress'-
6p
Proport~onal-±imit
6 cr
Critical stress
6y
Yield stress level
't
Et/E
stress
.,. 20
VII,,·
ACKNOWLEDGMENTS
The author is deeply ind.ebted to Dr o R o L o Ketter,
who supervised this Thesis
0
His most valuable advice and
suggestions are sincerely appreciated o
This study was carried out as part of the investi=
gation on
RESIDUAL STRESSES,
of Dr o Lo So Beedle,
Lehigh University,
under the general direction
at the Fritz Engineering Laboratory,
p:fwhich; Pr().fesS'Or Wo.1. o"Eney. _.1s the
Director, and Head of the Department of Civil En,gineeringo
<=
TABLE 1
~
21
CHEMICAL PROPERTIES OF 8WF31
HIGH S1'RENGTH TITANIUM STEEL
Chem=
icals
JIlIn
P
S
Va
Ti
1 09
0,,027
0 027
0004
0 0013
C
0,,15
%
0
0
Chem~
icals
Si
Ni
Cr
Mo
Cu
·0'0·22
0;08
0005
0 002
0 14
-.
%
0
.'
TABLE 2= PHYSICAL PROPERTIES OF 8WF31
HIGH STRENGTH TITANIUM STEEL
TAic1mess
in.0.
.0029
Yield Point
psi
55/ 720
Tensile Strength
psi
76,720
Elon~ation
2106
The above reports were supplied by the Manu£acturer.
=
TABLE 3
=
22
SUMMARY OF TENSION COUPON RESULTS
8WF31 (High Strength)
Specimen
E
No"
ksi
d .
P
ksi
6y(st)
ksi
, 6y
ksi
%
6 u1t
;3& Area
E1ong~. Redue=
ksi
ation
tion
30,400 45.
59020 : :55084
76048
28 028
59 025
T2
30,560
41,,4
55064 51,,41
76.048
2$015
58 93
~3
]1,600. 4507
57054 54062
....---T1
0
53065
48039
57058
53.019
75 016
28,,19
52 053
58014
T8
30,860
4209
60 .. 28
I
=
23
TABLE 4 - COMPARISON OF AVERAGE TENSION COUPON RESULTS
OF
Type
A...7 AND A=242 S~EELS
(All Values, in ksi)
Shape
8WF31 Wet>
A-7
Weighted
%6
8505
6p
6y (u)
30,010
32 00
39 1
3704
29)27 0
2707
4206
3507' 7707
29)820
30 09
3.909
37 00
83
" .
Flange
6p
6y
E
0
y
.
J
Flange
31/180
4403
5804
5404
81 06
31,690
4509
5805
5406
84
31 300
4406
5804
5405
82
-
8WF3l Web
A-242
Weighted
..
/
I
TABLE. 5 ... COMPARISON OF AVERAGE COMPRESSION COUPON RESULTS
OF A""7 AND A",,242 STEELS
(All Values inksi)
Type
8WF3l
A-7
'E
Shape
6p
./
%~
6
6y
y
3906
Flange'
28,940
3004
Web
30,000
3000. 4:Jo.:~' 6905
Weighted
29,200 13003' 4005
Flange
29/850
4508
54 02 8404
Web
29.680
4409
57 01
79
Weighted
29,830
4505
5409
8208
77
._,...
A';'242
8WF31
The A;"'7 Values are taken from Reference
I
75,
4
.
TABLE 6
,~
COMPARISON OF COMPRESSION ,COUPON
AND STUB COLUMN TEST RESULTS
(8WF31- A-242)
(All Values in ksi)
Ratio
A-242 'Steel
of
6
,p
Stub Column
Average
Compression.
Coupon
·'
•. _'.'.':
'
-,'
TABLE 7 -.. TABLE OFSPECIME:N NUMBERS
.
:",
T~n~~,C?n Coupons
TI, T2, T3, T4, T5, T6, T7, T8, T9
Compression Coupons
Residual Stress Measurement
Stub Column
Columns
CC ...I ,
,
CC...2
... 25
•
+
F!g. 1 ... /IDEALIZED RESIDUAL STRESS DISTRIBUTION,
6
Neglecting Residual Stress
6
__ ,L~ _..----..,./
Including
Residual Stress
d6
Et
='d€
Average (5 ... Eo Curve
of Se c t ion as a Whole
'E
Euler
L
r
Fig. 2 ... EFFECT OF RESIDUAL STRESS ON COLUMN STRENGTH
~
r
L
- - - -x-
Fig.
1
26
-u.
\\
\\
\\
II
II
II
<
II
II
'l
3 - BENT COLUMN WITH PARTIALLY YIELDED CROSS SECTION
8WF3l
I·
I.
)'
t
C-2
C-I
50
SoCol)
~l
I·
I_··_,--~
1. 12 ft .1
.1
0
ft
0
-
_
R.S.I~n
~
12 fto
..
I
Shaded Portion~ Discarded
Spec imen Numbers ~ See Table 7
Fig.
4 -
POSITIONS OF JJ.\fDIVIDUAL SPECIMENS
- 27
50
6
ksi
40
(A)
SpecimenT9
Cross-Sectional Area
0.648 sq in.
Young's Modulus 31,600 'ksi
(B)
Specimen T5···
Cross-Sectional Area
0.434 sq in.
Young's Modulus 32,300 ksi
30
20
10
0
1
2
3
4
5
6
7
8
fl( 10~.3
-
Fig. 5(b), TENSION COUPO\N
6 - E.
10
9
in/in.
DIAGRAM (A-242 STEEL)
8WF31
P
Oo432'~ I
60
50 -
lo802"r~
6
ksi
•
0 0599"
1.1_0
--_._--_.- ..
0 00 01..
H
t
IP
L3S'[[]
, - - CoO 02
0028~ H
tOo44411
30
. P
20
r8H~
T(~-2
10
[
o
~
-Jl-
1
.-..J..
~
..-1..- _
3
2
Figo 6 ., DIMENSIONS AND 6
c:=::::::...::=C=C=:J
=
E
DIAGRAMS
OF COMPRESSION COUPONS (A=242 STEEL)
4
em
Sa.w Cuts
0'
!~
-Ill" r-
[
.3 Y-6"
I:
)[
]
~
12 u- 0"
.
For Whittemore
Strain Gage
8WG31
Fig" 7
=
RESIDUAL STRESS DISTRIBUTION
BY SECTIONING NETHOD
29
"'" 30
Compression
Corrrr.'J!' e IS IS lon
-----
---]
,
....,.-~
-j
Flange Dlst1"':1.bution
.. a
!
~
1_--'-'_ - - J l .
:5
10
o
5
o
ksi
10
ksi
•
8WF31
High Strength .
lJ:'ension
Tension
I
Web! D1.s tr' ibut ion
1,,=------.------..-.,
. 10-.
5
~
ksi
---,-r---,-.
i
Fig o 8a
e----
Inner Surface
0---
Outer Surface
~.
RESIDUAL STRESS DISTRIBUTION OF
'( Sectioning Method)
~=242
STEEL
,J.
8WF31
. C(')'rrlJY.r" e E\ is:1 on
10
.
'.
1~.~i"~"=f~~"=~~~'cd
.
10 IG3:J..
•
.
. _
A ~~-4?
S+m
"1" (R'
a o l~J
'.,I::ic,l,
,.0Y
"---.
Ms.x:hrm.m Values
.... ~
--~------_
Test
Flange
'Web
Flange
Edge
Center
Genter'
1'!o
1------+-------4------4-------- --.----.-.
0
T-2
T. -O
.A~7
1205
------+_._-------~-----_.-
·7
~,~
A
.~I~,
.... {
0,"~
4.2
---_..
~
.?o
5.0..-..._.-
----~-----
'7
9 6
0
-------+---------+--------.....--------- -_........--......,_...
RoSa 1
~:2~:_.L, 140e
_..__~O 00__ . 201 _
F:lgo 8b
=
RESIDUAl~
0 .p.1:1
STRESS DISTRIBUTION
A "7 a.n
. d. ...A-..:....L.~~.
,")i·--; (~f'iTr;1""'IS'
"L:£J.li.t i
go)
,
i.,p'
..
.PosItions Where Str.ains
Were Measured
8WF31
(High. Strength)
--,'-----\.
•
(\
""00
\J
1/:"11•..'L'J
<;J
D1.a.~.i.
~
Gage
60
/
6
ksi.
1-1- 0
30
20
10 .
Figo 9
•
~
STUB COLUMN d ", 'E CURVES
eo,
33
30
ksl
20 .
o
~_-"-
__L - - _ - - ' -_ _"'--_-.J<..._.
20
1.0
30
50
uO
...&:-.&--._ _
60
() Cksi)
Fig o 10 ,~ 6 <~ E t
CURVE. DETERMINED FROM STUB COLUMN TEST
60 .
.50
6
. ks!
Euler
"30
20 '
~I
"'J
n
©
Wea.k A:riis
~
u
,)
n
o
o
~
20.
40
"
j
Test Results
o
i
!j
n
!
6
~
~
n
60
JL _
n
80
100
JL
_
120
_
~~~..JL._.........,"-
140
160
L
r'
Fl.g o 11
.
=
COLUMN CURVE FROJYI STUB COLUMN TEST
(Based On 1/10.000 Dial Gages)
180
figa 12 - LOAD=DEFLECrr'ION CURVE FOR
C~,l
400
P
kips
.
I"~
1-'
.1
L
ca.
r
=:
S4
9U
"
t
i
0
1 :in o
F'ig o 1.3
=
LOAD=DEFLECTION CURVE FOR
2 in o
C<~2
~{ (in)
r.::'.J
J r'
~?
8WF31
o
Fig o
~
14
=
DIMENSIONLESS COLUMN CURVES
Data Taken From Reference
4
r
~.
F go
15
<=>
STUB COLUMN 1.JEST SETUP
8WF31) SoOo"1
Fig o 16 = STUB COLUMN TEST IN PROGRESS
(8WF31) S oOo=1
36
37
Figo 17 ..,
8WF31 STUB COLUMN AT LOAD 455k
(Yield Lines
Fig o
First Vi ible
18 - AT LOAD OF 485k
•
F' go 19 '-' FLANGE SLIGHTLY BUCKLED AT LOAD soak
Figo 20
=
YIELDING CONDl'rIONS WHEN I.0AI) P y :::: 5040 3k
•
~
•
•
}i1ig o 2il
•
l!t
STUB COLUMN T'EST COMPLETED
Fig o 22 - ANOTHER VIEW OF COMPLETED
STUB COLUm TEST
39
•
=
.
•
igo 23
=
COLU}W SPECIHEN SETUP IN Soak
SCREW"" (PH:;
•
TEST'ING MACHINE
40
•
•
•
Figo
24 -
BOTTOM AND FIXTURE FOR COLUMN TEST
•
•
•
." 42
•
•
•
•
Fig o
•
25
~ COLUMN TEST IN PROGRESS
•
"" 43
•
.
...
Figo 26 - SUDDEN FA ILURE 9 AF'TER REACHING
OR ITICAL
•
•
LOAD
•
•
•
•
•
..
•
•
_ _ --J
Fig o 27
•
~
COMPLETED
TEST~
C-I
•
'-' 45
,
•
•
•
•
Figo 28
•
•
~
COMPLETED TEST, C-2
•
•
VI T A
George Chao-Chi Lee, first child of Dr. and Mrs.
S. 'Co Lee, was born on July 17, 1932 at Peiking, China.
He attended the Nati onal Taiw'an Uni versi ty in
•
•
the Department of Civil Engineering from September 1951
to June 1955.
Upon completion of his scholastic require-
ments at Taiwan Uni versi ty, he was called for military
service with the Engineering Corps of the Chinese Air
Force for a period of one year.
In September
1956,
he received the degree of B. S. in Civil Engineering.
He came to the United States in September 1956 as
a research fellow doing graduate work at Lehigh Univer'sity .and was re-appointed as a research assistant in
Fritz Engineering Laboratory in April 1957.
•
•
•