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RESIDUAL STRESS AND THE COMPRESSIVE PROPERTIES OF STEEL

Progress Report

MATERIAL PROPERTIES OF STRUCTURAL STEEL

by

Lambert Tall

(Not for Publication)

This work has been carried out as a part of an investiga­tion sponsored jointly by the Column Research Council, thePennsylvania Department of Highways and Bureau of Public Roads,and the National Science Foundation.

Fritz Engineering Laboratory

Department of Civil Engineering

Lehigh University

Bethlehem, Pennsylvania

April 1958

Fritz Laboratory Report No. 220A.28A

220A.28A SYNOPSIS

This report is the summary of certain aspects of the work

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on the general project "R~sidual Stress and the Con:q:>ressive Properties

of Steel", this phase being concerned with the relationship between

material properties and the strength of columns.

The overall objectives of the project were the determina-

tion of the behavior of columns containing residual stresses, the

magnitude and distribution of these stresses, and the development of

methods of predicting the influence of residual stresses on column

strength. As a necessary foundation for the complete study, the pro-

gram included a determination of the basic yield stress level of A.S.T.M.

A -7, mild structural steel of which columns of the type found in civil

engineering structures would be fabricated. This report is mainly con-

cerned with this basic yield strength.

The determination of the yield stress level and associated

properties, will give a better understanding of the behavior of mem-

bers made from this material. The results will therefore enable one

to obtain a more reaJ.istic meaning of the factor of safety used in

steel design today.

Methods and correlations used are shawn, so that the extent

and trends in the variation of the strength of steel will be apparent.

Both the elastic and plastic properties' are considered.-'\

Within the limits indicated, the correlation of the results

are good, although a greater sample of specimens would be expected to

limit further the range of variation for any particular parameter, par-

, ticularly in the case of residual stress prediction.

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TABLE OF CONTENTS

S-mOPSIS

I. THE YIELD STRESS

A. Introduction

B. Description

1. Yield Stress, Definition

2. Stub Column Tests

3. Tension Coupon Tests

4. Correlations

C. Results

1. The Static Level Of Yield Stress

2. The lMill Reports 1 For Yield Strength

3" Comparison or Mill Tests With The ~ys

4. Evaluation Of r?!ys, Static Level

Of The Yield Stress

5. Variation Of The Yield Strength

With The Strain Rate

6. Tension Versus Compression Coupons

7. Variation In Properties Of Specimens

From Web And Flange

@RESIDUAL STRESSES

A. Introduction And Description

B. Results

1. Residual Stress Distribution

In Wide Flange Shapes

2" Residual Stress From Stub Column Tests

3. Residual Stress Prediction

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Table of Contents

III. OTHER MATERIAL PROPERTIES

A. Introduction And Description

B. Results

1. Young f s Modulus, E

2. Comparison Of Coupon And Stub Colunm

Results For E

3. Strain Hardening Modulus, Est

4. The Ultimate Strength Of A Tension Coupon

5. Typical Stre"ss-Strain Curve

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IV. DISCUSSION 23

V. CONCLUS IONS 32

VI • ACKNOWLEDGMENTS 34..\VII. REFERENCES 35

" VIII.APPENDIX: 37

1. Nomenclature

2. Tables

3. Figures

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220A.28A

I. THE YIELD STRESS--A. JNTRODUCTION

At first glance, there are enough levels of yield stress to

satisfy even the most exacting-connoisseur of definitions. It would

appear that which ever reasonable value be estimated at random for

use in design, justification of it, to a greater or lesser degree,

exists. Further, it is common knowledge that increase in the speed

of testing of a coupon will increase the yield stress level, and that

such a value has little use, unless it is defined by a testing speed.

It is the purpose of this chapter to consider the factors that

have an influence on the yield stress, and to show how a prediction of

this value is possible from the mill reports. To deduce and substantiate

the conclusions, the mill coupon tests were simulated under strict speed

control in the laboratory. Further data were deduced from stub column

tests, using the full cross section. To make the study as complete as

possible, data from other investigations were also included where re-

quired.

B. DESCRIPTION

1. Yield Stress - definition

The following terms are relevant in describing the yield strength

of a steel coupon, see Figure 1.

-The upper yield point, OUy,"the first stress in a material, less

than the maximum attainable stress, at which an increase in strain

occurs without an increase in stress l' (ASTM definition of ryield

point r .)

-The lower yield point, (j y, the lowest level of yield stress imme-

diately following OUy.

220A. 28A -2

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-The yield stress level, Ojr, the average stress during actual yielding

in the plastic range, which rema:ins fairly constant, provided the

strain rate remains constant. (ASTM def:inition of yield strength:

lithe stress at which a material exhibits a specified limiting de­

viation from the proportionality of stress to strain. lI )

-The proportional limit, 6p, lithe greatest stress which a material is

capable of develop:ing without any deviation from proportionality

of stress to strain" (ASTM definition.) 6p is very closely equal

to O'y for a coupon, particularly if the coupon is annealed. This

is not necessarily the case for the cross section as a whole.

-Also, where no definite yield stress level may exist, as is the case

occasionally, a 0.2% offset is used to define a value for compara-

-tive purposes.

It is seen from Figure 1 that a great variation in the magnitude of the

stress associated with the different terms defined above does not exist.

This has lead to some confusion of terms.

Until recently, both the upper and the ldwer yield points have

been used as a basis for the estimation of the yield stress. Indeed,

it is common practice .:in testing coupons to record the yield as the

reading indicated_by the·free 'follower' pointer on th.e load indicator

dial, the actual load having dropped somewhat. This paper will define

the yield strength as the yield stress at the s.tatic level, that is,

the value for cry when the strain rate is zero. (The effect ()f strain

rate will be discussed :in section c-5.) Use of this static level is

logical, since most structural loads can be considered as primarily

static.

.220A. 28A

2. Stub Column Tests-A number of stub column tests, with material supplied by

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different manufacturers, were conducted so that an evaluation could be

made of the behavior of the full cross section of WF shapes. The results

obtained provided an important basis for correlation of the yield strength

with test coupons, and mill test data.

The stress-strain curve determined from such a stub colunm

test is of decided use in column strength predictions. As shown in Ref-

erence 1, the overall stress-strain picture enables use of the tangent

modulus concept. Further, other relevant data can be obtained, as shown

below, for the full cross section:

1. Young's Modulus, E.2. Proportional lilnit, op3. The rnaxilnum res idual stress (or=oy-or,), the

evidence of this being at the position ofthe first yield line on the Whitewash, orthe deviation from linearity of the load­deformation diagram. With as-rolled WFshapes, this yielding usually occurs atthe flange tips.

4. The static yield level, ()ys5. The overall effect of the residual stresses

on the cross section, as evidenced by. the .'Imee' of the stress-strain curve.

In general the speed of testing for these stub colunms may be

regarded as static2• Increments of load were applied slowly and once

yielding had begun, care was taken that both strain and load had stab­

ilized before readings were recorded8• The tests were conducted in

either a 5,000,000 pound capacity hydraulic or an 800,000 p01llld capacity

screw-type mechanical 1llliversal testing machine.

220A.28A -4

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~ Tension Coupon Tests

These tests covered a wider range of shapes than did the stub

column tests, due to both their ease of testing and economy.

The coupons were cut fr om the web and flange as shown in Figure

2, and then shaped to ASTH standards, (see Figure 3). The coupons were

all tested in a 120,000 pound Tinius Olsen universal testing machine, of

the screw-power-type with a positive control over the speed of the cross

head. In a few cases, the limited capacity of the machine requred that

the test be continued to rupture in a larger capacity testing machine •.,

Automatic electronic recording equipment was used to plot the load-strain

curve, which generally just reached into the strain hardening range, (see

Figure 11).

The tests were conducted so that the static level of yield stre~s

was also obtained. The speed of testing used was that recommended in Ref-

erence 3, being chosen so that the mill test of a steel manufacturer c'ould

be sinmlated. (Crosshead speed shall not exceed 1/16 in. per minute per

inch of gage length.)

From the load-strain curve then, the following data were ob-

tained; Young's Modulus, Proportional Limit, Upper and Lower Yield Levels

if any, the yield stress level at the strain rate used, the static yield

level,and, where it occurred on the recording paper, an estimation of the

strain hardening modulus. Combination of data from web and flange accord-

ing to their respective areas in the full cross section was employed to

show, by comparison, whether such methods will give an accurate indication

of the yield stress and other data.

The effect of strain rate on the apparent strength of steel

in testing has been given considerable attention, and data is presented

220A.28A -5

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that will enable predictions for the static yield strength knowing the

speed of test:ing. Although it has been known :in the past that the strain

rate has an effect, very little data was available.

1t.:. Correlations

Comparisons were made between the results of all the tests;

stub columns, coupons, mill reports, as well as data obtained in other

investigations.

The steel was supplied by Company IIAII· and by Company "B",

for both tension coupon and stub column tests. The results are shown

both separately and combined, for in some cases it was felt that com­

bination of the data obtained from the steels of the different companies

could lead to inconsistencies. The data where the values have been

combined will be useful in strength predictions when the orig:in of the

material in question is unknown •

C. RESULTS

1:. The Static Level of Yield Stress

Refer to. Section c-5 on strain rate.

(a) Stub Column Tests

From Tables II, III, and Figure 4, it is seen that:

material flAil () ys= 33.1 ksi mean value (20 specimens)

IIB" c)ys= 35.0 ksi mean value (13 specimens)

Average cJys= 33.9 ksi mean value (33 specimens)

Note: The 14 WF 426 had no apparent yield stress level, i.e. the

material continually strain-hardened.

220A.28A

(b) Simulated Mill Tests

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These are the weighted mean of the individual coupon tests. The indi-

vidual data is recorded in Tables IT and ITI, and in Figure 5.

-material "A" <J ys= 32.8 ksi mean value (22 specimens)

lIB" ifys= 34.6 ksi mean value (13 specimens)

Average CJ ys= 33.5 ksi mean·value (35 specimens)

2. The "Mill Reports" for Yield Strength

The mill report for the yield strength of steel is based on a

tension test of a coupon cut from the web of the particular shape carried

out in the manufacturer's own laboratory, as part of his control on pro-

duct ion. The tests are conducted at speeds allowed by ASTM and approxi-

mately the same as those advised in Reference 3. The results then give

the yield strength for a "dynamic" level a'yd, where· dynamic is used as

opposed to static. It will be further defined later •

The I'sirnulatedll mill tests were tension coupon tests conducted

in Fritz Laboratory as outlined in section B-3, on web coupons cut from

the WF shapes. "The speed of testing "s irnulated" that of mill laboratory

practice, and was according to the speed recommended in the previous.

paragraph.

(a) Mill Tests, Figure 6.

material "A" <ryd= 42.8 ksi mean value (24 specimens)

"B" cryd= 41.5 ksi mean value (14 specimens)

Average cryd= 42.3 ksi mean value (38 specimens)

!'i91!: 3000 material liB" mill tests gave: cYyd=44.1 ksi (Reference 4)

(b) "Sirnulated" Mill Tests, Figure 7.

material "All cJyd= 40.1 ksi mean value (24 specimens)

IlBIl 0'yd= 41.4 ksi mean value (13 specimens)Average cryd= 40.6 ksi mean value (37 specimens)

220A.28A -7

l:. COmparison of Mill Test Results with the C) ys

To allow a prediction to be made 'of the static level of yield

stress rs ys from the mill test reports, a comparison of these results was

made as a ratio of the former to the latter, (that is, \SysfJy mill tests.)

Tabulation of the results is shown in Tables II and III, with the distri-

bution shown in Figure 8. Except for some material "BII results, as shown

in Table III, the yield stress is taken as the weighted static value from

the coupon tests, it being shown later that such a value is equivalent to

that obtained from a stub column test.

(a) Comparison Using Mill Results, rsysfJy mill, Figure 8

material IIA", rati 0 =liB", ratio =

Average ratio =

76% mean value

84% mean value

79% mean value

(20 specimenf!)

(13 specimens)

(33 specimens)

•(b) Comparison Using lISimulated" Mill Results, Figure 8

These results have very little application and are recorded'

only for comparison. Assuming that the materials are equal, they do in-

dicate however that company IIA" appears to run its mill tests at a

slightly higher testing speed than company liB".

material IIAII ratio = 81% mean value (22 specimens)

IIBII ratio = 84% mean value (13 specimens)

Average ratio = 82% mean value (3.5 specimens)

l:!.:. Evaluation of cr"ys, Static Level of Yield Stress

by comparison of values from stub columns and from tension coupons.

This set of comparisons was made to see whether the static

yield stress ofa WF shape, obtained from the tension coupons by

weighting and averaging according to respective areas of flanges and

web, could ~pproximate the value of the static yield stress obtained

220A.28A

from a stub column test on the full cross section.

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• 0-ys stub columnRat~o: d"'ys weighted coupons , Figure 9

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material "All ratio = 99.1% mean value (18 specimens)

lIB" ratio =100.5% mean value ( 6 specimens)

Average ratio =99.5% mean value (24 specimens)

2.:. Variation of Yield Strength with the Strain Rate

The yield strength of steel is directly affected by the rate or

straining. This may be regarded as a property of steel, and the phenomenon

has been studied and observed on numerous occasions in the past'. Gen-

erally speaking the greater the speed of straining, the higher the yield

point tends to become, until the limit when. the ultimate load is reaohed

without yielding.

It is realized therefore that the definition of the testing

speed of a coupon is of the utmost :iJTIportance as a particular type of

steel could have an infinite number of values for the yield strength.

Actually, this is exactly what does happenl Nor do the specifioations

take account of size effect in coupons, and differences in testing rna':'

chines4. Although the ASTM has tentative specifications limiting the

maximum testing rate, it would appear that some investigators use lower

rates than others with the result that discrepancies exist as high as

20% in the measured value for yield strength. At this juncture it

should be noted that strain rate does not account for all the variation

between tests - it cannot account for material differences or manufac-

turing methods. However, the difference due to chemical and other man­

ufacturing properties can be more clearly evaluated if these superim-

posed artificial discrepancies of strain rate are removed.

220A.28A -9

This influence of strain rate was investigated by Mars'hman5.

This chapter will briefly describe the problems of strain rate and will

indicate some of the results that were obtained.

The greatest practical difficulty associated with strain rate

is its measurement. Although this is not difficult if specially measured,

it is not possible to use an indicated free moving crosshead speed as the

strain rate for any particular machine. This is particularly true with

an hydraulic testing machine. Due to the fact that during testing, the

machine itself is deforming, an adjustment Imlst be made to the indicated

free-running cross head speed to obtain the actual rate of straining. It

is in the elastic protion of the loading that this effect has its greatest

influence, for as the load increases, the strains and thereby the defor-

mations of the various parts of the machine also increase. 'l.'he result

•is that the indicated testing speed (free-running) is progressively de­

creased. This state of affairs continues till the yield point is reached.

At this instance, when the specimen starts to plastically deform, the

load is constant and no further elastic deformation of the machine can

take place. For such a case, the movement between the cross heads is

entirely due to the plastic yielding of the specimen. That is, except

for a negligible part of the strain rate being taken up with keeping tl+e

deformed testing machine in equilibrium under the applied, for practical

purposes now constant load, the specimen is "straining" at the indicated

free-running speed.

Although the indicated strain rate bel~T yield point is not

representative 'of the actual strain rate, and therefore cannot be used,

once the yield point has been reached and the load and strain rate have

stabilized, the indicated ratio of dynamic to static yield points has a

220A.28A -10

' .. definite level which is dependent on the testing speed. A plot of this

ratio versus testing speed is shmm. in Figure 10. It should be noted that

the curve is the result of a number of tests of plate specimens, (bar

stock.) All tests were carried out on the same mechanical testing machine.

The dynamic yield stress, O"yd, is defined as the yield stress at

a particular strain rate other' than' the zero strain rate.' The stat:i.c yield

stress is the limit case and is defined as the yield stress at the zero

strain rateo

Tests' have shown that the static yield level may be determined

without actually conducting the experiment in its entirety at a zero strain

rate, which, moreover, would be impossible. All that is required is that

the strain rate be decreased to zero in the plastic region and that a few

m~utes be taken to allow the load to decrease to the minimum. (In the

case of hYdraulic machines, care must be taken that the static level is

approached from the positive side ; that is, no strain reversal is to be

allowed.) The effect of this on a stress-strain curve is shawn in Figure

11, a typical stress-strain curve from the series of coupon tests run on

the screw-type mechanical testing machine. This static yield leve'l property

has not been proved conclusively on a large number of tests, but it is

felt that the series conducted' may be regarded as indicative of the be­

havior to be expected, due to their excellent correlation.

Figure 12 indicates a further observation tending to bear out

the foregoing conclusions; namely, that in the plastic yield range the

<Jyd depends on the testing speed, whereas, the r:rys, as obtained by

stopping the movement of the cross-head, is relatively constanto

£.:. Tension Versus Compression Coupons

Although no compression coupons were used in this series of

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tests, previous investigations have shown that, on the average, tension

and compression coupons give results that are almost indentica18. These

results and conclusions will be repeated here in summary form (see TabJ,e

V). Although these particular results are for one shape, 8WF31, exper-

ience with other shapes give the same indications.

Quoting from Reference 8:

liThe 'elimination of compression testing ofcoupons (in the case of rolled structuralsteel shapes) is thus considered as warranted,particularly in view of larger variation inproperties due to other causes. 1t

Compression testing of coupons is much more difficult as compared to the

case of testing tension coupons.

Considering the full cross-section, the static yield level as

determined from stub column 'tests was almost identical with that deter-

mined from the weighted mean of the tension coupqns as shown in Figure 9.

1:.. Variation in Properties of Specimens from Web and Flange

There is conflicting opinion on the sub ject of whether th~

shape and size of a specimen has any appreciable effect on its physical

properties. Previous investigations4,7 have shown that this effect

may exist in coupon testing, but the tests described in this report

seem to indicate that no conclusions can be made in either direction.

This se?tion presents a summary of certain results, shown in

Tables II and III and in some of the figures. The yield strength

,,'both at the static and the dynamic level is considered as is also the

ultimate strength.

(a) (5'ys, Static Yield Stress, refer to Figure 5.

From simulated mill coupon tests, weighted means:

220A.28A

material "Art mean = 32.8 ksi (22 specimens)

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range· below29 ksi: 14WF320 = 22 0 7 ksi

12WF190 = 26.800 67 = 2603

range 29-37 ksi: 100105,14WF 61,12WF 92,12WF 50,100 33,

16WF 88,12WF142,12WF 65,100' 66,

8WF 35

14WFll114WF 7812WF 53·100' 39

range above37 ksi: 00 31 =3709 ksi

8W.F 24· 37086WF1505 a, 4303.5WF18 0 5 =41 0 3

material rtBIi mean • 34.6 ksi (13 specimens)

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range 29-37 k6i~ 18WF'105,14WF 78,1M' 53,

6WF 25

100'88.,14WF61,10WF66,

14WF11112WF190

6WF15.5

range below29 ksi:

range above37 ksi:

The above sum:m.ary should be considered with Tables II and III.

It is then seen that in generalJl as would be expected, the heavier sec­

tions have a lower <5 ys Jl while lighter sections have a higher 6ys

than the mean o

Since the flanges are the. controlling factor in the determina-

tion of column strength of WF members both for buckling and direct loads,

the bit and oc:::: (Area of Flange/Area of Web) ratios were also considered~

The indications from the small number of.results on hand are that:

shapes with bit = approxo -10 or less, have U ys < 28 ksi

bit = approx. 18 or more, have .0'"ys > 37 ksi

220A.28A

shapes with 0('< approxo 25, have

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r 28>G"'ys orl crys >- 37 ksi

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The stub column values for ()ys were also considered. It may

be seen that the indications are exactly the Sallle as for the coupons,

although the results are less random, that is, the spread is narrower.I

(b) cryd, Dynalllic Yield Stress, Figure 6

mill test - web coupon results

In tPis case, the Sallle general indications hold as for the cases above.

This can be seen from the reasonably constant histogralll. It should be noted,

however, that the results are more random. Since cryd is not defined for

a particular strain rate, testing differences are probably present.

(c) o-ult. The Ultimate Stress, Based on Reduced Area.actual

Refer to Tables II, III and to Figure 20. (from simulated mill

coupon tests, weighted means.)

35 specimens were considered and to obtain a more realistic picture, the

ultimate stress was based on the reduced area at failure. From the histo...

gralll, it is seen that the spread of results is extremely narrow with only

the folloWing shapes not in the range 120-150 ksi.

material IIAII g

material liB II :

IBWFI05 = 110.5 ksi14WF228 = 187.512WF 53 = 114.5

14WF426 = 106.5 ksi14WF142 = 154.314WF 61 = 157.5

These results appear to be random displacements from the mean, rather

than due to any physical properties of the cross-section shape.

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III. RESIDUAL STRESSES-A. INTRODUCTION AND DESCRIPrION

The study of residual stresses has been intensified in the

last five years. This is mainly due to an increasing appreciation of'

their effect on the buckling strength of colurims. These studies have

brought to light many factors that have explained past failures of

correlation between experimental and predicted values for column strengths8•

While residual stresses have also been studied in built up columns, this

paper will only be concerned with the cooling initial stresses in ltas-

delivered It rolled shapes of A 7 type steel.

Residual stresses are the non-calculated, ~itial stresses that

are present in a structural member prior to the application of load. These,

in the main, are due to uneven cooling of the member during and after hot

rolling. However, residual stresses may also be formed by various fabri-

cation methods such as welding and cold bending. As a general rule, thej,,~

effect of these other types of initial stresses CJfJ less pronounced.

The measurement of residual stresses of the type in question

(longitudinal stresses) is best accomplished by the "sectioning" method,

whereby the member is measured before and after cutting into longitudinal

strips. This cutting releases the stresses enabling the sectioned strips

to deform freely according to the relaxation of their internal forces.

This method is explained at length in Reference 8~

A typical residual stress distribution diagram for a WF shape

is shown in Figure 13 where the terminology is also explained. Generally,

these distributions may be approximated quite well by straight line seg-

ments. From a knowledge of this distribution it is possible to predict

the average ()'-£, curve including the influence of this variable forthe

full cross section and the procedure is described in Reference 8.

220A.28A -15

It has been shown in these previous studies8 that, due to the

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symmetry of the residual stress pattern, an actual stub column test gives

a more accurate and far simpler means of obtaining the average 6-£ curve

than the lengthy calculations that are required starting from a measured

residual stress distribution. The importance of this average curve is that

the apparent tangent modulus values obtained can be related to the carrying

capacity of the member and thus column strengths can be predicted. It should

be pointed out, however, that while the uknee lf of the average C5"- £ curve

shows the effect of the residual stress distribution, it does not enable

the specific distribution to be determined. crrc , which can be determined, is

the largest inherent residual stress and defines the proportional limit.

B. RESULTS

1:. Residual Stress Distribution in WF Shapes

The results of the previous investigations are summarized in

Table VI, while Table V gives the individual detailed results. This will

give an indication of the distribution of residual stress in WF shapes.

In all cases the method of ttsectioning tt was used.

2. Residual Stress from Stub Column Tests- -----------....-..;;......._..--........~--.....---......-The limit of proportionality of the stress strain curve gives an

indication of the magnitude of the maximum compressive residual stress

that occurs in the flange, C5 rc.

( (j'rc = (Jy _ (Jp )

To take account of local high residual stresses and to obtain

by interpolation a basic value for (Jrc presumed to exist when these are

not present, a <S - E. curve of the type shown in Figure 1h was modif~ed

in the following manner~ The portion of the curve above. the proportional

220A.28A

limit, although with a. very slight curVature, may be considered as a

straight line. The tangent point of this line with the "knee" of the

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curve is then taken as a pseudo-proportional limit, thus defining what in

this report will be regarded as a basic value for cJ rc, when discussing

the results of stub column tests.

The following results which are shown in Figure 15 are of two

types, the actual residual stress average and, where necessary, this

average, modified value as explained above.

To show whether crr, the maximum residual stress as determined

from a stub column test, is a function of the yield stress or not, the

ratio rsr/ r:5ys has also been considered with 0'r both modified and un-

modified. The results are shown in Figure 16.

(a) ($r from Stub Column. Figure 15

material IIA" cr r .,. 13.5 ksi mean value. ()r.mod .,. 10.5 ksi mean value

material liB" err'" 14.6 ksi mean value

(Jr.mod = 12.6 ksi mean value

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average (Jr = 13.8 ksi mean value

cr r:mod = 11.1 ksi mean value

(19 specimens)(19 specimens)

( 7 specimens)

( 7 specimens)

(26 specimens)

(26 specimens)

...

(b) O'r/(J'ys from Stub Column. Figure 16.

material IIA" CSr /C5ys .,. 41.1% mean value (19 specimens)

()r /cJys.mod = 32.9% mean value (19 specimens)

material "B" (Sr/ crys = 41.5~ mean value ( 7 specimens)

0-r /cJys.mod = 35.6% mean value ( 7 specimens)

average crr/ (Sys .,. 41. 2% mean value (26 specimens)

6rjCJys.mod .,. 33.6% mean value (26 specimens)

220A.28A -17

~ Residual Stress Prediction

Attempts have been made in the pastlOto correlate the residual stresses

of a shape with its physical properties, such as b, d, t, 'W. This has als 0

been attempted in the present investigation. Unfortunately, the only state-

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ment that can be made regarding these studies is that no definite tendencies

seem to exist.

It is felt that S/iCient accuracy is obtained by estimating Value1')~from the tables of results' already at_ hand. )

220A.28A -18

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III. OTHER MATERIAL PROPERTIES

A. INTRODUCTION AND DESCRIPrION

The determination of tne yield strength of a material is usually

accompanied by the finding of the eLastic modulus. Furthermore, if the test

be on a coupon, the ultimate strength and strain hardening modulus are also

easily obtained.

This chapter seeks to present additional data on the following

properties:

I •. Young's modulus, E, and

2. Ultimate strength of a tension coupon.

The strain hardening modulus, Est, may also be obtained from

coupon and stub column tests, but its determination was not included in

this program.

The two moduli, E and Est, may be defined as the ratio of stress

to strain in the elastic and at the on-set of the strain hardening ranges.

E is a constant up to the proportional limit. Est is never constant, and

is usually defined at the onset of the strain hardening since it is this

value that is important in solving many stability problems.

The procedure of testing with tension coupons has been described

above. The results from these tests have been enumerated, and the Young's

Modulus will be compared also with the values obtained from stub column

tests.

B. RESULTS

1:. Young's Modulus, E.

Tables II and III show the actual experimentally determined

values for E from both coupon and stub column tests. Individual coupon

220A.28A .,.19

•

values are shown as well as a combined value for the cross section, weight-

ing the average according to the respective areas of flange and web. To

check this method, the results were then compared to those obtained from

the full cross section by stub column tests o

The experimental values for E, as determined from the coupon tests,

were obtained from the measUrement of the slope of the elastic portion of

the stress strain curve, a typical example of which is shown in Figure 11.

The accuracy is of an estimated order of 5-10%, which includes inaccuracies

of the automatic plotting, of the calibration of the gage and of the actual

measurement of the slope. The value of E for the complete cross section was

then obtained by averaging, according to weight, the individual values ob-

tained from coupon tests of web and flange.

Young's Modulus, as determined from a stub column test, is of an

estimated 5% accuracy, and is the measurement of the slope of a stress

strain curve plotted to an enlarged scale, from experimental results of de-

1formations over a lOU gage length as measured by the mean of two l"'O-,;";O""OO....--th

dial gages.

(a) E, Weighted Coupon Results, Figure 17.

It is noted that the flange has the lower value for E, as was the

case with the other properties obtained from the stress-strain curve.3

(21 specimens)material !lAIl E ." 31.2x10 ksi mean value

material '-'B" E = 31.lx103 ksi mean value (11 specimens).3

(32 specimens)average E = 31.2x10 ksi mean value

(b) E, Stub Column Results, Figure 1703

(19 specimens)material IlAIl E = 31.5x10 ksi mean value

material "B" E = 3004x10 3 ksi mean value ( 7 specimens)

average E = 31.2x103 ksi mean value (26 specimens)

220A.28A -20

~ Comparison of Coupon and Stub Column Results for E

To check the assumption for weighting the average for E with the

coupon tests as was done before with the other material properties, the

ratio for E for each particular section, obtained by the above two methods,

was compared. See Figure 18.

material E,couponE,stub column = 99.7% mean value (16 specimens)

material liB II

average

II

II

= 100.7% mean value ( 6 specimens)

= 100.0% mean'val~e (22 specimens)

..

l:. The Ultimate Strength of a Tension Coupon

Similarly to the method eIlfployed with the static yield stress,

the ultimate nominal stress in tension for a wide flange shape was deter-

mined ~y the weighted average of'the individual coupon tests for web and

flange. Further, to account for the reduction in area the ultimate strength

is also shown based on the percentage reduction recorded, which is a more

accurate indication of the· ultimate stress. The individual percentage

reductions have been combined according to the weighted average.

It is conceded that use of this method with coupon ultimate stren-

gth is probably extrapolating too far as no account is made of the changed

crystal structure due to the IInecking ll • The results should be indicative

•.

however, since the values for percentage reduction generally do not differ

greatly for flange or web from the same shape.

(a) O"ult from Weighted Coupons of "simulated" Tests, based on original

cross-sectional area, Figure 19•

material IIA" crult = 62.9 ksi mean value (23 specimens)

material "Bll O'ult = 65.3 ksi mean value (12 specimens)

average Cult = 63 ..7. ksi me·an value (35 specimens)

220A.28A

(b) <:Jultmod from Weighted Coupons, Based on Ultimate Cross-

-21

Sectional Area, Figure 20.

material ItA" <J'ultmod .. 134.9 ksi mean value (23 specimens)

material "B" C5'ultmod .. 135.0 ksi mean value (12 specimens)

average O'ult .. 134.9 ksi mean value (35 specimens)mod

average

(c) <Jult from Mill Tests (web), Figiire 21.

material IfAIf ()ult .. 66.3 ksi mean value (24 specimens)

material IfBit <Jult .. 68.2 ksi mean value ( 7 specimens)

<Jult .. 67.4 ksi mean value (31 specimens)

(d) C5'ult from Simulated Mill Tests (web coupons), Figure 22.

material lIA If \jult .. 63.5 ksi mean value (24 specimens)

material IIBIf O"ult .. 65.0 ksi mean value (13 specimens)

average 6ult .. 64.0 ksi mean value (37 specimens)

(e) Percentage Reduction in Area, Figure 23.

I. Web material itAII 49.6% (24 specimens)

material liB It 50.8% (14 specimens)

average 50.1% (38 specimens)

2. Flange material IIA't 54.0% (24 specimens)

material liB It 51.6% (14 specimens)

average 53.1% (38 specimens)

3. Weightedmean material itA It 53.3% (24 specimens)

material ItBIt 51.4% (14 specimens)

average 52.6% (38 specimens)

Average failure is on 47.4% of original area.

220A.28A -22

~ Typical Stress Strain Curve

A typical stress S:.rain curve has been drawn from the above results,

being an average obtained from the stub column tests and other tests con­

ducted. Only the initial portiop of the curve has been shown, neither the

strain hardening region nor the ultimate stress being included. Figure 24

220A.28A -23

IV. DISCUSSION-The following discussion embodies the conclusions and suggestions

that follow from the results above.

1. The yield strength has many definitions. The static yield

stress, crys however, is the preferred value as it is the

easiest to obtain·and also is the stress that corresponds best

to normal structural loading conditions. Further, it is inde-

pendent of time. In stub column tests, by allowing the load. to

IIsettle down", that is, to come to an equilibrium position after

a load. increment, it is the static value that is obtained. With

coupon tests, all that is required is that the rate of straining

be decreased to zero anywhere in the plastic yield range. This

is easily accomplished in mechanical and hydraulic testing ma-

chines, although with the latter a dial gage indicator is re-

quired to show movement of the cross head, and to guard against

strain reversal.

From the results (Figures 4, 5, and Section C-l) the approxi­

mate value for <Jys was 33.7 ksi, with a standard deviation of

3.8 ksi. This was the overall average for stub column and sim-

ulated mill (weighted average) tests. It is considered that

this value is close enough to be taken as the usually accepted

(j y = 33 ksi.

These results are also shown in a statistical form, both

as histograms, and as assumed normal distributions on probability

paper. This is further discussed in item 11 below.

220A.28A. -24

It is noted that the results were not dependent on chance

alone but on many manufacturing factors. For instance, it would

be expected that the comparatively large sections would give

small values for cry, while small sections would give larger

values. The amount of cold work, rate of cooling, etc., un­

doubtedly played a major role in this situati9'n.

,

2. Mill test results for the yield strength were approximately

27% higher than the true static level, due pr'obably to two causes:

a. mill tension tests are run on coupons cut from the web,

which being rolled thinner than the flange has about a

4-7% higher yield level than the flange.

b. the yield strength depends directly on the strain rate

as shown in Figure 10. Even with apparently small strain

rates" (approaching zero), (Jyd can be 5% greater than r:Jys"

whereas at normally acceptJ~d mill testing speeds, 13-18%

is a more realistic figurel

The strain rate has a pronounced effect. Therefore, unless.,.

it is specified for a given test the correlation of the result-

ing data with other test data is impossible. Indeed, in this

series of tests conducted on steel from the same lot, the simu-

lated mill (Fritz Laboratory) tests produced Gyd approximately

5% lower than did the mill tests. The former used the recom-

mended speed of the ASTM A6-54T (and A370-54T) while the test-

ing speed of the latter is not known although it should be

approximately the same. Testing machine variations could be

the factor, as discussed in item 4, below.

More consistent results were obtained for the

..

220A.28A

One of the more important objects of this investigation was

to see whether the yield stress could be defined by the mill

test. The results, Figure 8 and Section I-C-3, are varied. Com-

parison of the static yield level with both mill and simulated

mill results was considered. The range of distribution was

reasonably good and the average was equal to 79% for the ratio

<J"Ymill

ratio (J ys , with an average of 82%. (In all cases, cr ys<J"ysim.mill

is from weighted coupons.) This again brings up the question of

a standard straiI'l;. rate, and the comparatively good agreement of

the simulated mill results above (similar strain rate results

from steel of different manufacturers) would bear out the premise.

It is difficult to draw definite conclusions from these figures

above, particularly as previous investigations4 have obtained

85%± 5% as the ratio of <Jys , where \Jys refers to stub column<Jyd

tests.

From the above, it is suggested that 80%± 5% is a probable

value for cr ysO"ysm,ill·

3. The procedure described in the previous paragraph was for

the weighted tension coupons, weighted according to respective

areas of flange and web, but the same results would have been

obtained for crys from stub column tests. Figure 9 and Section

c-4 show that almost perfect correlation exists forC)ys between

stub column and weighted coupons.

220A.28A -26

Another result of this study is that the strength of the

full cross section of a wide flange shape may be estimated, with

complete confidence, from tension tests on coupon cut from flange

and web. Although economically this may be no saving, it does

•

enable a laboratory with testing machines of a limited capacity

to obtain reliable estimates. Unfortunately, \Jys and E are the

only properties that such coupon tests will supply, the important

OP and llknee II of the r:J - £ curve (showing effect of residual

stresses) for the full cross section cannot be determined.

4. The problem of strain rate and the determination of its

effect on the yield stress as shown above can only be overcome

by a substantial number of tests on a wide variety and type of

testing machine. Steel from the different manufacturers must

also be subject to exhaustive tests. Since the strain rate in

the elastic range is not too important if held within reasonable

limits, the basis for such a series of tests should be on the

free-running speed of the cross head. It is expected that the

outcome of such tests will show a similarity in ·the r<5Vd versus~

strain rate) curves for different wpes of testing machine and

steels. This trend has been indicated from the reasonable cor­

relation between Marshrnan5 and Romanelli6, the former testing

being carried out on a screw-type mechanical machine, whereas

the latter was on a hydraulic machine. Such tests would in-

dicate whether the difference for C>yd between simulated and

mill tests was due to the different testing machines or to dif-

ferent strain rates used o Up to the yield level and in the

220A.28A -27

strain hardening range the type of machine and size of specimen

has a much larger effect than in the plastic or yield range.

This result, however, seems to be of little practical interest.

If it is desired to determine this elastic effect of machine

deformation when the specimen is strained into the plastic range,

a series of strain gages should be attached over the full length

of the specimen to correlate the actual strain rate with the

"free-running" speed.

Tests ha~ demonstrated that a fast method of' obtaining \rys

is to decrease the strain rate to zero once or twice in the plastic

yield range (ensuring no strain reversal).

..

•

5. It was shown that compression and tension coupons give al-

most identical results • This statement is based upon the work

of previous investigations8• The difficult compression coupon

test can therefore be eliminated in all but confirmatory cases.

6. Generally speaking, heavier sections have a lower c:ry than

lighter sections. Similar general statements can be made for

bit and <X ratios.

7. From the stub column tests cond'l1cted, the indicated value

for <Jr is 13 ksi, (With a standard deviation of 4.5 ksi.) • This

is the mean value of the maximum compressive residual stresses

in the cross section and generally occurred at the flange tip•

Further, this value is the complement of the proportional limit

with respect to the yield stess, indicating that the average

value for the proportional limit of the sections tested was ap-

proximately 20 ksi.

..

220A.28A

The above value is a reaJistic estimation deduced from

Figure I, where the ttmodifiedtt values have also been taken

into slight consideration. Attention is drawn to Table VI

where the values 12.3 and 7.7 ksi (compression) are average

values for WF shapes of d/b .:::::. I., and >1.5 respectiveiy.

Since the histograms for the ratio ~rhave "become mucho-ys

wider, rather than narrower, in distribution, with respect to

the \5r histogram, it is concluded that () r is not a function

of the yield stress. See also Table IV. This has tended to be

confirmed by recent pilot tests on low alloy high strength steel

where crr was found to be of the same order of magnitude as11

was measured in A 7 steel •

8. The prediction of the residual stress distribution based

on mathematical relationships between the cross sectional phy-

sical properties has not been successful up to this time. How-

ever, a good estimation may be obtained from tabulated results

already available such as Tables V and VI of this report •

9. .3The YOung'lS modulus was found to be 31.2xlO ksi, with. - 3

a standard deviation of 1.'xlO ksi, the overall average

value obtained from all coupon and stub column tests conducted

in this series.

As with the yield stress~good estimation for the Young's

modulus of a full cross sectional shape may be obtained from

the weighted average of the coupon values.

No effects of size of cross section on the Young's modulus

was noted, among the relatively small number of specimens tested.

220A.28A

The values obtained in this series of tests showed both a

greater deviation among themselves, and a higher mean value,

than obtained in tests of other investigations. 7,8

10. The ultimate strength of tension coupons, Section III-B-4

Figures 19,21,22,lies within very definite bounds wit.h an average

of 64-67 ksi. (This is within the limits 60-72 ksi specified

by ASTI1 A7-55T). These measurements are based on the initial

•

•

cross sectional area. It should be noted that the simulated

mill tests gave somewhat lower results than the mill tests. How-

ever, this small difference was probably due to the slower strain

rate after the yield point of the simulated mill tests.

The ultimate strength based on ultimate cross section is

likewise within definite bounds with 'an average of approximately

135 ksi as, shown in Figure 20 •

The percentage reduction in area, although with a slightly

wider range as shown in Figure 23, is also reasonably consistent.

A difference of 5% between web and flange values was noted sug-

gesting that thickness of rolled section could have an effect.

Considering a weighted average for all specimens, the percentage

reduction in area is approximately 53%± 5%. (A standard devia­

tion of 4.6% was measured, assuming a normal distribution.)

11. The most advantageous manner of presenting the data of the

various tests is to have the group results for any parameter'

separate, rather than to have the results classified according

to the specimen. A logical outcome of this, then, is to have

the data tabulated in a statistical manner. This has been done

220A.28A ""3D

in two ways, by the histogram, and by ~ cumulative plot of re­

sults on probability paper, using the assumption of a normal

distribution.

Whereas the histogram is a plot of classified values accord-

ing to actual frequency of distribution in the tests, the cumu-

lative plot, and its line of best fit, is an attempt to obtain

a frequency distribution valid for all tests from the small

sample of tests at hand. It is obvious then, that if the histo-

gram were to be constructed from a sufficiently large number of

values, it would approach the actual frequency distribution for

the parameter considered. If this distribution be plotted on a

cumulative basis, the resulting curve is a cumulation distribu-

tion function, which again, if plotted on probability paper is

a straight line for a normal distribution. If the distribution

be skew, a plot on logarithmic probability paper would render

a straight line. The advantage of a straight line is that

•

the comparison of the statistical parameters becomes very simple.

The data obtained were comparatively small in number so

that an estimation of a normal distribution curve from the his-

togram was out of the question. However, .the number of resultsII

is sufficient for an estimation of a straight line in the cumu-

lative plot on probability paper. In practically every case,

the assumption of a normal distribution was reasonably true.

Although in some cases, such as Figure 21, a skew distribution

may have given a better approximation.

...

•

220A.28A -31

For a cumulative normal distribution, by synnnetry, the

mean value for the function considered is obtained from the

0.50 cumulative probability ordinate. (See Figure 4.) Further,

it may be shown.;L2,13,14, that the 0.841 ordinate (or the 0.159

ordinate) defines the standard deviation, s. For a normal dis­

tribution 68% of any sample of results is expected to fall

within the range x ± s, where x is the mean.

The standard deviation, also known as the standard error,

is a value for describing the scattering of the observations

about the mean. 12 ,13;14 o The straight line cumulative proba-

bility plot, by its slope, shows the range of the distribution,

e.g. the steeper the slope, the narrower the distribution, and

vice versa.

It should be noted, that when the experimental data are

plotted, the frequency is the ordinate of the curve, but that

once the line of best fit has been drawn arui hence the normal

distribution fixed, the ordinate then is the probability, use-

ful f or future estimations.

Generally, the curves w~e,plotted from the same classified

groupings as used for the histograms 0

A summary of the relevant statistical results is presented

in Table IV•

220A.28A -32

V. CONCliJSIONS-Continuing on from the previous chapter of discussions with re-

spect to the limited number of tests conducted, the following suggestions

become relevant:

1. This series of tests indicates the following probable values

for the material properties of the full cross section of a WF .

shape.

arc =

(Jys =

•

(on original area)

(on·reduced area)

percentage reductionin area

E =<5 ult

33 ksi with s = 4 ksi

13 ksi 5 ksi

20 ksi 5 ksi

3lxl03 ksi 1.5xl03 ksi

64 ksi{ 3 ~i

135 kSiJ Coupon Tests 11 ksi

53% 5%

•

2. The yield stress should be defined by the "static" yield stress

level for reasons discussed in Chapter IV.

3. The effect of strain rate on the yield stress level has been

discussed in Chapter 1. For authoritative conclusions re-

garding the influence of this variable, a substantial number

of tests on steels from different manufacturers should be con-

ducted using a wide variety and type of testing machine.

To obtain this more precise correlation between strain rate

and static yield stress level as well as between different

manufacturers and testing machines, it would be necessary

that the rate of testing of the mill coupons be observed for

•

220A.28A -33

each coupon test. Then Figure 10 could be substantiated, or

revised. This itself would allow the static yield stress of

any coupon to be immediately determined, knowing the dynamic

yield stress and the speed of testing.

4. This series of tests further indicated that the "static" level

of yield stress for a WF shape is 80%1: 5% of the mill test value

on a tension coupon cut from the web of the section. Standard-

ization to a definite testing rate may change this value.

5. The yield stress and Young's modulus for a given, shape can be

estimated accurately from test results on coupons cut from

flange and web, if the weighted average according.. to respective

areas is used. Th.:J.s is of use where only small capacity testing

machines are available.

6 1

• The elimination of compression testing of coupons is warranted'"Ji

I ' .in the case of rolled stru~tural steel shapes. Tension cou-

•

pons accomplish the same purpose with greater ease •

220A.28A -34VI. ACKNOWLEDGEMENTS-

This report presents a part of the theoretical and experimental

studies made on a research program on the influence of residual stres!3 on

column strength carried out at the Fritz Engineering Laboratory, Lehigh

University, Bethlehem,Pennsylvania, of which William J. Eney is Director.

The Pennsylvania Department of Highways and the Bureau of Public

Roads, the National Science Foundation and the Column Research Council

jointly sponsor the research program.

The author is greatly indebted to Dr. Lyrm S. Beedle and to Dr.

Robert L. Ketter. Their advice and suggestions are sincerely appreciated.

•

Professor A. M. Freudenthal of Columbia University suggested the plott~g

of the results as a cumulative function, on probability paper.

Many test specimens were prepared in the machine shop of Fritz

Engineering Laboratory. Sincere appreciation is expressed to Mr. Kenneth

R. Harpel, Foreman, and to the Laboratory Staff.

Messrs. George Lee, Robert Wagner and Theodore Galambos assisted

in the tests and in,the preparation of the data. Miss Grace Mann typed

•

the manuscript • Their cooperation is gratefully appreciated.

..

•

220A.28A

VII. REFEREN'CES

1. A. W. HuberTHE INFLUEN'CE OF RES IDUAL STRESS ON THE msTABILITY OFCOLUNNS, Fritz Laboratory Report No. 220A.22, LehighUniversity, May 1956.

2. A. W. HuberSTUB COI1JlYlN TEST, Fritz Laboratory Report No. 220A.16,Lehigh University, July 1956.

3. A. T. GozumCOUPON TESTmG, Fritz Laboratory Report No. 220A.15,Lehigh lJniversity, July 1954.

4. A. T. Gozum and A. W. HuberMATERIAL PROPERTIES, RESIDUAL STRESSES, AND COLUMNSTRENGTH, Progress Report, Fritz Laboratory Report No.220A.14, Lehigh University, November 1955.

5. J. c. MarshmanTHE INFLUEN'CE OF PLASTIC STRAm RATE ON THE YIELDSTRENGTH OF MILD STEEL, Unpublished, Lehigh University,June 1956 •

6. A. J. Romanelli_ INFLUEN'CE OF STRAm RATE ON YIELD STRESS LEVEL, Fritz

Laboratory, Lehigh University, 1955. Unpublished.

7. 1. Lyse and C. C. KeyserEFFECT OF SIZE AND SHAPE OF TEST SPECIMEN' UPON THE OB­SERVED PHYSICAL PROPERTIES OF STRUCTURAL STEEL,Proc. ASTM, Vol. 34, Part II, 1934.

. .

8. A. W. Huber and L. S. BeedleRESIDUAL STRESS AND THE COMPRESSIVE STRENGTH OF STEEL,Fritz Laboratory Report No. 220A.9, Lehigh University,December 1953.

9.. Y.Fujita. BUILT UP COLUMN STRENGTH, Ph.D. Dissertation, LehighUniversity, 1956.'

10. A. W. HuberRESIDUAL STRESSES m WIDE FLANGE BEAMS AND COL'(J}'lNS,Fritz Laboratory Report No. 220A.25, Lehigh University,July 1956. .

11. G. C. Lee and R. L. KetterTHE EFFECT OF RESIDUAL STRESS ON THE COMPRESSIVESTRENGTH OF MEMBERS OF HIGH STREN'GTH STEEL, FritzLaboratory Report No. 269-lA,Lehigh University,January 1958.

..

220A.28A. "36

12. R. S. Bm-ington and D. C. MayHANDBOOK OF PROBABILITY AND STATISTICS WITH TABLES,Handbook Publishers, Inc., Sandusky, Ohio, 1953.

13. A. HaldSTATISTICAL THEORY WITH ENGINEERThTG APPLICATIONS,John Wiley and Sons, Inco, New York, N.Y., 1952.

14 0 J. ToppingERRORS OF OBSERVATION AND THEm TREATMENT, The Insti­tute of Physics, London, 1955 •

.,

.1. Nomenclature

2. Tables

3. Figures

VIII. APPENDIX

"'37

-38

1. Nomenclature

b

d

E

s

t

w

E.

()

cr"y

0-ymill

Flange width

Depth of WF section between centerlines of flanges

Youngts modulus of elasticity

Strain hardening modulus

Standard deviation, a statistic measure of the scatteringof observations

Flange thickness

Web thickness'

Ratio, of area of flanges to area of web

Strain (in/in)

Stress

Yield stress

Yield stress of mill tension coupon, (as ob"tained from themill report).

CJys Yield stress at zero strain rate: "static" yield stress

(jyd Yield stress at a particular strain rate other than thezero strain rate: lIdynamic" yield stress

(5"uy Upper yield point, see pg. 4

c:5 ly Lower yield point, see pg. 4

r:::f p Proportional limit

<Sr Maximum residual stress determined from stub colunm test

<Jrc Residual stress at flange edges

<Jro Residual stress at flange center

() rw Residual stress at web center

2" Tables

-39

TABLE I

Schedule or Tests

No':Shape Material II All Material IIBII

coupon coupon~; test stub test stub

( simulated)' column (simulated) columnmill mill

8 18WFI05 x x x x9 l6WF 88 x x x x

10 14WF426 x x x11 14WF320 x x12 14WF228 x x

13 14WF142 x x x x14 14WFl1l x x x15 14WF 78 x x x x16 14WF 61 x x x 'x17 14WF 53 x x18 12WF190 x x x x19 12WF 92 x x20 12WF 65 x x21 12WF 53 x x x I x22 12WF 50 x x

23 10WF 66 x x x'24 10WF 39 x x25 10WF 33 x x26 8WF 67 x x27 8WF 35 x x28 8WF 31 x x29 8WF 24" x x.30 6WF15 oo5 x x x31 5WF1805 x x x,

.. Numhers, 220A Program, August 26~ 1954, Phases 4 and 5

·'

TABLE II

General Experimental and Analytical Data for Material IIA"

NOTEg All values are=irtckip~~nchrunits2

Area ' 'Area O(~ n>t <:n?C~do Clysmrtl

QUIt , <:1U1tNo. Shape Area Flanges Web ;area f1g o bit

stub stu stub mill -couponQ1"'AQ lATA ~olumn column column fl anQ'e web

8 18WF105 31.3 ._~1095 9032 2 036 13.0 12.8 "-r-c:==c::::> 29.8 43 0 1 62 08 4803 61.29 16WF88 2505 17092 7.55 2.37 ' 15.1 1806 309 31;,4 4203 6309 62.9 63.1

10 14WF426 12400 100~38 23.57 4040 5052 == === -:~ 38~2 . 6909 6404 73.411 14WF320 9305 69088 23057 2097 8 00 == === === 38.5 65.1 6107 590712 14WF228 6703 54019 13 009 4 014 9,,3 ,,905 === 2508 3802 6504 6208 6503

1

13 14WF142 41 09 33011 8079 3077 1407 12 00 === 3007 3701 6402 6506 68.3'14 14WFll1 32 01 25035 6072 3078 1609 10 02 === 33.0' 4500 71 00 6602 640515 14WF 78 22 03 16085 5045 3.09 1606, 10 02 === 2904 38 04 60.4 5903 590716 14WF 61 1709 12085 4096 2059 1509 == === === 4403 6608 6004 60 0017 14WF 53 == === == 1071 == == === == , 37 01 60 07 5809 550518 12WF190 5503 43066 11061 3076 7037 12 01 === 2406 34 01 68.6 6307 ' 61.619 12WF 92 27 00 20097 6 000 3050 14.3 19 08 10 04 ' 34·4 45.7 74 00 6903 690520 12WF 65 18 07 14024 4014 3044 20 0'6 1406 === 32 06 4403 6706 6208 610421 12WF 53 1507 11 076 3.87 3003 == ,1303 === 3500 4409 67 .. 8 61 03 6305

1

22 12WF 50 1403 10013 4 014 2045 13.0 1605 === 32.9 42 02 67 .. 5 6509 640723 10WF 66 1903 15021 4 002 3080 13.6 11.2 === 3302 4608 6803 6306 63.924 10WF-39 11.1 8011 2089 2080 1508 =- === 3702 41.9 62.7 6009 62.025 10WF 33 9,,8 7012 '2060 2 074 18 0 0 1101 === 3204 52 00 7408 60 06 61~1

26 8WF 67 1903 15004 4 0 20 3059 9 .. 18 8 09 === 2604 33.5 60 02 5907 570127 8WF 35 10 05 8023 2024 3068 16 0 2 1509 === 3509 4803 6403 6302 640728 8WF 31 9037 7 .. 24 2007 3.50 18$5 ' 606 === 36.1 44·4 6405 64·4 650029 8WF 24 7000 , 5016 1.79 2.88 16.7 24 .. 4 10.4 3904 47 .. 4 6902, 6502 700330 6WF1505 4 .. 57 3.16 '~ .. 34 2 037 22 .. 3 23,,3 308 43.0 51.1 66.4 6306 640031 5WF18 05 5031 4 021 1.05 4.18 12.0 604 --- 3807 48.8 65.6 63.1 64.4

" -, '

* No apparent yield load

TABLE II, Continued (a).- -

o-ys . o-ydo-ys Cf'ys

o-ys Stub cryd(Web) Clys WeightedNo. Shape Coupon Coupon o-ys O"Yd Column Coupon- OYd{Web)Flange Web Flange Web ~eighted lrleightec OYd OYmi11 ays Weighted , O"ymi11

Coupon .C0ll.pon Couponfo % % .• % %

8 18WF105 28:9 34.2 32/09 40 06 30 04 38.2 79.6· 70.7 98 0 0 94.3 74.99 16WF 88 3101 3109 39 .. 6 38.3 3104 39.2 8604 74.3 100 00 90.5 82.0

10 14WF426 == 30.4 -- 34.1 =- -- -- == -=- 89.3 --II 14WF320 22 .. 7 22,,8 2604 2604 22 0 7 26.4 86.0 59.0 68.6 86.2 -

==-

12 14WF228 -= 2906 -- 35.2 -- -- -- =- --- 92.2 - ....13 14WF142 28.4 32 0 7 33.8 38.9 29.3 34.9 83.8 79.2 104.7 104.9 75.314 14WF111 3205 33.2 38.9 39.4 32.7 39.0 83.8 7201 101,,0 87.5 83 0 015 14WF 78 28 0 8 30.4 3504 3306 29.2 .35.0 83.4 76.2 100.6 87.5 86.816 14WF 61 30 0 3 31,,4 36 00 3507 3006 3509 8502 69.0 =-- 80.5 85'0817 14WF 53 2906 29.6 4001 3607 29.6 -- -- 79.7 =-= 9807 80 0618 12WF190 2609 2605 29 .. 1 32.9 2608 2909 8907 8706 .91 08 9606 810519 12WF 92 33 02 35 00 4007 4104 33.6 40.8 82.3 73.5 102.4 . 90.8 810220 112WF 65 32 0 4 38,,6 41.9 38 06 3308 41.2 82 02 76.2 9604 87.0 87.621 12WF 53 33.4 37.6 38.5 46.3 34.4 -- -- 7605 101 08 103.3 740222 12WF 50 34.0 35.2 3908 43.1 3505 40 08 84.1 81.4 95.7 102 00 79.823 10WF 66 I 32 00 33.8 37.6 38.8 32 04 3709 85.5 69.2 102.6 8209 830724 10WF 39 34.2 36 01 41 03 44.7 34.7 42.2 82.2 82 07 --- 106.6 77.825 lOW 33 3401 3409 40.7 44.3 3403 41.7 8204 6600 94.5 85.3 770~ I

26 8WF 67 25.8" 28 03 30 02 3407 ~6-.3 3~h2 84lf3 78.6 100 04 103.6 76.27 8WF 35 34.7 37.5 40 .. 1 4407 35.3 -_. -- 73.2 10107 92 08 79.028 8WF 31

---

3703 39.7 44.3 48~8 3704 4503 8307 85.6 95.3 110.0 770729 8WF 24 36 .. 5 41.9 42 .. 0 48.5 3708 44.0 86.0 79.8 104.3 10203 78.030 6WF15.5 42.9 43.0 48.3 52.1 43.3 49.6 87.3 84,,7 99.2 102.0 83.331 5WF18,,5 40.7 ~3.8 4507 44.7 41.3 45.5 91.2 63.2 93 08 91.5 9208

I~f\)

TABLE II, continued (b)

Noo Shapeor or C"Ultmi11 crult Crultwei~ted %redn o= %redn o= Redno -(1"ultmodo- co pons~~

a:; Ci'Wetweb '!tleighted in area in area urea based onys o-ul"'tmillcolumn

modo coupon coupon % flange web weighted ~ of- redn ostub % average orig= area

column inal8 18WF105 42,,9% ===% 10L,3 51,,8 8205 5409 48,,9 53 .. 1 4609 110 059 16WF 88 5903 12 04 10103 62 09 98 .. 4 56.1 5407 56 .. 7 4303 145 00

10 14WF426 == 95 02 6600 .- 94 .. 3 52 00 30,,8 48,,2 5Ic8 127,,5==11 14WF320 i ....... ="". 10geO 61 02 94 00 54,,5 58 .. 1 55,,5 44,,5 137,,512 14WF228 36,,9 == 10000 6303 9805 69.8 51,,6 66,,2 33 .. 8 187,,5/13 14WF142 3901 == 9308 6602 10302 54.5 43 .. 3 52 .. 1 47 .. 9 138 0014 l4WFl11 30,,9 -= 110 00 6602 9303 55,,1 4909 5308 4602 1430515 14WF 78 3407 == 10103 5904 98 02 55,,1 54,,0 5407 4503 1310216 14WF 61 =- -~ 111 04 60 02 90,,0 5707 48 08 55 .. 2 44,,8 1340417 14WF 53 c:::lI~ =- 109 .. 4 - == -... 5505 5706 56 .. 2 - 43 .. 8 ==18 12WF190 4702 -- 11103 63 02 92,,2 54 .. 0 47,,4 52,,7 4703 133,,719 12WF 92 57,,6 3002 106,,4 6904 93 .. 8 5309 4804 52 .. 7 4703 1460620 12WF 65 44,,8 =- 11000 62,,6 92,,6 5703 52,,5 56,,2 43.8 143 0021 I 12WF 53 38 00 ~= 106 e8 61 09 91 .. 2 46,,7 4402 45,,9 5401 114 .. 522 I 12WF 50 50 02 -= 10403 6506 9701 4607 5003 4707 52 03 1250523 10WF 66 I 3307 -= 106,,8 6307 93 00 4807 4308 47 .. 7 5203 1210624 10WF 39 1 -= -- 101 03 61 02 9708 55,,2 5009 5402 45 08 1330525 10WF 33 3403 -= 12205 60 07 8102 52,,9 5600 53.8 4602 131" 526 8WF 67 ! 3307 ..= 10504 59.0 9801 /55" 5 5403 55 02 4408 131,,527 I BWF 35 I 44,,3 ~= 9904 63,,6 98 08 54,,0 46,,1 5202 4708 1330028 8WF 31 1803 ="" 99.3 64,,5 100,,0 51 6 1 49.7 50 .. 8 490e 1318129 8WF 24 6109 2604 98 03 6605 96 02 50 00 50 .. 4 51 .. 0 49 00 135.530 6WF15,,5 54,,2 8,,8 103 .. 8 63 .. 7 96 .. 0 54.0 53.7 53,,9 46,,1 138,,731 5WF18 ,,5 1605 -- 10108 63,,3 9607 5105 4507 5003 4907 12704

.'

TABLE 11 9 continued (c)

• ..

- -..

E E E EcouponNoo Shape coupon coupon stub Estub column

flange web weighted column %8 18WFI05 31..7 31.9 3108 30.8 103.49 16WF 88 30~6 32 0 9 31 03 31.8 9804

10 14WF426 -- 32.4 -- 3303 --II 14WF320 34 01 3300 3309 .,.- --12 14WF228 -- 33.0

I-- 29.6 --

13 14WF142 29~8 32.9 I 30 05 29.1 10408i

14I

14WFlll 3103 28.7 I 3007 3102 98.415 14WF 78 29~6 30.8 i 2909 32 00 930516 14WF 61 29.8 2708 I 2903 -- --17 14WF 53 30~3 30.6 I 30 04 -- --18 12WF190 38~4 3406 I 3707 32.7 11503

I19 12WF 92 I 29.7 . 33 00 I 30 04 3108 95.620 12WF 65 31.1 28,,8 I 30 06 3000 102 00 I21 12WF 53 33.2 30.,0 32 04 33.,8 950922 12WF 50 33.,8 29.6 32.6 32 09 990223 10WF 66 3108 30 07 3106 30.,1 105.024 10WF 39 31~3 30.5

I3101I -- --

25 10WF 33 30.5 30.4 30.5 29.2 1040526 8WF 67 30.2 30.7 3003 -- --27 8WF 35 30.2 32.2 30.,6 31.2 • 98.228 8WF 31 30.1 33~0 30 .. 8 30.2 102 0029 8WF 24 -- 34.4 -- 32.2 --30 6WF15 05 27.8 32 05 29 02 33.5 87.231 5WF18.5 29~9 29.6 29.8 32.4 92.0

...- . ~.. -- - ._~ -

.'

TABLE III

General Experimental and Analytical Data for Material "Bl!

NOTE~ All values arein kip-inch units o

No o Shape Area Area Area 4'13 CJrc orc ays <JultFlanges Web area flanges stub modo stub oy CT"ult coupon

area web column stub column mill mill flange webcolumn

8 18WFI05 30 06 2100 905 2 021 1304 -- 33 00 3707 62.4 6102 61.59 16WF 88 2507 1801 706 2.38 2303 9.1 3404 41 06 6803 6505 6403

10 14WF426 4040 6807 660811 14WF320 2 097

I12 14WF22813 14WF142 40.6 32.0 805 3.76 18 01 38.7 51.2 7401 7003 71.314 ' 14WFlll 3.78 63.2 64.415 14WF 78 23.2 1705 506 3.13 14.8 35 08 42.3 6808 6405 660916 14WF 61 18.1 13 00 500 2 060 901 36.7 4402 68.4 6408 6503

i 17 14WF 53! 18 12WF190 5507 4401 1107 3077 1103 3002 3906 6807 66 02 6706i

19 12WF 9220 12WF 65 36 .6 -~i- 39.7-:i-21 12WF 53 1507 1107 3095 2.97 1203 35.0 35.1 66.9 64 01 640822 12WF 50 36.0-:i- 42 06-'ri-

I 23 10WF 66 3068 39.9 63.3 620524 10WF 39 35.9-:i- 41. 2'~i-

25 10WF 3326 8WF67 31.4* 43.0-:i-27 8WF 35 36.7-:i- 40.0*28 8WF 31 37.4* 43.3-:i-29 8WF 24 34.3-:i- 39.8-'ri-.30 6WF15.5 64·0 63.631 5WF18.5 67.1 65.2

--6WF2·5 _I· ,: , .. ".. -.. , - , .- _.......... ,-.,. ,•....- . "'"".. ', _. ,-. ,. ____.0.1. 3 ,61....4-.

~'from prevIous investigations

-

TABLE III, continued (a)

ery-sc~gen ~s <5d OYs ays oy stub or ~.

No o Shape coupon iJeig ted weighted scolumn - (JysOYd oymill oysweifihted OYs

flange web f'lange web modocoupon coupon % % %co pon stub stub

column colurrm

8 18WFI05 3305 31 02 3904 3800 32 08 39 00 8401 8700 100 06 40079 16\& 88 34 01 3406 4102 39 08 3403 40 08 83.8 8205 6708 2605

10 14WF426 2804 2904 3207 3105 2806 3205 88 0011 14WF32012 14WF22813 14WF142 37.8 38 05 45 0 0 4502 38 00 4501 8403 7402 101.8 46 08

14 14WFl11 33 0 0 37 00 3902 43 08 3309 4001 840715 J.4WF 78 3406 3701 4007 44 02 3501 4105 84·7 8208 102.1 410416 14WF 61 36 01 36 06 42 02 4207 3603 4203 85.8 8202 101,,2 24 0817 14WF 5318 12WF190 3005 3204 33 08 39.2 30.9 3409 8805 7800 97,,7 34.1

I19 12WF 92

l 9202*20 12WF 65!21 12WF 53 35.2 35.2 41.4 4004 35 02 100.3 99.5 35 0222 12WF 50 84. 5~-23 10WF 66 34 02 36 06 41.,7 4101 35.524- 10WF 39 8701*25 lOWE' 3326 8WF 67 72.8*27 8WF 35 91.8*28 8WF 31 86.2*29 8WF 24- 86 .2~-

30 6WF15.5 36.6 37.4- 42.4- 43.( 36.831 s'WF18.5 37.2 38.0 40.0 46.E 37.,4

·.6WF2-5 .. .- 4 " 34.9..." '.. :. ,..~~_."' ..,-. _.,. ~ '. , '-"~ ..--~, ..:.~ ~..-~·".l' ,.......~,._ .... ·2 ... 1:: ~""'" '" . , , . ,- . '., ....'" ...'.- Co ." •....,., ... . ' ._'" ~ , . ......... ..."..., .. '----. .•. ~ ,.

.... '", _ ......., .. "-~':.~ "',"' r-' ~.::'! - Y~,'~ - C, ~- ~. f .~-- -- .-- ,"

TABLE III, continued (b)

Shape ~lt %redno in 1% redn o Redoarea CJult 0 mod 0

Ecoupon Ecoupon E EcouponNoo we gnted area in area ~ o:f based oncoupon stub Estub:flange web weighted original redo area :flange web weighted po1umna.verage c~lumn .

8 18WF105 61e3 5609 5002 5408 45 e2 13508 2903 28.2 28.9 28~·6 101.1

9 16WF 88 69.3 52 02 4705 5007 4903 132 05 3000 2904 29 08 31 07 90 0910 14WF426 68e5 33.7 4407 3507 6403 10605 33.8 3506 34.111 14WF320 5405 5801 5505 440512 14WF22813 14WF142 7007 5309 5101 5402 45 08 154.3· 3008 3109 31eO 33e8 9108

14 14WF111 6303 5503 4409 53.0 47 00 13408 3206 31.2 32 0315 14WF 78 6502 4805 5305 4907 5003 12906 3004 3201 30.8 2705 112 0016 14WF 61 6501 5502 6704 5807 41 03 157 .. 5 31 .. 7 32.2 3109 30 .. 4 1050.017 14WF 5318 12WF190 6604 5305 48 03 52 .. 2 4708 13900 =- 29.4 -- 30e9 -=

19 12WF 9220 12WF 6521 12WF 53 6402 5109 4205 49.6 5004 12706 3200 27.4 3008 29 08 1030522 12WF 50.23 10WF 66 6302 51 00 5300 5103 48 .. 7 129 08 30 .. 9 29.0 30 .. 5

- --._~- - -

24 10WF 3925 10WF 3326 8WF 6727 8WF 35 .28 8WF 3129 8WF 24 50 04 50.0 50.2 49 .. 830 6WF15.5 6308 5401 5401 54.1 4509 13808 3101 32.0 30.831 5WF18.5 66.7 51..5 45 .. 7 50.2 44.8 133.9 31.9 30.9 31.7

I' ..j:::"" .-'J '..

TABIE IV

Statistical Results Assurn:i.ng a Normal D:istribution -48

Mean s AverageNo. of ksi ksi No. of lVlean s

FiEl. Description Mat'l. Snecimens Snecimens ksi ksi

4 b O'ys Stub Column A 20 33.1 5.1B 14 35.0 .2.2 34 33.9 3.8

5 b ()ys Sim. }1ill A 22 32.8 4.7B 13 34.6 2.5 35 33.5 3.8

6 b <Jyd Mill (web) A 24 42.8 5.0B 14 4105 3.5 38 42.3 4.4

7 b ($ yd Sim. Mill (web) A 24 40.1 600B 13 4104 3.3 37 40.6 4.9

8 b cS ys/ifyd (Mill) A 20 76.4% 6.1%

t~22 8102% 4.9%

(jys/fSyd S~. 'Mill 13 83.8% 4.3% -

15 b(l) (j'rc (max.)stub column A 19 13.5 402B 7 14.6 4.3 26 13.8 4.7

15 b(2) cr rCmod (max.. ) stubcOIU;Jlll1 A 19 10.5 4.2

B 7 12.6 3.4 26 11.1 4.1

16 b(l) 6r ;'6ys A 19 '4101% 11.1%B 7 41.5% 1207% 26 41.2% 12.6%

16 b(2) (Jrmod/6"ys A 19 32.9% 1303%B 7 3506% 9.4 % 26 33.6% 1200%

17 b(l) E, -weighted coupons A 21 }1.2 1.4B 11 31.1 1.1 32 31.2 l.~

xlif xlO17 b(2) E, stub columns A 19 31.5 1.6

B 7 30.4 1.5 26 31.2 1.6-xl03 xl03

18 b E/E, comparison of17 (a) & 17 (b) A 16 99.7% 601%

B 6 10009% 10~4% 22 100.0% 7.8%

19 b <S'" ult Sim. Mill A 23 62.4 2.8(weighted) B 12 65.3 302 35 63.7 3.0

20 b crultmod"'Siril.. Mill A 23 134.9 10.1(based on reduced ~ 12 13500 12..5 35 134.9 11.1area)

I

21 b c:r lilt (web) -A 24 66.3 3.6I

Mill Test

I B 7 68.2 2.6 31 6607 3.3

TABLE IV - Continued-49

AverageNo. of Mean s No. of Mean I s

Fi~. Descrintion Matt 1. Snecimens ksi ksi Snecimens ksi ksi

22 b cr- ult Sim. Mill(web) ·A 24 63.5 4.4

B 13 65.0 2.0 37 64.0 3.6, ,

23 bel) % red. in area I A web 24 ' 49.6 6.4A flange 24 54.0 4.2 24 53.3 4.6

23 b(2) % I ~~. webI 11 50.8red. in area 7.7B flange 11 51.6 5.7 11 51.4 6.0

23 bO) % re.d. in area A 24 53.3 4.6weighted average, B 11 51.4 6.0 38 52~6 4.7tension coupontests.

TABLE V

Summary

Material E 0p Guy °ydI

IAl Flailge 29$900 (9) ~~ 30Q6,(6)'~ 38 .. 4 (8)~~ 38 .. 0 (9)';~

Web 28$750 ( 2) 2605 (2) 4207 (2). 42 .. 7 ( 2)

Ave o· -. 2";~1( 29 $580 (11) 2906 (8) 39~ 4 (1O) 39 .. 2 (11)

IA2 Flange 30~120 (3) 39 08 (3) 39 .. 8 (3)

1:82 Flange 28~940 ( 6) 30" 4 (6) 3906 (6) 39.6 .( 6)Web 30 9 000 ( 2) 30.° (2) 43.6 (2) 43.3 (2)

Aveo-2 29 9 200 (8) 30.3 (8) 4006 (8) 40.5 (8)

TOTAL Ave o-2 29 9 580 ( 22) 2906 (16) 40. ° (21) 39.8 (22)

Tension Coupons (as-delivered)(.A.verage Value s in ksi J

IAl Flange 30 9 23 0 (3) 4208 (3) 39 .. 1 (3)Web 30 9 200 (1) 4408 (1) 43.3 (1)

Aveo=2 30 9 210 (4J 43.3 (4) 4001 (4)

IA2 Flange 30 9 010 (9) 320° ( 6) 3901 (9) 3704 (6)Web 29 9 270 (3) 2707 ( 2) 4206 ( 2) 35.7 (2)

Ave.=2 29 9 820 (12) 30 09 (8) 3989 (11) 3700 (8)

IB2 Flange 30 9 090 (3) 4385 (3)' 40.5 (3)Web 30~200 (1) 4606 (1) 44.2 (1)

Ave o=2 30 9 120 (4) 44.2 (4) 41.4 (4)

TOTAL Ave.=2 29 9 970 (20) 30.9 (8) 410 6 (19) . 38.9 (16)

,Mill Report Tension Test (as-delivered)

Web == -= -- 43.3

~~umber of specimens~f'~eighted average in proportion of flange and web areas.

,

TABLE VI

Residual Stresses Due to Cooling in WF Shapes

Stress Flange Edge F1an~e Center· Web Center·in ksi max. avgo min.· max. avg~ min. max. avg. min.

Columns ...5o~ . ...1203 =18~7 1605 406 -.3'Q. 7 1705 3.9 -1505d/b-1.5

\

f

:Beams -4.1 -7.7 -10.8 .19.7 14.6 8.3 -808 -16.3 .,.29.5d/b 1.5 -

tension = +compression ~ ciD

These are results 'of all tests conducted in Fritz EngineeringLaboratory on Research Project No. 220A~0

TABLE VII

Cooling Residual Stresses in WF Shapes(Average Values)

l\. 11t::--:--:=1<:::::> '

TYPE I TYPE II - TYPE III

SHAPE wit d/b --ore oro ° ' TYPE REMARKSrw

1 4WF 13 0811 101022 ~100'0 40.0 505 II

2 5WF18"5 0632 1 0018 = 7"17 -200 1605 II/III center beam oncoo1in~ bed

3 5WF1805 0632 1 0 018 ';'10,,6 3 02 60.0 II edge beam oncooling 'bed

4 6LC15" 5 0892 1.. 000 -1501 1005 -009 I/Il light column

.5 8WF 24' 0616 1.,138 -10.. 2 0,,5 17b5 III/II .-

6: .8WF 31 0665 1 a OOO -13.09 506 9'b3 II'

7 8WF 31' 0665 1<:i 000 -11'05 101 1505 II/III sarne heat, diff-erent ro11in~s

8 8Wl;' 31 0665 1,,000 -17·",,5 402 500 II

9 8WF 31 " 665 1,,000 -160;1 1001 L3 IIII different heat

10 8WF 67 0616 1,,088 = 905 =307 1505 III

11 12314·' '0893 3~000 = 401 803 -808 I beam

12 12WF50 0579 10510 - 5,,5 902 -1500 I

13 12WF65 "644 10011 =1807 ,1605 -1505 I

14 14WF43 0584' L711 - 805 1907 -2905 I on cooling bed(slow coolingrate)

15 14WF43 0584 10711 - 805 2402 ..;41 00 I cooled separate-ly - (high cool-ing rate)

16 14WF426 0 619 10126 -1708 805 1400 II- J

17 36WF3.50 0665 20990 -1008 1403 -1500 I beam

30 Figures

...-5.3

IIIIIIIIIIIII

~.h- ...0.002

t1=F

Plast ie Range

Unit Strain

-54'

Strain Hardening

Stress-Strain Curve

Figure 1

GRAPHICAL DEFINITION OF TERMS

-.55

,I II II I

I :: . I

. I ,I II II JI II I

I ;t IL..)

Fleur- 2

SHOYmGPOSn'IO. 01'TBNSIOlf COUPOlTS omnOM FLAlTGE ABD WBB

OF A WF SHAPE.

= 3ft

~ !-------"__.~~~..a..-~""--~I~r.-_....--.-.....-----=..:;-.2::~·..---,.-:1...---..-.1

•

Figure 3

DnmNSl;ONS OFTDSION COUPON

(Shaped to ASTH'Specifioation)

30a~

II

- 56'

Material "A"20 Speoimens

Frequenoy

~

25 30 13533.1

40 45 ksi

(fys

40~ ..

~I

Pi&eq".ncy.~ '.

30

20

Material "B"14 Speoimens

10,\

25 30 40 45 ksi

0­ys

".:' ".

30

Frequency%

20

10

Average34 Speoimens

()ys

45 ksi4030o ~I--r~-+--"'-f-,""'+-..,..-!Io,~h-""""~-.-,....+..,.-..,I--;

:353309

Figure. ·4(a),'..'

SJfUB COLUMN TEST RESULTS

The Stat io Level Of Yield Stress , r:fysHistograms

p'

o

0 0 998

Line for s

33.1 '. ....,----

35.0 0 ---

33.9 •

"All: 20 Specimens, Mean =

liE II : 14 Specimens, Mean =

34 Specimens, Mean =Average:

/

/ Material/

/ Material/

Line for Mean0.500

0.841

00002

0098

0095p"

0094.per!.--ler! 0 080.0

c.U0.70'8

~ 0060P-t

0050CD 0040P-

ori 0030.pc.U 0020.--l

§;::S 00 ;LO

0

0005

0002

4540

o. 000 l+----r---...--..._l---.,....-.....---t----r---..---._....-.........---.-----r---:,---.or---r-oooor--....,..--..,.-,....-.,.--,----.---,----,-.,--,

20 25 30 35

Figure 4{ b)

STUB COLUl~ TEST RESULTS

The Static Level Of Yield Stress,_ 0ys

Normal Distribution Probability Curves \.Jl.-J

- 58

Frequency%

30

20'.

s::ell

~·1.•1

II

. ~teri~l "An22 Specimen.s

(jys45 ksi .40353025

o -,-+~~+-r-+ .....-+-.-+·.....1 -+-r-+-..-+...,.....,f-r-+-r-+-.I1.

32 Q 8

40

Average35 Specimens

Material "B"·13 Specimens

IIIII1 _.-

c--

.-

I I

30

10

20

25 30 35 403406

@~

30 II

I20 I

Frequency%

10

°

Frequency%

25 30 :35 40 45 ksi3305

Figure 5(a)

SIMULATED MILL TESTS(Weighted Mean Of Flange And Web Coupons)

The Static Level~Of Yield Stress, aysHistograms

..

•

0.998

0---

•

. - ----32.834.633.5

Mean =Mean =Mean =

•

22 Specimens,13 Specimens,35 Specimens,

flA" :."BII :

/~/,

/0/~~terial

/ Material// Average:

Line for Mean

Line for s0.8 1

0.02

0098

0095~

~ 0.90r-l·rl 8.D o. 0co.g 0 0 70~ 0.60

Pot 0050~ 0 0 40

orl.j..J 0.30co

r-l 0.20~EO6 0.10

0.05

0.002

. 0 . 000 I-t-..,..........---,--r-r--.,.....-.,-~-r---r--r-,........,..-.,--r---r----r--r-,........,..-.,-...,..---r----r---.20 25 30 35 L~O 45 G"ys ks i

Figure 5(b)SIMUIATED MILl, TESTS

(We ighted Mean- Of Flan.ge And Web_ CoupoIls)

~The Static Level Of Yield Stress,. 6ys ·

Normal Distribution Probability Curves

- 60

30 ~~I

20 I

Material "A"j

Frequency 24 Specimens%

10

0' cr'ymill

35 40 45 50 55 ksi42 0 8

30

35

20. Frequency

% 10

°+-,-,--I-r-l-r-+--.-+-rJj4-r-+-r-+-t---r--t-+--,L,

40: 45 50 55ksi4105

Material "B"14 Specimens

crymill

It

Freq%en.cy

30

20

10

§~II

Average38 Specimens

crymill

5040 454203

35O-l-f-t-+-r-+--'C-+-"-+~~-h-4-r-+-.-+--r-+---r-11

55 ksi

Figure 6(a)

MILL TESTS (Web Coupons)The Dynamic Level Of Yield Stress, rrydHistograms

00999 o ,

00998

//

/'

lIA II ~ 24 Spee-:imens, Mean := 420 18 "----Material liB 1I : 14 Specimens, Mean = 4105 0-----

Average t 38 Specimens, Mean = 4203 •

Line for Mean

Line for s

0 098

0 095l>:>.p 0 090.r! 0 8 1..-J.r! 0 080..0ttl 0 070..00 0 060H

P-t 0 050Q) 0040l>'r! 0 030.jJ

rxi 0 020,....;:::s

,....;:::s 0010

0

0005

0 002

00002

o

35 40 45Figure 6( b)

MILL'TESTS- (WEB COUPONS)The Dynamle~ tevel'"oi:'rYi~ld -Stress,

Norma.l Distribut lon Probab ility°Ymil1Curves

55 6ymill ks i

- 62

20Fre-

quency 10%

025 30

I

35 49 454001

50

Material nAil .

24 Spe.c imens

55 ksi

30

Fre- 20., quency

% 10

025 30 35

§~IIIII

I

50

Material lIBlI

13 Specimens

O'Yd

55 ksi

§~I

20 II

Fre- I Averagequency I 37 Specimens

% 10 III O'ydI0

25 30 35 40: 45 50 55 ksi

40 0 6

Figure 7(a)

SIMULATED MILL TESTS (Web Coupons)The Dynamic Level Of Yield Stress, O'Yd

Histogr-ams

009999 o •.

0 0 998/

Line for Mean

Line for s

o. 00

0010 Material "A fI :; 24 Specimens,0

,Mean: 40.10005 / ----

Material liB fI :; 13 Specimens,0002 '/ Mean = 41~4 0-----

/Average :: 37 Specimens,

Mean - 40.6 •00002

t- 0080;=1 0070~ 0 060,2 0050~ 0040

P-i 0030~ 0020

ori.j..)

tilr-l

§::so

550yd ksi

5045403530o0000 1 +-~--r---,---;---I~,...---r-....,--;---,----,.-;--,...--r-....,--;-......,..--..,.-r--,...-...,.-....,---r-......,..---,.-r--..,.--...,.--,..........,

25

Figure 7(b)SIMULATED'''MILL -TESTS (WEB COUPONS)"

The ,Dynamic ,Level or, Yield Stress, <1yd

Normal Distribution Probability Curves

... 64

(a) Mi~l 'Test..~ , with ~ys from weighted coupon averagec1ymi11

Material "A"20 Specimens

90 %85

JI

III

IIIII

0-+-1--r-+-"-+-...-+~-r-+t.,---t--1-+-"'-+.....--Jf-;-+-r-r-.-,

65 70 75: 80I

76 .. 4

30

10

20Frequency

%

( )<J'"vs

b Simulated Mill Tests, ~vyd

20

Frequency 10%

§~III Material "A"

22 Specimens

95 %90

o +-,--,-.."...,......,-,...,.-...--+-.--1-r-+-r-+--1-1

+-r--+-r-I-.,.-T....,.-,,+--r--t--T

65 70 75 80! 8581 .. 2

ter ia1 liB"Specimens

95 %9080 I 858308

7570

§- ~ -

I Ma.I 131.---1I

,-- III

r--II

I I I 1 Io65

30

10

20

40

Frequency. %

Figure 8(a)- r ....

RATIOS OF STATIC YIELD STRESS TO MILL YIELD STRESSHist ograms.

00999

.

0.998

• • o

0.98

p., 0095~

.r! 0090r-l.r! ',D 0.80oj

.g 0.70rt 0060

0.50(I)

:> 0.40.r!~ 0030oj

r-l 0.20§6 0.10

0.05

0.02

0.002

008 1

o. 00

Line for s

Line for Mean

/

Material "A": 20 SpecimensMean = 76.4 • ---

Material. TlA Tl : 22 SpecimensMean = 81.2 () ----

Material TlBl!: 13 SpecimensMean = 83;8 • ----

Figure 8(b)

RATIOS OF STATIC YIELD STRESS TO MILL YIELD STRESS

'Normal Distribution' Probability Curves

- 66

1 "A"imens

105 %I1100I

9901

9590

- IIII Materia- I 18 SpecIII- III

I

II

!T I' Io

30

10

40

Fre=quency

% 20

~ys Stub Column

dys Weighted Coupon

Figure 9

RATIO OF STATIC YIELD STRESS, STUB COLUMN TO WEIGHTED COUPONS

Histogram

500

. .

I·

•

1." 00-+------r---r----,----r--~--r_-_.__--1

o

Strain Rate

Figure 10

- 67

micr 0- inche sinch-seconds

°ydCURVE SHOWING - AS A FUNCTION OF STRAIN RATE,

CJys

USING THE ~ FREE RUNNING~ CROSSHEAD SPEED

(Fig. a, of Reference 5)

..

30~-_.

Loadin

Kips

20

10

80-t------r---~----r--------,~--......----..,-----r------r---

o 2 6Elo~gation in Inches ~_ (?5 x ~O~)

Figure II--TYPICAL LOAD-DEFORMATION CURVE FOR COUPON' TENSION TEST

Strain Rate = 98 ~ioro=inchirlch=sec o

(}yd = 3402

50

Strain Rate 235micro=inch

=:inch~seco

(Jyd =: 350440

Stressin 30

Kips

20

10

f .-., .._~

" .~. '-, ~ ~.

o 00005 00010 0.015

Str~in i~ Lnch~s per Inch,.··.1

Figure:12STRESS~STRAIN CURVE FOR FLAT PLATE TENSION COUPON,

SHOWING EFFECTS OF DIFFERENT STRAIN RATES

0.020

- ~O

11Compressiou.~;_~ ~-I"~C ompres s ion

Stress KSI

-5 -10 -15

T-O

+10

=2

-1

8WF31

WEB DISTRIBUTION

FLANGE DISTRIBUTION

+10

T-O

+ 5

I=:0+10

...-lD)

I=:CD

E-t +15

=15 -10I IStress

1"

--~T=O

~'T=1

o -ir---T=2

-

~;<1'r c --- (Jro drw

-1309 5.6 903-11 .. 5 101 1505=12 05 4.2 500----------'-------------- --- ..... _.. __ .

AVERAGE RESIDUAL STRESSES (KSI)-------------_._-

Figure 13(a)

RESIDUAL STRESS DISTRIBUTIONS (AS DELIVERED)(Throe Specimens)

P

I

FLANGEDISTRIBUTION

. /'O"ry

(Jryo

(Jrt

(+ )

+(-)/O"rx o

WEBDISTRIBUTION

II

1, I

II

~

I

P,

( -)

~t/

~( +)

'1: Residual St~ess

In WF Shape2: Partially Yielded Cross-Section

- Nomenclature

Figure 13(b)

RESIDUAL STRESSES: DISTRIBUTION AND NOMENCLATURE

, ," ,

" ,

. .: .. ~ ". ,... ". ..~..

- 72

'..~ .

.. .'. '

, '"

modi:ried

---proportional limit

"

1\'

"1 :

rJys

b ~IP.eUdot-proportton.l limit

j<1ro

Stress

i .

, I .

"j, -'

. ;"

,

..

Strain

, .Figure 14

MODIFICATION OF STUB COLUMN STRESS-STRAIN CURVEWITH HIGlL LOCAL RESIDUALST~ES~~S. ·IN FLANGES

.' h-

'. \

, : .:,".

" ,.\, , , .:

,

.3:0

20

Frequency% 10

Material 'A'19 Specimens

(! = 0'r rc

','',,­'~'-'.

~;.

Material 'A';t9 Specimens.

= a:d rCmod

30 ksi

30

20

20Ip.lOo5i

~

o

O'

- IIIIII

-6

~r mo

iII I

o

30

10

Frequenoy% 20

.' ','

,..Average

26 Specimens

20 kai

30Frequenoy

• %20

10

00 10

20 ka~

Average26 Specimens

'/

(Jr modo

1101..

Figtl.:re '15{a)HISTOGRAMS OF THE MAXIMUM EESIDUAL STRESS

IN THE FLANGES OF STuB COLUMN, orc

~.

. #'~00500 Line for Mean ~

/.~.Y'/ Material "All:

~ • Material "B":• ~. 0 Average:

A~.

0 0 999

00998

0098i>J

0095.porirl 0090°rl,Doj

0 080,D0

0070HPoi

0060Q)

0050P-°ri

0040.pojrl 0 030§

0.20::s0

0.10

0.05

0.02

00002

0.8 1 Line for s

..

•o

19 Specimens,

7 Specimens,26 Specimens,

•9

Mean == 1305---­

Mean == 1406 0----­

Mean = 13.8. ----

o.000 15" --;-..,..-"Q'.--"-1-0,--,.......r-r-"'-""""1-S-r--..,.-....,...--r---r-

2""0-or--r--r---r--

2'T"5---r---,r---""'-""-3-'O-,~-r-c-k-S i

Figure 15< b) 1MAXIMUM RESIDUAL STRESS IN THE FLANGES OF STUB COLUMN, (Jrc

Normal Distribution Probability Curves

0.9999 •

0.998

Line for 'Mean

Line for s

Material nAif ~ 19 Specimens, Mean = 10.5 • ---,,/"

/ Material HB 11: 7 Specim.ens, Mean = 1206 0 -----,,-

/ Average: 26 Specimens, Mean = 11.1 •

o. 00

0.98

0095~

+J 0.90·rir-I·ri 0.80.0cd 0.70.00

0.60HP-I 0050(\)

0 040P-·ri 0030+Jcd

r-I 0 020::3S

0010::30

0.05

0.02

0.002

20 6rcmod ks i1510o.0001 ....--;,..--.,..--r---o--.,..---,--.,..---r--..,.--.,.---,r--~---r"-..,.--..,..-I-r-----

5

Figure 15( b) 2-

MAXIMUM RESIDUAL STRESS IN THE FLANGES QF_STUB., C0.-LVMN, c1rcmod

Normal Distributi"on Probability. -

Curves

/:,

,.

err-crys

(a) Material flAil19 Specimens

70 %6020 . 30 . 4~ .~

. j 41~1. I ..

III

IIII \---,,.--..,

IIIII

10

-"'"

~(

.--

-

~-~ II

I Ioo

<1r04---r--4-~+-4--I-+1+-+--I--+--!-r-~..., - mod

. -0 .•. ,.: .10 .. 20 30: 40 ·50, 60 70 % (fys3209

30

10

20Freqgency.

% 10

30

20Frequency

%

..

..

(b) Average26 Specimens.,

§~III

Oi-.....,---,-~-+--+-+--+--+,......,-If--+-+--+--+---+ o"ro 10 20 30 49 .5'0 60 70% (fys

4102§

30

20Freq%ency

10

30

20

10

o 10 20 30 : 403306

60 70 %

Figure 16(a).'" "".

HISTOGRAM OF THE RATIO OF RESIDUAL STRESSTO STATIC YIELD. STRESS

• ...

0.9999

0.998

0098§.~

0095 ~p,-I-:l 0 090 • •·rl 0 0841 Line for.--l s 0

orl 0080,.0oj

0070 0.0 7·0H 0060 00 Line for- MeanPoi 0050 00Q) 0.40:>·rl-I-:l 0.30oj

.--l 0020~ 0

;:::s 0.10 ; /'0

0.05 .p Material "A II : 19 Specimens, Mean = 41 01 • ---4

0.02 Material liB 11 : 7 Specimens, Mean = 41.5 0-,---

Average: 26 Specimens, Mean = 41.2 •

0.002

/

70 %656055504540353020o .000 104-I----<;>----r---,.----~-___,.--__r_--_r_--_r__--,_-___,.--.....,

15

Figure 16{ b) 1

RA TIO OF RESIDUAL STRESS, <1rc ~ TO STATIC YIELD STRESS

Normal Distribution Probability Curves

,0 010

/Material T1ATl : 19 Specimens, Mean 32.9= .---0.05 ,-

/' Material llB T! : 7 Specimens, Mean = 35.6 0----

0.02 ,- Average: 26 Specimens, Mean = 33.6 •/'

r

009999

0 0998

0.002

0.841

Q. 00

Line for s

Line for Mean

..

o

•

o .0001---......-....,.--..,....--0--.....,.----,---...,.---,..--.....,..---.,....-----,5 10 15 20 25 30 35 40 45 50 55 %

Figure 16(b}2

RATIO OF RESIDUAL STRESS, drcmod,TO STATIC YIELD STRESS

Normal Distribution Probability'Curve~--

.. -,'-, ..

. ....

- 79

valtte's:47

al "A" ,.'imens-

- ~.I MateriI 21 .Sp.e.cI- I

I I Al'So 2-.' ~ 330

- I 370II I II

21 3~ 3 ... I 3) 3L

(a)Weighted 30Coupons

E

,':'

lues:

xl03 ksi

gemens'

j Avera.I 32 Speci

/ I, I

Al$P 3 va-I ' 3309I

I 3707- 3401

II l 11

2~I I

- 3) 3 32 33o

30

20Frequency

%10

30E

al "Animens0·3values·: .

33 .. 333 .. 833.. 5--

3xl0 3 ksi

i Materi-

I 19 SpecI AlaI. . ,

-/'

29 30 '3 I 32 3a

(b)

Stub,.Colunms 20

Freqgenci/0 10

E

ge ._. Emens

-Avera

J 26 Speci- r-'Also ", vI j

I..

J."

I·"- .. II

fI

21 3b 31 I 3 3I311,,2

F:tgure- 1T( a)

YdUNG~S }!ODU'WS'· FROM TtWE!G:HTEDII COUPONS AND STUB COLUMNSHistogram1?

30

a

20Freque:Q:cy.

% 10

..

0.9999

00998

• ..

o oG

0098• • • e • • •

0095p., 0.90 0.8.j.j 1 Line for sor!

M0.80.r!

,.0ttl 0.70.g 0060

0 0500H 0050 Line for MeanP-I

<D 0040i> 0.30or!

.j.j

ttl 0020 0 Material IIAII: 21 Specimens, Mean = 31.2 .. ---,-j

PE 0 010 #. Material liB II ~ 11 Specimens, Mean :: 31.1 0----p 0

0 #.-

0005 Average: 32 Specimens, Mean = 31.2 •b70002

0.002

30 31 32 33 34 35 36

F'igure 17(b)1

YOUNG'S MODULUS FROM If'WEIGHTED Tr COUPONSNormal- Distribution Probability Curves CD

o

• .. •

00999

Line for s

_0 0 /'/'

Material lIA I! ~ 19 Specimens, Mean =: 31.5 • ---

'. Mate:rial TlBI! : 7 Specimenf?, Mean = 30.4 0-·---

Average~ 26 Specimens, Mean :::: 31.2 •

0.841

o . 0

/'+-=-0---"-•.L5~0~0__-=L=in=-=e for Mean,o.._--- 0/

•

0 0998

0 098

0095p.. 0 0 90.p

or!,..--j 0.80.,.-j

,.00070aj

,.00 0 060H

0 050~

(j) 0.40:> 0.30.r-i.paj 0 020

,..--j;::sE 0.10;::s

00005

0002

0.002

0.000127 29 30 31 32 33 34 35 X 10 3 ksi

F' i gure 17 (b )2

YOUNG'S MODULUS FROH STUB COLUMNS

Normal Distr ibUtlon -Probab-ili ty Curve s

- 82

Material "A"16 Specimens

120 %110I100I

99,,7

90

..

-II

II

Io

30

40

10

20

Frequency%

..

Average22 Specimens

o %9

-III

-

-

-

I I0 11~ 12'

o

30

40

10

Frequency% 20

•

100,,0

E coupon

Estub column

Figure l8(a)

COMPARISON OF COUPON AND STUB COLUMN RESULTS FOR E

Hist ogr-ams

L

..

009999 o ••

0.998

t---

0-----

16 Specimens) Mean = 99.7

6 Speci~en~, Mean = 100.9

22 Specimens, Mean = 100.0 0-------

o

"A 1/ :

"B 11 ~

Average:

./"/

/

Line for s--------------------.£-"-~-_.r__~...-=c---

Line for Mean

~ ..---' /"--- ~.--- //' Material

A( Material

00841

0.500

0.98

0095l»~ 0090r-l

:8 0.80

2 0070~ 0060

P-t 0050~ 0.40

*rI 0.30.p

.::l 0 020§::J 0010o

0.05

0.02

0.002

o 90 100 110

Figure 18(b)

COMPARISON OF COUPON-AND STuB COLUMN RESULTS FOR ENormal~Distribution PrDbability Curves'

J - 84··-

30 Material "A"23 Specimens

" 20Frequency

% 10W"IOS\i

0cJult

60 65 70 ksi

62,,4

Material "B"12 Specimens

°Ult70 ksi55

r--+--

,--

I--

....-

I I I:o

30

10

20Frequency

%

..

30

Frequency% 20

Average35 Specimens

.-

.. 165I

63,,7

O'u1t70 ksi

Figure 19(a)

SIMULATED MILL GOUPGNRES\1!ll'$ WEIGHTED AVERAGEULTI~TE .... STRESS. ~..

Hist ograms

..

0.9999 •o

0.998

0.002

0.300.20

0.10

0.05 .•

0.02

0.98

0.95

~ 0.90 0.8~1... _ !,j, Line for sr-f -'LL~~_----d.~'-IOL-~~,

•..-l 0.80+J

.2 0.70o 0.60H ~. sOO

P-t 0.50Q) 0.40P-

e..-l+J

c;Ur-l

§::3o

Material

Average:

//

//

/

23 Specimens,

12 Specimens,

35 Specimens,

Mean == 62.4 .- --

Mean == 65.3 0-·-·

Mean = 63.5 •

70 ksi656055

o•000 l"'---r--~....,--..,..-.,...---r--~-r---...,..-o()---r----,r---r---r'-.,...-.....,----,.--r---..,..-.,...-.....,--.,

50Figure 19(b)

SIMUIATED MILL COUPON RESULTS; -WEIGHTED-AVERAGE,-ULTIMATE STRESSNormal-Distribution- Pr'obability Curves'

- 86

, .. . ~~.:.;' -

ia1 liB"eoimens

u1tmod

190 kei

Material "A fI

23 Speoimens

1701.50

§~I

110

110

()Mater12 Sp

0-

0' -~.

V I J I J

4

3

1

2

2Frequency

%1

3Frequency

%

•

3Frequency

% 2

1

130 II

13409

Average3.5 Speoimens

FIgure 20 (-a)

SIMULATED MILL COUPON RESULTS = WEIGHTED AVERAGE/ ULTIMATE·· STRESS, BASED· ON REDUCED AREA

Histograms

•_.

0.9999 o ..•

flAil : 33 Specimen~, Mean = 134.9 .. - - -HB fl : 12 Specimen~, Mea,n = 135.0 0 -0--.

35 Specimens, Mean = 134.9 •

••....

Line for s

Line for

~

o :b'~:.. ::/.~/ Mater ial

//Mate!,~al

Average:

O. 00

00841

0.002

0.98

l» 0.95-+oJ 0 0 90orlrl-rl

0.80.g,D 0.700H 0060

P-t0.50

OJ0.40l>

orl0.30-+oJ

cOrl 0020:::s!=ll» 0010

0

0005

0002

110 120 130 160 170

Figure 20(b)-

SIMULATED MILL'COUPON RESULTS - WEIGHTED AVERAGE, ULTIMATE STRESS,BASED-ON REDUCED-AREA

Normal Distribution Probability Curves

- 88

,

Material "A"24 Specimens

80 ksi7565 7066 .. 3

60

-' II

.--1I

- rI--

-r--

nI I .1o

20

30

10

Frequency

%

s::• ttl

~I

3I

I AverageI 31 Specimens

2Frequency

%1

C1ult

60 65 70 75 80 ksi

66.7

Figure 21( a) f

MILL COUPON TESTS (WEB)'1YLIf:CMATE STRESS

Histograms

L

.. .....

0.9999

0.998

/0098

0095

0.90 0 8 1~.p 0.80.r!.-l 0.70.r!,D 0060cd 0 00,D 0.50aH 0.40P;

Q) 0.30? 0020'r!.pcd 0.10rl;:3s 0.05;:3

0

0.02

0.002

Line for s

Line- for Mean

//

0

//

/ Material "A 1I :

/ Material liB 1I :

/ Average:

••o

24 Specimens,

7 Specimens,

31 Specimens,

••o

Mean = 66.3 .---Mean = 68.2 0----

Mean = 66.7 •

O'ult

75 ksi7065o•000 l..---r----()----,.-.....,..---,--...,---,---~-r______,-___.-__,_-....,....-...,.._-._____.,

60

Figure 21(b)

MILL COUPON TESTS (WEB) ~ ULTIMATE STRESS

Normal Distribution· Probability Curves

30.,

20t Frequency

% 10

055 60

20

C1ult

ksi

- 90

O"ult

ksi

Material "B"13 "Specimens

.Ma. ter ial "A"24 Specimens

Average37 Specimens

§

fIIII

: . 5 7063.5

§

~

60 6? 70 75 80II

i I~~ .

• I

55

-~

-

i---

- .p---

I . I 1 Io

30

40.

10

30

20

40

Frequency%

Frequency%

70

•

'10

55 60 : 656401

0

F1gure.22(a)

75 80C1ult

ksi

SIMULATED MILL COUPON TESTS (WEB)

ULTIMATE STRESS·

Histograrns

l

•

o

.---

,A•

13 Specimens,Mean = 6).0 0 ----

37 Specimens,Mean = 64.0 e----

-::-. '"-. ,

24 Specimens,Mean = 63.)

IlB" :

-- ---..----~---

Material

Average:

-//J

//

/0

// Mater ial IlA Il :

//

Line for s------'-------

Line for Mean"'-"-"'-"'-"~--==-.... _._------..._..

0.998

00002

0.98

p., 0.9)..p

0 •.90 I·rl 0.841rlorl

0.80,Dm,D 0~70 \0H 0.60

fl10.)0 a o. SOO

I.

Q)

0040P-·rl.p 0.30mrl 0.20::sE::s 00100

0 00)

0.02

Figure 22(b)

SIMULATED MILL COUPON TESTS (WEB) - ULTIMATE STRESS

Normal Distribution Probability Curves

- 92

WebMaterial "A"24 Specimens

Also: 30 .. 8(14WF426)

FlangeMater ial "A"

. 24 Specimens.

Also: 64 .. 8. (14WF228)

60554540

IIIiIII

0+-.-+--r+-r-+--r-1h-++--r--+-r--t-1--f-'-T""+"'T""t-,--,.....,.....,

¥OI

4906

30

20Frequency

%10

20

10

60450-h"""r--'l~-r-+-r-+--r-1h-+-r--+-r-+--,r-+-T"""T"""T""T~

40

30

•

20Freq%ency .

10

40 45 60 . %.

Weighted Average38 Specimens

.:" ..::'

(I Figure 23Ca)

PERCENTAGE REDUCTION IN AREATENSION COUPON TESTS

Hist·ogram

l

r

009999 o

00998

0----

e----

Material "A" (Web):24 Specimens

Mean =: 49.6

Material "A" (Flange):24. Specimens

Mean::::: 54.0Mater tal "A"

Weighted Average24 Specimens

:: 53.3

/~

//

//

//

Line for Mean

4~

/,#1

~/fj.~ a

/~Q----8.b.f-4......l L~in!,£e"'_____'fLo~r~s~__=__----------L~Y---

/ .../. //'

/ e./00500

00002

0.98

p., 0.95+>..-t 0.90.--l.r!.n 0080l:\l.n0 0070HIli 0060

(1) 0050po

0040.r!+>l:\l 0030

.--l

§ 0020:J

0 0.10

0005

0.02

70 %6560554$403530o00 00l+---.r---r---~----,r----''''''''-O---...-----..,.-----r----r-----r

25

Figure 23(b)1PERCENTAGE REDUCTION IN AREA - .':rENS1C)}JGOUPON r:rES'l'E), tlMATERIAL "A"

Normal Distribution Probability Curves

.'0 0 9999 • • o

0----

e----

.-----

•

o

.• ~ j

./~/ ' 0

o / /8/

/

'Materia141 "BII (Web):Specimens, Mean = 50.8

.' Material "B" (Flange):14 Specimens, Mean = 51.6

Average (Weighted)14 Specimens, Mean = 51.4

0.500 Line for Mean-"-------- ------.----".:.....::.::.::=-----/;fAt-----

008Ul Line for s~=!:j,~---=-= ~=--=---------~<-------

00998

0098

0 0 95

0090

00800.70006000500 0400<300 020

0.10

0005

0002

0.002

70 %605040

o0000 l+--<;>---.--r----,r__~~-..,..___r_-,......._,____,-~___r-,.............___,r___,___,.-..,..___r____;_,

30

Figure 23( b) 2PERCENTAGE REDUCTION IN AREA ~ TENSION COUPON TESTS, MATERIAL liB II

Normal Distribution Probability Curves

r

009999 o.•

.----

.----

.~~f//if: Material"nAT! (Weighted Average):

. 24 Spec imens, Mean = 5303-

Material-TlB"TI (Weighted Average):14 Specimens , Mean::: 5104 0 --. --.

Average· (A& B) :38 Specimens~ Mean =

oo

•

/

Line for s

0.500 Line for Mean-1-=-=...£.---=-::.--------.-------~'Grr_--------

00998

00002

0 098

h 0 095+>·rl 0 090~

·rl.0 0 080cd.0 00700H 0.60P-;

CD 0050p. 0.40·rl

+> 0.30cdM 0020::::lS::::l 0.100

0005

0 002

605040

o 0 000 l+---r-----lt--...,.--.,.--,---,--r--r----,---,...,.----,--.,..---,--or---r----r--,-----,--.,....-....,

30

Figure 23(b)3

PERCENTAGE REDUCTION IN AREA~~~TENSION COUPON TESTSWEIGHTED"" AVERAGE OF <MATERIAL flA If AND MATERIAL liB"

Normal Distribution . Probabil-ity Curves

- 96cJys = 3307

Average from33 stub column

and 35 weightedtension coupon tests

J 3

(1rc,..I-

2 := 1909

Stressksi

1 31 02 x 10 3

o Strain in/in.

Typical Stress-Strain Curve For Stub ColumnAverage From Test Results

(j. s = 33.0

= 200,0

30 "

c:f =: 13 0 0rc

10 '.

20Stressksi

,o-IL------r------r------r-----....,.-------r

oStrain in/in.

L

Suggested Typical Stress=Strain CurveForWF Stub Column Test

Figure 24