Welded Columns

HYBRID STEEL COLUMNS

by

N. R. NagarajaRao, P. Marek, and L. Tall

Fritz Engineering LaboratoryDepartment of Civil Engineering

Lehigh UniversityBethlehem, Pennsylvania

May 1969

Fritz Laboratory Report No. 305.2

305.2

TABLE OF CONTENTS

-i

ABSTRACT ii

1. INTRODUCTION 1

2. THEORETICAL ANALYSIS 3

Strength of an Ideal Column 3

Tangent Modulus Strength 6

Ultimate Load and the Load Deflection Curve 8

Eccentrically Loaded Columns 9

Local Buckling 9

3. EXPERIMENTAL STUDIES 11

Description 11

Tension Specimens 11

Residual Stress 12

Stub Column 12

Pinned-End Columns 13

Local Buckling 14

4. DISCUSSION OF RESULTS 16

Ultimate Load 16

Column Tests 16

Price - Strength Ratio 18

5. CONCLUSIONS 20

6. AC KNOWLE DGEMENT S 23

7. NOTATION 25

8. FIGURES AND TABLES 27

9. REFERENCES 47

305.2

ABSTRACT

This report presents the analysis and results

of a theoretical and experimental investigation to

determine the strength of hybrid steel columns.

The investigation was made on centrally­

loaded welded H-shaped columns with high-strength

steel flanges and low-strength steel webs.

The tangent modulus and ultimate load, the

mechanical porperties of the materials, the actual

residual stress distribution and local buckling were

taken into consideration for the theoretical analyses

of column curves. The predictions were verified by

tests.

The experimental study included five hybrid

shapes, fabricated from flame-cut or universal-mill

-ii

plates. The following tests were conducted: tension

specimen coupon, resid~al stress measurements, stub

column tests and pinned-end column tests with a

slenderness ratio of 65.

The study showed that the column strength of.~

..

305. 2

hybrid shapes can be predicted from the actual residual

stress distribution by assuming a hypothetical residual

stress in the web equal to the qifference in yield

strength of flange and web.

The investigation was completed by a

discussion of approximate estimation of residu~l stress

distribution and its magnitude,local buckling

considerations and elastic stress of webs at the

"working" load.

For slenderness ratios up to 70, the A5l4

homogeneous steel columns are usually the most

economical; for ratios from chart 50 up to 70, hybrid

columns may lead to a price reduction.

-iii

305.2

1. INTRODUCTION

-1

.

The hybrid steel column is a special type of

component ~tructural member that consists of higher-

strength steel flanges and a lower-strength steel web.

Much information is already available about the use of

hybrid beams,(l) which frequently offer significant

material cost savings over homogeneous beams, but there

has not yet been extensive theoretical and experimental

analysis of the behavior of hybrid steel columns.

This paper is a contribution to hybrid section

analysis and gives a description of the theoretical

analysis and tests executed at Lehigh University and

the comparison of results and discussion about the

usefulness of compression members composed of two

different types of steel.

greater detail in Ref. 2.

The study is described in

The concept of hybrid shapes has been applied

to structural members in bending, by placing a stronger

material in a position where it can resist higher

stresses, thus using materials according to their

strengths. Such explanations are not satisfactory for

centrally loaded ideal columns, with no region of lower

305.2 -2

stresses; already in the case of beam-columns the hybrid

cross section may offer some savings. Another interesting

problem that suggests the study is the reinforcing of old

columns to carry heavier loads by adding high-strength

steel cover plates.

A knowledge of residual stresses in hybrid

sections and information about the behavior of centrally

loaded colum~s are necessary in considering design

recommendations for both columns and beam-columns. For

these reasons, an investigation was made on welded H­

shapes, with high-strength steel flanges and low-strength

steel webs, with respect to:

a. The difference in the yield stresses of the

materials used,

b. The residual stress distribution caused by

fabrication of plates and by welding,

c. The local buckling characteristics,

d. The out-of-straightness of the column.

305.2

2. THEORETICAL ANALYSIS

-3

Strength of an Ideal Column

The strength of a column may be defined by its

bifurcation or buckling load, (at which a theoretically

straight column is indifferent to its deflected shape),

and by its ultimate load (the maximum load that a

column can carry, defining the transition from a stable

to an unstable configuration). A review of the past

(34)work is p~ovided in several papers.' Research in

the last decade has underlined the great influence of

( 5 )residual stress distribution on column strength.

The tangent modulus and recuded modulus buckling

theories are applicable with some modification to

" . "d 1 (3,6)columns contalnlng reSl ua stresses.

In determining the column curve for a hybrid

steel column, the main problems are caused by the

difference in yield stresses of the component material

and by the residual stresses. A simple method presented

here, uses the residual stress itself as a tool to

transform a jybrid shape into a homogeneous shape.

It is assumed that the stress-strain curve of

the web steel and flange steel are both idealized as

shown in Fig. 1.

An ideal hybrid H-shape is shown in Fig. 2.

-4

and

The yield stresses are crf

for the flange, crw

for the web,cr

w- = a «1.0). The entire web yields when thecr

faverage stress is cr and further loading is tr?nsferred

w

to both flanges only. Column curves for this ideal

column as shown in Fig. 3 are derived as follows:

For the flange area Af

and w~b area Aw

' the

load to cause yielding on the complete section,

Py ='lAfcr f + Awcr wI

and the" moment of inertia

I

and

with

then

For

2 2r = Ar .

w

( 1 )

( 3 )

305.2 -5

At a = L/r =c

= C1

( 4 )

At the load corresponding to a = a , the web yieldsw

andcompletely, and Ix

Prespectively, and P

y

IY

:1= aa

f

reduce to Iex

and Iey

X-axis Buckling

I Af

2ex r

fi3= =I 2

A r

I2 ex

P. E I 27T

Ar-- = .a

f2

a fL

( 5 )

aa

f= i3 . ( 6 )

At a = a , L/r = c $ I a = c 2w .

For a = a , the column curve is given by Eq. 6. Thew

maximum value of ala f is

( 7 )

aa

f= = y < 1.0

For convenience,

and the corresponding slenderness ratio,

L/r = c$ I y = C3

to have PIP reach 1.0 when the entirey

shape yields, the PIP ordinates are divided by andy

( 8 )

Eqs. 2 and 6 rewritten as

C2

P mfor <= a a

P (L/r)2 'wy

( 9 )

305.2

C2

13.p m fpr cr >= crp

(L/r)2 wy

where CC=m ../Y

Y-axis Buckling

-6

(10 )

(11 )

I~ 1.0

I

CJ t-p

--CJ

fP

Y

when the web yields so that although

= (L~r)2

cr for cr <-- CJfcrf

2P

=(L~;) for cr < CJ fP

Y

Tangent Modulus Strength

Similar to homogeneous columns, the tangent

( 2 )

modulus load can be found by two methods: (1) using

the tangent modulu~ obtained by a stub column test

d (2) . h ·d 1 d""b· (3,5)an uSlng t ~ reSl ua stress lstrl utlon. .

Although the stub column method has not been

used to predict the tangent modulus curve in this

investigation, stub column tests were conducted to

obtain other important characteristics of hybrid columns. \\

3 a5.2

The residual stress distribution of hybrid

-i

shapes is described in Section 3. Some modifications

were made to the measured distributions in order to use

them for computing column curves with the help of a

digital computer.

The following assumptions were made for the

mechanical properties:

- an idealized stress-strain relationship

- the material is homogeneous

- plane cross~sections remain plane after

deformation

the residual stress is constant along

each fiber in the cross section and axial

symmetry of cross section and residual

stress exists

- the hybrid shape may be transformed into

a homogeneous shape as described above.

computer

The tangent modul~s

( 2 )program are shown

curves obtained by a

in Figs. 4 (a) through

(e) • The portions of curves shown dotted are for the

shapes without residual stresses.

In Fig. 5, the tangent modulus column curve

305.2 -8

for buckling about the y-axis for the hybrid column is

shown with the slenderness ratio non-dimensionalized.

Also shown are the CRC column curve and tangent modulus

very important fbr y-axi~ buckling. Furthermore, it

shows that the curves for columns with A441 flanges

are significantly above those of A7 welded columns and

that the column curve for the shape with A441 flame

cut flanges is very close to the CRC curve. For

comparison, also a column curve for a flame-cut welded

h 12H79 f A36 I d " I d d (7)s ape, , 0 stee gra e 1S. 1nc u e .

comparison of all shown column curves confirms the

The

effect of arjay, as a ja decreases, column strengthr y .

increases.

Ultimate Load and the Load Deflection Curve

The theoretical load deflection curves, .such

as the one shown in Fig. 6, were obtained after

simplifying the computation by the assumption of a

single sine wave initial deflection curve and after

modifying the actual measured residual stress distribution

for perfectly symmetrical distribution about the

geometrical axes of the section. The maximum value of

305.2

the load in each of the load-deflection curves is the

theoretical ultimate load of that column for the

-9

corresponding slenderness ratio. No initial out-of-

straightness was assumed. The ultimate strength column

curves obtained by plotting tbese ul~imate loads and

slenderness ratios are shown in Figs. 7 (a) to (e).

Eccentrically Loaded Columns

The research program was concerned with the

investigation of centrally loaded columns. Due to

fabrication error, unsymmetrical residual stress

d.istribution, or eccentrici ty of the load, the actual

column may have significant out-of-straightness and

the method of computing the load-deflection curve

must be modified. The computer program for centrally

loaded columns was adjusted to compute the load­

deflection curve, taking eccentricity into consideration.

Figu~e 8 shows the computed load-deflection curves for

shape No. IV, with e = 0, e = 0.1 in. and e = 0.20 in.

and L/r = 65. These curves indicate that the ultimate

loads are less than the tangent modulus load by about

15% and 20% respectively.

Local Buckling

In hybrid shapes, web buckling may be of some

305. 2

concern because the web may be partially or wholly

inelastic at working load. Flange buckling can be

considered without difficulty, since it will be

-10

mostly elastic. The width-thickness ratio of the

web must be such that the web does not buckle even

if it has yielded completely.

Plate buckling in the inelastic range has

been investigated in the past in connection with

plastic design, see Ref. 11. The buckling of plates

containing residual stresses has been analyzed in Refs.

8 and 9. According 'to the conclusions, local buckling

in the plastic range is prevented when A ~ 0~52 if the

ends are fixed and A < 0.58 if the ends are simply

supported.

305.2

Description

3. EXPERIMENTAL STUDIES

-11

The study included five hybrid shapes, which

are described in Table 1. The hybrid columns were

\'

fabricated from flame-cut plates or UM plates (No. II)

which were not subjected to any cold-bending or

straightening. The component plates were 20 ft. long.

The shapes after welding also were not straightened or

cold-bent or trimmed in any way.

shown in Fig. 2.

The cross section is

The tests conducted on these shapes were:

tension specimen coupon tests, residual stress

measurements, stub column tests, and pinned-end tests.

Tension Specimens

Coupon tests were used to obtain mechanical

properties and to ascertain that the right type of

steel had been used. The results of tests are ~iven

in Table 2. As shown, all steels except the A441 steel

web of No. IV showed more than the specified stress

level. The coupon dimensions were in accordance with

ASTM 'f" . (10)specl lcatlons.

The specimens were 3 ft.

305.2

Residual Stress

Residual stress measurements were made by the

h d f.. (12)

met 0 0 sectlonlng.

long and one spcimen was taken from each hybrid shape.

The results for all shapes are shown in Figs. 9 and 10.

-12

The shape of the residual stress distribution corresponds

to the usual distribution in homogeneous columns and in

the flange tips of universal mill plates and of flame-

cut plates.

Stub-Column

Stub column tests provide an average stress-

strain curve of the whole cross section, including

the effect of residual stresses. Stub columns are

short columns long enough to retain the residual stress

distribution in normal column and short enough not to

fail by column buckling. The length of such columns

is prescribed in Ref. 13; the test columns were 24

inches long. Strains were measured after alignment

by 0.0001 in. dial gages over a gage length of 10

inches. Stub columns shapes Nos. I, IV, V, were

tested in a 5 million pound hydr~ulic testing machine,

while those with A441 flanges (No. II and III) were

tested in an 800,000 pound mechanical testing

machine. The results of the stub column tests are

given in Table 3 and in Figs. 11 (a) to (c).

305.2

Pinned-End Columns

Pinned-end column tests verify the prediction

of column strength made on the basis of the residual

stress distribution or of stub column tests, and

pr0vide information on the behavior of the shapes used

-13

as columns. One column of each shape was tested as a

pinned-end column. With a length of 8 ft; and a

slenderness ration of 65, axial load was applied

through special fixtures which simulate a pinned-end

condition about the y-axis and a fixed-end condition

about the x-axis (Ref. 14). Strains were measured

by means of SR-4 A-I type strain gages of I" gage

length placed at the mid-height of the column and near

both enns. They were also used to align the columns

so that the load would be exactly central at mid­

height and as close as possible to central at the

ends. The columns had a slight initial out-of-

straightness and were bent in single curvature. The

maXlmUffi out-of-straightness measured was at the mid­

height. (See Table 4) Load was applied in small

increments and the lateral deflection at mid-height

was measured by a 0.001 in. dial gage and also with

a transit and 0.01 in. scales at quarter points on

the length of the column. The rotations at the ends

we~E n~dsured by a 0.0001 in. dial gage and level bar.

305.2

The results of the pinned-end column tests

are shown in Table 4. The test results exceed the

predicted values by 1% (No. I and No. IV), by 10%

(No. III) and by 6% (No. V). The test result is 4%

below the predicted value for shape No. II. Based

on the limited number of tests, a reasonably good

prediction can be made with the measured residual

stress distribution and the computer program.

The load-deflection curves of the column

-14

tests are shown in Fig. 12. The ultimate load was

reached when the lateral deflection was about 0.1" for

all columns, except shape No. IV.

A comparison of the predicted and actual

load-deflection curves can be made with the help of

Fig. 13. The prediction of the load-deflection curve

is complicated, since in an actual column such factors

as out-of~straightness, eccentricity of load and

unsymmetrical residual stress distribution, all

influence the behavior considerably.

Local Buckling

Flanges - The width-thickness ratio for the

webs and flanges of the H-shapes used in this

305.2

study were 16 and 12 respectively. These are

-IS

comparatively low values, and therefore, local

buckling did not occur in the stub column tests

until strains were well in the plastic range.

It was also observed that local buckling

occurred in the flange first, and by the time

the web started to buckle, the flanges were

severely buckled. Thus it was found for the

test'specimens that the width-thickness ratio

of the flange was the critertion for strength.

Webs - The stress-strain curves for the webs

obtained from pinned-end column tests are

shown in Fig. 14. The strains were measured

at the mid-height of columns and in the

middle of the web on both sides and averaged.

From the load-deflection curves of the columns

shown in Fig. 12, it is seen that the mid-

height deflection is negligible up to 60%

of yield load. Therefore, it can be assumed

that the cross section at mid-height is

subjected to a negligible amount of bending

stress and the strains recorded are due

essentially to the axial load.

305.2

Ultimate Load

4. DISCUSSION OF RESULTS

-16

The theoretical tangent modulus column curves

and ultimate load curves for the hybrid shapes have

shown that the strength of these columns is much higher

than that of welded homogeneous A36 columns.

The computation of the tangent modulus load

is simple compared to the ultimate load calculation.

As shown for columns with A514 flanges (Fig. 7),

PufP t l=::t 1.0, and it i's therefore not necessary to

compute the ultimate load. For columns with A441

steel flanges, PufPt = 1.05, whereas for welded

columns of A36 steel PufPt may be as high as 1.25.

The hybrid columns tested in this study had ultimate

loads of about 75 per cent of the yield load. Welded

H columns of A36 steel of comparable slenderness ratio

, ( 3 )have such a high value.

Column Tests

The hybrid columns with A514 flanges failed

suddenly after reaching the ultimate load.

In Section 2, the local buckling considerations

of the columns tested were mentioned. The width-

305. 2

thickness ratio specified by AISC for allowable stress

design may be used for flanges since the working

stresses in the flanges can be expected to be within

the elastic limit; the validity of these ratios has

not been, confirmed by tests.

As far as the webs are considered, the column

tests results described in Section 3 lead to the

following comments:

If it is assumed that the factor of safety

for these columns is 2.0, the columns of Shapes Nos.

I, IV, V, II and III would have working loads of

0.38 P , 0.37 P , 0.42 P , 0.37 P and 0.42 PY Y Y Y Y

-17

respectively, based on pinned-end column tests. This

shows tnat all shapes except No. I will have their

webs well within the elastic limit. If it is desired

that the average stress in the web be within the

yield stress, then A36 ahd A514 steels should not be

used in the same shape.

The values of width-thickness ratio of web

as used in the AISC specification are not very

restrictive for A36 or A441 steels. The li.miting

ratios would be 42 and 34 respectively. These vall.:r;:;s

were intended for the condition that the webs are

305.2

allowed to strain-harden. The webs of hyb~id shapes

- 18

would have strained not more than ~e when the entirey

shape is in plastic state. Hence, the recommended

values are conservative.

P~ice-Strength Ratio

A relationship between price-to-strength ratio

and slenderness ratio can be developed with the aid of

column curves and cost data. Figure 15 shows such

curves which are based on the theoretical cross-

sectional areas and ~he ave~age net mill prices, 1969

level. The prices used in the calculation are: A514,

15 cents/lb; A441, 12 cents/lb; A36, 9 cents/lb.

Figure 15 shows that A514 steel columns should be

economical for low slenderness ratios. For slenderness

ratios larger than about 70, A36 steel is progressively

suitable. The combination of A514 and A441 with A441

and A36 steel respectively, not only reduces the dead

load to be carried, but may also bring economical

savings. For a reliable comparison, further factors

should be taken into consideration, for example

fabrication, transportation and errection, any of

which may change the price relationship shown in Fig. 15.

The price relationship of the hybrid shape

No. 5 in comparison with the homogeneous shapes lS

305.2 -19

shown in Figure 16. The price of the hybrid section

(6" x 1/2" flanges, A514 steel and 6" x 3/8" web,

A441 steel) is compared for each slenderness ratio

with the prices of homogeneous columns, all having

the S2me allowable load. The ultimate load for hybrid

sectiGn No.5 was obtained from Fig. 7c; the factor of

safety and allowable stresses for A36, A441 and A514

steel grades are those of the AISC specification.

As shown in Fig. 15B fc,r ,very low slenderness ratios

up to about 45, A514 steel is most economical; for

slenderness ratios above 75, A36 steel is the

c h e ape st. For s 1 end ern e s s r a't i 0 s fro m 4 5 up to 7 5 ,

use of the hybrid section may reduce the price by

more than 10 per cent.

30 S. 2

5. CONCLUSIONS

-20

The typical tests conducted on hybrid shapes

were coupon tests, residual stress measurements, stub

column tests and pinned-end column tests. Residual

stress measurements made on welded plates of A7, A36,

A4 41 and A514 steels were used to estimate the residual

stresses in hybrid shapes. The actual residual stresses

in the hybrid shapes were used to compute the tangent

modulus column curve and the ultimate load curve by a

digital computer. These curves were verified by tests.

The following are the important conclusions

of this study:

1. The residual stress distributions are similar in all

three shapes with A514 steel flanges. The tensile

residual stress at the flame-cut flange tips ranges

from 30 ksi to ,70 ksi, and is about 25 ksi at the

welds (average through the thickness). The

compressive residual stress is about 20 ksi. The

webs have high tensile residual stress in the

immediate vicinity of the welds and a compressive

residual stress of about 10 ksi over the remaining

area.

305. 2 -21

2. The column strength of hybrid shapes can be predicted

from the actual residual stress distribution and by

assuming a hypothetical residual stress in the web

equal to the difference in yield strength of flange

and web.

3. The tangent modulus column curves show that the

column strength reduction due to residual stresses

is small (no more than 10%) for shapes with A5l4

steel flanges; also, the hybrid column with A44l

flame-cut flanges is stronger than the column with

A441 Universal Mill flanges, and the hybrid

column with A44l flame-cut flanges has a tangent

modl~lus curve very close to the CRC curve.

4. For shapes with A514 steel flanges, the ultimate

load is only slightly higher (up to one per cent)

than the tangent modulus load. The ultimate load

for the shape with A44l flame-cut flanges is about

5% greater than the tangent modulus load. For

t~2 hapewith A441 Universal Mill flanges, the

ultimate load is considerably greater than the

tangent modulus load at the low slenderness ratios

(up to 20 per cent).

5. Local buckling considerations requir~ that the webs

must not buckle up to a strain of twice the yield

strc:in (2€ ).Y

The width-thickness ratios of webs

must not exceed 42 for A36 steel. The flanges may

305. 2 -22

be designed with respect to requirements of allowable

stress design. Further research into the plastic

behavior of A441 and A514 steels are necessary to

make definite recom~endation~.

5. The pinned-end test columns carried the predicted

ultimate load within 5 per cent.

7 . The col u mn t est s s howe d, t hat at the "w 0 r kin g If, loa d

the webs of all shapes except No. I (A514 flanges

and A35 webs) were elastic.

8. For slenderness ratios up to about 70, the A514

homogeneous steel columns are usually the most

economical; for ,slenderness ratios from about 50

up to 70, hybrid columns with A514 flanges may

bring a price reduction and can be taken into

consideration.

9. The information obtained on the behavior of the

hybrid shapes should be taken into consideration

in future column curve studies. This will be

part i cularly tr'u::! if din e:rent co I umn de sign

curves for different shapes and steel graJes

will be developed. Only then will the more

reliable and logical price comparison be made.

305.2

6. ACKNOHLEDGEMENTS

-23

This report is based on a research program

"Hybrid Steel Columns" conducted at the Fritz

Engineering Laboratory, Department of Civil Engineering,

Lehigh University, Bethlehem, Pennsylvania. The

Pennsylvania Departm~nt of Highways, the U.S. Department

of Commerce - Bureau of Public Roads, and the Column

Research Council jointly sponsored the research.

Task Group 1 of the CRC under the Chairmanship

of John A. Gilligan provided valuable guidance. Special

thanks are due to Lynn S. Beedle, Director of Fritz

Laboratory for his helpful suggestions throughout the

program.

The United States Steel Corporation donated

part of the high-strength steel used in the columns,

and acknowledgement is due also to the Bethlehem Steel

Corporation, in particular, to Jackson L. Durkee and

J. Smith for arranging the fabrication of the columns,

and for donating two columns.

Kenneth Harpel, Foreman, and his assistants

at Fritz Lab were very helpful in the testing.

Kuo Yu assisted in all phases of the program.

Ching­

The

305.2

figures were drawn by J. Izquierdo, J. M. Gera and

Mrs. Sharon Balogh. Special thanks are due to Miss

Joanne Mies for typing the report.

-24

305.2

7. NOTATION

-25

A

E

cm

Area of cross section

Area of flanges

Area of web

Constants

Young's Modulus

Tangent Modulus

I ,

I ,e

L

KL

P

Py

Pt

Pu

r

t

I , Ix Y

I Iex' ey

Moment of inertia of a section

Moment of inertia of the elastic

area of a partly yielded cross section

Length of a column

Effective length of a column

Load on a column

Yield load

Tangent modulus

Ultimate load

Radius of gyration of entire section

Thickness 6f flange

a crBuckling Istress = P /A

cr

af

aw

ay

a.,S,y

Yield stress of flange

Yield stress of web

Yield stress in general

Constants

305.2

€Y

It

Strain

Yield strain; a IEy

Non-dimensional slenderness ratio

of a plate or column

-26

305.2 -27

8,. TABLES AND FIGURES

305.2

TABLE I

Hybrid Shapes in Test Program

Steel GradeNo. Flange Web

I A5l4 A36

II A441(UM) A36

III A44l A36

IV A5l4 A44l

V A5l4 A44l

UM - Universal Mill Plates

-28

305.2

TABLE II

TENSILE SPECIMEN RESULTS OF STEELS USED

IN HYBRID SHAPES

(Laboratory Tests)

-29

ShapeNo.

I

II

III

IV

V

Flange

A514

A441UM

A441

A514

A514

(Jy

(ks i)

110

50

51

106

104

(J ul t

(ksi)

121

76

78

117

117

Web

A36

A36

A36

A441

A441

(J

Y(ksi)

40

39

39

49

53

(J ul t

(ksi)

67

66

72

75

305.2

TABLE III

RESULTS OF STUB COLUMN TESTS

-30

Shape Flange Web Yield Load PNo. y

From From Pi':

Coupons Stub Column y

P if: Py Y

(kip) (kip)

I A514 A36 750 774 1. 03

II A441Ul"! A36 388 393 1. 01

III A441FC A36 394 403 1. 02

IV A514 A441 746 779 1. 04

V A514 A441 743 735 o .99

FC = Flame-Cut Plate

305.2

TABLE IV

RESULTS OF PINNED-END COLUMN TESTS

-31

Shape Max-imum Predicted Test ResultsNo. Out-of- Load

Straight-P P P P P (p ) Test

ness + u u u u u u( in. ) (kips) P (kips) P it': P it': it': (p ) Predicted

y y u u

I 0.06 572 0.75 581 0.78 o .75 1. 01

II 0.06 294 0.76 283 0.73 o .72 0.96"

III 0.02 315 0.80 334 o .85 0.83 1. 06

IV 0.10 574 0.77 580 0.78 0.74 1. 01

V 0.09 561 0.75 619 0.83 0.84 1.10

+ This occurred at mid-height of columns.

Based on coupon strengths of flange and web.

Based on stub column tests.

305.2

Fig. 1 Ideal Stress-Strain Curve

~"

L .-------1-----.

6"

1~111-1._~61_' I

-32

Fig. 2 Cross Section of a Hybrid Steel Column

305.2 -33

E

V-axis

P (Cm)2Py = L/r

( )

2..f- ~ CmPy- L/r

o C3 C Cm C2 CIL/r

AI1.0

Yt-A ___.-+'"'

0-Of X-axis

a

o

ay

1.0

P/Py

Fig. 3 Column Curves for a Hybrid H-Shape Without

Residual Stress

Q

305.2 -34

Euler Curve

0.2 ResidualStressDistribution

Shope :# Iflong. A514 6"IiW.b A36 6"~

--- - Without Residuol Stress

--With Residual Stress

d­E

a

a 20 40 60Llr

80 100 120

1.0 Y-QxisyI X-axis

0.8 x-~x

~JShop. #4

y ""Fla",~e A514 6-1 112

0.6W.b A441 6',~,;

-- - - Without Residual StressPIP,

3~+ ~--Wit h Residua I Stress b

0.4 ~0 40ksi Euler Curve

°fl -f02 Residual I 2

StressDistribution

a 20 40 60 80 100 120

Llr

c

Euler Curve

Shop. # 5flong. A514 6','1;W.b A441 6"\'

----Without RllicluGl Stress--With Residual Stress

Y-axis

X-axis

+--Jr\t!'d~Oksi ~

~3

+ I 2

Residual .StressDistribution

0.2

1.0 -­YI

0.8 x-=p-xy ""

0.6

PIP,

0.4

a 20 40 60

Llr

80 100 120

Fig. 4 Tangent Modulus Column Curves (A5l4 Flanges)

365.2

PIp,

1.0

O.B

0.6

0.2

Yield------------------~~

I

X-Oli.----l, \, \

i=±:::1~I~\\\\

Residual StressDistribution

'i-oxi,

Shop. #2Flgn;_ A44t1 UN 6-. ~.Web A36 6- • '5,8-

- - - Without R..idual Siren

--With Re,ldual Sir•••

Eullr Curve d

-35

of10-, :R••ldual Sfren ~ +Distribution

40 k$i

o

1.0

O.B

0.6

P/Py

0.4

0.2

0

20

20

40

40

60Llr

60

L/r

BO

BO

100

Y·oIII

100

120

Snape" ;,FlanQe A441 6·. 'It:.

(Flam. Cut)Web A36 ft. "8-

---Without R••ldual Sft...

- With R..lduol Sims

120

e

Fig. 4 Tangent Modulus Column Curves (A44l Flanges)

A36 FC Welded12 H79

•".".'" ". ' ......

' .. ' ..'"

A7~ .y

I

IIy

'..'. ".

0.2

0.8

0.6

0.4

P/FY

305.2 -36

Shape Flange Web Curve Test Point

I A514 A36 ----- 0

2 A441 A36 ------ X3 A441 A36 _._.- +

(Flame -cut)4 A514 A441 _._-_._.- 0

5 A514 A441 _.._..- A

A7 A7 .................. •A36 A36 -_._-

1.0 A 514 Flanges

a 0.4 0.8 1.2 1.6

A=_I ~Py ~.h.Tr AE r

Fig. 5 Non-dimensional Column Curves for Y-Axis

Buckling

305.2

P/Py 0.8

Shape :# IA514 8 A36b =6"

L/r = 504030

-37

o 0.05. I

0.10

Yc/ b

0.15

1.0

P/Py 0.8

o

1.0

P/Py 0.8

Shope #4A514 a A36b= 6"

20

I I I

0.05 0.10 0.15Yc/ b

Shape :# 5A514 8 A441b =6"

50 4030

oI I

0.05 0.10

Yc/ b

0.15

Fig. 6 Theoretical Load-Deflection Curves

305.2Shape :#: IA514 a A36b = 6"

La

-37

P/Py 0.8

L/r = 504030

a 0.05 0.10

Yc/ b

0.15

1.0

P/Py 0.8

a

1.0

P/Py 0.8

Shope #4A514 a A36b=6"

20

, I I

0.05 0.10 0.15Yc/ b

Shape :#= 5A514 a A441b = 6"

50 4030

oI I

0.05 0.10

Yc/ b

0.15

Fig. 6 Theoretical Load-Deflection Curves

305.2 -38

a

120

Euler Curve

1008060Llr,

4020

Shope'" I

Flange A514 6'",Web A~6 6',,,..

--Tangent Modulus--Tangent Modulus

Without Residual Siress

-----Ultimote LoadTest Result

o

0.4

06

1.0 r-----_......y=iel!!....-_--\t

y \

t,,,.~''''+\J-+:-+

L

0.8

0.2

PIP,

b

+ J Euler Curve

L

Shape :# 4

Flange A514 6', V;Web A441 6'"

-- Tongent Modulus

- - Tangent ModulusWithout Residual Stress

---- Ultimate LoadTesl Result

it-l "'''00 .",+\r-0.6

0.8

1.0r--_0;.-=

0.2

PIP,

0.4

o .' 20 40 60Ltr,

80 100

': ,~:

.. ::-.'~'~~!

! ~~.":~~Y

08

0.6

PIP,

0.4

02

Sholle #: 5

Flange A514 6Ml 1ti

Web A441 6',3~'

-- Tongent Modulus

--Tongent ModulusWithout Residual Siress

-----Ullimote Load• Test Result.

d­[

Euler Curve

c

o . '20 40 80 .100 120

".. ~'. ,"

Fig. 7 Ultimate Load Column Curves (A5l4 Flanges)

y

tIY (Buckling Alis)

Shop. # 2Flang. A441 6', ~2

Web A36 6-13,8'-- Tangent Modulus- - Ton gent Modulus

Without Residual Stress-- --- Ultimat. Load (e· 0)

• Ttst Result

305.2

1.0

08

0.6

PIP,

0.4

0.2

0 20 40 60 80Llr,

100 120

Euler Curve

d

-39

0.6

PIP, Shop. # 3 Euler CurveFlonoe A441 6', "2' y

0.4 IW.b A36 6"3t;

I-- Tangent Modulus

0.2--Tongent Modulus I

Without Residual Stress Y (Buckling Alis)

-~---UltimQte Load (e-O)Test Result

0 20 40 60 80 100 120.·Llr,

e

Fig. 7 Ultimate Load Column Curves (A44l Flanges)

PIP,

Fig. 8 Load-Deflection Curve for Centric and

Eccentric Loaded Column

305.2+75.

+63

.+74

• +62

-40

+73

Shope '*' IFlanoe: A514

JWeb: A36

o Outer Facee Inner Face

+60

a

+69..+61

• .+73 0+77 e .+71

e+54

c

.+49

o Outer Face• Inner Face

0-12

oo

+71 _

Shope #5

Flanoe: A514

Web: A441

+49.

b

' 50ksi

0+45

I ,

o Outer Foee• Inner Face

+29

Shope '*' 4Flanoe: A514

Web: A441

+530

+75------"1

+550 0+59

e e+70

Fig. 9 Residual Stress Distribution in Hybrid

H-Shapes (A5l4 Flanges)

305.2e+58

e

-14

-II

aShope #2 0 Outer Face

FlanQe : A441 UMe Inner Foee

Web: A36

-10

-19

ee+59

e+68

-41

Shope # 3

FlanQe :A441flame-cut

Web: A36

-61e

+24

ee+.61

b

0 Outer Foeee Inner Face

I I I I

0ksi

50

Fig. 10 Residual Stress Distribution in Hybrid

H-Shapes (A441 Flanges)

305.2 -42

t Locol Buckiino in Flanoe

Shape # IT••• T·3

Flono' ASI4

Web A36

P .774 L'" 24in

aL/r·16

12106Strain in/in

0.8

1.0'

i/'

I

0.6;

/PIP, i

0.4 /;ii

0.2 ,!

./0 2

•• ••T-7 T-2.

A514 A514,./

A441 A441

PIp, 77911. 73511. b-<>-

STRAIN in.lln.

141210

Shop. •• ••Te.t m T-15

FlonQt A441 A441(Flame-Cut)

P/Pyw•• A•• A'. C~ .00' 40"

Curve

Locol BuckllnQ In Flonge

STRAIN in.! in

Fig. 11 Stub Column Stress-Strain Curves

305.2 -43

1.0

1.61".4

0.84

PulPy

0.75

0.74

1.2

Web

A36

A441

A441

1.0

A514

A514

A514

Flan\le

5

4

L= 8'-0" ltr =65

Note: Pycorresponds to Stub. ColumnTest Result

Shape

0.8

\\,I:--8I,,,

0.6OA0.2

I

o

0.4

0.2

Pmax =619k (Shape :fI: 5)

._.~-__ _ k

0.8' Pmax=58Ik(:fI:IL r--------- P

max-580 (Shape:fl:4)

.~.- - -.,...:' .~--.\ ./ /' ---- --==._---./. ------ ------I / ------ -----.....-

0.6Ii! -----! II i

IIiii

P/Py

8 (in), ,::.

b

Shape Flan\le Web PulPy

2 A441 A36 0.72

3 A441 A36 0.83

(Flame Cull

L= 8'-0" L/r • 65

Note: Py corresponds to Stub ColumnTest Result

\\II

r 8,III

0.2

08 Pmax=283k

! ----.L (Shape:fl: 2)I ./. =""- ~

!./ .~---=..::-=:::::===--06! I

P/Py !iI'OA.

i

o 0.2 OA 0.6 0.8 1.0 1.2 IA 1.6

8 (in)

Fig. 12 Experimental Load-Deflection Curves

305.2

1.0

P/Py

0.4 Shope Flange Web Theory Test

2 A441 A36 ~--- -<>--3 A441 A36 -- ---t:--,.

,'-0.2 (Flame Cut)

-44

a 0.2 0.6

8 (in)

0.8 1.0

Fig. 13 Theoretical and Experimental Load Deflection Curves

=:E--SR-4 Strain Gages

305.2

1.0

P/ Py

1.0

. ., -..---

5

Strain in/in

Shape:lf: 5A441 Web

6 7

-45

b

0.8

0.6

P/Py

0.4

o

Shope # 2

A36 Web

2 3 4 5

Shope #3

A36 Web

6 7

a

Fig. 14

Strain in/in

Stress-Strain Curves of Webs in Pinned-End

Column Tests

305.2

Fig .15

Fig. 16

-46

cents/ft/kip

1.0

o 20 40 60 eoL Ir

Price-to-Strength versus Slenderness Ratio.

(Homogeneous Shapes)

._. · -i iTTTT r~'

INote' At any slendemess ratIo aU shopes

2 - I, tarr, ,,,'("me j""awr t, '---'-----'---'-'-'--"---t--'---"--o 10 20 30 40 50 60 70 80

L/r

Price of the Hybrid Shape No.5 versus Price

of Homogeneous Shapes.

/

305.2 -47

8. REFERENCES

1. DESIGN OF HYBRID STEEL BEAMS - Report,Subcomm~ 1 on Hybrid Beams and Girders,Joint ASCE-AASHO Comm. on FlexuralMembers. Jouin. Struct. Div., ASCEJune, 196~.

2. N. R. NagarajaRaoTHE STRENGTH OF HYBRID COLUMNS, Ph.D.Dissertation, Lehigh University, April,1965. University Microfilms, Inc.,Ann Arbor, Michigan.

3. tall, L., Editor-in-ChiefSTRUCTURAL STEEL DESIGN,The Ronald Press, 1964.

4. Salmon, E. H.COLUMNS, A TREATISE ON THE STRENGTH ANDDESIGN OF COMPRESSION MEMBERS, OxfordTechnical Publications, London, 1921.

5. Beedle, L. S. and Tall, L.BASIC COLUMN STRENGTH,Journ. Proc.ASCE ST7, July, 1960.

6. Tall, L.RECENT DEVELOPMENTS IN THE STUDY OFCOLUMN BEHAVIOR, Journ. Inst. Eng.,Australia, Vol. 36, No. 12, Dec., 1964.

7. McFalls, R. and Tall, L.A STUDY O~ WELDED COLUMNS MANUFACTUREDFROM FLAME-CUT PLATES, Welding Journal,April, 1969.

8. Ueda, Y. and Tall, L.INELASTIC BUCKLING OF PLATES WITH RESIDUALSTRESSES. IABSE - Publications 1967,Zurich.

9. Nishino, R. and Tall, L.RESIDUAL STRESS ANf LOCAL BUCKLINGSTRENGTH OF STEEL COLUMNS, FritzLaboratory Report No. 29D.ll, LehighUniversity, 1965.

305.2

10. ASTM Specifications - A370-55.

11. Haaijer, G. and Thurliman, B.ON INELASTIC BUCKLING IN STEEL,Trans. ASCE, Vol. 125, p. 308, 1960.

12. Huber, A. W. and Beedle, L. S.RESIDUAL STRESS AND THE COMPRESSIVESTRENGTH OF STEEL, Vol. 33, Dec., 1954.

13. Louis, H., M~rincek, M. and Tall, L.STUB COLUMN TEST PROCEDURE, DocumentA-282-61, International Institute ofWelding, Annual Conference, Oslo, 1962.

14. Hu1)er, A. W.FIXTURES FOR TESTING PIN-END COLUMNS,ASTM, Bulletin No. 234, Dec., 1958.

-48