axial capacity of concrete infilled cold-formed steel columns

7/23/2019 Axial Capacity of Concrete Infilled Cold-Formed Steel Columns

1/17

Missouri University of Science and Technology

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Axial capacity of concrete inlled cold-formed steelcolumns

C. Y. Lin

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2/17

Ninth International Specialty Conference on Cold-Formed Steel Structures

St. Louis, Missouri, U.S.A., November

8-9,1988

AXIAL CAPACITY

OF CONCRETE INFILLED

COLD FORMED STEEL COLUMNS

by

C.Y. Lin

ABSTRACT

In

this

experiment,

a to ta l

of 18 specimens were

tes ted

to demonstrate

the

behavior

and strength of the concrete in f i l l ed cold-formed s tee l

columns

subjected

to

axial

loads.

The

variables

considered

in

th i s

investigation

included

the concrete strength, the

shape

and

thickness

of

cold-formed s tee l and the length

width

ra t io LID) of the specimen.

Test

resul ts

indicated

that

the

axial

capacity and the res idual post-crushed

strength

of

the

inf i l led concrete

are

functions of

the thickness

of

the

cold-formed

s tee l and

the shape

of

the

sect ion. The ci rcular cold-formed

s tee l sect ion provides be t te r

confinement

on concrete prior and af te r the

crush

of the inf i l led concrete.

Based

on the t es t

resul ts

an equation

with

confining

coeff ic ient C was

proposed for calculating the

axial

capacity

of the concrete in f i l l ed cold-formed s tee l column.

Further

study

has to

be carried out

to evaluate

the confining coeff ic ients

for

rectangular

sect ions

with

different aspects ra t ios .

INTRODUCTION

In

general

pract ice ,

l a te ra l

confining reinforcements such as

t ies or

spi ra ls are

commonly

used in reinforced

concrete

columns to offset the

st rength loss

due

to

spall ing of concrete

cover, to increase the capacity

of the column

and to

sustain

large

deformations without a

s igni f icant

st rength loss . The effect iveness of l a te ra l

confinement depends

upon

the

s ize and spacing of the l a te ra l reinforcement.

Currently,

to carry axial

s tee l section,

sect ion.

2

,3 ,4

cold-formed

s tee l

sect ions are

commonly designed

as

columns

10ads

However, due

to

thinness of

the

cold-formed

the capacity i s generally control led by buckling of the

When a

th in

cold-formed s tee l sect ion i s in f i l l ed with

concrete

to

serve

as

a

column, the

concrete

and the thin cold-formed

s tee l

provide

l a te ra l

confinement to

each other continuously. The

effect

of

confining pressure on

the compressive

st rength of concrete has

been

studied and an

e

5

uation

was

developed to predict the compressive st rength

of

the concrete.

In previous

experiments,

the concrete was tes ted

within

a pressure

chamber, in which the

l a te ra l

pressure

was maintained

constant over the

ent i re loading process.

When concrete

is

confined by

elas t ic material ,

the confining

pressure

varies

with

the

longitudinal

deformation.

In

Professor ,

Department

of Construction Engineering

National

Taiwan

Ins t i tu te of

Technology

Taipei, Taiwan,

R.O.C.

443


3/17

addit ion, due to the compatibi l i ty, the cold-formed s tee l not

only

provides l a tera l confinement on concrete, but also carr ies longitudinal

load with concrete.

This

paper presents some experimental data on

the axial

capacity of

the concrete inf i l led cold-formed s tee l column. Concrete

materials

with

different strengths were used in the experiment. The effects of thickness

of

the cold-formed s tee l and the shape

of

the

column

on the

axial

capacity

of concrete

in f i l l ed

columns were invest igated.

No

conventional

reinforcements were

used in

ei ther

longitudinal

or transverse direction.

TEST

PROGRAM

In

this

invest igat ion, a to ta l of 18

specimens

were

fabricated and

tested. The concrete

for

a l l 18 specimens was produced with Type I

portland

cement. Local sand

and aggregate with maximum size of 2 mm were

used.

Three mixing proportions were used to

obtain

different concrete

s t rengths .

The shapes of cold-formed s tee l columns, s tee l thicknesses,

and specimen lengths are

given

in Table 1 All specimens

were tes ted in a

MTS

closed-loop

servo

control led hydraulic tes t machine with a

constant

loading

ra te . Displacement

was

measured

by a

dial

gage f i t t ed

paral le l to

the

specimen between the base plate and loading head.

To

evaluate

the

s t ra in in

both

longitudinal and transverse

direct ions ,

s t ra in gages were

placed

on the s tee l surface. The specimen was loaded

with small

increments

over the ent i re loading process.

TEST RESULTS

AND

DISCUSSION

Stress-Strain

Relationship

The

typical

s t ress -s t ra in curve for the

concrete in f i l l ed

cold-formed

s tee l

column is shown

in

Fig. 1 The s t ress -s t ra in curve

can

be

divided

in to

three segments.

Between

point

0 and

point

A is the elas t ic range.

From

point

A

to

point B is the post-cracked range, in which the inf i l led

concrete i s

cracked.

Point

B

i s

the

beginning

of the post-crushed

range,

which indicates

the

res idual

st rength

of the confined

crushed concrete.

The modulus of e las t i c i ty of concrete E

c

the deflect ion and

the

s t ra in

El

corresponding to the maximum concrete st rength f ~ c of the

composite

construct ion

are

shown

in

Table 2.

The

modulus

of

e las t i c i ty

of

the

confined

concrete i s not s igni f icant ly affected by the thickness of

confining s tee l and the shape of the section. The s t ra in El

corresponding

to the maximum s t ress f ~ c

is not

affected

by concrete

strength. For

the

concrete with higher strength,

the

s t ra in

El

was

compensated by

the

higher modulus of e las t i c i ty . When

the

s t ra in

exceeded El the concrete inside the cold-formed s tee l sect ion was

par t ia l ly damaged. The

s t ress

of the composite sect ion i s

graduately

reduced, with increasing s t ra in . The

s t ress

s tabi l ized when the s t ra in

reached E2. The reduction

in s t ress

~ f ~ c

between

El and

E2

i s a

function

of the

thickness

of confining s tee l the shape of column

sect ion

and the inf i l led concrete strength. As shown in Fig.

2,

a smaller

st rength reduction ~ f ~ c i s observed

for the

sect ion confined by thicker

s tee l section. Comparing the section with different geometries as shown

in

Fig.

3, a larger ~ f ~ c was observed in rectangular sections,than


4/17

5

circular

and

square

sections.

As shown in Fig. 4,

almost equal

post-crushed strength was observed for

specimens with

different concrete

strengths This

indicates

tha t the

specimen

with higher concrete

strength

yielded with

la rger strength

reduction ~ f ~ c

Ultimate Strength

The compressive

strength

of the

confined

concrete f ~ c

is

commonly

expressed

as:

5

f ~ cp

where

specified compressive strength

of

concrete

c confining coeff ic ient

p confining pressure

The confining pressure provided by a circular

cold-formed

s tee l

section,

as shown in Fig. 5,

can

be

calculated

as

where

p

2

f

t

s

D

p confining pressure

fs tensi le s t ress

in confining

s tee l

t

thickness of

cold-formed s tee l

D diameter

of

circular section

1)

2)

For a square

section,

an equivalent circular

section

was proposed for

calculating

the confining pressure provided by cold-formed

s tee l

as shown

in Fig.

6.

Thus,

Eq

2) can

also

be applicable

for

calculating the

confining pressure. When

a rectangular section i s confined by cold-formed

s tee l two different

equivalent

circular sections may

be

proposed as shown

in Fig. 7. In

this

study, a shorter dimension

is

adopted

to

calculate the

diameter

of

the

equivalent circular

section for

the rectangular

section.

The axia l

capacity

of

the

concrete

in f i l led

cold-formed s tee l depends

upon how the s tee l section

i s

considered in calculation. The cold-formed

s tee l can be transformed into concrete by the

modular

ra t io

Es/Ec

or

by

super position, in which s teel and concrete are

considered separately.

I f the

cold-formed s tee l

i s

considered as

the

longitudinal reinforcement

in a reinforced concrete

column, then the

axia l

capacity

of the column

P

n

can

be

calculated

as:

3)


5/17

446

where

area

of concrete core

compressive strength of confined concrete

area

of cold-formed s tee l

yield strength of

cold-formed

steel

By

knowing

the value of

P

n

from

experiment, the concrete strength

fbc1 can

be

calculated

from

Eq.

(4)

P - A

f 1 = n ty (4)

0.85

A

c

The

calculated

fbc1, as shown

in Table 2,

is

greater

than fb

used

in

this

experiment. This

indicates that the cold-formed

s tee l

not only

carr ies

the

axial load in the

longitudinal

direction, but also provides

l a tera l confinement

on the

concrete

inside

the

steel

section.

From

Eqs.

(1),

(2) and (4), the confining coefficient can

be

calculated

and

denoted

as C1 from Eq. (5);

P - A f - 0.85A f

n s t

y

c C ___

D

__

)

0.85A 2f t

c y

The

confining

coefficient

C1

for

each specimen

was

calculated

and

shown

in Table

3.

(5)

During the tes t ,

large

deformations in the

longitudinal direction

were

observed. The thin, cold-formed s tee l buckled in the

longitudinal

direction and separate from the

concrete

long

before

the rupture

of

steel

was

observed.

Thus

the compatibility

between

concrete

and steel

is not

valid.

Hence,

the transformed area

method is

not applicable in strength

calculation. According to the t es t

resul ts

as shown in Table 2, the

average concrete s t ra in in the

longitudinal

direction reached

0.01

when

the specimen reached i t s axial capacity fbc.

At

this

stage,

with

a

Poisson s rat io of 0.15-0.20

for

concrete, the

s t ra in

in the transverse

direction

could

be

as

high

as 0.002, which exceeds

the

yield s t ra in of the

confining

steel . I f the cold-formed steel is

only

considered as a

confining

material in

the

transverse direction and the

contribution

in the

longitudinal

direction

is ignored, then,

The confined concrete strength, fbc2

can

be

calculated

by Eq. (7)

(7)

In

Eq.

(7) the value

C

can then

be

calculated

by

Eq.

(8) and

denoted

as C2;


6/17

447

C2

(8)

The

value

of

C2

for

each

specimen was also

calculated and

shown in

Table 3.

Comparing

the values of C and C2 calculated

from

tes t

resul ts for sections with the same

shape,

a larger variat ion in

C

was

observed. In calculating C1 i t

was

assumed

that

the

confining

s tee l

carried

the

axia l

load in the

longitudinal direc t ion and

provided

confinement

on

concrete in the t ransverse direc t ion simultaneously.

Hence, the thickness

of s tee l plays

a

very important role

in

the

calculation of C1.

Smaller

C was observed

for

the

thicker section.

On

the

other hand, when

the

confining

s tee l only

provided

confinement on

concrete

in

the t ransverse direc t ion,

a re la t ively

uniform C2

was

observed. Thus, the ult imate axia l

capacity

of the concrete

in f i l l ed

cold-formed

s tee l column can be predicted more accurately by

using

Eqs.

(6)

and

(7), with

C

3.2 for

circular

sections,

C

1.9

for square

sections,

and

C 1.5 for rectangular sections

In this

experiment,

different C values were obtained for square

and

rectangular

sections.

This indicates that the

C

value i s

a

function of

the aspect

rat io of the rectangular section.

Thus,

further investigation

has to be conducted

to

study the C value for sections with different

aspect

rat ios .

Failure

Modes

The s tee l

section

used in this experiment was

cold-formed

from th in

s tee l plate and then welded

along

the longitudinal direc t ion. The weld

was

designed

to develop the fu l l

strength

of the s tee l

section.

The

weld

l ine for

square

and rectangular sections

was located

very

close to the

corner of the section. According

to

t es t results 14 out of 18 specimens

fai led

by

rupture of confining

s tee l

in

the longitudinal direc t ion

as

shown in Fig.

8. For of those

14

specimens, the ruputure occurred

ei ther

a t top

or bottom

of the

specimen,

and for

10

of

them

the

rupture

occurred along

the weld l ine . The rupture zone is

l imited to

1 to 1-1/2 D

of the section regardless the length of the member. Reviewing the C

values for those

specimens

ruptured along the weld l ines no s ignif icant

difference was observed for circular sections

and

square

sections.

However,

lower C values were

observed for rectangular sections

D 14

and

D-18.

This difference

may be contributed by poor

welds.

For

those

3

specimens which did not fa i l in rupture of

s tee l section,

the

tes ts

were

stopped

when the

tes t machine reached i t s

maximum

stroke.

CONCLUSIONS

This exploratory tes t

program

demonstrated

the axial capacity

and

behavior

of

the

concrete

in f i l l ed cold-formed

concrete.

Based

on the

resul ts

discussed

in

th is

paper, the

following

conclusions

may

be

drawn:


7/17

448

1. For

the

concrete infi l led

steel

columns with the same length,

the

longitudinal st rain

E

corresponding

to the maximum stress f tc

remains constant

regardless

the concrete strength, the shape of the

section,

and

the thickness

of confining

steel .

The

st rain E

varies

with

the length

of

the

element.

A

shorter element

yielded with a

higher value of E1'

2. The post-crushing strength of the

confined

concrete is a function of

the thickness of confining material and the shape of the

section.

Larger strength

reductions,

bftc

in square

and

rectangular sections

were observed.

No

s ignif icant difference

in residual , post-crushed

strength of the in f i l l ed

concrete

was observed for concrete with

different

in i t ia l

strengths f t .

3. The rupture of confining steel in square and rectangular sections

occurred

at

the corner

of

the

section

in

the t ransverse

direction,

while

the

rupture

mostly

occurred

a t ei ther

top or bottom of the

column in the

longitudinal direction.

The rupture zone

is

l imited

to

1 to 1-1/2 D of the section regardless the length of the member.

4.

The axial capacity

of

the column

can

be more

accurately predicted

by

Eq. (6), in which the

cold-formed

steel

only provides l a te ra l

confinement on concrete, and the axial capacity provided by the

cold-formed

steel

in the

vert ical

direction i s ignored in

strength

calculation. The circular section has a higher confining coefficient

than the square and

rectangular sections.

The

confining

coefficient C

for the rectangular section is a function of i t s aspect

rat io . Thus,

further

study

has

to

be

carried

out

to evaluate the

confining

coefficient for rectangular

sections

with different

aspect

rat ios.

APPENDIX I - REFERENCES

1.

Yu W.W. Cold-Formed

Steel Design,

John Wiley and Sons, Inc. , New

York, 1985, 545pp.

2.

Shil l ing,

C.G., Buckling

Strength

of Circular Tubes,

Journal

of the

Structura l

Division, ASCE Proceedings, Vol. 91, Oct. 1968.

3.

Miller, C.D., Buckling of

Axially

Compressed

Cylinder, Journal

of

the Structural Division,

ASCE Proceedings, Vol. 103,

Mar. 1977.

4. Sherman, D.R.,

Structura l

Behavior of

Tubular Sections,

Proceedings

of the Third

Internat ional

Specialty Conference on Cold-Formed

Steel

Structures,

University

of

Missouri-Rolla,

Nov. 1975

5. Park, R. and Pauley, T., Reinforced Concrete Structures, John Wiley

and Sons,

Inc.,

New York, 1975,

769pp.

APPENDIX I I - NOTATIONS

The

following

symbols

are

used

in

this

paper:

Ac = area of

concrete

core


8/17

C

z

D

f

c

H

t

9

area of

cold formed

steel

width of square

and

rectangular cold formed

steel

sections

confining coeff ic ient

confining

coeff ic ient

confining

coeff ic ient

diameter

of

circular cold formed

steel

section

specified compressive strength of concrete

maximum

compressive stress of confined concrete

reduction

in s t ress between

El and Z

tensi le

stress

in

cold formed

steel

yield

stress of

cold formed

steel

depth of rectangular section

confining pressure

axial

capacity

of column

thickness

of cold formed steel

st r in corresponding to

maximum

stress

s tabi l ized st r in corresponding to post crushed concrete


9/17

450

Table 1

Proper t ies

of Specimens

specimen specimen

steel

specimen A A

no.

dimension thickness

length

c

s t y

c

cm

2

2

cmxcm)

cm)

cm)

ton)

kg/cm

D l

5< > 0 07

48

177

8 3

230

D2

5< >

0 07

80 177

8 3

230

D4

5< > 0 14

80 177 16.5 230

D6

5< >

0 21

80

177

24.7 230

D7 15x15

0 07

48 225 10 5

230

D8

15x15

0 07

80 225

10 5

230

Dl0

15x15

0 14

80 225 21.0

230

D12

15x15

0 21

80

22.5

31.5

230

D

13

15x20

0 07

48 300 12 3

230

D14

15x20

0 07

80

300 12 3

230

D

16

15x20

0 14

80

300

24.5

230

D18

15x20

0 21

80

300

36.8

230

E l

5< >

0 07

48 177 8 3

344

E6

5< >

0 21

80 177

24 7

360

E7

15x15

0 07

48

225

10 5

344

E 10 15x15

0 14 80

225

21.0

360

E

15 15x20 0 14 48

300 24.5

344

E 18

15x20

0 21

80

300 36 8

360


10/17

451

Table 2. Mechanical

Proper t ies of

Test Specimens

specimen

\

El E2

( , f l

e 2

-2

(10

-2

ern/

ern

ee

2

no.

(kg/ern )

ern

(10

ern/em)

(kg/em)

D1

22300

0.65 1.354 2.922

124

D2 34320

0.725

0.906 1.656

74

D4 37250

0.70

0.875

3.312

59

D6

35850

1.10 1.375

3.063

38

D7

22280 0.60 1.250 2.135

90

D8

41180

0.575 0.719

1.875

135

D10 29890

0.70

0.875 1.750

72

D12 30110

0.65

0.813

2.219 74

D13

20976

0.70

1.302

3.542

142

D14 35960 0.60

0.750 1.438

88

D16 39600 0.50

0.625 1.250

107

D18

44290 0.525

0.656

1

781

56

E1

40400

0.45

0.938

5.730

148

E6

56600 0.70 0.875 6.250

113

E7 31500

0.43

0.896 2.500

179

E10

41411

0.65

0.813

2.000

154

E15

42240

0.50

1.04

4.170

170

E18 44370

0.55 0.688 2.188

156


11/17

452

Table

3 es t

Resul t s

specimen

P

f

f

Failure

Mode

n

eel

C

1

cc2 C

2

(kg/ cm

2

(kg/

no. (ton)

cm

2

Longitudinal

Transverse

D1

54.9 310

3.43

310

3.43

Middle

Non-Weld

D2 52.4 293

2.70

296

2.83 Bottom

Weld

D

71.1

363

2.85

402 3.68

Bottom

Non-Weld

D6

80.3

370 2.00 454

3.20

Middle

Weld

ave:2.75

ave:3.285

0:0.59 0:0.36

D7

56.9 243

0.56

253 0.99 Top

Non-Rupture

D8

62.4 271 1.

76

277

2.02 Top

Non-Weld

D1

72.6

270 0.86

322 1.97

Bottom

Non-Rupture

D12

80.9

258 0.40

358 1.83

Middle

Weld

ave:0.90

ave:1.70

0:0.61

0: 0.48

D13

81.1

273

1.84

273 1.

71

Middle

Non-Rupture

D14

71.9

234

0.17

240

0.43

Top Weld

D16

89.9

257

0.58

300

1.50

Bottom

Weld

D18 86.1

194

-0.51

287

0.81

Bottom

Weld

ave:0.52

ave :1.113

0:0.99

0:0.59

E1

75.9 450

4.55

429 3.60 Top

Weld

E6

109.5 443

1.67

620

3.71

Top

Weld

ave:3.11

ave:3.66

0:2.03

0:0.08

E7

76.2 344 0

339 0

Middle

Non-Rupture

E1 99.3

409

1. 78

441 1.74 Top

Weld

ave:0.87 ave:0.87

0: 1. 23

0: 1. 23

E15 119.6

373 0.62 399 1.15

Bottom

Weld

E18

129.3

263

0.53

431

1.13

Bottom

Non-Weld

ave:0.58

ave:

1.14

0:0.06 0:0


12/17

3

A

2

'

0

o

.

U

l

U

l

Q

J

I

1

o

O

1

2

3

S

t

a

i

n

c

m

/

c

m

x

1

F

g

1

T

c

s

t

e

s

s

t

a

i

n

c

v

3

'

E

2

b

.

U

l

U

l

Q

J

I

1

0

D

6

=

2

m

)

A

_

D

4

=

O

.

1

m

)

D

2

=

O

.

0

m

)

0

2

4

6

S

t

a

i

n

c

m

/

c

m

x

F

g

2

S

t

e

s

s

t

a

i

n

c

v

f

o

s

p

m

e

w

i

h

d

i

e

r

e

n

t

s

t

e

e

l

t

h

i

c

k

n

e

s

s


13/17

3

2

C

E

0

-

b

O

O

J

;

+

r

n

1

0

D

(

e

i

c

u

l

a

r

D

1

q

e

D

1

r

e

e

t

a

a

0

2

4

6

S

t

a

i

n

-

2

c

m

/

c

m

x

O

)

F

i

g

.

3

S

t

e

s

a

i

n

c

v

f

o

r

s

p

m

e

w

i

h

d

i

e

r

e

n

t

s

h

3 2

C

E

0

b

O

O

J

;

+

r

n

1

0

D

7

(

=

2

3

0

c

j

{

c

m

2

)

E

(

=

3

4

4

k

c

m

2

)

c

0

2

4

6

S

t

a

i

n

c

m

/c

m

x

1

)

F

i

g

.

4

S

t

e

s

a

i

n

c

v

f

o

r

s

p

m

e

w

i

1

d

i

e

r

e

n

t

f

c


14/17

455

-

_

1/---'- _. . . -1 1-_

t

Y

D

Fig. 5 Confinement on c i rcu la r sec t ion .

B

i

.. //---

'...:-

1

.

-

b ~

/ _.

0

-

\

..

.

B

\

.

\ ~ .

.

~ h

,-

. .

./.;/

t

Y

Fig. 6 Equivalent confinement on square sec t ion .

t f

Y


15/17

56

Fig Equ iva len t con: ine nent on r ec t angu l a r s e c t i o n


16/17

57

Fig

ai lure

modes


17/17

axial capacity of concrete infilled cold-formed steel columns

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