material ch26

8/12/2019 Material Ch26

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STEEL-CONCRETECOMPOSITE COLUMN-II


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Interaction curve for compression and uni-

axial bending

0

P/Pp

M/Mp0

1.0

1.0

M

P

C

B

A

D

Resistance of Members in Combined

Compression and Uni-axial Bending

Interaction Curve for Compression and Uni-axial

Bending


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Interaction curve using the simplified method according to UK

National Application Document for EC4 (NAD)

Pc

A

B

C

P

MMp0

Pp

0


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MB=Mp

Zero axial force

Stress distributions for the points of the interaction curve

for concrete filled rectangular hollow sections

y

Poin t Bck

y

sk

hnx

y

ckPoin t A y sk

Pp

No moment

x


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Mb=Mp

PC=Pc

Point C ck y sk

2hn

x

y

Stress distributions for the points of the interaction curvefor concrete filled rectangular hollow sections


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Variation in the neutral axis positions

ck

2 y

Pc2hn

y

x

P P

eo

Initially imperfect column under

axial compression

Analysis of Bending Moments due to SecondOrder Effects


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The second order effects on bending moments

should be considered if :

(2) Elastic slenderness conforms to:

In case the above two conditions are met the

correction factor k,

0.1P

P

(1)cr

0.2

1.0

P

P1

1k

cr


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Resistance of Members under combined

Compression and Uni- axial Bending

where

M design bending moment

moment resistance ratioMp plastic moment resistance

pM90M


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Interaction curve for compression and uni-axialbending using the simplified method

1.00

c

P/Pp

M/Mp

1.0

k

d

d

A

B

C


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whend c

whend <

c

c axial resistance ratio due to the concrete,

d design axial resistance ratio,

reduction factor

c

d

1

c

d

1

11

p

c

P

P

pP

P


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Combined Compression and

Bi-Axial Bending

Three conditions to be satisfied are:

9.0

9.0

pyy

y

pxx

x

M

M

M

M

0.1pyy

y

pxx

x

M

M

M

M


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x

y

0.9x xMx/ Mpx

My/Mpy

0.9 yy Moment interaction curve for bi- axial

bending


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where

when d c

when d< c

when d c

when d< c

xc

dx

x

1

yc

dy

y

1

xc

dx

1

11

yc

dy

1

1

1


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Design Steps for columns with axial load

and uni-axial bending

List material properties : fy,fsk, fck, Ea,Es, Ec

List section properties A a, A s, A c, Ia, Is, Ic

Design checks

STEPS IN DESIGN


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(1) Evaluate plastic resistance, Pp

Pp

= Aa

fy

/a

+c

Ac

fck

/c

+ As

fsk

/ s

(2) Evaluate effective flexural stiffness, (EI)e for short

term loading in x and y direction

(EI)e=EaIa+ 0.8 EcdIc + EsIs

(3) Evaluate non-dimensional slenderness, in x

and in ydirections from equation,

x

y

2

1

cr

pu

P

P


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where

Ppu = A afy+ cA cfck+ A sfsk

and

(4) Check for long-term loading

The effect of long term loading can be neglected if

Eccentricity, egiven by

e = M/P 2(cros s sect ion d imension )

2

2

e

cr

EIP


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the non-dimensional slenderness in the plane of

bending being considered exceeds the limits given

in Table 6 ( Composite Column - I)

(5) Check the resistance of the section under

axial compression for both x and yaxes.

P


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(6) Check for second order effects

Isolated non

sway columns need not be checkedfor second order effects if

22.015.0 and

= reduction factor due to column buckling.

For both the axes

P / Pc r 0.1 0.2


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(7) Evaluate plastic moment resistance about the plane

of bending under consideration.

Mp= y( Zpa-Zpan) + 0.5 ck(Zpc-Zpcn) + sk ( Zps- Zpsn)

(8) Check the resistance against axial compression

and uni-axial bending

M0.9 MP

where

moment resistance ratio


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Design Steps for columns with axial load

and bi-axial bending

List material properties: fy, fsk, fck, Ea, Es, Ec

List section properties A a, A s, A c, Ia, Is, Ic

Design checks


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(1) Evaluate plastic resistance, Pp

Pp= A afy/a+ c A cfck/c+ A sfsk/ s

(2) Evaluate effective flexural stiffness,

(EI)ex and (EI)ey, for short term loading

(EI)ex= EaIax+ 0.8 EcdIcx + EsIsx

(EI)ey=EaIay+ 0.8 EcdIcy + EsIsy


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(3) Evaluate non-dimensional

slenderness,

andx y

2

1

xcr

pu

xP

P

2

1

ycr

pu

y

P

P


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(4) Check for long term loading

The effect of long-term loading can be neglected if

Eccentricity, egiven by

e = M / P 2 ( cros s sect ion dimension)

(5) Check the resistance for axial compression about

both the axes.

P


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(6) Check for second order effects Isolated non sway

columns need not be checked if:

P / (Pc r)x 0.1 for bending about x-xaxisP / (Pc r)y 0.1 for bending about y-yaxis

(7) Evaluate plastic moment resistance for axial

compression and bi-axial bending

Mpx= [y( Zpa-Zpan) + 0.5 ck(Zpc-Zpcn) + sk ( Zps- Zpsn) ]x

Mpy=[ y( Zpay-Zpan) + 0.5 ck(Zpcy-Zpcn) + sk ( Zpsy- Zpsn) ]y


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material ch26

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