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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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