Week 3 Challenge
1) Height of column =10m
Restrained in mid height.
10m long column is restrained at ends in both Y-Y and Z-Z direction.
Hence the actual length=5m
a) Braced frame and shear wall
The effective length factor for bottom column is fixed and top of column is free.
=2xL
=2X5
=10m
b) Unbraced frame with a pinned base
=2xL
=2x5
=10m
c) Unbraced frame with fixed base
=1.2xL
=1.2X5
=6m
2) For rolled steel section
Fy=250N/mm2
Fu=410N/mm2
E=2X105N/mm2
For top roller and bottom fixed
KXL=1.2X3=3.6m
For ISMB300
h=300, bf=200, Lf=12mm
h/bf=300/200=1.5
h/bf>1.2, tf<=40mm
It belongs to building class 'a'
from sp-6 steel table.
γmin=γyy=25.4mm
design compressive strength
Pd=AcxFcd
Fcd=(Fy/γm0)/Φ+[Φr-γr]0.5
Φ=0.5[1+∝(λ-0.2)+λ2]
λ=√(fy/fce)
fce=π²E/(KL/r)²
fce=π²x2x105/(3600/28.4)²
=122.84N/mm²
λ=√(250/122.840)=1.426
for building class 'a' '∝' imperfection factorfrom IS-800:2007 Table-7
∝=0.21
Φ=.5[1+0.21(1.426-0.2)+(1.426)²]
=1.645
fcd=(250/1.1)/1.645+[(1.645)²-(1.42)²]0.5
=92.19N/mm²
Pd=AcxFcd
=56.26x92.19
=5186.80KN
3)L=2m, P=400KN, Fy=210MPa, K=1
KL=2000mm
Let Fcd=80N/mm²
Areq=400x10³/80=5000mm²
πD²/4=Areq
D=√(5000X4/π)=80mm
For circular hollow section (semi compact)
D/t<=88ε²
e=√(250/fy)=1.09
Let t=8mm
80/8<=88x1.09²
D=80mm t=8mm
λ=KL/r
r=80/2=40mm
λ=2000/40=50
Circular sections are under buckling class a
using table 9a
KL/r fcd@fy=210
Pd=Acxfcd=5000x1.76=880,000KN
4) Assuming fcd=135N/mm
Area required=1000x1000/135=7407.40mm²
Try 2 ISMC250 @ 298.2N/mm² (SP-6-1)
Area provided =2x3867=7734mm²
r22=99.4mm
distance will be maintained so as to get
ryy>r22
Actual slenderness ratio(KL/r)=1x10000/99.4=100.60
Since it is a leced column
(KL/r)=1.05x100.60=105.63
From table 9C of IS 800 of buckling class C table-10
fcd=107-(105.63-100/110-100)x(107-94.6)
fcd=100.018N/mm²
Load carrying capacity=7734x100.015
=7735.39>100KN
Hence OK
Spacing between channels
let it be a clear distance'd'
Now Ixx=2x3816.8x104
=7633.6x104mm4
Iyy=2[219.1x104+3867(d/2+23)²]
equating Iyy to Ixx we get
[(d/2+23)²]=4368.5
d/2+23=66.09
d=86.18mm
provide 90mm spacing
Horizontal spacing=90+23+23=136mm
vertical spacing=136xsin 45ºx2
=192.304mm