Q# Using AISC column specifications, determine the safe axial loads on W 310x107 section used under following conditions (a) hinged ends and a length of 10 m (b) built-in ends and unsupported length of 10 m (c) built-in ends and a length of 10 m braced at mid point. Use proportional limit for steel as 380 MPa and Modulus of elasticity equal to 200 GPa. Take properties of section from internet or recommended books. Furthermore discuss in detail about the variation of column capacity with the variation of conditions.
SOLUTION
Given data
Properties of steel section
Column section W 310×107
Gross area
of cross sectipn Ag = 13600 mm²
Radii of
gyration rx= 135mm
ry = 77.2mm
Restrain
Along x
direction
Along Y direction
Unsupported
length of column Lx = 10m unsupported length of
column Ly = 10m
Bottom
end
: pinned
Bottom end : pinned
Top
end
: pinned
top end : pined
Calculations
Yield
stress of steel Fy = 380 Mpa
Modulus of
elasticity of steel E = 200000
Mpa
Effective
length factors Kx
= 1
Ky = 1
= 74.07
for; λe
‹, 1.5, Fa = (0.658 λe²)Fy λe ›
1.5, Fa = (0.877/ λe²)
Fy
Since Kx Lx / rx ‹
Ky Ly / ry , KyLy/ ry controls
λe
=
= 1.80 > 1.50
λe ‹, 1.5, Fa = (0.658 λe²)Fy
λe ›
1.5, Fa = (0.877/ λe²) Fy
therefor,c ritical stress, Fa = 103.2 Mpa
hence,
design axial strength of column, ɸͤe P n = ɸe Fa Ag
=0.9 ×103.2×13600
= 1263.0 kN
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