Buckling
of Columns
*Example: A steel, simply-supported,
wide flange column, W 10 x 60, of
length, L, is subjected to
compressive loading P as shown in the figure below. Let L = 18 ft. For steel E = 30 x 106 psi. Find the smallest load for column buckling. |
Strategy: Calculate the critical load by
applying Pcr = n π2EI/L2 . Note: The critical buckling load
depends on the sizes of the moment of inertia and the From tables for
wide-flange beams: I11 =
341 in4 and I22 = 116 in4
Next consider the buckled
mode shape. The mode shape for
buckling with no mid-span restraint Is a single sine wave. So n
= 1. Now the column is free to
buckle in any direction. It will
buckle first in the “weakest” direction. So select I22 . Pcr
= Pcr = π2 (30 x 106)(116)
/ [(18)(12)2 lb =
7.36 x 105 lb The figure below shows a
top view of the deflected column. |
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