GATE CE 2024 Set 2 — Question 39
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Structural Engineering → Stress, Strain & Beams → Buckling of Columns
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Question
A homogeneous, prismatic, linearly elastic steel bar fixed at both the ends has a slenderness ratio () of 105, where is the bar length and is the radius of gyration. The coefficient of thermal expansion of steel is . Consider the effective length of the steel bar as and neglect the self-weight of the bar.The differential increase in temperature (rounded off to the nearest integer) at which the bar buckles is
Correct answer
(A) 298 ^
Solution
1.The Euler buckling load for a column is .
2.The thermal force developed in a fixed-end bar due to temperature increase is .
3.At the point of buckling, :
Since , where is the radius of gyration:
4.Given and , the effective slenderness ratio is:
.5.Substitute the values:
.
Rounding to the nearest integer, we get .
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