GATE CE 2014 Set 1 — Question 36
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Structural Engineering → Torsion, Stress Transformation & Columns → Euler's Column Theory
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Question
If the following equation establishes equilibrium in slightly bent position, the mid-span deflection of a member shown in the figure is
If is amplitude constant for , then

If is amplitude constant for , then
Correct answer
(C) y = a sin (nπ x)/(L)
Solution
The differential equation for the buckling of a column is given by:The general solution is .
For a member pinned at both ends (as shown in the figure), the boundary conditions are:
Substituting back into the solution:
(where is the amplitude constant).
For a member pinned at both ends (as shown in the figure), the boundary conditions are:
1.At
2.At
For a non-trivial solution (), .Substituting back into the solution:
(where is the amplitude constant).
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