GATE ME 2022 Set 1 — Question 16
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Engineering Mechanics → Beams & Columns → Euler's Theory of Columns
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Question
A uniform light slender beam AB of section modulus is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight as shown. If the maximum value of to avoid buckling of the beam AB is obtained as , where is the ratio of circumference to diameter of a circle, then the value of is
Correct answer
(A) 0.0924 m⁻²
Solution
1.Analyze the forces at point B:
Let be the tension in the cable CB and be the axial compressive force in the beam AB.Resolving forces vertically at B: .
Resolving forces horizontally at B: .
2.Euler's Buckling Load:
The beam AB is pinned at both ends (A is a pin joint, and B is effectively pinned by the cable and weight).The critical buckling load for a pinned-pinned column is given by:
where .
3.Equate axial force to critical load:
To avoid buckling, . The maximum value of occurs when .4.Find :
Given , we have .Continue learning with Success Tracker
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