GATE ME 2020 Set 2 — Question 48
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Strength of Materials → Beams & Columns → Euler's Theory of Columns
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Question
Uniaxial compression test data for a solid metal bar of length is shown in the figure.
The bar material has a linear elastic response from O to P followed by a nonlinear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is ________ mm (round off to one decimal place).
Correct answer
55 to 58
Solution
1.Material Properties: From the stress-strain curve, the yield stress and the corresponding strain .
Young's Modulus .2.Buckling Condition: For a pinned-pinned column, the Euler critical buckling stress is:
For a circular cross-section, and , so .
3.Design Requirement: To prevent buckling before yielding, .
.
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