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An initially stress-free massless elastic beam of length L and circular cross-section with diameter d(d<< L) is held fixed between two walls as shown. The beam material has Young's modulus E and coefficient of thermal expansion α.
If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to
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- d
- d2
- d3
- d4
- d
Correct Option: B
| By Buckling load, P = | |
| l2 |
Force due to change in temperature,
| σ = | = lα∆T | |
| A |
P = Alα∆T
| = A l α∆T | ||
| l2 |
| ∝ ∆T | ||
| A |
| ∆T ∝ | ||
| d2 |
∆T ∝ d2
