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A cantilever beam having a square cross-section of side \(a\) is subjected to an end load. If \(a\) is increased by 19%, the tip deflection decreases approximately by
- 19%
- 29%
- 41%
- 50%
Correct answer: 50%
Solution
For a cantilever with end load, tip deflection is proportional to \(1/I\). For a square cross-section, \(I\propto a^4\), so increasing \(a\) by 19% makes deflection scale by \(1/(1.19)^4\approx 0.5\), i.e. about a 50% decrease.
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