Question

A cantilever beam having square cross-section of side a is subjected to an end load, If a is increased by 19% , the tip deflection decreases approximately by

• A. 19%
• B. 29%
• C. 41%
• D. 50%

Answer 1

The correct option is D 50%

For cantilever beam,
$\delta =\frac{w{L}^3}{3EI}$
$I=\frac{a^4}{12};\delta =\frac{4w{L}^3}{E{a}^4}$
${\delta }^{\prime }=\frac{4w{L}^3}{E(1.19a{)}^4}=0.498\delta$
% decrease in deflection = $\frac{{\delta }^{\prime }-\delta }{\delta }=50.13\%$