Question

A cantilever beam of rectangular cross-section is 1 m deep and 0.6 m thick . If the beam was to be 0.6 m deep and 1 m thick then the beam would be

• A. Weakened by 60%
• B. Strengthened by 60%
• C. Weakened by 40%
• D. Strengthened by 40 %

Answer 1

The correct option is C Weakened by 40%

$Z_1=\frac{b{d}^2}{6}=\frac{0.6\times 1}{6}=0.1m{m}^3$

$Z_2=\frac{d{b}^2}{6}=\frac{1\times {0.6}^2}{6}=0.06m{m}^3$

Thus, % change in strength ,

$=\left|\frac{Z_2-Z_1}{Z_1}\right|\times 100=\left|\frac{0.06-0.1}{0.1}\right|\times 100=40\%$

(weakened)