Question

A rectangular timber beam is cut out of a cylindrical log of diameter D. The depth of the strongest timber beam will be

• A. $\sqrt{\frac{1}{2}}D$
• B. $\sqrt{\frac{2}{3}}D$
• C. $\sqrt{\frac{5}{8}}D$
• D. $\sqrt{\frac{3}{4}}D$

Answer 1

The correct option is B $\sqrt{\frac{2}{3}}D$

For strongest beam, the section modulus should be maximum.

Breadth of beam = $\frac{D}{\sqrt{3}}$

Depth of beam = $\sqrt{\frac{2}{3}}D$

Section modulus = $\frac{D^3}{9\sqrt{3}}$

Moment of inertia = $\frac{D^4}{27\sqrt{2}}$