Question

Consider a simply supported beam of length 50h with a rectangular cross-section of depth h and width 2h. The beam carries a vertical point load P at its mid- point. The ratio of the maximum shear stress to the maximum bending stress in the beam is

• A. 0.02
• B. 0.10
• C. 0.05
• D. 0.01

Answer 1

The correct option is D 0.01

${\tau }_{max}=\frac{3}{2}\frac{P_{max}}{A}=\frac{3P_{max}}{4h^2}=0.75\frac{P_{max}}{h^2}$

${\tau }_{max}=\frac{0.75}{h^2}\frac{P}{2}=\frac{0.375P}{h^2}[\because P_{max}=\frac{P}{2}]$

$M_{max}=\frac{PL}{4}=\frac{P\times 50h}{4}=12.5Ph$

$Z=\frac{b{h}^2}{6}=\frac{h^3}{3}$

${\sigma }_{max}=\frac{M_{max}}{Z}=\frac{12.5Ph\times 3}{h^3}=37.5\frac{P}{h^2}$

$\therefore \frac{{\tau }_{max}}{{\sigma }_{max}}=\frac{0.375}{37.5}=0.01$