Question

A simply supported beam of span L carries a concentrated load W at mid-span. If the width 'b' of the beam is constant and its depth is varying throughout the span , then what should be its mid-span depth , when design stress is 'f' ?

• A. $\sqrt{\frac{6WL}{bf}}$
• B. $\frac{6WL}{bf}$
• C. $\sqrt{\frac{3WL}{2bf}}$
• D. $\frac{3WL}{2bf}$

Answer 1

The correct option is C $\sqrt{\frac{3WL}{2bf}}$

The bending moment diagram of the beam is BM at point x from simply supported end.

$M_x=\frac{W}{2}x$

Section modulus $Z_x=\frac{b{d}_x^2}{6}$

$But,f=\frac{M_x}{Z_x}$

$\therefore d_x=\sqrt{\frac{3Wx}{bf}}$

$at,x=L/2,d_{\left(L/2\right)}=\sqrt{\frac{3WL}{2bf}}$