Question

A simply supported beam of span L carries a point load W at midspan. The breadth 'b' of the beam along the entire span is constant. Given, f = permissible stress is bending, for a beam of uniform strength, the depth of the beam at any cross-section at a distance 'x' from the support would be

• A. $\frac{6Wx}{fb}$
• B. $\sqrt{\frac{6Wx}{fb}}$
• C. $\frac{3Wx}{fb}$
• D. $\sqrt{\frac{3Wx}{fb}}$

Answer 1

The correct option is D $\sqrt{\frac{3Wx}{fb}}$


For a beam of uniform strength
BM at distance x = Moment of resistance of beam

$\frac{W}{2}x=\sigma z$

$\frac{W}{2}x=\frac{fb{d}^2}{6}$

$d=\sqrt{\frac{3Wx}{fb}}$