Question

A simply supported beam of constant width and varying depth and uniform strength is subjected to a cental concentrated load. The depth of the beam ${}^{\prime }{d}_x^{\prime }$ at a distance 'x' from one of the supports is proportional to

• A. $x^{1/2}$
• B. $x^{1/3}$
• C. x
• D. $x^2$

Answer 1

The correct option is A $x^{1/2}$


Bending moment at a distance x(L/2) from end.

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

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

$\frac{P}{2}x=\sigma \frac{b{d}_x^2}{6}$

$d_x\propto x^{1/2}$