Question

A homogeneous prismatic simply supported beam is subjected to a point load F. The load can be places anywhere along the span of the beam. The very maximum flexural stress developed in the beam is

• A. $\frac{3FL}{2B{D}^2}$
• B. $\frac{3FL}{4B{D}^2}$
• C. $\frac{2FL}{3B{D}^2}$
• D. $\frac{4FL}{3B{D}^2}$

Answer 1

The correct option is A $\frac{3FL}{2B{D}^2}$

Max. bending stress,

${\sigma }_{max}=\frac{M_{max}}{Z}$

Section modulus,

$Z=\frac{I}{y_{max}}=\frac{B{D}^3/12}{D/2}=\frac{B{D}^2}{6}$

BM will be maximum when load is mid-span,

$\therefore M_{max}=\frac{FL}{4}$

$\therefore {\sigma }_{max}=\frac{FL/4}{B{D}^2/6}=\frac{6FL}{4B{D}^2}=\frac{3FL}{2B{D}^2}$