Question

An 8 m long simply- supported elastic beam of rectangular cross-section (100 mm x 200 mm) is subjected to a uniformly distributed load of 10 kN/m over its entire span. The maximum principal stress(in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at 2 m from the support is

• A. 90

Answer 1

The correct option is A 90
at 2 m from support
Bending moment, $M=40\times 2-10\times 2\times 1=60KN-m$
Shear force, $V=40-(10\times 2)=20KN$
At external compression edge (top fibre)
Shear stress ($\tau =0$)
Bending stress, $\sigma =\frac{MY}{I}$
$=\frac{(60\times {10}^{6}N-mm)\times 100mm}{\frac{100\times {200}^3}{12}}m{m}^4=90N/m{m}^2$
$=90MPa$
Since this edge is free from shear stress, hence it is a principal plane.
Thus maximum principal stress $=90MPa$