Question

A cantilever beam with square cross-section of 6 mm side is subjected to a load of 2 kN normal to the top surface as shown in the figure. The Young's modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope (in radian) at Q (20 mm from the fixed end) is _________ .

• A. 0.1587

Answer 1

The correct option is A 0.1587
Slope ${\theta }_Q-{\theta }_O$ = $\frac{1}{EI}$ [Area of diagram till Q]

Area of diagram till 'Q'

$[\frac{1}{2}\times 100\times 2\times {10}^5]-[\frac{1}{2}\times 80\times y]$

Calculating ; y from properties of similar triangles,

$\frac{y}{2\times {10}^5}=\frac{80}{100}$

y= 160000 Nmm

Area of diagram till Q

$\Rightarrow [\frac{1}{2}\times 100\times 2\times {10}^5]-[\frac{1}{2}\times 80\times 160,000]=3600000N.m{m}^2$

${\theta }_Q=\frac{1}{210\times {10}^3\times I}\times 3600000$

$I=\frac{b{d}^3}{12}=\frac{b^4}{12}=108m{m}^4$

${\theta }_Q=\frac{1}{210\times {10}^3\times 108}\times 3600000$

= 0.1587 rad