Question

A 3 m long simply supported beam of uniform cross section is subjected to a uniformly distirbuted load w=20 kN/m in the central 1 m as shown in the figure.

If the flexural rigidity (EI) of the beam is $30\times {10}^6$ $N-m^2$, the maximum slope (expressed in readians) of the deformed beam is

• A. $0.681\times {10}^{-4}$
• B. $0.943\times {10}^{-4}$
• C. $3.611\times {10}^{-4}$
• D. $5.910\times {10}^{-4}$

Answer 1

The correct option is C $3.611\times {10}^{-4}$


$F_1=\frac{1}{2}\times 1.5\times \frac{15}{EI}=\frac{11.25}{EI}$
$F_2=\frac{\frac{2.5}{EI}\times 0.5}{2+1}=\frac{1.25}{3EI}$
R=F1-F2
$=\frac{11.25}{EI}-\frac{1.25}{3EI}=\frac{33.75-1.25}{3EI}$
$\frac{32.5}{3EI}=\frac{65}{6EI}$
$\Rightarrow V_A$ in conjugate beam
$=\frac{-65}{6EI}$
$\Rightarrow {\theta }_A$ in real beam
$\frac{65}{6\times 30\times {10}^{-4}}rad$