Question

A simply supported beam of length $L$ is subjected to a varying distributed load sin $\left(3\pi x/L\right)N{m}^{-1},$ where the distance $x$ is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

• A. zero
• B. $L/3\pi$
• C. $L/\pi$
• D. $2L/\pi$

Answer 1

The correct option is B $L/3\pi$

$Load,W=\underset{o}{\overset{L}{\int }}sin\left(\frac{3\pi x}{L}\right)dx=\frac{2L}{3\pi }$

Vertical reaction,

$R_1=R_2=\frac{L}{3\pi }\left(duetosymmetricalloading\right)$