Question

A cantilever beam of span ${}^{\prime }l{}^{\prime }$ carries a uniformly varying load of zero intensity at free end and 'w' per meter length at the fixed end. What does the integration of the ordinate of the loading diagram between the limits of free and fixed ends of the beam give?

• A. B.M at fixed end
• B. S.F at fixed end
• C. B.M at free end
• D. S.F at the free end

Answer 1

The correct option is B S.F at fixed end


$\text{We know}\frac{dF}{dx}=W_x\Rightarrow dF=W_x.dx$

$\int dF=\int W_{x}dx$

$F=\underset{0}{\overset{l}{\int }}{W}_x.dx$

$F_{fixed}-F_{free}=\underset{0}{\overset{l}{\int }}{W}_x.dx$

S.F. at free end is zero

$\therefore F_{fixed}=\underset{0}{\overset{l}{\int }}{W}_x.dx$

$\therefore$ S.F. at fixed end is calculated.