Question

The magnitude of moment at end 'A' for the beam shown in figure below will be ______ kN-m


(EI is constrif)

Answer 1

The correct option is A 15
Let the reaction at the roller (R) be redundant

$\therefore {\left({\Delta }_B\right)}_{AB}={\left({\Delta }_B\right)}_{BC}$

$\Rightarrow \frac{5\times {\left(4\right)}^4}{8EI}-\frac{R{\left(4\right)}^3}{3EI}$

$=\frac{5{\left(2\right)}^4}{8EI}+\frac{R{\left(2\right)}^3}{3EI}$

$\Rightarrow R=6.25kN$

Moment at A,
$M_A=R\times 4-5\times 4\times 2$

$=6.25\times 4-5\times 4\times 2$

$=25-40$

$=-15kN-m$

Therefore, the magnitude of moment at A = 15 kN-m.