## Question:

The beam is pin-connected at $A$ and rocker-supported at $B$.Determine the reactions at the pin $A$ and at the roller at $B$.

Given:

$F$ = $500$ $N$

$M$ = $800$ $N.m$

$a$ = $8$ $m$

$b$ = $4$ $m$

$c$ = $5$ $m$

## Step-by-step

$\alpha =atan\left( \frac { c }{ a+b } \right)$

$\circlearrowleft \sum { { M }_{ A } }$ = $0$ ;$\quad \quad \quad -F\frac { a }{ \cos { (\alpha) } } -M+{ B }_{ y }a$ = $0$

$\quad \quad \quad \quad\quad\quad \quad \quad \quad { B }_{ y }=\frac { Fa+M\cos { (\alpha) } }{ \cos { (a) } a }$

$\quad \quad \quad \quad\quad\quad \quad \quad \quad { B }_{ y }$ = $462$ $N$

$\underrightarrow { + } \sum { { F }_{ x } } =0;\quad \quad -{ A }_{ x }+F\sin { (\alpha )=0 } \quad \quad { A }_{ x }=F\sin { (\alpha ) } \quad \quad\quad\quad\quad\quad\quad { A }_{ x }$ = $192$ $N$

$+\uparrow \sum { { F }_{ y } } =0;\quad \quad -{ A }_{ y }-F\cos { (\alpha ) } +{ B }_{ y }=0\quad \quad { A }_{ y }=-F\cos { (\alpha ) } +{ B }_{ y }\quad \quad { A }_{ y }$ = $180$ $N$