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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

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