## Question:

Replace the loading by an equivalent resultant force and couple moment acting at point $A$.

Units Used:

$kN$ = ${ 10 }^{ 3 }$ $N$

Given:

$w$ = $6$ $\frac { kN }{ m }$

$F$ = $15$ $kN$

$M$ = $500$ $kN.m$

$a$ = $7.5$ $m$

$b$ = $4.5$ $m$

## Step-by-step

${ F }_{ R }$ = $\frac { 1 }{ 2 } w(a+b)+F\quad { F }_{ R }$ = $51.0$ $kN$

${ M }_{ R }$ = $-M-\left( \frac { 1 }{ 2 } wa \right) \left( \frac { 2 }{ 3 } a \right) -\left( \frac { 1 }{ 2 } wb \right) \left( a+\frac { b }{ 3 } \right) -F\left( a+b \right)$ $\quad \quad { M }_{ R }$ = $-914$ $kN.m$