## Question:

Replace the distributed loading by an equivalent resultant force and specify where its line of action intersects member $AB$, measured from $A$.

Given:

${ w }_{ 1 }$ = $200$ $\frac { N }{ m }$

${ w }_{ 2 }$ = $100$ $\frac { N }{ m }$

${ w }_{ 3 }$ = $200$ $\frac { N }{ m }$

$a$ = $5$ $m$

$b$ = $6$ $m$

## Step-by-step

${ F }_{ Rx }$ = $-{ w }_{ 3 }a\quad \quad \quad \quad \quad \quad \quad \quad\quad\quad\quad\quad { F }_{ Rx }$ = $-1000$ $N$

${ F }_{ Ry }$ = $\frac { -1 }{ 2 } \left( { w }_{ 1 }+{ w }_{ 2 } \right) b\quad \quad \quad \quad \quad \quad \quad \quad { F }_{ Ry }$ = $-900$ $N$

$-y{ F }_{ Rx }$ = ${ w }_{ 3 }a\frac { a }{ 2 } -{ w }_{ 2 }b\frac { b }{ 2 } -\frac { 1 }{ 2 } \left( { w }_{ 1 }-{ w }_{ 2 } \right) b\frac { b }{ 3 }$

$y$ = $\frac { { w }_{ 3 }a\frac { a }{ 2 } -{ w }_{ 2 }b\frac { b }{ 2 } -\frac { 1 }{ 2 } \left( { w }_{ 1 }-{ w }_{ 2 } \right) b\frac { b }{ 3 } }{ -{ F }_{ Rx } } \quad \quad \quad \quad \quad \quad \quad y$ = $0.1$ $m$