## Question:

Wind has blown sand over a platform such that the intensity of the load can be approximated by the function $w$ = ${ w }_{ 0 }{ \left( \frac { x }{ d } \right) }^{ 3 }$ Simplify this distributed loading to an equivalent resultant force and specify the magnitude and location of the force, measured from $A$.

Units Used:

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

Given:

${ w }_{ 0 }$ = $500\frac { N }{ m }$

$d$= $10$ $m$

${ w }_{ x }$ = ${ w }_{ 0 }{ \left( \frac { x }{ d } \right) }^{ 3 }$

## Step-by-step

${ F }_{ R }$ = $\int _{ 0 }^{ d }{ w(x)dx\quad \quad \quad \quad \quad } { F }_{ R }$ = $1.25$ $N$

$d$ = $\frac { \int _{ 0 }^{ d }{ xw(x)dx } }{ { F }_{ R } } \quad\quad\quad \quad \quad \quad \quad d$ = $8$ $m$