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:

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

$d$ = $10$ $m$

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

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:

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

$d$ = $10$ $m$

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

Units Used:

[latex]kN[/latex] = [latex]{ 10 }^{ 3 }[/latex] [latex]N[/latex]

Given:

[latex]{ w }_{ 0 }[/latex] = [latex]500\frac { N }{ m }[/latex]

[latex]d [/latex]= [latex]10[/latex] [latex]m[/latex]

[latex]{ w }_{ x }[/latex] = [latex]{ w }_{ 0 }{ \left( \frac { x }{ d } \right) }^{ 3 }[/latex]

Accepted Answer

[latex]{ F }_{ R }[/latex] = [latex]\int _{ 0 }^{ d }{ w(x)dx\quad \quad \quad \quad \quad } { F }_{ R }[/latex] = [latex]1.25[/latex] [latex]N[/latex]

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

Question : Wind has blown sand over a platform such that the intensity ...

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