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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

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