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Determine the equivalent resultant force and couple moment at point O.

Units Used:

kN = { 10 }^{ 3 } N

Given:

a = 3 m

{ w }_{ O } = 3\frac { kN }{ m }

{ w }_{ (x) } = { w }_{ O }{ \left( \frac { x }{ a } \right) }^{ 2 }

Step-by-step

{ F }_{ R } = \int _{ 0 }^{ a }{ w(x) }  dx\quad \quad\quad \quad \quad \quad { F }_{ R } = 3 kN

{ M }_{ O } = \int _{ 0 }^{ a }{ w(x) } (a-x)dx\quad \quad \quad { M }_{ O } = 2.25 kN.m

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