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Replace the loading by an equivalent resultant force and couple moment acting at point A.

Units Used:

kN = { 10 }^{ 3 } N

Given:

w = 6 \frac { kN }{ m }

F = 15 kN

M = 500 kN.m

a = 7.5 m

b = 4.5 m

Step-by-step

{ F }_{ R } = \frac { 1 }{ 2 } w(a+b)+F\quad { F }_{ R } = 51.0 kN

{ M }_{ R  } = -M-\left( \frac { 1 }{ 2 } wa \right) \left( \frac { 2 }{ 3 } a \right) -\left( \frac { 1 }{ 2 } wb \right) \left( a+\frac { b }{ 3 } \right) -F\left( a+b \right) \quad \quad { M }_{ R } = -914 kN.m

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