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The beam supports the distributed load caused by the sandbags. Determine the resultant force on the beam and specify its location measured from point A.

Units Used:

kN = { 10 }^{ 3 } N

Given:

{ w }_{ 1 } = 1.5 \frac { kN }{ m } \quad a = 3 m

{ w }_{ 2 } = 1 \frac { kN }{ m } \quad b = 3 m

{ w }_{ 3 } = 2.5 \frac { kN }{ m } \quad c = 1.5 m

Step-by-step

{ F }_{ R } = { w }_{ 1 }a+{ w }_{ 2 }b+{ w }_{ 3 }c\quad \quad \quad { F }_{ R } = 11.25 kN

{ M }_{ A } = { w }_{ 1 }a\frac { a }{ 2 } +{ w }_{ 2 }b\left( a+\frac { b }{ 2 } \right) +{ w }_{ 3 }c\left( a+b+\frac { c }{ 2 } \right)

{ M }_{ A } = 45.563 kN.m\quad \quad d= \frac { { M }_{ A } }{ { F }_{ R } } \quad \quad d = 4.05 m

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