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Replace the loading by an equivalent resultant force and specify its location on the beam,measured from point B.

Units Used:

kip = { 10 }^{ 3 } Ib

Given:

{ w }_{ 1 } = 800 \frac { Ib }{ ft }

{ w }_{ 2 } = 500 \frac { Ib }{ ft }

a = 12 ft

b = 9 ft

Step-by-step

{ F }_{ R } = \frac { 1 }{ 2 } a{ w }_{ 1 }+\frac { 1 }{ 2 } ({ w }_{ 1 }-{ w }_{ 2 })b+{ w }_{ 2 }b\quad \quad \quad\quad\quad\quad { F }_{ R } = 10.65 kip

{ F }_{ R }x = -\frac { 1 }{ 2 } a{ w }_{ 1 }\frac { a }{ 3 } +\frac { 1 }{ 2 } \left( { w }_{ 1 }-{ w }_{ 2 } \right) b\frac { b }{ 3 } +{ w }_{ 2 }b\frac { b }{ 2 }

x = \frac { -\frac { 1 }{ 2 } a{ w }_{ 1 }\frac { a }{ 3 } +\frac { 1 }{ 2 } \left( { w }_{ 1 }-{ w }_{ 2 } \right) b\frac { b }{ 3 } +{ w }_{ 2 }b\frac { b }{ 2 } }{ { F }_{ R } } \quad \quad \quad x = 0.479 ft

\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad x = 0.479 ft

( to the right of B )

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