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Replace the distributed loading by an equivalent resultant force, and specify its location on the beam, measured from the pin at C.

Units Used:

kip = { 10 }^{ 3 } Ib

Given:

w = 800 \frac { Ib }{ ft }

a = 15 ft

b = 15 ft

\theta = 30 deg

Step-by-step

{ F }_{ R } = wa+\frac { wb }{ 2 } \quad \quad \quad { F }_{ R } = 18 kip

{ F }_{ R }x = wa\frac { a }{ 2 } +\frac { wb }{ 2 } \left( a+\frac { b }{ 3 } \right)

x = \frac { wa\frac { a }{ 2 } +\frac { wb }{ 2 } \left( a+\frac { b }{ 3 } \right) }{ { F }_{ R } } \quad \quad \quad x = 11.7 ft

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