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The loading on the bookshelf is distributed as shown. Determine the magnitude of the equivalent resultant location, measured from point O.

Given:

{ w }_{ 1 } = 2\frac { Ib }{ ft }

{ w }_{ 2 } = 3.5\frac { Ib }{ ft }

a = 2.75 ft

b = 4 ft

c = 1.5 ft

Step-by-step

Guesses\quad \quad R=1Ib\quad \quad d = 1 ft

Given \quad \quad { w }_{ 1 }b+{ w }_{ 2 }c\quad = R

\quad \quad\quad { w }_{ 1 }b\left( a-\frac { b }{ 2 } \right) – { w }_{ 2 }c\left( \frac { c }{ 2 } +b-a \right) = -dR

\left( \begin{matrix} R \\ d \end{matrix} \right) = Find (R,d) \quad \quad R = 13.25 Ib \quad \quad d = 0.34 ft

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