Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 4 - Force System Resultants - Section 4.9 - Reduction of a Simple Distributed Loaded - Problems - Page 196: 142

Answer

$$ \begin{aligned} & F_R=15.0 \mathrm{kN} \\ & d=3.40 \mathrm{~m} \end{aligned} $$

Work Step by Step

Summing the forces along the $y$ axis $$ \begin{aligned} +\uparrow\left(F_R\right)_y=\Sigma F_y ; \quad-F_R & =-2(6)-\frac{1}{2}(2)(3) \\ F_R & =15.0 \mathrm{kN} \downarrow \end{aligned} $$ Now Summing the Moments about point $A$, $$ \begin{aligned} C+\left(M_R\right)_A=\Sigma M_A ; \quad-15.0(d) & =-2(6)(3)-\frac{1}{2}(2)(3)(5) \\ d & =3.40 \mathrm{~m} \end{aligned} $$
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