Engineering Mechanics: Statics & Dynamics (14th Edition)

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

Chapter 7 - Internal Forces - Section 7.1 - Internal Loadings Developed in Structural Members - Problems - Page 355: 14

Answer

$\begin{aligned} & M_C=-15.0 \mathrm{kip} \cdot \mathrm{ft} \\ & N_C=0 \\ & V_C=2.01 \mathrm{kip} \\ & M_D=3.77 \mathrm{kip} \cdot \mathrm{ft} \\ & N_D=0 \\ & V_D=1.11 \mathrm{kip}\end{aligned}$

Work Step by Step

$$ \begin{aligned} & ↺+\Sigma M_B=0 ; \quad-A_y(14)+2500(20)+900(8)+3000(2)=0 \\ & A_y=4514 \mathrm{lb} \\\\ & \rightarrow \Sigma F_x=0 ; \quad B_x=0 \\ & +\uparrow \Sigma F_y=0 ; \quad 4514-2500-900-3000+B_y=0 \\ & B_y=1886 \mathrm{lb} \\\\ & ↺+\Sigma M_C=0 ; \quad 2500(6)+M_C=0 \\ & M_C=-15000 \mathrm{lb} \cdot \mathrm{ft}=-15.0 \mathrm{kip} \cdot \mathrm{ft} \\\\ & \rightarrow \Sigma F_x=0 ; \quad N_C=0 \\ & +\uparrow \Sigma F_y=0 ; \quad-2500+4514-V_C=0 \\ & V_C=2014 \mathrm{lb}=2.01 \mathrm{kip} \\\\ & ↺+\Sigma M_D=0 ; \quad-M_D+1886(2)=0 \\ & M_D=3771 \mathrm{lb} \cdot \mathrm{ft}=3.77 \mathrm{kip} \cdot \mathrm{ft} \\\\ & \pm \Sigma F_x=0 ; \quad N_D=0 \\ & +\uparrow \Sigma F_y=0 ; \quad V_D-3000+1886=0 \\ & V_D=1114 \mathrm{lb}=1.11 \mathrm{kip} \\ & \end{aligned} $$
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