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 353: 1

Answer

$\begin{aligned} & N_C=0 \\ & V_C=-386 \mathrm{lb} \\ & M_C=-857 \mathrm{lb} \cdot \mathrm{ft} \\ & N_D=0 \\ & V_D=300 \mathrm{lb} \\ & M_D=-600 \mathrm{lb} \cdot \mathrm{ft}\end{aligned}$

Work Step by Step

Support Reactions: $ \begin{aligned} & ↺+\Sigma M_B=0 ; \quad 500(8)-300(8)-A_y(14)-0 \\ & A_y=114.29 \mathrm{lb} \end{aligned} $ Intermal Forces: $ \begin{aligned} & \text { 士 } \Sigma F_x=0 \quad N_C=0 \\ & +\uparrow \Sigma F_y=0 ; \quad 114.29-500-V_C=0 \quad V_C=-386 \mathrm{lb} \\ & ↺+\Sigma M_C=0 \\ & M_C+500(4)-114.29(10)-0 \\ & M_C=-857 \mathrm{lb} \cdot \mathrm{ft} \\ & \end{aligned} $ Applying the equations of equilibrium to segment ED we have $ \begin{gathered} \rightarrow \Sigma F_s=0 ; \quad N_D-0 \\ +1 \Sigma F_y=0 ; \quad V_D-300=0 \quad V_D=300 \mathrm{lb} \\ ↺+\Sigma M_D=0 ; \quad-M_D-300(2)=0 \quad M_D=-600 \mathrm{lb} \cdot \mathrm{ft} \end{gathered} $
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