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: 13

Answer

$\begin{aligned} & N_D=0 \\ & V_D=3.00 \mathrm{kip} \\ & M_D=12.0 \mathrm{kip} \cdot \mathrm{ft} \\ & N_E=0 \\ & V_E=-8.00 \mathrm{kip} \\ & M_E=-20.0 \mathrm{kip} \cdot \mathrm{ft}\end{aligned}$

Work Step by Step

Support Reaction. $ \begin{array}{ccc} ↺+\Sigma M_B=0 ; & 5(6)+6-A_y(12)=0 & A_y=3.00 \mathrm{kip} \\ ↺+\Sigma M_A=0 ; & B_y(12)-5(6)+6=0 & B_y=2.00 \mathrm{kip} \\ \pm \Sigma F_X=0 & B_x=0 & \end{array} $ Internal Loading. Referring to the left segment of member $A B$ sectioned through $D$ $ \begin{array}{lll} \pm \Sigma F_x=0 ; & N_D=0 & \\ +\uparrow \Sigma F_y=0 ; & 3.00-V_D=0 & V_D=3.00 \mathrm{kip} \\ ↺+\Sigma M_D=0 ; & M_D+6-3.00(6)=0 & M_D=12.0 \mathrm{kip} \cdot \mathrm{ft} \end{array} $ Referring to the left segment of member $B C$ sectioned through $E$, $ \begin{array}{llll} \pm \Sigma F_x=0 ; & N_E=0 & & \\ +\uparrow \Sigma F_y=0 ; & -V_E-1.5(4)-2.00=0 & V_E=-8.00 \mathrm{kip} & \text { } \\ ↺+\Sigma M_E=0 ; & M_E+1.5(4)(2)+2.00(4)=0 & M_E=-20.0 \mathrm{kip} \cdot \mathrm{ft} & \end{array} $
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