Question 6.116: The structure is subjected to the loading shown. Member AD i...
The structure is subjected to the loading shown. Member AD is supported by a cable AB and roller at C and fits through a smooth circular hole at D. Member ED is supported by a roller at D and a pole that fits in a smooth snug circular hole at E. Determine the x, y, z components of reaction at E and the tension in cable AB.
\Sigma M_y=0 ; \quad-\frac{4}{5} F_{A B}(0.6)+2.5(0.3)=0
F_{A B}=1.5625=1.56 \mathrm{kN}
\Sigma F_z=0 ; \quad \frac{4}{5}(1.5625)-2.5+D_z=0D_z=1.25 \mathrm{kN}
\Sigma F_y=0 ; \quad D_y=0
\Sigma F_x=0 ; \quad D_x+C_x-\frac{3}{5}(1.5625)=0 (1)
\Sigma M_x=0 ; \quad M_{D x}+\frac{4}{5}(1.5625)(0.4)-2.5(0.4)=0
M_{D x}=0.5 \mathrm{kN} \cdot \mathrm{m}
\Sigma M_z=0 ; \quad M_{D z}+\frac{3}{5}(1.5625)(0.4)-C_x(0.4)=0 (2)
\Sigma F_z=0 ; \quad D_{z^{\prime}}=1.25 \mathrm{kN}
\Sigma M_x=0 ; \quad M_{E x}=0.5 \mathrm{kN} \cdot \mathrm{m}
\Sigma M_x=0 ; \quad M_{E x}=0.5 \mathrm{kN} \cdot \mathrm{m}
\Sigma M_y=0 ; \quad M_{E y}=0
\Sigma F_y=0 ; \quad E_y=0
\Sigma M_z=0 ; \quad D_x(0.5)-M_{D z}=0 (3)
Solving Eqs. (1), (2) and (3):
C_x=0.938 \mathrm{kN}
M_{D z}=0
D_x=0
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