Question 7.137: The traveling crane consists of a 5-m-long beam having a uni...
The traveling crane consists of a 5-m-long beam having a uniform mass per unit length of 20 kg/m. The chain hoist and its supported load exert a force of 8 kN on the beam when . Draw the shear and moment diagrams for the beam. The guide wheels at the ends A and B exert only vertical reactions on the beam. Neglect the size of the trolley at C.
Support Reactions: From FBD (a),
\hookrightarrow +\Sigma M_A=0 ; \quad B_y(5)-8(2)-0.981(2.5)=0 \quad B_y=3.6905 \mathrm{kN}
+↑\Sigma F_y=0 ; \quad A_y+3.6905-8-0.981=0 \quad A_y=5.2905 \mathrm{kN}
Shear and Moment Functions: For 0 \leq x<2 \mathrm{~m} [\mathrm{FBD}(\mathrm{b})],
+↑\Sigma F_y=0 ; \quad 5.2905-0.1962 x-V=0
V=\{5.29-0.196 x\} \mathrm{kN}
\hookrightarrow +\Sigma M=0 ; \quad M+0.1962 x\left(\frac{x}{2}\right)-5.2905 x=0M=\left\{5.29 x-0.0981 x^2\right\} \mathrm{kN} \cdot \mathrm{m}
For 2 \mathrm{~m}<x \leq 5 \mathrm{~m} [\mathrm{FBD}(\mathrm{c})] \text {, }
+↑\Sigma F_y=0 ; \quad V+3.6905-\frac{20(9.81)}{1000}(5-x)=0
V=\{-0.196 x-2.71\} \mathrm{kN}
\hookrightarrow +\Sigma M=0 ; \quad 3.6905(5-x)-\frac{20(9.81)}{1000}(5-x)\left(\frac{5-x}{2}\right)-M=0M=\left\{16.0-2.71 x-0.0981 x^2\right\} \mathrm{kN} \cdot \mathrm{m}
