Answer to Question #234435 in Mechanical Engineering for RUTH

Question

A copper tube having a cross-sectional area of 2 000 mm2 and a length of 300 mm is placed between two rigid caps. Four 22-mm-diameter steel bolts are symmetrically arranged parallel to the axis of the tube and are lightly fastened. Find the stress in the tube if the temperature of the assembly is raised by 70 °C. What load will each bolt carry at the raised temperature? (Let EST = 200 GPa; Ec u = 100 GPa; aST = 12 x 10"6 / o C; ac u = 16 x 10-6 /°C.)

Answer 1

Part 1

$P_1=4P_2=31.67462 kN\\ Stress \space in \space the \space tube, \sigma_1= \frac{P_1}{A_1}= \frac{31.67462*10^2}{2000}= 15.837MPa$

Part 2

$\delta_1+\delta_2= \Delta L_1+\Delta L_2= L( \alpha_1 - \alpha_2)\Delta T= 300*70*(16.5-13)*10^{-1}\\ \frac{P_1L}{A_1E_1}+\frac{P_2L}{A_2E_2}=L*(16.5-13)*10^{-6}*70\\ \frac{4P_1}{2000*117*10^3}+\frac{P_2}{380.1327*190*10^3}=(16.5-13)*10^{-6}*70\\ P_2=7918.65503 n$