Question

0.7 mm 6 BL Problem 3 - Thermal Stress (25 pts) The center rod CD of the assembly is heated from T, = 25°C to T2 = 200°C using electrical resistance heating. At the lower temperature T, the gap between C and the rigid bar is 0.7 mm. Determine the force in the rods AB and EF caused by the increase in temperature. Rods AB and EF are made of steel, and each has a cross-sectional area of 125 mm². CD is made of aluminum and has a cross-sectional area of 375 mm². E, = 200 GPa, Eat = 70 GPa, and cal = 23(10-)/°C. 240 mm 300 mm

Answer 1

0.7 nimi .6, ܟܘ 280 inni;») mini

By equilibrium of forces;

$\sum F_y =0$

$\Rightarrow P_a - 2P_s = 0$

$\Rightarrow P_a =2P_s$

By compatibility equation;

(Sa)t - (Sa)p - (83)p = 0.7

$\Rightarrow (\alpha_a l_a)(T_2-T_1) - \frac{P_al_a}{A_aE_a} -\frac{P_sl_s}{A_sE_s} = 0.7$

$\\\Rightarrow (23\times10^{-6} \times240)(200-25) - \frac{(2P_s)(240)}{(375)(70\times10^3)} -\frac{P_s(300)}{(125)(200\times10^3)} = 0.7$

$\\\Rightarrow P_s = 8783\;\;N$

Answer:

OR