Answer to Question #153653 in Mechanical Engineering for Badshah

Question

The two cylindrical rod segments are fixed to the rigid walls such that there is a gap of 0.01in between

them when T1 = 60^oF. Determine the larger temperature T2 required in order to just close the gap

without producing stresses in the rods? Each rod has a diameter of 1.25in. Take (alpha)al = 13 x 10^-6 in/in ^oF,

Eal = 104 ksi, (Alpha)cu = 9.4 x 10^-6 in/in ^oF, Ecu = 15 x 10³ ksi.

Answer 1

a)=$\Delta Cu + \Delta Al = 0.01$

$L cu D cu (T2-T1) + L al D al (T2-T1) = 0.01$

$T2 = 112.4 F$

b)= $[-(12\times9.4\times10$ ^-6) $- (6\times13\times10$ ^-6)]+$\alpha [ \frac{12} {10^4}+ \frac{6}{1.500^4}]$ = 0.01

= 34.87Ksi