Do not round intermediate calculations. Give your final answer(s) to three signi

Question

Do not round intermediate calculations. Give your final answer(s) to three significant figures. A brass link (Eb = 105 GPa. alpha b = 20.9 Times 10-6/ degree C) and a steel rod (Es = 200 GPa. alpha 5 = 11.7 Times 10-6/ degree C) have the dimensions shown at a temperature of 25 degree C. The steel rod is cooled until it fits freely into the link. The temperature of the whole assembly is then raised to 50 degree C. Determine (a ) the final stress in the steel rod. (b) the final length of the steel rod.

Explanation / Answer

After cooling, the lenght of rod decreases by 0.36 mm so as to fit in the brass link.

l = (T)

=> 0.36 *10-3 = 11.7 *10-6 (T)

T = 30.77 oC

Tc = -5.77 oC

(b) the whole assembly is heated to 50 oC,

length of steel rod is same as length of brass link.

Lb = Li + b*(T) = 253.522 mm

length of steel rod = 253.522 mm

(a) when heated to 50 oC, steel rod would have expanded to (253 + 11.7*10-6*(50-(-5.77)) = 253.652 mm

The compression in length= e = 0.13 mm

Stress developed = E * e = 200 *109 *0.13/1000 = 26001800 Pa = 26.002 Mpa

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