Question

A copper collar is to fit tightly about a steel shaft whose diameter is 7.0000 cm at 20° C. The inside diameter of the copper collar at that temperature is 6.9760 cm. After the collar is heated and fitted about the steel shaft, it begins to cool. What is the tensile stress in the copper collar when its temperature returns to 20° C?

____________________N/m2

Answer 1

L_co = original diameter of copper collar at 20 C, = 6.9760 cm

L_so = original diameter of steel shaft at 20 C, = 7.0000 cm

_c = coefficient of thermal expansion of copper = 17 x 10^-6

_s = coefficient of thermal expansion of steel = 13 x 10^-6

T_i = initial temperature = 20 C

T_f = Final temperature = T

T = Change in temperature = T - 20

Final length of diameter of copper collar = Final diameter of steel shaft

L_co (1 + _cT) = L_so (1 + _sT)

(6.9760) (1 + (17 x 10^-6) T) = (7.0000) (1 + (13 x 10^-6) T)

T = 869.82 C

F = tensile strength of copper = 2 x 10⁸ Pa

tensile stress is given as

Stress = F _cT

Stress = (2 x 10⁸) (17 x 10^-6) (889.82)

Stress = 3.025 x 10⁶ N/m²