Answer to Question #187188 in Mechanical Engineering for harry

Question

A brass tie bar of length 500 mm and diameter 20 mm undergoes a change in temperature

from 25°C to 135°C. The linear expansivity of copper is 19 × 10−6°C−1 and its modulus of

elasticity is 84 Gpa.

i) Determine the change of length that takes place.

ii) Determine the compressive force induced in the bar if it is rigidly held and expansion is prevented.

Answer 1

Given:

Length of brass bar(L)= 500mm

Diameter of brass Bar (d) = 20 mm

Change in temperature $(\Delta T)$ = 135-25=110 ⁰C

The coefficient of linear expansion($\alpha$)=19x10^-6 /^oC

Modulus of elasticity (E)=84GPa=84x10³ N/mm²

Solution:

(i) Change in length ($\Delta L$ )=$L\times\alpha \times \Delta T$ =500 x 19x10^-6 x 110 =1.045 mm

(ii)The compressive force (F) = $E\times \alpha \times \Delta T\times Area(A)$ =84x10³x19x10^-6x110x $\frac{\pi\times{20}^2}{4}$

F= 55.125 kN