Answer to Question #188968 in Mechanical Engineering for Beryllium

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

i) dl = $\alpha$l∆T = 19 x 10^-6 °C^-1 x 500 mm x (135 - 25)°C = 1.045 mm

ii) F = $\sigma$A = $\alpha$TEA = 19 x 10^-6 °C^-1 x 84 x 10⁹ Pa x (135 - 25)°C x $\pi$(0.01)² = 55.15 kN