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.
i) dl = \alphal∆T = 19 x 10-6 °C-1 x 500 mm x (135 - 25)°C = 1.045 mm
ii) F = \sigmaA = \alphaTEA = 19 x 10-6 °C-1 x 84 x 109 Pa x (135 - 25)°C x \pi(0.01)2 = 55.15 kN