PROBLEM A bridgeis constructed ofa material having an expansion coefficient of 2

Question

PROBLEM A bridgeis constructed ofa material having an expansion coefficient of 20 x 106 °C and an elastic modulus of 2 x 10 Pa. Expansion joints are placed in the bridge every 50 m and are of 2 cm spacing at 20°C. On a very hot day the temperature on the top surface of the bridge reaches 60°C (1) Will the expansion gaps have closed? If so, at what temperature do they do so? (2) Calculate the stress set up in the bridge after the expansion gaps close. If the cross sectional area of the bridge What recommendations would you make if you saw this bridge at the design stage? rs is 5 m, what force is generated (3)

Explanation / Answer

Given,

Expansion coefficient, a = 20 x 10-6 /c

elongation in length = [20x10-6] x (60 - 20) x 50 = 0.04 m = 4 cm

Now available space is 2 cm, sorry the gaps will close and compress against each other

FOR CLOSING OF GAPS

elongation length = 2 cm = 0.02 m = [20x10-6] x (T - 20) x 50

=> T = 40 C

Now STRAIN = 0.02/(50 + 0.04) = 4x10-4

STRESS = Y x STRAIN = 2x1011 x 4x10-4 = 80 MPa [compressive stress]

FORCE = (STRESS) x (AREA) = 80 MPa x 5 = 400 MN = 4 x 108 N

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