Problem # p004

Thermal expansion

The device displayed below consisting of the beam ABC supended on the two cables "1" and "2" is initially installed with the rigid beam ABC exactly horizontal. Beam ABC and both cables are of negligible weight.

By how much does the vertical position of point C change if the entire assembly heats up by 100°C ?

Assume that the vertical distance h between the support points for the two cables is unaffected by the temperature change.

NOTE : The angle between beam ABC and the horizontal will be only a few degrees leaving the horizontal distance between the points A, B, and C practically unchanged.

    Cable 1 :
Length = 4.5 m
Coefficient of thermal expansion = 16·10-6 1/°C

Cable 2 :
Length = 3.5 m
Coefficient of thermal expansion = 32·10-6 1/°C

Horizontal distances :
a = 3 m , b = 5 m