Problem # 025

Thermal Expansion and Stress

A column of length L is sitting on a rigid floor. At installation time there is a gap d between the top of the column and the rigid ceiling above.

The distance between ceiling and floor is constant for the purpose of this problem.

  • Length of column : L = 2.5 m
  • Initial gap : d=0.8 mm
  • Coefficient of thermal expansion : 12*10-6 1/oC
  • Modulus of Elasticity : E = 200 GPa

  1. By how much must the temperature of the column rise in order for the gap d to close ?
  2. What is the normal stress in the column at a temperature 50 oC above that at installation time ?