Problem: The steel bar AB has a 10 x 10 mm square cross section and is held by pins which are a fixed distance apart and are located at a distance e = 0.9 mm from the geometric axis of the bar. At temperature To the pins are in contact with the bar and the force in the bar is zero. Determine the increase in temperature for which the bar will just make contact with point C if d = 0.3 mm. Use E = 200 GPa and a coefficient of thermal expansion of 11.7 x 10-6 oC-1.
Solution: The cross section is square, so A and I are easily computed. Here's a summary of the data:
Using the secant formula (equation 10.31), I get
Using equation 10.30,
It should be remembered that the P's are axial forces which, in this case, are caused by the thermal expansion. Thus, we can use the axial deformation and thermal expansion equations:
1 This is problem 11.56 from Beer & Johnston's Mechanics of Materials, 2nd Edition.