Calculation of Thermal Stresses
Fortunately, it is possible to calculate the magnitude of these stresses or forces.
Young's modulus is used to find help find the force or stress on an object subject to simple tension or compression. To recall, tension occurs when an object is pulled or stretched, and compression occurs when an object is squeezed or pushed in. Engineers give the elastic modulus the symbol E. E varies according to the material, not to its shape or size. In SI units, E is 200x109 N/m2 for steel, 20x109 N/m2 for concrete, and for brick it is 14x109 N/m2.
The force per unit area in terms of Young's modulus and the dimensionless strain ΔL/L0 is:
1) F/A = E ΔL/L0
In SI units, where force is measured in Newtons and area in meters, E is in N/m2. From the first equation in the aforementioned article on thermal expansion, we know that the linear thermal expansion is:
2) ΔL = L0αΔT or ΔL /L0 = αΔT
Substituting the term for ΔL /L0 from 2 into equation 1 we find:
3) F/A = EαΔT = αEΔT
This equation allows us to calculate what may possibly happen to our material under thermal stress if it is not allowed to contract expand properly. We use our calculations and compare it with ultimate strength of material parameters for tensile, compressive, and/or shear strength to find if a substance will buckle or fracture under thermal stress. For a review of these terms, it is recommended that you read the Bright Hub article on materials engineering.
Thermal stress is the reason why engineers build bridges with expansion joints, and why concrete sidewalks and bridges are built with expansion spaces. Lack of proper spacing between concrete slabs to effects such as cracks, as you can see here.