Temperature Effects on Structures

Thermal stress and strain are internally introduced into component or structure due to thermal expansion or contraction of the material. (+ expansion, - contraction)

• Relatively modest temperature changes can cause comparable stresses and strains to those produced by ordinary external loads.
• If the structure is free to expand or contract, only thermal strains will be introduced.
• If expansion and contraction is constrained, thermal stresses (and possibly strains) will be introduced.

Bridges and Power Lines

Compensating for Thermal Expansion to Maintain Part Accuracy

 

Thermal Strain

Linear coefficient of thermal expansion, α - relates thermal strain to changes in temperature (units: 1/K, 1/^oC, 1/^oF)

Assumptions

• homogeneous material
• isotropic material
• temperature increase is uniform throughout material

Material Room-Temperature CTE  (x10-7 in/inoF) Lead 159 Aluminum 128 Brass 104 Bronze 101 Steel, Stainless 99 Copper 93 Plaster 76 Marble 73 Nickel 70 Iron, wrought 67 Steel, carbon 65 Iron, cast 59 Concrete 55 Concrete masonry 52 Glass 50 Granite 47 Slate 44 Limestone 44 Rubble masonry 35 Brick masonry 34

Material Room-Temperature CTE  (x10-7 in/inoF) parallel to grain perpendicular to grain Fir 21 320 Maple 36 270 Oak 27 300 Pine 36 190 To find degrees Celsius, first subtract 32 from the degrees Fahrenheit and then multiply by 5/9.     From Building Construction Illustrated, 3rd Ed by F.D.K. Ching and C. Adams, Wiley, 2000, p. 7.46.   elemental CTE

Temperature-displacement relation  

Solution technique for indeterminate structures with thermal stresses

1. generate equilibrium equations
2. generate compatibility equations
3. generate force-displacement equations
4. generate temperature-displacement equations
5. simultaneously solve all equations