Thermal Stresses

Thermal Stress: Temperature changes cause the body to expand or contract. The amount δT, is given by

where α is the coefficient of thermal expansion in m/m°C, L is the length in meter, T_i and T_f are the initial and final temperatures, respectively in °C. 

• The stress caused by internal forces created to resist thermal deformations. If temperature deformation is permitted to occur freely, no load or stress will be induced in the structure.
• In some cases where temperature deformation is not permitted, an internal stress is created. The internal stress created is termed as thermal stress.

For a homogeneous rod mounted between unyielding supports as shown, the thermal stress is computed as:

Deformation due to temperature changes;

Deformation due to equivalent axial stress

where σ is the thermal stress in MPa, E is the modulus of elasticity of the rod in MPa. If the wall yields a distance of x as shown, the following calculations will be made:

where σ represents the thermal stress.

Coefficient of Thermal Expansion (α) and Elastic Modulus (E) :

If the temperature rises above the normal, the rod will be in compression, and if the temperature drops below the normal, the rod is in tension.