C2.3 Thermal Deformation

Engineering structures are subject to varying temperatures throughout the day, causing them to expand/contract. If say the thermal expansion is restricted (e.g. due to fixed supports), we have what we call thermal stress that develops in the structure.

That is why in bridges, we see expansion joints that are placed to allow space for thermal expansion. Without the space, the expansion will be restricted and thermal stresses develop.

Expansion joint for thermal expansion

C2.3 Thermal Deformation

Engineering structures are subject to varying temperatures throughout the day, causing them to expand/contract. If say the thermal expansion is restricted (e.g. due to fixed supports), we have what we call thermal stress that develops in the structure.

That is why in bridges, we see expansion joints that are placed to allow space for thermal expansion. Without the space, the expansion will be restricted and thermal stresses develop.

Expansion joint for thermal expansion

We need to quantify the degree of thermal expansion to see how it translates into stress. Here’s the formula:

Thermal deformation formula

Note:

α is the linear thermal expansion coefficient (units: ^oC^-1 or K^-1). It gives the strain per unit change in temperature.
ΔT is the change in temperature (units: ^oC or K)
L is the length of the member (units: m)

We can use this displacement relation in our compatibility equation, and together with the equations of equilibrium we can solve for the reactions due to thermal loading.

Let’s look at an example now.

We need to quantify the degree of thermal expansion to see how it translates into stress. Here’s the formula:

Thermal deformation formula

Note:

α is the linear thermal expansion coefficient (units: ^oC^-1 or K^-1). It gives the strain per unit change in temperature.
ΔT is the change in temperature (units: ^oC or K)
L is the length of the member (units: m)

We can use this displacement relation in our compatibility equation, and together with the equations of equilibrium we can solve for the reactions due to thermal loading.

Let’s look at an example now.