Thermal Stress Calculator

The thermal stress calculator tells you the stress on the object due to any thermal load. The thermal stresses are a result of a change in temperature. Thermal loads on a structure include temperature changes that could be due to operating, like components of engines or heat exchangers (learn more about heat exchangers through our LMTD calculator) pipes and valves, being exposed to heat. It could also be a change in temperature due to weather, say, a considerable temperature drop in cold weather or a hot summer day in deserts.

Thermal stress is prevalent in objects like boilers, pipelines, and valves. Exposure to thermal loads could cause changes in dimensions as the structures expand or contract.

Have you noticed cracked footpaths? That occurs due to thermal stress in the concrete. Thermal expansion (see thermal expansion calculator) from heat leads to deformation in steel railway tracks or cracks in brittle materials that can cause catastrophic structural failure. Most engineers give allowances for such designs; for instance, you can observe small gaps between tracks that allow for thermal expansion. This allowance is set considering the coefficient of thermal expansion of stainless steel or any other material used in construction. The applicability of this concept is not limited to construction but it is also valuable for medical sciences to design dental filings and in machinery to devise gears, shafts, coupling, rivets, and boilers to name a few.

To this end, this article explains the thermal expansion formula and thermal stress.

Before getting into thermal stress (for mechanical stresses, refer to our stress calculator), let's look at thermal load? — It is the load acting on a structure caused by movements due to thermal expansion. This load is higher in the case of restrained structures that do not account for any movement of parts.

The load causes stress on the structure; that stress is known as thermal stress. In other words, the change in temperature makes the structure expand or contract. This movement causes mechanical stress on the structure, which we call thermal stress. It depends on the expansion rate of the material and the temperature gradient.

Now that you know what thermal stress is, you can use the thermal stress equation to estimate it:

where:

• $\sigma_t$ – Thermal stress;
• $\alpha$ – Coefficient of thermal expansion;
• $E$ – Young's modulus; and
• $\Delta T$ – Change in temperature.

What is temperature gradient? — It is the change in temperature per unit length of a material. It is expressed in the temperature units such as °F or °C and K. For a unit length sized sample, the temperature gradient is:

where:

• $T_f$ – Final temperature; and
• $T_i$ – Initial temperature.

To calculate thermal stress:

1. Enter the coefficient of linear thermal expansion, $\alpha$.
2. Fill in the Young's modulus of the material, $E$.
3. Insert the initial temperature, $T_i$.
4. Enter the final temperature, $T_f$.
5. The calculator will return the thermal stress.

In the Results part, you can also check the temperature difference, $\Delta T$.

Estimate the thermal stress in a copper bar if it is heated to a temperature of 50 °C from a temperature of 20 °C. Take the coefficient of thermal expansion of copper as $17 \times 10^{-6} \text{ K}^{-1}$ and Young's modulus as 110 GPa.

To calculate thermal stress in the bar:

1. Enter the coefficient of linear thermal expansion, $\alpha = 17 \times 10^{-6} \text{ K}^{-1}$.
2. Fill in the Young's modulus of the material, $E = 110 \text{ GPa}$.
3. Insert the initial temperature, $T_i = 20 \text{ °C}$.
4. Enter the final temperature, $T_f = 50 \text{ °C}$.
5. Using the thermal stress formula:

The table below contains Young's modulus and coefficient of thermal expansion for metals and alloys. You can use the data from the table to find stresses due to thermal expansion in pipes or thermal stress in concrete.