 # Thermal expansion

Thermal expansion  and thermal stress can become problematic for structural members. In other words, the engineers have been witnessed on several failures due to this phenomenon.

In simple words, When temperature increases the materials is going to expand. Let’s make it as simple as possible: heating causes expansion.

### Thermal expansion

The amount of thermal expansion is actually a function of 3 different parameters.

1. The amount of change in temperature
2. the initial length of the object
3. The material itself.

linear expansion coefficient is a parameter that helps us to account for the effect of material specifications. This coefficient has been measured by some experimental test for each material, so you can find it in most of engineering books. Thermal expansion formula

Ok let’s give you an example to clarify this formula. Here we have a steel structure. a 6 meter aluminum beam has been installed in 20 degrees c. we want to estimate the length of this beam in a cold winter when temperature decreases to about -30degrees. The linear expansion coefficient has been given in the figure below.

### When is thermal stress?

Thermal expansion happens only when there is nothing to stop it. So if there is no barrier ahead, heating will cause no force, just a an increase in dimensions.

But what if the end of the bar is constrained? In this figure, for example, the beam is fixed at the ends so linear expansion is impossible. And when the temperature increases the barrier is going to suppress  any tendency of the beam for elongation. In other words,  the barriers apply a reaction force to prevent the expansion. These reaction forces create a degree of internal stress inside the material which is called thermal stress. In such cases the amount of thermal stress can be estimated by this formula. How thermal stress is created Thermal stress formula