Temperature Effects and Stress Due to Temperature Change

As we know, for any material changes in temperature result in volume change. An increase or decrease in temperature results in the expansion or contraction of a structure.

To better understand this phenomenon, consider a steel wire with a length,, fixed at one end and free on the other end, is subjected to a temperature rise of . The wire will elongate by , as shown below:

The increase in the length, , is related to the changes in temperature by the following equation:

                                                            (1)

In this equation,  represents changes in temperature in degrees Fahrenheit (), l is the original length, and is the coefficient of thermal expansion (or thermal coefficient) with the units of  depends on the material type. The following shows the values of  for a few commonly used building materials:

Material
Aluminum	0.00128
Stainless Steel	0.00099
Copper	0.00093
Mild Steel	0.00065
Concrete	0.00055
Masonry	0.00035
Wood	0.00030

                                              

As can be seen from the above table, aluminum has larger  value than steel. This means that, subjected to the same temperature variations, aluminum structures undergo larger changes in volume than similar steel structures.

If the structure is prevented from movements (restrained) while subjected to a temperature change, stresses will develop.

Consider the same piece of wire used before with both ends restrained undergoing a temperature rise of . Since both ends of the wire are prevented from movement, stresses develop in the wire, forcing it to buckle.

To find how much these stresses are and what parameters they depend on, we first consider the wire without one of the end supports subjected to a temperature increase of .
The wire extends by , and the wire’s length becomes .

Now, we push the right end of the wire to go back to its original length. This is the force that would have developed in the wire if both ends were restrained when the temperature was raised.

As we know, the stress, , in the wire due to the force, , is:

where  is the cross-sectional area of the wire.
We also remember that the modulus of elasticity, , is defined as:

Where  is the strain, defined as:

Substituting equation (4) into (3):

Substituting equation (1) into (5):

or

The above equation shows the relationship between the changes in temperature and the stress developed in the restrained structure.

For aluminum and steel spatial structures undergoing extremely large temperature variations this may become an important issue to consider. However, in most typical cases of spatial structures the temperature effect may be neglected since the developed stresses are negligible.

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