Lecture 27

Lecture 27:

Thermal Stresses

The size of a body will change as the ambient temperature fluctuates, expanding as it rises and contracting as it falls. For example, cracks in an asphalt highway which were there all winter, dissapear during the summer. The asphalt closes the cracks as it expands in the summer heat but they will reappear in the cold of winter as the material shrinks. This repetative cycle of expansion and contraction results in significant temperature stresses in construction material.

Within the ordinary climatic temperature range experienced by buildings, the change in dimension has conveniently been found to be approximately proportional to the change in temperature. The amount of dimensional change that will take place is determined by a factor known as the coefficient of thermal expansion (alpha). This describes the change in length (or width) of a member per unit length of the member. The values below describe some of the coefficients of thermal expansion for some common materials.

COEFFICIENTS OF THERMAL EXPANSION PER degree F

Wood	0.000 0030
Glass	0.000 0044
Concrete	0.000 0060
Cast Iron	0.000 0061
Steel	0.000 0065
Wrought Iron	0.000 0067
Copper	0.000 0093
Bronze	0.000 0100
Brass	0.000 0104
Aluminum	0.000 0128

These values describe the change in length per unit of length for one degree F temperature change. Some tables list the coefficients for a 100F temperature change. Similar tables may be found for the temperature change based on Centigrade rather than Fahrenheit. These are not only used to determine the values for expansion, but for contraction or shortening as well.
The equation used in determining the deformation is as follows:

Delta L = (alpha)(delta T)(L)
Where:

delta L= total change in length, inches (total deformation)
alpha = coefficient of thermal expansion
delta T = temperature change
L = length in inches

Note that the equation does not include a variable for the cross-sectional area. Every construction material will expand and contract with changes in temperature; regardless of the cross-sectional area.

Thermal Strain

Temperature stresses can cause significant loads for high-rise and long-span structures. In both cases the initial design and construction detailing must allow for these dimensional changes to prevent excessive stresses and strains.