If the temperature of a material is increased, there will be expansion in the material (except ice) and if the temperature is decreased, there will be contraction in the material. If these expansion and contraction occur freely there will be no stress in the material and if these expansion or contraction is prevented then stress will be setup in the material which is known as temperature of thermal stress.
δl = l0αΔt
where δl is change in length; l0 is original length; α is coefficient of linear expansion; and Δt is change in temperature.
Thermal stress = EαΔt
Example 12.11: A composite bar consisting of aluminium and steel components as shown in Figure 12.19 is connected to two grips at the ends at a temperature of 100°C. Find the stress in the two rods when the temperature falls to 60°C (i) if ends do not yields, and (ii) if ends yield by 0.5 mm. Assume Esteel = 2 × 105 MPa, EAl = 0.7 × 105 MPa, αsteel = 1.17 × 10−5 per degree centigrade, αAl = 2.34 × 10−5 per degree centigrade. Cross-sectional areas of aluminium and steel bars are 400 and 250 mm2, respectively.
Figure 12.19 Compositer Bars with Fixed Ends
Solution:
There is contraction in the bars due to decrease in temperature.
If contraction is free change in length,
When contraction is prevented tensile stress are produced in the rod.
Loads in two rods will be same.
Case I: When ends do not yield.
Total contraction = Contraction in aluminium + Contraction in steel
Case II: When the ends yield by 0.5 mm.
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