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Learning Goal:
To solve for thermal stresses in statically indeterminate bars subject to a temperature change.
Most materials change in size when subjected to a temperature change. For a temperature change of a homogenous isotropic material, the change in length of a bar of length I due to a temperature change AT can be calculated as d = aATL, where a is the linear coefficient of thermal expansion-a property of the material the bar is. made from.
For a member that is not constrained, this expansion can occur freely. However, if the member is statically indeterminate, the deflection is constrained. Thus, changes in temperature will induce internal thermal stresses. The compatibility condition is that the changes in length due to the temperature change and to the induced stress must cancel each other out, &T + 8 = 0, where
NL
with N being the induced internal AE
SF
=
normal force, positive for tension.
Figure
A
< 1 of 2
B
>
Part A Calculate thermal stress
The round bar shown (Figure 1) has a diameter of 7.4 cm and a length of 8 m. The modulus of elasticity is E= 130 GPa and the linear coefficient of thermal expansion is 1.6x10-5
K
Transcribed Image Text:<U4 - Ch4 Tutorial
Thermal Stress
Learning Goal:
To solve for thermal stresses in statically
indeterminate bars subject to a temperature
change.
Most materials change in size when subjected to a
temperature change. For a temperature change of a
homogenous isotropic material, the change in
length of a bar of length I due to a temperature
change AT can be calculated as &T=&ATL,
where a is the linear coefficient of thermal
expansion-a property of the material the bar is
made from.
For a member that is not constrained, this
expansion can occur freely. However, if the member
is statically indeterminate, the deflection is
constrained. Thus, changes in temperature will
induce internal thermal stresses. The compatibility
condition is that the changes in length due to the
temperature change and to the induced stress must
cancel each other out, or + 6 = 0, where
NL
dF = AE
normal force, positive for tension.
Figure
with N being the induced internal
< 1 of 2 >
B
Part A - Calculate thermal stress
The round bar shown (Eigure 1) has a diameter of 7.4 cm and a length of 8 m. The modulus of
elasticity is E= 130 GPa and the linear coefficient of thermal expansion is 1.6x10-5
1
K
Express your answer with appropriate units to three significant figures.
▸ View Available Hint(s)
Value
If the bar originally has no internal normal forces and the temperature decreases by AT=22
K, what is the thermal stress developed in the bar?
Submit
▾ Part B - Multiple materials
4
Value
Submit
Units
Express your answer with appropriate units to three significant figures.
View Available Hint(s)
< Return to Assignment
The right half of the bar from Part A is replaced with a material that has a₂ = 4x10-5
but
the same modulus of elasticity (Eigure 2). What is the thermal stress developed for the entire
bar when the temperature decreases by AT-22 K from a temperature where there is no
stress in the bar?
?
Units
< 5 of 5
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