2. Temperature changes occur:
High speed travelling objects, parts & vehicles.
Heat engines and rocket engines.
Boilers, furnace etc.
Effect of temperature change :
Mechanical expansion & significance
Changes in material properties.
Expansion due to heat: Analogy:
Strains induced internally.
Hence stress induced .
3. Thermal stress effects:
Block of material
subjected to an increase
in temperature
B’
Changes in temperature produce expansion or contraction of
materials and result in thermal strains and thermal stresses
Thermal strain εT is proportional to the temperature change ΔT :
εT = α (ΔT) (Where α is coefficient of
thermal expansion)
Sign convention for thermal strains : Expansion is positive and
contraction is negative
4. Relation between stress (Ϭ) and
change in temperature (ϪT).
• Suppose we have a bar subjected to an axial load.
ε = σ / E
• Also, we have an identical bar subjected to a temperature change ΔT.
εT = α (ΔT)
• Equating the above two strains we will get:
σ = E α (ΔT)
Increase in length of a prismatic
bar due to a uniform increase in
temperature
1
2
3
5. Thermo-elastic stress &
strain relations:
Fig:A Fig:B
Uniform rise in temperature
(unconstrained)
Hence uniform change in
dimension.
Non-uniform change in
temperature and
hence uneven stress
development
T=T(t, x, y, z)
6. Total strain = normal strain (αT) + strain due
to stress components
€x = бx –ν (бy + бz) + Δ α T
E
€y = бy –ν (бx + бz) + Δ α T
E
€z = бz –ν (бx + бy) + Δ α T
E
} Total strains at each
point
8. General results
When the temperature distribution is known, the problem
of thermoelsticity is used to determining 15 functions :
6 stress components
6 strain components
3 displacement components
So as to satisfy 15 equations :
3 equilibrium equations
6 stress- strain relations
6 strain – displacement relations
Displacement boundary conditions (linear distribution):
T(x, y, z, t) = a(t) + b(t)x + c(t)y d(t)z
