Short Notes: Thermal Stresses | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


Thermal Stresses
Thermal stress is created by thermal expansion or contraction. Thermal stress can 
be destructive, such as when expanding gasoline ruptures a tank
Thermal Stress: Temperature changes cause the body to expand or contract. The 
amount 5T, is given by
6 t =aL(Tf —T,)= a L ± T
where a is the coefficient of thermal expansion in m/m°C, L is the length in meter, T; 
and Tf are the initial and final temperatures, respectively in °C.
• The stress caused by internal forces created to resist thermal deformations. If 
temperature deformation is permitted to occur freely, no load or stress will be 
induced in the structure.
• In some cases where temperature deformation is not permitted, an internal 
stress is created. The internal stress created is termed as thermal stress.
For a homogeneous rod mounted between unyielding supports as shown, the 
thermal stress is computed as:
&
Deformation due to temperature changes;
6 t = aLAT
Deformation due to equivalent axial stress
Page 2


Thermal Stresses
Thermal stress is created by thermal expansion or contraction. Thermal stress can 
be destructive, such as when expanding gasoline ruptures a tank
Thermal Stress: Temperature changes cause the body to expand or contract. The 
amount 5T, is given by
6 t =aL(Tf —T,)= a L ± T
where a is the coefficient of thermal expansion in m/m°C, L is the length in meter, T; 
and Tf are the initial and final temperatures, respectively in °C.
• The stress caused by internal forces created to resist thermal deformations. If 
temperature deformation is permitted to occur freely, no load or stress will be 
induced in the structure.
• In some cases where temperature deformation is not permitted, an internal 
stress is created. The internal stress created is termed as thermal stress.
For a homogeneous rod mounted between unyielding supports as shown, the 
thermal stress is computed as:
&
Deformation due to temperature changes;
6 t = aLAT
Deformation due to equivalent axial stress
PL aL
$ 1
AE E
S r ^ i
ctLAT—
< tL
cr= aATE
where a is the thermal stress in MPa, E is the modulus of elasticity of the rod in 
MPa. If the wall yields a distance of x as shown, the following calculations will be 
made:
S T = x+Sr
a lA T = x + — 
E
where a represents the thermal stress.
Temperature Stresses in Taper Bars:-
4PL .
Stress = aLAT = —- — -— 
irdjd; E
Temperature Stresses in Composite Bars:-
St2 = 5,! + dp]
8t i — 8,1 = 8 P i + S P2
At ( a ^ ! - ) = P 1 ^ £
+
u \
A1 E2
p
At ( a 2— a i ) 
1
+
' A ] P ] A,F >
a) origin
Coefficient of Thermal Expansion (a) and Elastic Modulus (E):
Page 3


Thermal Stresses
Thermal stress is created by thermal expansion or contraction. Thermal stress can 
be destructive, such as when expanding gasoline ruptures a tank
Thermal Stress: Temperature changes cause the body to expand or contract. The 
amount 5T, is given by
6 t =aL(Tf —T,)= a L ± T
where a is the coefficient of thermal expansion in m/m°C, L is the length in meter, T; 
and Tf are the initial and final temperatures, respectively in °C.
• The stress caused by internal forces created to resist thermal deformations. If 
temperature deformation is permitted to occur freely, no load or stress will be 
induced in the structure.
• In some cases where temperature deformation is not permitted, an internal 
stress is created. The internal stress created is termed as thermal stress.
For a homogeneous rod mounted between unyielding supports as shown, the 
thermal stress is computed as:
&
Deformation due to temperature changes;
6 t = aLAT
Deformation due to equivalent axial stress
PL aL
$ 1
AE E
S r ^ i
ctLAT—
< tL
cr= aATE
where a is the thermal stress in MPa, E is the modulus of elasticity of the rod in 
MPa. If the wall yields a distance of x as shown, the following calculations will be 
made:
S T = x+Sr
a lA T = x + — 
E
where a represents the thermal stress.
Temperature Stresses in Taper Bars:-
4PL .
Stress = aLAT = —- — -— 
irdjd; E
Temperature Stresses in Composite Bars:-
St2 = 5,! + dp]
8t i — 8,1 = 8 P i + S P2
At ( a ^ ! - ) = P 1 ^ £
+
u \
A1 E2
p
At ( a 2— a i ) 
1
+
' A ] P ] A,F >
a) origin
Coefficient of Thermal Expansion (a) and Elastic Modulus (E):
Material
a (10- 6 m/ m /oC)
E (106 Pa)
Aluminium 24 69
Steel 11.7 200
Concrete 11 20-28
Masonry 7 7-21
Wood 3.5 -4.5 8-15
Glass S O 66
Plastic 122-144 2-2.8
If the temperature rises above the normal, the rod will be in compression, and if the 
temperature drops below the normal, the rod is in tension.
“ steel ~ a concrece ~ 12 X 10 6/-C 
a Alumlnlwn > a Brass ^ a Copper -> “ Steel