Thermal Shock
DOE-HDBK-1017/2-93
THERMAL STRESS
In the simple case where two ends of a material are strictly constrained, the thermal stress can
be calculated using Hooke's Law by equating values of
from Equations (3-1), (3-2), and
Dl
l
(3-3).
E
=
=
(3-3)
stress
strain
F/A
Dl
l
or
=
(3-4)
Dl
l
F/A
E
aDT =
(3-5)
F/A
E
F/A =
EaDT
where:
F/A =
thermal stress (psi)
E
=
modulus of elasticity (psi)
a
=
linear thermal expansion coefficient (°F-1)
DT
=
change in temperature (°F)
Example: Given a carbon steel bar constrained at both ends, what is the thermal stress when
heated from 60°F to 540°F?
Solution:
a
=
5.8 x 10-6/°F (from Table 1)
E
=
3.0 x 107 lb/in.2 (from Table 1, Module 2)
DT
=
540°F - 60°F = 480°F
Stress = F/A = EaDT = (3.0 x 107 lb/in.2) x (5.8 x 10-6/°F) x 480°F
Thermal stress = 8.4 x 104 lb/in.2 (which is higher than the yield point)
Rev. 0
Page 3
MS-03
