Thermal Stress Calculator
Calculate the stress induced in a fully restrained member due to a temperature change.
Thermal Stress
192.0 MPa
Thermal Stress vs Elastic Modulus (E)
सूत्र
## Thermal Stress in Restrained Members When a material cannot expand or contract freely, temperature changes produce internal stresses. ### Formula **sigma_thermal = E alpha delta_T** where E is the elastic modulus, alpha is the coefficient of linear thermal expansion, and delta_T is the temperature change. Heating a restrained member produces compression; cooling produces tension.
हल किया गया उदाहरण
A steel rail (E=200 GPa, alpha=12e-6 /deg C) heated by 80 deg C while fully restrained.
- 01Free strain = 12e-6 x 80 = 9.6e-4 = 0.000960
- 02Thermal stress = 200,000 MPa x 0.000960 = 192 MPa
- 03This is 77% of steel yield (250 MPa), highlighting why expansion joints are critical.
अक्सर पूछे जाने वाले प्रश्न
What are typical thermal expansion coefficients?
Steel: 12e-6 /deg C, Aluminium: 23e-6 /deg C, Copper: 17e-6 /deg C, Concrete: 10-12e-6 /deg C, Invar (nickel alloy): 1.2e-6 /deg C. Aluminium expands nearly twice as much as steel.
What if the member is only partially restrained?
If the member can expand partially, the actual stress is reduced proportionally. For a member with partial fixity, sigma = E alpha delta_T x (1 - ratio_of_free_expansion_allowed).
Why do bridges have expansion joints?
Without joints, a 100 m steel bridge heated by 40 deg C would try to expand by about 48 mm. The resulting compressive stress (96 MPa) could buckle the structure. Expansion joints allow free movement.
सीखें