# THERMAL STRESS IN A BAR

Thermal Stress Calculator has been developed to calculate stress of a restrained bar when the temperature of the bar is uniformly changed.

If the temperature of a bar , which is placed between two fixed supports, is increased by ∆T, the bar cannot expand due to restraints imposed on its ends. The supports exert equal and opposite forces on the bar to keep it from elongating. Thus, a state of stress is created in the bar. This thermal stress is proportional to the temperature change ∆T, coefficient of thermal expansion (α) and elastic modulus (E) of bar material and thermal stress formula is given in the "List of Equations" section.

### Thermal Stress Calculator: INPUT PARAMETERS Parameter Value Elastic Modulus [E] GPa ksi Linear Expansion Coefficient [α] m/m°C in/in°F Initial Temperature [t0] °C °F Final Temperature [t1]

 RESULTS Parameter Value Thermal Stress [σT] --- MPa psi ksi Temperature Change [∆T] --- ---

Note: Use dot "." as decimal separator.

Note: Negative stresses are compression stresses.

### Supplements:

 Link Usage Material Properties Thermal expansion coefficient and elastic modulus values of steels, aluminum alloys, cast irons, coppers and titaniums. Linear Thermal Expansion Calculator Calculates linear thermal expansion of an unrestrained bar when the temperature of the body is uniformly changed. Thermal Stress in a Unifrom Plate Calculates stress of a restrained unifrom plate when the temperature of the plate is uniformly changed.

### List of Equations:

 Parameter Equation Thermal Stress [σT] σT = -(∆T)αE

### Reference:

• Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill, Chapter 2.10
• Budynas.R , Nisbett.K . (2014) . Shigley's Mechanical Engineering Design . 10th edition.  McGraw-Hill , , Chapter 3.17
• Young.W.C., Budynas.R (2011). Roark's Formulas for Stress and Strain, 8th Edition . McGraw-Hill, Chapter 16