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Bar Restrained With Spring Uniform Heat Applied Calculator

Heat Transfer Engineering

Bar Restrained With Spring and Uniform Heat Applied Calculator and Equations

A bar rigidly mounted with uniform heat applied will expand and exert force and axial stress onto itself and adjoining surfaces.

When a structural element is subjected to a change in temperature, it will either expand or contract depending on whether the temperature change is an increases or decrease. I the element is restrained, the attempt ar expansion or contraction will induce stresses into the structure.

The formula for determining if and how much axial force is applied onto the bar and spring by the thermal expansion is:

Eq. 1

P = α 1 L 1 ( T T o ) 1 + α 2 L 2 ( T T o ) 2 1 / C + L 1 / A 1 E 1

C = spring rate for L2 at its final temperature T. This spring may be real or represent another structure.

Restraint with Spring, Uniform Heat
Figure 1 Restraint with Spring, Uniform Heat


A = area of contact
L1 = length rigid bar
L2 = length spring
P = load
E1 = modulus of elasticity
E2 = modulus of elasticity spring
α1 = coefficient of thermal expansion bar
α2 = coefficient of thermal expansion spring
T = temperature initial
To = temperature final

  • Bell Helicopter Structural Design Manual, 1977