Related Resources: calculators

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

${\displaystyle P=\frac{-<!--\; -\; -->{\mathrm{\alpha <!--\; \alpha \; -->}}_1{L}_1(T-<!--\; -\; -->T_o{)}_1+{\mathrm{\alpha <!--\; \alpha \; -->}}_2{L}_2(T-<!--\; -\; -->T_o{)}_2}{1/C+L_1/A_1{E}_1}}$

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

Figure 1 Restraint with Spring, Uniform Heat

Where

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
T_o = temperature final

• Bell Helicopter Structural Design Manual, 1977

Related

• Bar Restrained One End and Gap on Other Formula and Calculator
• Restrained Beam Thermal Expansion Force Axial Stress Calculator
• Linear Thermal Expansion Equation and Calculator
• Pipe Expansion Thermal Loop Equations and Calculator
• Fastener Thermal Expansion Equation and Calculator
• Compression Tension Stress Linear Thermal Expansion Equation and Calculator
• Thermal Linear Expansion of AISI 303 Stainless Steel
• Stress Concentration Cylinder feature with Axial Loading Stress concentration on a selected radius of a shaft with axial loading.
• Solid Shaft Equivalent of Hollow Shaft of Same Length Equal Strength Formula and Calculator
• Cylinder Interference Press Fit Design Equations and Calculator
• Torsion Stress Calculator and Equations Torsion is the twisting of an object due to an applied torque . It is expressed in newton meters (N-m) or foot-pound force (ft-lbf).