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Plate Joints with Dissimilar Materials Loads Calculator and Equations

Fastener, Bolt and Screw Design Torque and Force Calculations

Sheet / Plate Joints with Dissimilar Materials Loads Calculator and Equations

When dissimilar materials are subjected to a uniform temperature change from the same initial temperature, T₀, to a final temperature T and T₂ , the loads induced into the clamped materials are as follows.

Preview Load Effects Due to Temperature Calculator

For heating of sheet 1 or cooling of sheet 2
Eq. 1
${\displaystyle P=\frac{{\mathrm{\alpha <!--\; \alpha \; -->}}_1(T-<!--\; -\; -->T_0)-<!--\; -\; -->{\mathrm{\alpha <!--\; \alpha \; -->}}_2(T_2-<!--\; -\; -->T_0)-<!--\; -\; -->(g_1+g_2)/L}{1/A_1{E}_1+1/A_2{E}_2}}$ The force P will be compressive in 1 and tensile in 2

For heating of sheet 2 or cooling of sheet 1

Eq. 2
${\displaystyle P=\frac{{\mathrm{\alpha <!--\; \alpha \; -->}}_2(T_2-<!--\; -\; -->T_0)-<!--\; -\; -->{\mathrm{\alpha <!--\; \alpha \; -->}}_1(T_1-<!--\; -\; -->T_0)-<!--\; -\; -->(g_1+g_2)/L}{1/A_1{E}_1+1/A_2{E}_2}}$ The force P will be compressive in 2 and tensile in 1

Figure 1, Single Bolt

Figure 2, Two or Three Bolts

Where

A₁ = Section area of plate 1
A₂ = Section area of plate 2
L = length
g₁ = gap plate 1
g₂ = gap plate 2
E = modulus of elasticity
T₀ = Initial temperature
T₂ = final temperature plate 1
T = final temperature plate 2
α₁ = Coefficient of thermal expansion plate 1
α₂ = Coefficient of thermal expansion plate 2
P = load

• Bell Helicopter Structural Design Manual, 1977

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