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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 EquationsWhen dissimilar materials are subjected to a uniform temperature change from the same initial temperature, T_{0}, to a final temperature T and T_{2} , 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

$P=\frac{{\alpha}_{1}(T-{T}_{0})-{\alpha}_{2}({T}_{2}-{T}_{0})-({g}_{1}+{g}_{2})/L}{1/{A}_{1}{E}_{1}+1/{A}_{2}{E}_{2}}$
The force P will be compressive in 1 and tensile in 2

For heating of sheet 2 or cooling of sheet 1

Eq. 2

$P=\frac{{\alpha}_{2}({T}_{2}-{T}_{0})-{\alpha}_{1}({T}_{1}-{T}_{0})-({g}_{1}+{g}_{2})/L}{1/{A}_{1}{E}_{1}+1/{A}_{2}{E}_{2}}$
The force P will be compressive in 2 and tensile in 1

Figure 1, Single Bolt

Figure 2, Two or Three Bolts

Where

A_{1} = Section area of plate 1

A_{2} = Section area of plate 2

L = length

g_{1} = gap plate 1

g_{2} = gap plate 2

E = modulus of elasticity

T_{0} = Initial temperature

T_{2} = final temperature plate 1

T = final temperature plate 2

α_{1} = Coefficient of thermal expansion plate 1

α_{2} = Coefficient of thermal expansion plate 2

P = load

- Bell Helicopter Structural Design Manual, 1977

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