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Partially Restrained Square Plate in Frame Uniformly Heated Stress Calculator and Equations

Heat Transfer Engineering

Partially Restrained Square Plate in Frame, Uniformly Heated Stress Calculator and Equations

Uniformly Heated Rectangular Plate Restrained in the X and Y Directions by a Frame Plate Calculator and Equations for Stress

Preview Partially Restrained Square Plate in Frame, Uniformly Heated Stress Calculator

Eq. 1

${\displaystyle {\mathrm{\sigma <!--\; \sigma \; -->}}_{x1}={\mathrm{\sigma <!--\; \sigma \; -->}}_{y1}=\frac{-<!--\; -\; -->E_1{\mathrm{\alpha <!--\; \alpha \; -->}}_1(T_1-<!--\; -\; -->T_0)}{(1-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->})}}$

Eq. 2

${\displaystyle {\mathrm{\sigma <!--\; \sigma \; -->}}_2=-<!--\; -\; -->A_a/A_2{\mathrm{\sigma <!--\; \sigma \; -->}}_{x1}=-<!--\; -\; -->A_1/A_2\mathrm{\sigma <!--\; \sigma \; -->}{}_{y1}}$

Eq. 3

${\displaystyle K=\frac{1-<!--\; -\; -->\frac{{\mathrm{\alpha <!--\; \alpha \; -->}}_2(T-<!--\; -\; -->T_0)}{{\mathrm{\alpha <!--\; \alpha \; -->}}_1(T_1-<!--\; -\; -->T_0)}}{1+\frac{E_1{A}_1}{(1-<!--\; -\; -->\mathrm{\mu <!--\; \mu \; -->})(E_2{A}_2)}}}$

Eq. 4

A₁ = a t₁

Eq. 5

A₂ = 2 w t₂

Figure 1 - Partially Restrained Square Plate

Figure 2 Restrained Square Plate Section View

Where

E₁ = modulus of elasticity plate 1
E₂ = modulus of elasticity plate 2
α₁ = coefficient of thermal expansion plate 1
α₂ = coefficient of expansion plate 2
T = Reference temperature
T₀ = temperature frame plate
T₁ = temperature center plate
µ = Poisson's ratio
A₁ = surface area plate 1
A₂ = surface area plate 2
K = calculated constant
σ_x1 = stress plate 1
σ_x2 = stress plate 2
a = width and height
w = width of plate frame
t₁ = thickness plate 1
t₂ = thickness plate 2

• Bell Helicopter Structural Design Manual, 1977

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