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### Short Rectangular Membrane Stress and Deflection Calculator

Short Rectangular Membrane Stress and Deflection Design Calculator and Equations

Figure 1 shows a short rectangular membrane (a / b < 5 ) clamped on four sides under a uniform pressure p.

The deflection at the center of this membrane given by

Eq. 1

$\delta ={n}_{1}a\sqrt[3]{\frac{pa}{Et}}$

where n1 is given in figure 1

The stress at various locations on short rectangular membranes are given by following equations for which the values of the coefficients n2 through n7 are given in figure 2.

Center of plate ( c = b / 2, y = a / 2 )

Eq. 2
${f}_{x}={n}_{2}\sqrt[3]{{p}^{2}E{\left(\frac{a}{t}\right)}^{2}}$

Eq. 3
${f}_{y}={n}_{3}\sqrt[3]{{p}^{2}E{\left(\frac{a}{t}\right)}^{2}}$

Center of short side (x = b / 2, y = 0

Eq. 4
${f}_{x}={n}_{4}\sqrt[3]{{p}^{2}E{\left(\frac{a}{t}\right)}^{2}}$

Eq. 5
${f}_{y}={n}_{5}\sqrt[3]{{p}^{2}E{\left(\frac{a}{t}\right)}^{2}}$

Center of long side ( x = 0, y = a / 2 )

Eq. 6
${f}_{x}={n}_{6}\sqrt[3]{{p}^{2}E{\left(\frac{a}{t}\right)}^{2}}$

Eq. 7
${f}_{y}={n}_{7}\sqrt[3]{{p}^{2}E{\left(\frac{a}{t}\right)}^{2}}$

It should be noted that the maximum membrane stress at the center of the long side of the plate

Figure 1, Short Rectangular Membrane Clamped on Four Sides

Where

p = pressure
fmax = calculated stress
E = modulus of elasticity
a = length
b = width
t = thickness of membrane
δ = deflection
µ = poisson's ratio

Figure 2 Coefficients for Equations 1 - 7
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• Bell Helicopter Structural Design Manual, 1977

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