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### Short Rectangular Membrane Stress and Deflection Calculator

Flat Plates Stress, Deflection Design Equations and Calculators

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.

Preview: Short Rectangular Membrane Stress and Deflection Design Calculator

The deflection at the center of this membrane given by

Eq. 1

$\delta ={n}_{1}a\sqrt[3]{\frac{pa}{Et}}$where n_{1} 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 n_{2} through n_{7} 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

f_{max} = calculated stress

E = modulus of elasticity

a = length

b = width

t = thickness of membrane

δ = deflection

µ = poisson's ratio

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- Bell Helicopter Structural Design Manual, 1977

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