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### Long Rectangular Membrane Design Calculator and Equations

Flat Plates Stress, Deflection Design Equations and Calculators

Long Rectangular Membrane Stress and Deflection Design Calculator and Equations

Figure 1 shows a long rectangular membrane (a / b > 5 ) clamped along the two long sides.

Preview: Long Rectangular Membrane Stress and Deflection Design Calculator

The maximum deflection of this membrane is at the center and is given by

Eq. 1

$f}_{max}={\left[\frac{{p}^{2}E{b}^{2}}{24(1-{\mu}^{2}){t}^{2}}\right]}^{1/3$Eq. 2

$\delta =\frac{b}{8}{\left[\frac{24(1-{\mu}^{2})pb}{Et}\right]}^{1/3}$

Figure 1, Long Rectangular Membrane Clamped on Two Sides

A long rectangular plate may be considered to be a membrane if P / E (b / t )^{4}

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

- Bell Helicopter Structural Design Manual, 1977

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