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Long Rectangular Membrane Design Calculator and Equations

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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

${\displaystyle f_{max}={\left[\frac{p^{2}E{b}^2}{24(1-<!--\; -\; -->{\mathrm{\mu <!--\; \mu \; -->}}^2)t^2}\right]}^{1/3}}$

Eq. 2

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

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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