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### Flat spring cantilevered design equations and calculator

**Beam Stress Deflection Equations and Calculators
Spring Design Equations and Calculators **

Flat spring design equations and calculator: This spring is often used to overcome operating space limitations in various products such as electric switches and relays. The equations are based on standard beam formulas where the deflection is small.

Flat spring cantilevered design equations and calculator.

Deflection:

eq. 1

F = 4P L^{3} / E b t^{3}

eq. 2

F = 2 S_{b} L^{2} / 3 E t

Load:

eq. 3

P = S_{b} b t^{2} / 6 L

eq. 4

P = E b t^{3} F / 4 L^{3}

Stress, Bending:

eq. 5

S_{b} = 6 P L / b t^{2}

eq. 6

S_{b} = 3 E t F / 2 L^{2}

Thickness, Spring:

eq. 7

t = 2 S_{b} L^{2} / 3 E F

eq.8

t = ( 4 P L^{3} / ( E b F ) )^{(1/3)}

Where:

P = Load, (lbs),

L = Active length subject to deflection (inches),

b = Widest width of spring (in),

E = Modulus of Elasticity in Tension, (lbs/in^{2}),

t = Thickness, (in),

S_{b} = Stress, bending (lbs/in^{2}),

F - Deflection, for on active section (in)

Reference:

Machinery Handbook, 27th edition

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