**Related Resources: calculators**

### Tapered Flat spring cantilevered Design equations and calculator

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

Flat spring design equations and calculator: The equations are based on standard beam formulas where the deflection is small.

Flat spring cantilevered design tapered geometry equations and calculator.

Deflection:

eq. 1

F = 5.22 P L^{3} / E b t^{3}

eq. 2

F = 0.87 S_{b} L^{2} / E t

Load:

eq. 3

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

eq. 4

P = E b t^{3} F / ( 5.22 L^{3 })

Stress, Bending:

eq. 5

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

eq. 6

S_{b} = E t F / 0.87 L^{2}

Thickness, Spring:

eq. 7

t = 0.87 S_{b} L^{2} / E F

eq.8

t = ( 5.22 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