Related Resources: calculators

Flat spring cantilevered design triangular geometry 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 triangular geometry equations and calculator.

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Deflection:

eq. 1
F = 6 P L³ / E b t³

eq. 2
F = S_b L² / E t

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Load:

eq. 3
P = S_b b t² / 6 L

eq. 4
P = E b t³ F / 6 L³

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Stress, Bending:

eq. 5
S_b = 6 P L / b t²

eq. 6
S_b = E t F / L²

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Thickness, Spring:

eq. 7
t = S_b L² / E F

eq.8

t = ( 6 P L³ / ( E b F ) )^(1/3)

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Where:

P = Load, (lbs),
L = Active length subject to deflection (inches),
b = Widest width of spring (in),
E = Modulus of Elasticity in Tension, (lbs/in²),
t = Thickness, (in),
S_b = Stress, bending (lbs/in²),
F - Deflection, for on active section (in)

Reference:

Machinery Handbook, 27th edition