Cubic Parabola Shape Fixed End Single Concentrated Force Applied Beam Deflection

Beam Deflection, Stress, Strain Equations and Calculators
Area Moment of Inertia Equations & Calculators

Beam Cubic Parabola Shape Deflection Equation Calculator with Variable Shape Fixed End Single Concentrated Force Applied

  • Cross Section: Rectangle: width z variable, depth y constant
  • Elevation: Cubic Parabola
  • Plan: Cubic Parabola

Cubic Parabola Shape Deflection Equation Calculator

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Equations

Cubic Parabola

k (Constant) = z / y

I2 = b3 d / 30

c = b / 2

Ss = I2 / c

Cubic Parabola

b1 = k h

Deflection at A:

f = ( 6 P / b1 E ) ( l / h )3


Where:

E = Modulus of Elasticity psi

(N/mm2)

I = Moment of Inertia in4 (mm4)
P = Force lbf (N)
f = Deflection inches (mm)
Ss= Section Modulus in3 (mm3)
a, b, c, d, x, l = Some distance as indicated inches (mm)

References:

  • Civil Engineering Formulas, Tyler G. Hicks, PE International Engineering Associates

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