### Deflection Calculator 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

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** Equations **

k (Constant) = z / y

I_{2} = b^{3} d / 30

c = b / 2

S_{s} = I_{2} / c

b_{1} = k h

Deflection at A:

f = ( 6 P / b_{1} E ) ( *l* / h )^{3}

Where:

E = | Modulus of Elasticity | psi |
(N/mm |

I = | Moment of Inertia | in^{4} |
(mm^{4}) |

P = | Force | lbf | (N) |

f = | Deflection | inches | (mm) |

S_{s}= |
Section Modulus | in^{3} |
(mm^{3}) |

a, b, c, d, x, l = |
Some distance as indicated | inches | (mm) |

References:

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