### Beam Deflection and Stress for Variable Shape Fixed End Single Concentrated Force Applied

**Beam Deflection, Stress, Strain Equations and Calculators**

Area Moment of Inertia Equations & Calculators

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

- Cross Section: Rectangle width b constant and depth y variable.
- Elevation 1) Top straight line and bottom patabola. 2) Complete parabola.
- Plan: rectangle

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** Equations **

S_{s} = I / c_{2}

c_{2} = (5 b) / 8

I_{2} = (19 b^{3} d) / 480

y^{2} = (6 P x) / (b S_{s} )

h = (6 P* l* / b S_{s})^{1/2}

f = ( 8 P / b E ) ( *l* / h )^{3}

Where:

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

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

P = | Force | lbf | (N) |

h = | Deflection | inches | (mm) |

S_{e}= |
Section Modulus | ||

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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