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

Ss = I / c2

c2 = (5 b) / 8

I2 = (19 b3 d) / 480

y2 = (6 P x) / (b Ss )

h = (6 P l / b Ss)1/2

f = ( 8 P / b E ) ( l / h )3

Where:

E = Modulus of Elasticity psi

(N/mm2)
I = Moment of Inertia in4 (mm4)
P = Force lbf (N)
h = Deflection inches (mm)
Se= 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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