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 / c₂

c₂ = (5 b) / 8

I₂ = (19 b³ d) / 480

y² = (6 P x) / (b S_s )

h = (6 P l / b S_s)^1/2

f = ( 8 P / b E ) ( l / h )³

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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