Solid Round Beams Deflection Calculation

This Online Mechanical calculator is helpful in knowing the deflection of a solid round beams. The deflection of a spring beam depends on its length, its cross-sectional shape, the material, where the deflecting force is applied, and how the beam is supported.
The equations given here are for homogenous, linearly elastic materials, and where the rotations of a beam are small.

Table of Contents:

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Formula

MI for Solid Round = (PI * Diameter⁴) / 64
Deflection = (Length³ * Force) / (3 * E * MI)
Bending Stress = (Force * Length) / (MI / (0.5 * Height))

Where,
MI = Moment of Inertia
E = Modulas of Elasticity in psi

It assumes the beam is supported on one end and the force is applied to the other end.

Example:
Length (Inches) = 15
Diameter (Inches) = 5
Force (Pounds) = 20
Material = Steel

Solution:
Apply Formula:
MI for Solid Round = (PI * Diameter⁴) / 64
Deflection = (Length³ * Force) / (3 * E * MI)
Bending Stress = (Force * Length) / (MI / (0.5 * Height))
Deflection = 0.0000244461 (Inches)
Bending Stress = 24.446199258915122 (PSI)