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# Beam Deflection Calculator

Select the term you want to calculate, enter the values of required input fields, and click calculate button using beam deflection calculator

Table of Contents:

## Beam Deflection Calculator

This Online beam deflection 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.

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

## Formula

**MI for Solid Round = (PI * Diameter ^{4}) / 64 Deflection = (Length^{3} * Force) / (3 * E * MI) Bending Stress = (Force * Length) / (MI / (0.5 * Height))**

**Where,**

MI = Moment of Inertia

E = Modulas of Elasticity in psi

## How to calculate the deflection of a solid round beam?

**Example**

Length (Inches) = 15

Diameter (Inches) = 5

Force (Pounds) = 20

Material = Steel

**Solution:**

**Apply Formula**:

MI for Solid Round = (PI * Diameter^{4}) / 64

Deflection = (Length^{3} * Force) / (3 * E * MI)

Bending Stress = (Force * Length) / (MI / (0.5 * Height))

**Deflection = 0.0000244461 (Inches)**

**Bending Stress = 24.446199258915122 (PSI)**