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# Solid Rectangular Beams Deflection Calculation

This online Mechanical Engineering Calculator is to compute the defection of simple solid rectangular beams. It assumes the beam is supported on one end and the force is applied to the other end perpendicular to the width. Bending stress is also calculated.

Table of Contents:

Formula

**MI for solid rectangle = ((Height ^{3}* Width) / 12) 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

If bending stress exceeds the materials yield strength it will be permanently deformed and not return to its original shape.

**Example:**

Calculate the beam deflection of a solid rectangle.

Length (Inches) = 15

Width (Inches) = 10

Height (Inches) = 5

Force (Pounds) = 20

Material = Steel

**Solution:**

**Apply Formula:**

MI for solid rectangle = ((Height^{3}* Width) / 12)

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

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

**Deflection = 0.0000072 (Inches)**

**Bending Stress = 7.19999999999999 (PSI)**