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Builders use hollow rectangular beams in construction because such beams can withstand the forces of shearing and bending in both the x- and y-directions. They are also resistant to torsional forces, much more so than I-beams. This online Mechanical Engineering Calculator is to compute the deflection of hollow rectangular beams. The bending stress is also calculated.

Hollow Rectangular Beams Deflection Calculation

Table of Contents:

**Formula**

**MI for hollow rectangle beams = (Width * Height ^{3}) - (Inside_width * Inside_height^{3}) / 12**

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

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

**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 deflection of hollow rectangle and its bending stress.

Length (Inches) = 5

Width (Inches) = 10

Height (Inches) = 15

Wall Thickness (Inches) = 5

Force (Pounds) = 10

Material = Steel

__Solution__:

**Apply formula**:

MI for hollow rectangle beams = (Width * Height^{3}) - (Inside_width * Inside_height^{3}) / 12

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

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

**Deflection = 4.938271604938271e-9 (Inches)**

**Bending Stress = 0.13333333333333333 (PSI)**