# Hollow Rectangular Beams Deflection Calculation 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
 Length (Inches): Width (Inches) : Height (Inches) : Wall Thickness (Inches) Force (Pounds) : Material : --Select-- Steel Titanium Brass Aluminum Carbon Fibre Garolite Polycarbonate Nylon UHMW Wood Deflection : Inches Bending Stress : PSI
Formula
MI for hollow rectangle beams = (Width * Height3) - (Inside_width * Inside_height3) / 12
Deflection = (Length3 *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 * Height3) - (Inside_width * Inside_height3) / 12
Deflection = (Length3 *Force / (3 * E * MI)
Bending Stress = (Force * Length) / (MI / (0.5 * hHeight)
Deflection = 4.938271604938271e-9 (Inches)
Bending Stress = 0.13333333333333333 (PSI)

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