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Five Beam Deflection Calculators (Solid/Hollow, Round,Rectangular,Triangular )

I mostly use these calculators for leaf spring design.

Limitations:

  • Beam length to height ratio should be greater than 10.
  • Deflections greater than 10% of the beam length might be less accurate.
  • If bending stress exceeds materials yield strength results will be invalid.

For reference there is a handy chart at the bottom of this page for yield strength.

Deflection calculator for solid retangular beams
Input Output

Length (inches)

Width (inches)

Height (inches)

Force (pounds)

Deflection (inches)
Bending Stress (psi)
Energy (joules)

This is a Javascript calculator to compute the defection of simple rectangular beams. It assumes the beam is supported on one end and the force is applied to the other end perpendicular to the width. (Like a diving board).

Bending stress is also calculated. If bending stress exceeds the materials yield strength it will be permamently deformed and not return to its original shape.

Enter the length, width and height and then select the material from the drop down menu. Click COMPUTE and read the deflection value in the output panel. I use it to help design small leaf springs. Potential energy in the beam/spring is also computed.

The formula is: Deflection =W*L^ 3/ 3*E*I
Where W is force, L is length, E is Modulas of Elasticity in psi, and I is Second Moment of Inertia.
Moment of inertia is calculated by (width * thickness^3) / 12 .

Bending stress is computed by: (Force*Length) / (I / (0.5*height))

A product of Dales Homemade Robots, Copyright 2007 by Dale A. Heatherington

Deflection calculator for solid triangular beams
Input Output

Length (inches)

Width (inches)

Height (inches)

Force (pounds)

Deflection (inches)
Bending Stress (psi)
Energy (joules)

This is a Javascript calculator to compute the defection of solid triangular beams. It assumes the beam is supported on one end and the force is applied to the other end perpendicular to the width. (Like a triangle shaped diving board with the pointed end over the water).

Bending stress is also calculated. If bending stress exceeds the materials yield strength it will be permamently deformed and not return to its original shape.

Enter the length, width and height and then select the material from the drop down menu. Click COMPUTE and read the deflection value in the output panel. I use it to help design small leaf springs. Potential energy in the beam/spring is also computed.

The formula is: Deflection =6*W*L^3 / E*width*thickness^3
Where W is force, L is length, E is Modulas of Elasticity in psi.

Bending stress is computed by: (6*Force*Length) / (width*thickness^2)

A product of Dales Homemade Robots, Copyright 2012 by Dale A. Heatherington

Deflection calculator for hollow retangular beams
Input Output

Length (inches)

Width (inches)

Height (inches)

Wall thickness (inches)

Force (pounds)

Deflection (inches)
Bending Stress (psi)
Energy (joules)

This is a Javascript calculator to compute the defection of hollow rectangular beams. It assumes the beam is supported on one end and the force is applied to the other end perpendicular to the width. (Like a diving board)

Bending stress is also calculated. If bending stress exceeds the materials yield strength it will be permamently deformed and not return to its original shape.

Enter the length, width, height and wall thickness and then select the material from the drop down menu. Click COMPUTE and read the deflection value in the output panel.

The formula is: Deflection =W*L^ 3/ 3*E*I
Where W is force, L is length, E is Modulas of Elasticity in psi, and I is Second Moment of Inertia.
Moment of inertia is calculated by ((width * height^3) - (inside_width * inside_height^3)) / 12 .

Bending stress is computed by: (Force*Length) / (I / (0.5*height))

A product of Dales Homemade Robots, Copyright 2007 by Dale A. Heatherington

Deflection calculator for solid round beams
Input Output

Length (inches)

Diameter (inches)

Force (pounds)

Deflection (inches)
Bending Stress (psi)
Energy (joules)

This is a Javascript calculator to compute the defection of simple round beams. It assumes the beam is supported on one end and the force is applied to the other end.

Bending stress is also calculated. If bending stress exceeds the materials yield strength it will be permamently deformed and not return to its original shape.

Enter the length and diameter then select the material from the drop down menu. Click COMPUTE and read the deflection value in the output panel.

The formula is: Deflection =W*L^ 3/ 3*E*I
Where W is force, L is length, E is Modulas of Elasticity in psi, and I is Second Moment of Inertia.
Moment of inertia is calculated by (pi * D^4) / 64 .

Bending stress is computed by: (Force*Length) / (I / (0.5*diameter))

A product of Dales Homemade Robots, Copyright 2007 by Dale A. Heatherington

Deflection calculator for round tube beams
Input Output

Length (inches)

Diameter (inches)

Wall thickness (inches)

Force (pounds)

Deflection (inches)
Bending Stress (psi)
Energy (joules)

This is a Javascript calculator to compute the defection of simple round tubular beams. It assumes the beam is supported on one end and the force is applied to the other end.

Bending stress is also calculated. If bending stress exceeds the materials yield strength it will be permamently deformed and not return to its original shape.

Enter the length, diameter (OD) and wall thickness then select the material from the drop down menu. Click COMPUTE and read the deflection value in the output panel.

The formula is: Deflection =W*L^ 3/ 3*E*I
Where W is force, L is length, E is Modulas of Elasticity in psi, and I is Second Moment of Inertia.
Moment of inertia is calculated by (pi * (OD^4 - ID^4)) / 64 .

Bending stress is computed by: (Force*Length) / (I / (0.5*OD))

A product of Dales Homemade Robots, Copyright 2007 by Dale A. Heatherington

Material Tensile Strength Table
1020 Steel 65,000
1040 Steel 90,000
1080 Steel 140,000
12L14 Steel 60,000
4130 Steel 97,000
4140 Steel Annealed 98,000
4140 Steel Hardened 156,000
Titanium 6AL4V 130,000
303 Stainless Steel 90,000
5052-H32 Aluminum 33,000
6061-T6 Aluminum 45,000
2024-T361 Aluminum 72,000
7075-T6 Aluminum 76,000
Yellow Brass 71,000
Polycarbonate 10,500
Delrin 10,000
Nylon 11,500
PVC 7000
UHMW 4000

Disclaimer:The information and programs on this site are provided "as-is," without any express or implied warranty. In no event shall Dale A. Heatherington be held liable for any damages arising from the use of information or programs on this website.

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