Beam Deflection Calculator

Make use of our beam deflection calculator to find maximum deflection of the beam (simple-supported or cantilever) after a certain load is carried on it. Calculates the effect of beam bending depending upon the magnitude and location of the object placed on it.

How To Calculate Beam Deflection?

Following beam deflection formulas will help you out in determining the respective beam deflections for certain loads it carries:

Simply-Supported Beam:

Midspan Load:

\(𝛿_{max}=\dfrac{PL^{3}}{48EI}\)

Load at Any Point:

\(𝛿_{max}=\dfrac{Pb\left(3L^{2}-4b^{2}\right)}{48EI}\)

Uniform Load:

\(𝛿_{max}=\dfrac{5wL^{4}}{384EI}\)

Uniformly Varying Load:

\(𝛿_{max}=\dfrac{0.00652wL^{4}}{EI}\)

Triangular Load:

\(𝛿_{max}=\dfrac{wL^{4}}{120EI}\)

Moment Load at Some Support:

\(𝛿_{max}=\dfrac{ML^{2}}{9\sqrt{3}EI}\)

Cantilever Beam:

For these specific types of beam, our steel i beam deflection calculator different equations that are as follows:

End Load:

\(𝛿_{max}=\dfrac{PL^{3}}{3EI}\)

Load at Any Point:

\(𝛿_{max}=\dfrac{Pa^{2}\left(3L-a\right)}{6EI}\)

Uniform Load:

Uniformly Varying Load (Case 1):

\(𝛿_{max}=\dfrac{wL^{4}}{30EI}\)

Uniformly Varying Load (Case 2):

\(𝛿_{max}=\dfrac{11wL^{4}}{120EI}\)

Moment Load at End:

\(𝛿_{max}=\dfrac{ML^{2}}{2EI})

How to Use This Beam Deflection Calculator?

To use this beam deflection calculator, follow the below-mentioned steps:

• Select the “Beam Type” and “Load Type.”
• Enter the length of the span and the point load.
• Input the modulus of elasticity and moment of inertia.
• Hit the “calculate” button.

References:

From the source of Wikipedia: Deflection (engineering), Beam deflection for various loads and supports, Units
From the source of Lumen Learning: Stress, Strain, and Elastic Modulus, Tensile or Compressive Stress, Bulk Stress