Enter the deflection, length, modulus of elasticity, and moment of inertia into the calculator to determine the load on a cantilever beam. This calculator can also evaluate any of the variables given the others are known.
Cantilever Load Formula
The following formula is used to calculate the load on a cantilever beam.
L = (P * L) / (E * I)
Variables:
- L is the deflection of the beam (m)
- P is the load applied at the end of the beam (N)
- L is the length of the beam (m)
- E is the modulus of elasticity of the beam material (Pa)
- I is the moment of inertia of the beam’s cross-sectional area (m^4)
To calculate the load on a cantilever beam, multiply the load applied at the end of the beam by the length of the beam. Divide this result by the product of the modulus of elasticity of the beam material and the moment of inertia of the beam’s cross-sectional area.
What is a Cantilever Load?
A cantilever load is a force that is applied to a structure, typically a beam or a pole, that extends horizontally and is only supported at one end. This type of load creates a bending effect on the structure, causing it to flex and potentially deform or break if the load is too heavy. The amount of load a cantilever can bear depends on the material’s strength and the length of the overhang.
How to Calculate Cantilever Load?
The following steps outline how to calculate the Cantilever Load using the given formula:
- First, determine the load applied at the end of the beam (P) in Newtons (N).
- Next, determine the length of the beam (L) in meters (m).
- Next, determine the modulus of elasticity of the beam material (E) in Pascals (Pa).
- Next, determine the moment of inertia of the beam’s cross-sectional area (I) in meters to the power of 4 (m^4).
- Finally, calculate the deflection of the beam (L) using the formula: L = (P * L) / (E * I).
- After inserting the values of the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge:
Load applied at the end of the beam (P) = 500 N
Length of the beam (L) = 2 m
Modulus of elasticity of the beam material (E) = 2.1 x 10^11 Pa
Moment of inertia of the beam’s cross-sectional area (I) = 4.5 x 10^-6 m^4
