Enter the load, length, modulus of elasticity, and moment of inertia into the calculator to determine the deflection of the beam. This calculator can also evaluate any of the variables given the others are known.
Steel Deflection Formula
The following formula is used to calculate the deflection of a steel beam.
δ = (5 * W * L^4) / (384 * E * I)
Variables:
- δ is the deflection of the beam (inches)
- W is the load on the beam (pounds)
- L is the length of the beam (inches)
- E is the modulus of elasticity of the steel (psi)
- I is the moment of inertia of the beam’s cross section (in^4)
To calculate the deflection of a steel beam, multiply the load on the beam by the fourth power of the length of the beam, then multiply the result by 5. Divide this result by the product of 384, the modulus of elasticity of the steel, and the moment of inertia of the beam’s cross section.
What is a Steel Deflection?
Steel deflection refers to the degree to which a structural element is displaced under a load. It may occur in beams, columns, or trusses due to forces such as wind, gravity, seismic activity, or even the weight of occupants and furniture. The amount of deflection in a steel structure is a crucial factor in its design as excessive deflection can lead to structural failure or damage to attached materials.
How to Calculate Steel Deflection?
The following steps outline how to calculate the Steel Deflection using the given formula:
- First, gather the values of the variables: W, L, E, and I.
- Next, substitute the values of the variables into the formula: δ = (5 * W * L^4) / (384 * E * I).
- Finally, calculate the Steel Deflection using the formula.
- After inserting the values 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:
W = 500 pounds
L = 60 inches
E = 30,000,000 psi
I = 500 in^4
