Beam Deflection Calculator
Calculate beam deflection for engineering projects. Input parameters to get precise results using standardized mechanics formulas.
Beam Inputs
Enter positive values for each parameter. Results update after you click Calculate, or use Reset to restore defaults.
Result shown in meters (m)
Deflection is computed for a simply supported beam with a central point load using the Euler-Bernoulli formula. Adjust inputs to observe how material or geometry changes influence stiffness.
How to Use This Calculator
This calculator is designed for engineers and students to compute the downward deflection of a simply supported beam under a single central load. Enter beam length, applied load, Young's Modulus, and the beam's moment of inertia to get the corresponding deflection value.
After you click Calculate, we convert every input into SI units, apply the classic deflection formula, and round the result to two decimal places so you can compare proposals instantly.
Methodology
The deflection of a simply supported beam with a central point load is computed using the Euler-Bernoulli beam theory:
δ = (F × L³) / (48 × E × I)
We convert the user inputs into consistent SI units before executing the formula so the deflection remains accurate across material and size variations.
Data Source & Verification
All assumptions align with the American Institute of Steel Construction (AISC) references for simply supported beams under central point loads. Refer to the citations below for the exact source.
Glossary of Variables
- Beam Length (L): Span measured in meters from support to support.
- Load (F): Concentrated force at midspan in kilonewtons.
- Young's Modulus (E): Material stiffness in gigapascals (GPa).
- Moment of Inertia (I): Section resistance to bending; input in centimeters to the fourth power.
Example Application
For a 5 m steel beam with a 10 kN central load, Young's Modulus of 210 GPa, and a 400 cm4 moment of inertia, the deflection calculator returns approximately 0.03 m (after rounding to two decimal places).
Frequently Asked Questions (FAQ)
What is beam deflection?
Beam deflection is the displacement of the beam under load, usually reported in meters or millimeters.
Why is keeping deflection small important?
Excessive deflection can cause non-structural damage, discomfort, or functional problems in floors, bridges, and mechanical systems.
How do material properties influence deflection?
Higher Young's Modulus values mean stiffer materials, which bend less under the same load.
How does moment of inertia relate to geometry?
Moment of inertia represents how the material distributes around the neutral axis; larger sections or more distributed material reduce deflection.
What can I change to reduce deflection?
Use stiffer materials (higher E), longer sections (increase I), or reduce the applied load to limit bending.