Beam deflection calculator
Deflection of a simply supported beam under uniform or point load.
Fill in the fields and the result will appear here automatically.
Estimates maximum midspan deflection of a simply supported beam. It supports a uniform load over the full span or one force at midspan, with constant EI, linear elasticity and small displacements. Creep, shear deformation, dynamics and stability are not checked. The load unit changes with the scheme.
How it works
Formula and logic
Uniform load: δ = 5qL⁴/(384EI), with q in kN/m. Midspan force: δ = FL³/(48EI), with F in kN. L is in m, E in GPa and I in cm⁴; EI = 10·E·I in N·m², and deflection is shown in mm. Inputs are positive and finite. Relative deflection is 1/(L/δ); L/250 is a fixed numerical comparison, not a code check.
Example
With E = 10 GPa, I = 1000 cm⁴, L = 3 m and uniform q = 2 kN/m, EI = 100,000 N·m² and deflection is 21.094 mm. L/250 is 12 mm; this compares numbers and does not establish beam suitability.
Fields and units
- Load scheme — list option
- Load — kN/m or kN
- Span — m
- Modulus of elasticity — GPa
- Second moment of area — cm⁴
How to use
- — Choose uniform load in kN/m or a midspan force in kN.
- — Enter span in metres, modulus in GPa and second moment of area in cm⁴.
- — Use properties about the bending axis and add self-weight to distributed load.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- MIT, Roylance: elastic simply supported beam deflection, midspan force and uniform load
- Limitation
- Preliminary calculation of the stated elastic model. It does not replace structural checks for applicable requirements, loads and material properties.
FAQ
Why does deflection grow so sharply with span?
At unchanged q, E and I, uniform-load deflection scales with L⁴: from 3 to 4 m the factor is (4/3)⁴ ≈ 3.16. For an unchanged midspan force it scales with L³. Increasing I can offset this growth; for a rectangle of fixed width, I scales with h³.
What does a deeper section buy?
The second moment of area grows as the cube of the depth: a 50×200 joist is 2.37 times stiffer than a 50×150. That is why beams are set on edge rather than flat — the same section works far harder.
What does 1/250 mean?
The ratio is written as 1/(L/δ): a denominator of 250 means δ = L/250. The separate L/250 row is a fixed comparison in this calculator; the applicable limit depends on the project and structural requirements.
Is the beam's own weight included?
Not automatically. Add self-weight to the uniform load when it belongs in your load case. Density and section area are not inputs here.