Simply supported beam deflection, center load
Enter the span, the load, the elastic modulus and the section moment of inertia to get the midspan deflection and peak moment. Good for a quick check of a beam.
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How to use it
- Enter span length, point load, elastic modulus and section moment of inertia.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Maximum deflection δ = P L³ ÷ (48 E I) at midspan. Maximum moment M = P L ÷ 4. Each support reaction = P ÷ 2.
Example
Inputs: Span length = 4 m, Point load = 10 kN, Elastic modulus = 200 GPa, Section moment of inertia = 2,000 cm⁴. Result: Maximum deflection: 3.333 mm; Maximum bending moment: 10 kN·m; Reaction at each support: 5 kN.
Limits and caveats
- Assumes linear elastic material, small deflection and a load exactly at midspan.
- Does not include the beam self-weight and does not check strength or code limits.
Questions about this tool
What elastic modulus should I use for steel?
Structural steel is about 200 to 210 GPa; aluminium is about 70 GPa.
Where do I get the moment of inertia?
From the steel section tables of the maker, or compute it for simple shapes with the section moment of inertia calculator.
What deflection is allowed?
Many codes use limits such as L/360 for floors under live load. Check the code that applies to your project.