Simply supported beam deflection, uniform load
A uniform load is the usual case for roofs and floors. Enter the load per metre with the span and section properties.
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How to use it
- Enter span length, uniform 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 = 5 w L⁴ ÷ (384 E I) at midspan. Maximum moment M = w L² ÷ 8. Each support reaction = w L ÷ 2.
Example
Inputs: Span length = 6 m, Uniform load = 5 kN/m, Elastic modulus = 200 GPa, Section moment of inertia = 8,000 cm⁴. Result: Maximum deflection: 5.273 mm; Maximum bending moment: 22.5 kN·m; Reaction at each support: 15 kN.
Limits and caveats
- Assumes an even load over the full span and linear elastic material.
- Add the beam self-weight to the uniform load if you want it included.
Questions about this tool
How do I add the beam self-weight?
Convert its mass in kg per metre to kN/m by multiplying by 9.80665 ÷ 1000, then add it to w.
Which deflects more: a uniform or a centre load of the same total?
The centre point load. A uniform load with the same total gives 5/8 of that deflection.
Is kN/m the same as N/mm?
Yes. 1 kN/m equals exactly 1 N/mm.