Simply Supported Beam Center Deflection Calculator
Calculate simply supported beam center deflection with transparent engineering inputs and the displayed formula.
Run deterministic checks for missing or mixed units, physical bounds, detectable out-of-range values and formula applicability. This is not an engineering approval or a complete code/compliance check.
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PROFENG provides this tool for engineering screening and educational use. Check the calculation basis, units, physical assumptions, applicable standards, safety factors, equipment data and project-specific requirements before design, procurement or operation.
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Why use this simply supported beam center deflection calculator?
Calculate simply supported beam center deflection with transparent engineering inputs and the displayed formula. The displayed relationship is δ = FL³/(48EI).
What this calculation does
This calculator determines maximum deflection from center point load, span, young's modulus, second moment of area. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
Formula and engineering variables
δ = FL³/(48EI)
| Variable | Definition | Unit | Working guidance |
|---|---|---|---|
force | Center point load | N | Illustrative screening band: 0 to about 100,000 N. This is not a design limit. |
length | Span | m | Illustrative screening band: 0 to about 40 m. This is not a design limit. |
modulus | Young's modulus | GPa | Illustrative screening band: 0 to about 2,000 GPa. This is not a design limit. |
inertia | Second moment of area | m⁴ | Illustrative screening band: 0 to about 1 m⁴. This is not a design limit. |
Ranges above are screening guidance or physical bounds where stated. They are not code limits or manufacturer ratings.
Calculated outputs
- Maximum deflection (mm): force*Math.pow(length,3)/(48*modulus*1e9*inertia)*1000
Worked example
- Center point load (force) = 10,000 N
- Span (length) = 4 m
- Young's modulus (modulus) = 200 GPa
- Second moment of area (inertia) = 0.00008 m⁴
(10000)*Math.pow((4),3)/(48*(200)*1e9*(0.00008))*1000 = 0.833 mmMaximum deflection: 0.833 mmAssumptions
- Loads and geometry are represented by the idealized relationship shown.
- Material behavior is treated according to the simple formula, typically linear-elastic where relevant.
- Units and section properties are consistent with the displayed equation.
Limitations
- Stress concentrations, fatigue, dynamics, buckling interaction, tolerances and manufacturing effects may require dedicated analysis.
- Apply appropriate design factors and the governing component or machinery standard before final design.
- Beam is prismatic, linearly elastic and slender enough for the classical small-deflection beam model.
- Load is concentrated at midspan and supports are idealized as simple supports.
- Shear deformation and second-order effects are neglected.
- The displayed default values are a worked example only; replace them with traceable project or measurement data.
Formula source and acknowledgement
Relationship used: δmax = FL^3/(48EI) for a simply supported beam with a concentrated load at midspan.
The relationship used here follows Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, David F. Mazurek, Mechanics of Materials 8th edition (2020), McGraw Hill.
Credit for the underlying method belongs to the cited author(s). PROFENG presents its own implementation and wording and is not affiliated with or endorsed by the authors or publishers.
Limits of use for this relationship
- Beam is prismatic, linearly elastic and slender enough for the classical small-deflection beam model.
- Load is concentrated at midspan and supports are idealized as simple supports.
- Shear deformation and second-order effects are neglected.
Read the PROFENG methodology for formula sourcing and automated checks →
How to use it
Start with the inputs shown above, review the assumptions or options, then generate the result. Where the tool creates a file, keep the original until you have opened and checked the downloaded output.
Frequently asked questions
What does Simply Supported Beam Center Deflection Calculator calculate?
This calculator determines maximum deflection from center point load, span, young's modulus, second moment of area. Use it for first-pass mechanics and machine-design calculations with explicit loads, geometry and material inputs.
What formula does Simply Supported Beam Center Deflection Calculator use?
The calculator uses δ = FL³/(48EI). Every input used by the implementation is listed in the variable table on this page.
How is the worked example for Simply Supported Beam Center Deflection Calculator checked?
PROFENG substitutes the displayed default values into the implemented relationship and compares the result against automated verification cases where an independent verifier is available.
What assumptions matter most for Simply Supported Beam Center Deflection Calculator?
Loads and geometry are represented by the idealized relationship shown. Material behavior is treated according to the simple formula, typically linear-elastic where relevant. Units and section properties are consistent with the displayed equation.
Can I use this result for final design or procurement?
Use it as an engineering screening calculation. Final design, procurement, operation or compliance decisions require project-specific data and the applicable engineering method, standard or manufacturer information.
QA, changelog and corrections
Last QA update: 30 September 2026.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks, independent cross-checks for calculators, and unit round-trip checks for converters where applicable.
Changelog
30 September 2026 – source/indexation status, metadata and correction pathway reviewed. Engineering tools display the automated verification label only when they are inside the passing Part 3 verification scope.