Idealized elastic mechanicsEntered comparison
Beam Deflection
Calculator
Evaluate one closed-form, prismatic, linear-elastic load case using verified inputs.
What you enter
Enter E and an optional L/x comparison directly. The worksheet does not choose stiffness, load combinations, creep/cracking treatment, or an acceptance limit.
Who it's for: structural engineers comparing an idealized elastic deflection at construction documents against a user-selected serviceability limit.
Elastic response
mm, N, MPa, mm⁴
Idealized deflection—
Maximum elastic deflection
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Before you rely on this result
Confirm the idealization, units, loads, effective stiffness, span, and entered comparison basis.
How to use this calculator
1
Verify the idealization
Use only one of the four exact boundary/load patterns.
2
Enter effective properties
Supply E and I appropriate to the modeled response; the worksheet provides no material presets.
3
Enter the matching load
Use N/mm for full UDL or N for the modeled point load.
4
Compare cautiously
Any entered L/x ratio is user selected; full serviceability and strength design remains separate.
The formula
SS UDL: 5wL⁴/(384EI). SS midspan point: PL³/(48EI). Cantilever UDL: wL⁴/(8EI). Cantilever tip point: PL³/(3EI).
Worked example
Example
L 5,000 mm, w 10 N/mm, E 200,000 MPa, and I 50,000,000 mm⁴ in the simply supported UDL idealization give about 8.14 mm.
When this estimate will be off
- One idealized elastic prismatic load case only.
- Does not include combinations, continuity, shear deformation, cracking, creep, shrinkage, composite action, vibration, stability, or connection flexibility.
- An entered L/x comparison is not selected or validated by the worksheet.
- A comparison result is not member adequacy or compliance.
Frequently asked questions
A common mistake: One idealized elastic prismatic load case only.
No. It means only that this idealized elastic result is not greater than the entered arithmetic comparison. All other serviceability and strength checks remain.
Sources
- Verified structural-analysis basis — must establish equations, effective properties, loads, and comparison criterion
This free Beam Deflection Calculator is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.