Engineering
Beam Deflection Calculator
Estimate elastic midspan deflection and maximum bending moment for a simply supported prismatic beam under a centered point load. The page explains converted modulus and inertia units, serviceability interpretation, stiffness, support assumptions, and the structural checks not covered by the closed-form equation.
Center deflection (mm)-
Maximum bending moment-
Load-to-deflection stiffness-
Span-to-deflection ratio-
Decision view
Simply supported center-load response
Simply supported center-load responseThe entered point load acts at midspan; the elastic deflection curve, maximum moment, and span-to-deflection ratio correspond to this specific load case.
Exact scenario comparisonCenter point load (N) changes while all other entered assumptions remain constant.
| Center point load (N) | Center deflection (mm) | Maximum bending moment | Load-to-deflection stiffness | Span-to-deflection ratio |
|---|
How to use Beam Deflection Calculator
- Confirm that the real beam is reasonably represented by simple supports and one centered point load.
- Enter clear span, elastic modulus, and second moment of area about the correct bending axis.
- Compare deflection and moment with applicable strength, stability, serviceability, vibration, and connection requirements.
Calculator guide
Understanding Beam Deflection Calculator
A simply supported beam with one center point load has a recognizable symmetric deflected shape. The calculator pairs the formula with that shape, support conditions, maximum moment, stiffness, and span-to-deflection ratio.
Calculation method
How the calculation works
Apply the elastic simply-supported center-load formula using converted modulus and section inertia units. For a centered point load, δmax = PL³/(48EI) and Mmax = PL/4. The calculator converts GPa to Pa and cm⁴ to m⁴ before reporting deflection in millimetres.
Model identification
Use this formula only for the matching load case
Support and load placement control both the coefficient and deflected shape.
If any condition changes, select a matching beam formula or perform a more complete analysis.
Worked situations
Practical examples
- A 5 kN center load on a 3 m span with E = 200 GPa and I = 850 cm⁴ gives about 1.654 mm deflection.
- Maximum ideal bending moment is 3.75 kN·m at midspan.
- The corresponding span-to-deflection ratio is approximately 1,814.
Better inputs
Useful tips
- Use the section inertia about the bending axis; strong-axis and weak-axis values can differ greatly.
- Add self-weight and other loads using compatible superposition formulas when linear elastic assumptions remain valid.
- Check actual end restraint: fixed, continuous, cantilever, and semi-rigid beams use different equations.
Before relying on the result
Limitations and common mistakes
- Self-weight, distributed loads, off-center loads, shear deflection, and support settlement are excluded.
- Yielding, local or lateral-torsional buckling, residual stress, creep, cracking, composite action, and fatigue are not checked.
- This preliminary equation does not replace code design, load combinations, connection design, or qualified structural review.
Reference
Key terms
- Elastic modulus
- Material stress-to-strain stiffness within the modeled elastic range.
- Second moment of area
- Geometric property governing bending stiffness about a selected axis.
- Deflection
- Calculated transverse displacement from the unloaded beam line.
- Simple support
- Ideal support condition allowing end rotation without moment restraint.
Important note
Calculated from the entered values using the displayed engineering relationship. Confirm design values, load cases, safety factors, standards, and field conditions with a qualified professional.
Frequently asked questions
Why does span have such a large effect?
The center-load deflection formula contains L cubed, so modest span increases can substantially increase movement.
Is the maximum moment at midspan?
Yes for a simply supported beam with one centered point load.
What is cm4 in the inertia input?
It is centimetres to the fourth power; the calculator converts it to metres to the fourth internally.
Does a high span-to-deflection ratio mean the beam is safe?
It indicates smaller modeled deflection relative to span, but strength, stability, vibration, and code checks remain separate.