How to Read a Bending Moment Diagram
Learn how support conditions and load placement affect bending moment shape, maximum values, and where beam reinforcement or section capacity is most critical.
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Advanced Structural Beam Calculator 2026
Beam Calculator – Bending Moment, Shear Force & Deflection
Estimate maximum bending moment, shear force, and elastic deflection for common beam cases in seconds. This beam calculator is built for early-stage structural checks, construction planning, steel beam comparisons, timber beam review, and reinforced concrete member concept design.
Select the beam support condition, choose the loading type, enter span, load, elastic modulus, and moment of inertia, then receive a clean engineering-style result summary with units and interpretation notes.
Simply supported and cantilever beam options.
Point load and uniformly distributed load calculations.
Outputs bending moment, shear force, deflection, and span ratio.
Responsive layout for mobile, tablet, and desktop.
What this beam calculator covers
Use it for quick load-response checks before detailed structural design.
- Maximum bending moment in kN·m for common beam cases.
- Maximum shear force in kN for support and load planning.
- Elastic deflection in mm using E and I values.
- Useful for steel, timber, concrete, and composite beam studies.
- Preliminary estimates only; final design requires code verification.
4
Beam Cases
Simply supported and cantilever beams with point or distributed loading.
3
Key Outputs
Bending moment, shear force, and maximum elastic deflection.
2026
Engineering Ready
Designed for modern construction estimating and preliminary structural planning.
100%
Mobile Friendly
Large input fields, clear result cards, and smooth scrolling on all devices.
Beam Calculator for Bending Moment, Shear Force & Deflection
Choose your beam type and load condition, then enter the span, load, Young's modulus, and second moment of area. The calculator uses standard elastic beam equations for preliminary analysis.
Selected Beam Case-
Maximum Bending Moment0.00 kN·m
Maximum Shear Force0.00 kN
Maximum Deflection0.00 mm
Span / Deflection RatioL / -
Engineering NotePreliminary estimate only
Why Use This Beam Calculator in 2026?
Modern construction projects need fast feasibility checks before detailed modeling. This beam calculator gives engineers, contractors, estimators, and students a quick way to compare member behavior and understand the effect of span, load, stiffness, and support condition.
Bending Moment Calculator for Common Beam Cases
Estimate maximum bending moment for simply supported beams and cantilever beams using point load or uniformly distributed load cases. This helps identify critical flexural demand before choosing a steel section, timber joist, or reinforced concrete member.
Shear Force Calculator for Support Reactions
View maximum shear force values that are useful for preliminary web shear review, stirrup planning, support bearing checks, and connection demand estimates during early project design.
Beam Deflection Calculator With Span Ratio
Calculate elastic deflection in millimeters and convert it into a span-to-deflection ratio. This makes serviceability review easier when comparing member options or assessing whether a beam is too flexible.
Beam Design Inputs That Matter Most
Small changes in span, load, and stiffness can create large changes in deflection and bending demand. Use these input sections carefully to improve estimate accuracy.
Beam Span Length
Span is one of the most influential variables. Moment usually increases with span squared for distributed loads, while deflection can increase with span to the third or fourth power depending on load case.
Point Load or Uniform Load
Point loads may represent equipment, concentrated reactions, or heavy partitions. Uniform loads may represent slab loads, live loads, roofing, flooring, self-weight, or distributed storage loads.
Section Moment of Inertia
The second moment of area controls bending stiffness. A deeper beam generally gives much higher stiffness than a shallow beam with the same material because inertia increases strongly with section depth.
How To Use the Beam Calculator
Follow these steps to calculate bending moment, shear force, and deflection using a consistent unit system.
1
Select Beam Case
Choose simply supported or cantilever behavior and select whether the load is a center point load or uniformly distributed load.
2
Enter Span & Load
Input the beam length in meters and the load value in kN or kN/m depending on the selected load case.
3
Add E and I
Use a material preset or enter a custom elastic modulus, then add the section's moment of inertia in cm⁴.
4
Review Results
Check the maximum moment, maximum shear, deflection, and span ratio before moving to detailed structural design.
Beam Calculator Formulas for Moment, Shear & Deflection
The formulas below are standard closed-form elastic beam equations for common preliminary engineering checks. They assume small deflection, linear elastic behavior, prismatic sections, and idealized supports.
Simply Supported Point Load
For a central point load P: maximum moment M = PL/4, maximum shear V = P/2, and maximum deflection δ = PL³/(48EI).
Simply Supported UDL
For a full-span uniform load w: maximum moment M = wL²/8, maximum shear V = wL/2, and maximum deflection δ = 5wL⁴/(384EI).
Cantilever End Load
For a point load at the free end: fixed-end moment M = PL, maximum shear V = P, and free-end deflection δ = PL³/(3EI).
Cantilever UDL
For a full-length uniform load: fixed-end moment M = wL²/2, maximum shear V = wL, and free-end deflection δ = wL⁴/(8EI).
Beam Calculation Examples
These sample values show how different spans, loads, and support conditions affect bending moment, shear force, and deflection.
| Beam Case | Span | Load | E | I | Max Moment | Max Shear | Max Deflection |
|---|---|---|---|---|---|---|---|
| Simply Supported - Point Load | 6 m | 25 kN | 200 GPa | 8,000 cm⁴ | 37.50 kN·m | 12.50 kN | 7.03 mm |
| Simply Supported - UDL | 5 m | 8 kN/m | 200 GPa | 6,500 cm⁴ | 25.00 kN·m | 20.00 kN | 5.01 mm |
| Cantilever - End Point Load | 3 m | 12 kN | 200 GPa | 9,000 cm⁴ | 36.00 kN·m | 12.00 kN | 6.00 mm |
| Cantilever - UDL | 2.5 m | 5 kN/m | 200 GPa | 7,500 cm⁴ | 15.63 kN·m | 12.50 kN | 1.63 mm |
| Timber Joist - UDL | 4 m | 2.5 kN/m | 11 GPa | 4,200 cm⁴ | 5.00 kN·m | 5.00 kN | 18.05 mm |
| Concrete Beam - Point Load | 7 m | 40 kN | 30 GPa | 120,000 cm⁴ | 70.00 kN·m | 20.00 kN | 7.94 mm |
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Read ArticleCalculate Beam Moment, Shear & Deflection Now
Use this free beam calculator for early design checks, engineering study, construction planning, and quick comparison of support conditions, load cases, and member stiffness.
Beam Calculator FAQ
Common questions about bending moment, shear force, deflection, stiffness inputs, and safe use of beam calculation results.
Bending moment is the internal rotational effect caused by loads acting on a beam. It is commonly measured in kN·m and is used to check whether a beam section has enough flexural capacity.
Shear force is the internal force that tends to slide one part of the beam past another. It is important for web shear design in steel beams and stirrup or link design in reinforced concrete beams.
Deflection affects serviceability, finishes, partitions, drainage, appearance, and user comfort. A beam may have adequate strength but still fail serviceability requirements if it deflects too much.
Use the elastic modulus for your material and grade. Typical preliminary values are around 200 GPa for structural steel, about 70 GPa for aluminium, around 10 to 14 GPa for many timber products, and variable values for concrete depending on strength and aggregate.
The second moment of area, also called moment of inertia of area, describes how a beam section resists bending. Higher I values usually mean a stiffer beam with lower deflection for the same span and load.
No. This calculator is for preliminary estimates and educational use. Final design must include load combinations, material strength checks, code requirements, stability, support detailing, connections, fire performance, durability, and professional engineering review.