Bending Moment Calculator

Calculate bending moment for simply supported, cantilever, and fixed beams under point loads and UDL. Real-time results with beam diagrams and step-by-step formulas.

📐

Bending Moment Calculator

Select beam type and loading condition, enter dimensions and load values to instantly calculate the maximum bending moment with diagrams and step-by-step formulas.

Max Bending Moment

—

Settings & Actions

Output Unit

Decimal Precision

Beam Configuration

Beam Type

Load Type

Beam Lengthⓘ

Length Unit

Load Magnitude (N)ⓘ

Force Unit

Press Esc to reset

Quick Presets

Beam Diagram

What is a Bending Moment Calculator?

A Bending Moment Calculator is a structural engineering tool that computes the internal bending moment at any cross-section of a beam subjected to external loads. Bending moment is the algebraic sum of moments of all forces acting on one side of a section, and it determines how much a beam will bend under load.

This calculator supports four beam configurations — simply supported, cantilever, fixed (both ends), and overhanging — combined with point loads, uniformly distributed loads (UDL), and multiple point loads. Results are displayed in Nm, kNm, lb-ft, lb-in, and kip-ft simultaneously.

The tool renders real-time bending moment diagrams (BMD) and shear force diagrams (SFD) using SVG, making it easy to visualize beam behavior without specialized software.

How to Use the Bending Moment Calculator

Step-by-Step Guide

1Select the beam type (simply supported, cantilever, fixed, or overhanging)
2Choose the load type — point load, UDL, or multiple point loads
3Enter the beam length and select the length unit
4Enter the load magnitude and select the force unit
5For point loads at any position, use the slider to set the load location
6View the maximum bending moment, reactions, and diagrams instantly

Key Features

✓Real-time calculation as you type
✓4 beam types — simply supported, cantilever, fixed, overhanging
✓4 load types — center point, any position, UDL, multiple loads
✓Interactive load position slider
✓Live bending moment and shear force diagrams (SVG)
✓Multi-unit output — Nm, kNm, lb-ft, lb-in, kip-ft
✓Reaction force display (R_A and R_B)
✓Calculation history with localStorage persistence
✓Export results as TXT file
✓Quick presets for common engineering scenarios

Bending Moment Formulas

Beam Type	Load Type	Formula	Location
Simply Supported	Center Point Load	M = (F × L) / 4	At center
Simply Supported	Point Load at 'a'	M = F·a·b / L	At load point
Simply Supported	UDL (w N/m)	M = (w × L²) / 8	At center
Cantilever	End Point Load	M = F × L	At fixed end
Cantilever	UDL (w N/m)	M = (w × L²) / 2	At fixed end
Fixed (Both Ends)	Center Point Load	M = (F × L) / 8	At supports
Fixed (Both Ends)	UDL (w N/m)	M = (w × L²) / 12	At supports

Example Calculations

Beam	Load	Length	Max Moment
Simply Supported	1000 N (center)	4 m	1000 Nm
Cantilever	500 N (end)	2 m	1000 Nm
Simply Supported	200 N/m (UDL)	6 m	900 Nm
Fixed	2000 N (center)	8 m	2000 Nm
Cantilever	100 N/m (UDL)	3 m	450 Nm
Simply Supported	5 kip (center)	20 ft	25 kip-ft

Real-World Applications

🏗️

Structural Beams

Calculate bending moments in floor beams, roof beams, and bridge girders to ensure structural integrity.

🏢

Building Design

Architects and structural engineers use bending moment calculations to size beams in buildings and frames.

⚙️

Machine Design

Shafts, axles, and machine frames experience bending loads that must be analyzed for safe operation.

🌉

Bridge Engineering

Bridge beams and girders are designed based on maximum bending moments from traffic and dead loads.

🎓

Engineering Education

Bending moment is a core topic in mechanics of materials and structural analysis courses.

🔩

Manufacturing

Press frames, crane booms, and conveyor structures all require bending moment analysis.

Frequently Asked Questions

What is bending moment?

Bending moment at a cross-section of a beam is the algebraic sum of moments of all forces acting on one side of that section. It represents the internal resistance of the beam to bending. The SI unit is Newton-meter (Nm).

What is the difference between bending moment and shear force?

Shear force is the algebraic sum of all transverse forces acting on one side of a section, while bending moment is the sum of moments of those forces. Shear force causes sliding failure; bending moment causes bending failure. The bending moment diagram is the integral of the shear force diagram.

Where does maximum bending moment occur?

For a simply supported beam with a center point load, maximum moment occurs at the center. For a cantilever, it occurs at the fixed support. For UDL on a simply supported beam, it occurs at the midspan. In general, maximum moment occurs where shear force is zero.

What is UDL in beam analysis?

UDL stands for Uniformly Distributed Load — a load spread evenly along the entire length of the beam, measured in N/m or kN/m. Examples include the self-weight of a beam, floor loads, and snow loads on roofs.

How does a fixed beam differ from a simply supported beam?

A simply supported beam has pin and roller supports that allow rotation at both ends. A fixed beam has both ends rigidly connected, preventing rotation. Fixed beams develop end moments (hogging) and have lower maximum bending moments than simply supported beams for the same load.