Shear Force & Bending Moment Diagram Calculator
Draw shear force and bending moment diagrams for beams under various loading conditions
Calculator
Enter beam parameters and loads to calculate shear forces, bending moments, and generate diagrams.
Shear Force Diagram (SFD)
Bending Moment Diagram (BMD)
About the Shear Force & Bending Moment Diagram Calculator
The Shear Force & Bending Moment Diagram Calculator is a practical tool for engineers, designers, and students to analyze beams under various loading conditions. By entering the beam type, length, point loads, and uniformly distributed loads (UDL), you can calculate shear forces and bending moments along the beam and generate detailed diagrams for structural analysis and design.
What You Can Calculate
- Maximum Shear Force (Vmax): The peak shear force in the beam for the given loading.
- Maximum Bending Moment (Mmax): The maximum bending moment occurring along the beam.
- Shear Force Diagram (SFD): Visual representation of shear forces along the beam.
- Bending Moment Diagram (BMD): Visual representation of bending moments along the beam.
Formulas Used in the Calculator
- Simply Supported Beam with Point Load at Distance a from Left Support:
- Left Reaction: RA = P × (L - a) / L
- Right Reaction: RB = P × a / L
- Shear Force: V(x) = RA (x < a), V(x) = -RB (x ≥ a)
- Bending Moment: M(x) = RA × x (x < a), M(x) = RB × (L - x) (x ≥ a)
- Simply Supported Beam with Uniformly Distributed Load (UDL):
- Vmax = w × L / 2
- Mmax = w × L² / 8
- Cantilever Beam with Point Load at Free End:
- Vmax = P
- Mmax = P × L
- Cantilever Beam with UDL:
- Vmax = w × L
- Mmax = w × L² / 2
How to Use the Calculator
- Select the beam type (simply supported or cantilever).
- Enter the beam length and units (m, cm, mm).
- Provide any point loads and their position from the left support.
- Optionally, add a uniformly distributed load (UDL) along the beam.
- The calculator automatically computes the maximum shear force, maximum bending moment, and generates the corresponding SFD and BMD diagrams.
- Adjust inputs to analyze different loading scenarios and beam configurations.
Applications of Shear Force & Bending Moment Analysis
- Structural Design: Evaluate beam strength under various loads for safe design.
- Bridge and Building Engineering: Analyze support reactions, shear forces, and bending moments in beams and girders.
- Mechanical Components: Assess stresses in shafts, levers, and other beam-like structures.
- Education & Research: Learn shear force and bending moment concepts and verify analytical calculations.
- Design Optimization: Adjust load placements and beam dimensions to ensure safety and efficiency.