Advanced Load Case
Beam Deflection Calculator for 3 Point Loads
Analyze a simply supported beam with three discrete point loads, including reactions, deflection, shear, and moment diagrams.
Use meters for geometry, kN for point loads, GPa for E, and cm^4 for I.
Calculation Inputs
Beam Diagram
Calculation Basis
Assumptions & Limits
- The model represents 2D bending response only and does not include torsion.
- Supports are idealized as analytical boundary conditions.
- Construction stages, nonlinearity, and settlement effects need a more detailed model.
Reference Basis
- Documentation: Advanced beam methodology
- Documentation: Engineering Review
- Matrix stiffness method references
- Elastic beam theory references for validation checks
Shear Force Diagram
Bending Moment Diagram
Response Summary
| Left support | V = 11.00 kN |
| Right support | V = 11.00 kN |
Calculation Method
Beam model
General form
K d = F
Current model
Supports: Left support @ 0.00 m, Right support @ 6.00 m. E = 210.0 GPa, I = 4,500 cm^4.
Result
Linear superposition of three point-load responses
Load setup
General form
F = F_point + F_distributed
Current model
P1 = 6.00 kN @ 1.20 m; P2 = 10.00 kN @ 3.00 m; P3 = 6.00 kN @ 4.80 m. No distributed load.
Result
Max deflection = 8.01 mm
Internal response
General form
M(x) = E I y''(x), V(x) = dM/dx
Current model
Max |M| = 22.20 kN*m, max |V| = 11.00 kN.
Result
Reactions solved at 2 support locations
Model Assumptions
- The beam is simply supported at both ends.
- All three point loads act vertically in the same plane.
- The model is linear elastic and based on Euler-Bernoulli beam theory.
Related Tools
- This page solves the combined response of three point loads on one span rather than forcing the user into repeated single-load calculations.
- The response is assembled through a reusable advanced beam solver, so reactions and internal force diagrams stay coherent even when the three loads are asymmetric.
- If the real beam includes partial fixity, torsion, or large deformation effects, this one-dimensional elastic model should be treated as a preliminary check.