Multi-Span Support
2-Span Continuous Beam Solver
Solve for reactions and internal forces in a two-span continuous member using finite element analysis.
Use meters for geometry, kN for point load, kN/m for UDL, 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
| L | V = 12.38 kN |
| Center | V = 33.25 kN |
| R | V = 6.37 kN |
Calculation Method
Beam model
General form
K d = F
Current model
Supports: L @ 0.00 m, Center @ 4.00 m, R @ 8.00 m. E = 210.0 GPa, I = 8,560 cm^4.
Result
Euler-Bernoulli beam under linearly varying distributed load
Load setup
General form
F = F_point + F_distributed
Current model
P = 12.00 kN @ 2.00 m. w: 5.00 to 5.00 kN/m over 0.00-8.00 m.
Result
Max deflection = 1.02 mm
Internal response
General form
M(x) = E I y''(x), V(x) = dM/dx
Current model
Max |M| = 14.80 kN*m, max |V| = 18.79 kN.
Result
Reactions solved at 3 support locations
Model Assumptions
- The member is continuous over a central support.
- Supports are located at 0, L/2, and L.
- Linear elastic material response is assumed throughout.
Related Tools
- Continuous beams redistribute moments into the supports, allowing for longer spans or smaller sections compared to simple spans.
- A uniform load is applied over the full length of both spans in this configuration.
- Support settlement effects are not included in this basic elastic model.