Structural Cluster
3-Span Continuous Beam Solver
Solve for internal forces and deflections in a three-span member, typical for large building frames and bridge spans.
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 = 18.80 kN |
| S2 | V = 46.08 kN |
| S3 | V = 32.95 kN |
| R | V = 13.17 kN |
Calculation Method
Beam model
General form
K d = F
Current model
Supports: L @ 0.00 m, S2 @ 4.00 m, S3 @ 8.00 m, R @ 12.00 m. E = 210.0 GPa, I = 12,400 cm^4.
Result
Euler-Bernoulli beam under linearly varying distributed load
Load setup
General form
F = F_point + F_distributed
Current model
P = 15.00 kN @ 2.00 m. w: 8.00 to 8.00 kN/m over 0.00-12.00 m.
Result
Max deflection = 1.08 mm
Internal response
General form
M(x) = E I y''(x), V(x) = dM/dx
Current model
Max |M| = 21.77 kN*m, max |V| = 26.20 kN.
Result
Reactions solved at 4 support locations
Model Assumptions
- The member is continuous over three supports internally (total 4).
- Supports are equally spaced at 0, L/3, 2L/3, and L.
- Global stiffness matrix approach for hyperstatic systems.
Related Tools
- Triple span members significantly reduce peak deflection compared to simple spans via moment redistribution.
- The central span often experiences a 'lift' effect if external spans are heavily loaded, or vice versa.
- Ideal for roof purlins and floor joist systems with intermediate supports.