Advanced Load Case
Fixed-Fixed Beam Point Load Deflection Calculator
Estimate reactions, end moments, deflection, shear, and bending response for a fixed-fixed beam under a point load.
Use meters for geometry, kN for point load, 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
Validation Examples
These check cases show how key pages compare against known elastic beam benchmarks or symmetric reference cases.
Fixed-fixed midspan point-load benchmark
Case setup
L = 5.0 m, P = 12.0 kN at mid-span, E = 210 GPa, I = 6200 cm^4
Validated metric
Maximum deflection
Reference
Reference result: 0.60 mm
Calculator
Calculator result: 0.60 mm
Check
Difference: 0.00%
Benchmark: classical fixed-fixed point-load formula delta_max = P L^3 / (192 E I)
Shear Force Diagram
Bending Moment Diagram
Response Summary
| Left fixity | V = 6.00 kN, M = 7.50 kN*m |
| Right fixity | V = 6.00 kN, M = -7.50 kN*m |
Calculation Method
Beam model
General form
K d = F
Current model
Supports: Left fixity @ 0.00 m, Right fixity @ 5.00 m. E = 210.0 GPa, I = 6,200 cm^4.
Result
Euler-Bernoulli beam with fixed end restraints
Load setup
General form
F = F_point + F_distributed
Current model
P = 12.00 kN @ 2.50 m. No distributed load.
Result
Max deflection = 0.60 mm
Internal response
General form
M(x) = E I y''(x), V(x) = dM/dx
Current model
Max |M| = 7.50 kN*m, max |V| = 6.00 kN.
Result
Reactions solved at 2 support locations
Model Assumptions
- Both beam ends are fully fixed in rotation and vertical displacement.
- The point load acts vertically at the selected coordinate.
- The model assumes constant E and I along the member.
Related Tools
- This page addresses fixed-fixed beam behavior directly instead of approximating it with a simply supported beam and correction factors.
- Because the support restraints are explicit, the solver also returns fixed-end reaction moments rather than only vertical reactions.
- Real end fixity may be lower than ideal full fixity, so connection flexibility should still be judged separately.