Structural Case
Propped Cantilever Deflection Calculator
Analyze a beam fixed at one end and pinned at the other (propped cantilever) under point or uniform loading.
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
| Left fixity | V = 13.91 kN, M = 14.77 kN*m |
| Right support | V = 7.34 kN |
Calculation Method
Beam model
General form
K d = F
Current model
Supports: Left fixity @ 0.00 m, Right support @ 4.50 m. E = 210.0 GPa, I = 4,500 cm^4.
Result
Euler-Bernoulli beam under linearly varying distributed load
Load setup
General form
F = F_point + F_distributed
Current model
P = 10.00 kN @ 2.25 m. w: 2.50 to 2.50 kN/m over 0.00-4.50 m.
Result
Max deflection = 1.48 mm
Internal response
General form
M(x) = E I y''(x), V(x) = dM/dx
Current model
Max |M| = 14.76 kN*m, max |V| = 13.67 kN.
Result
Reactions solved at 2 support locations
Model Assumptions
- The left support is a full rotation-resistive fixity.
- The right support is a simple vertical pin/roller.
- Elastic member behavior using 1D Finite Element Analysis.
Related Tools
- This is a classic statically indeterminate beam. The reactionary force at the prop reduces the mid-span deflection compared to a pure cantilever.
- Fixed-end moment is calculated precisely using the stiffness matrix method.
- Verify the actual rotational stiffness of the 'fixed' end in reality, as partial fixity is common.