Structural Case
Propped Cantilever Rechner
Analysieren Sie einen einseitig eingespannten Рё einseitig gestuetzten Balken (Propped Cantilever) unter Punkt- oder Gleichlast.
Use meters for geometry, kN for point load, kN/m for UDL, GPa for E, and cm^4 for I.
Calculation Inputs
Beam Diagram
Berechnungsgrundlage
Assumptions & Limits
- Das Modell bildet nur 2D-Biegeverhalten ohne Torsion ab.
- Lager werden als idealisierte Randbedingungen angesetzt.
- Fuer Bauzustand, Nichtlinearitaet oder Setzungen ist eine weitergehende Modellierung noetig.
Reference Basis
- Dokumentation: Methodik fuer Advanced Beams
- Dokumentation: Engineering Review
- Matrix-Stiffness-Method Referenzen
- Elastische Balkentheorie fuer Plausibilitaetschecks
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
Allgemeine Form
K d = F
Aktuelles Modell
Supports: Left fixity @ 0.00 m, Right support @ 4.50 m. E = 210.0 GPa, I = 4,500 cm^4.
Ergebnis
Euler-Bernoulli beam under linearly varying distributed load
Load setup
Allgemeine Form
F = F_point + F_distributed
Aktuelles Modell
P = 10.00 kN @ 2.25 m. w: 2.50 to 2.50 kN/m over 0.00-4.50 m.
Ergebnis
Max deflection = 1.48 mm
Internal response
Allgemeine Form
M(x) = E I y''(x), V(x) = dM/dx
Aktuelles Modell
Max |M| = 14.76 kN*m, max |V| = 13.67 kN.
Ergebnis
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.