Description du projet
Un porte-à-faux est entièrement encastré à l'extrémité gauche et chargé par un moment fléchissant selon le schéma suivant. The problem is described by the following set of parameters. Small deformations are considered and the self-weight is neglected in this example. Determine the maximum deflection uz,max.
Matériau | Elastic-Plastic | Module d’élasticité | E | 210000.000 | MPa |
coefficient de Poisson | ν | 0.000 | |||
Module de cisaillement | G | 105000.000 | MPa | ||
Plastic Strength | fy | 240.000 | MPa | ||
Géométrie | Porte-à-faux | Périmètre | L | 2.000 | m |
Largeur | w | 0.005 | m | ||
Épaisseur | t | 0.005 | m | ||
Load | Moment fléchissant | M | 6.000 | Nm |
Solution analytique
The cantilever is loaded by the bending moment M. The quantities of this load are discussed at first. The moment Me when the first yield occurs and the ultimate moment Mp when the structure becomes plastic hinge are calculated as follows:
The bending moment M causes the elastic-plastic state. The cross-section in the elastic-plastic state is divided into the elastic core and the plastic surface, which is described by the parameter zp according to the following diagram.
The elastic-plastic moment Mep in the cross-section has to equal to the bending moment M. The curvature κ results from this equality.
The total deflection of the structure uz,max is calculated using the Mohr's integral.
Paramètres RFEM
- Modeled in RFEM 5.16 and RRFEM 6.01
- The element size is lFE= 0.020 m
- Geometrically linear analysis is considered
- The number of increments is 5
- Shear stiffness of the members is neglected
Résultats
Material Model | Solution analytique | RFEM5 | RFEM6 | ||
uz,max [m] | uz,max [m] | Ratio [-] | uz,max [m] | Ratio [-] | |
Orthotrope plastique 2D | 1.180 | 1.190 | 1.008 | 1.190 | 1.008 |
Isotropic Plastic 2D/3D, Plate | 1.173 | 0.994 | 1.173 | 0.994 | |
Isotrope plastique 1D | 1.180 | 1.000 | 1.180 | 1.000 | |
Isotropic Nonlinear Elastic 2D/3D, Plate, Mises | 1.190 | 1.008 | 1.190 | 1.008 | |
Isotropic Nonlinear Elastic 2D/3D, Plate, Tresca | 1.190 | 1.008 | 1.190 | 1.008 | |
Isotrope plastique 1D | 1.180 | 1.000 | 1.180 | 1.000 |