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07.12.2020

VE0019 | Flexion plastique - Charge de moment

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

Références
  1. Licence, J. (1990). Théorie de la plasticité. New York : Macmillan, 1993