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009019
2020-12-07

VE0019 | Пластический изгиб – моментная нагрузка

Описание работы

Консоль полностью защемлена на левом конце и загружена изгибающим моментом согласно следующему эскизу. 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.

Material Elastic-Plastic Мод. упруг. E 210000.000 MPa
поперечная деформация ν 0.000 -
модуль сдвига G 105000.000 MPa
Plastic Strength fy 240.000 MPa
Geometry Cantilever Длительность L 2.000 m
Ширина w 0.005 m
толщина t 0.005 m
Load изгибающий момент M 6.000 Nm

Analytical Solution

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.

RFEM Settings

  • 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

Результаты

Material Model Analytical Solution RFEM 5 Rfem 6
uz,max [m] uz,max [m] Ratio [-] uz,max [m] Ratio [-]
Ортотропная пластическая 2D 1.180 1.190 1.008 1.190 1.008
Isotropic Plastic 2D/3D, Plate 1.173 0.994 1.173 0.994
Изотропная пластичная 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
Изотропная пластичная 1D 1.180 1.000 1.180 1.000

Ссылки
  1. Люблинер, J .: (1990). Теория пластичности. Нью-Йорк: MacMillen, 2015


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