Plastic hinges are imperative for the Pushover Analysis (POA) as a nonlinear static method for the seismic analysis of structures. In RFEM 6, plastic hinges can be defined as member hinges. This article will show you how to define plastic hinges with bilinear properties.
With the orthotropic elastic-plastic material model, you can calculate solids with plastic material properties in RFEM 5 and evaluate them according to the Tsai‑Wu failure criterion. The Tsai-Wu criterion is named for Stephen W. Tsai and Edward M. Wu, who published it in 1971 for plane stress states.
The elastic‑plastic material model in RFEM 5 allows you to calculate surfaces and solids with plastic material properties and to carry out a stress evaluation. This material model is based on the classic von Mises plasticity.
In RFEM, orthotropic plastic analyses using the Tsai‑Wu plasticity criterion have been possible for quite some time now. The hardening modulus Ep,x or Ep,y can be used to consider the hardening of the material during the iterative calculation.
In the "Material Model - Isotropic Nonlinear Elastic" window, you can select the yield laws according to the von Mises, Tresca, Drucker-Prager, and Mohr-Coulomb yield rules. This makes it possible to describe the elasto-plastic material behavior. The yield function depends on the principal stresses or the invariants of a stress tensor. The criteria apply to 2D and 3D material models.
The elastic deformations of a structural component due to a load are based on Hooke's law, which describes a linear stress-strain relation. They are reversible: After the relief, the component returns to its original shape. However, plastic deformations lead to irreversible deformations. The plastic strains are usually considerably larger than the elastic deformations. For plastic stresses of ductile materials such as steel, yielding effects occur where the increase in deformation is accompanied by hardening. They lead to permanent deformations - and in extreme cases to the destruction of the structural component.
When designing a steel cross-section according to Eurocode 3, it is important to assign the cross-section to one of the four cross-section classes. Classes 1 and 2 allow for a plastic design; classes 3 and 4 are only for elastic design. In addition to the resistance of the cross-section, the structural component's sufficient stability has to be analyzed.
The following article describes designing a two-span beam subjected to bending by means of the RF-/STEEL EC3 add-on module according to EN 1993-1-1. The global stability failure will be excluded due to sufficient stabilizing measures.
Orthotropic material laws are used wherever materials are arranged according to their loading. Examples include fiber-reinforced plastics, trapezoidal sheets, reinforced concrete, and timber.
Pushover analysis is a nonlinear structural calculation for seismic analysis of structures. The load pattern is inferred from the dynamic calculation of equivalent loads. These loads are increased incrementally until global failure of the structure occurs. The nonlinear behaviour of a building is usually represented by using plastic hinges.
SHAPE‑THIN cross‑section properties software determines the effective section properties of thin‑walled cross‑sections according to Eurocode 3 and Eurocode 9. Alternatively, the program allows plastic design of general cross‑sections according to the Simplex Method. In this process, plastic cross-section reserves are iteratively calculated for elastically determined internal forces. The following example describes the effective cross-section properties in the notching area of a rolled I-section. Afterwards, the results are compared with the plastic analysis.
Prior to the analysis of steel cross‑sections, the cross‑sections are classified according to EN 1993‑1‑1, Sec. 5.5, with respect to their resistance and rotation capacity. Thus, the individual cross-section parts are analyzed and assigned to Classes 1 to 4. The cross-section classes are determined subsequently and usually assigned to the highest class of the cross-section parts. If plastic resistance is to be applied to further design of cross-sections of Class 1 and Class 2, you can analyze the elastic resistance of cross-sections as of Class 3. In the case of cross-sections of Class 4, local buckling occurs even before reaching the elastic moment. In order to take this effect into account, you can use effective widths. This article describes the calculation of the effective cross-section properties in more detail.
RF-/STEEL EC3 allows you to perform plastic design checks of cross‑sections according to EN 1993‑1‑1, Sec. 6.2. You should pay attention to the interaction of loading due to the bending and axial force for I‑sections, which is regulated in Sec. 6.2.9.1.
The following article describes the design of a single-span beam subjected to bending and compression, which is performed according to EN 1993‑1‑1 in the RF-/STEEL EC3 add-on module. Since the beam is modeled with a tapered cross-section and thus it is not a uniform structural component, the design must be performed either according to General Method in compliance with Sect. 6.3.4 of EN 1993‑1‑1, or according to the second-order analysis. Both options will be explained and compared, and for the calculation according to the second-order analysis, there is an additional design format using Partial Internal Forces Method (PIFM) available. Therefore, the design is divided into three steps: design according to Sect. 6.3.4 of EN 1993‑1‑1 (General Method), design according to the second‑order analysis, elastic (warping torsion analysis), design according to the second‑order analysis, plastic (warping torsion analysis and Partial Internal Forces Method).
The following example presents a comparison between a shell model and a simple member model performed in RFEM. In the case of the shell model, there is a beam suspended in surfaces, which is modeled with restraints on both sides due to the boundary conditions. This is a statically indeterminate system that forms plastic hinges when overloaded. The comparison is carried out on a member model that has the same boundary conditions as the shell model.