Study of Inelastic Behavior of Reticular Structures of Steel Bars - Phenomena of Plastification

Technological advancement has increasingly helped solve engineering problems, but the designer who does not seek knowledge of the physical behavior of materials and mathematical techniques to solve them runs the risk of not being able to interpret the results provided by structural software. Computational techniques do not provide the exact solution of engineering problems, they provide approximations to the intervals where the solution of the differential equations governing the mechanics of the continuum are inserted. The engineer who does not know how to idealize the engineering problem in his mind will not be able to model the problem in the computer. One of the most intriguing and peculiar engineering problems is the plastification phenomenon of metallic objects.


I. INTRODUCTION
Structural analyzes are made in first-order theory in wich the equilibrium of the structure is studied in the indeslocated position, and in second-order theory where equilibrium is studied in the displaced position. The stability of the structure can only be studied in second order theory. According to Chen (et. Al., 1996) in the study of the resistence and stability of structures it is necessary to do:  Check the inelastic behavior of the materials;  Check the flexibility of the connections;  Check second order effects due to geometry change. The consideration of physical and geometric nonlinearities are pre-requisites for the beginning of the understanding of the plastification effects of steel structures.

Fig.1: Load-displacement characteristics of general analysis types.
The types of structural analyses are the First and Second Order Elastic Analyses and First and Second Order Inelastic Analyses, as shown in the figure above. In order to understand and delineate the plastification effects of steel structures, Chen (1) proposes the Advanced Structural Analysis, which consists of a technique that seeks to introduce into the behavioral models of the elements representative of the structure and its materials the closest hypotheses of reality and, together, sophisticated numerical and iterative procedures to estimate the non-linear behavior of these structures. In this way, the advanced analysis encompasses the nonlinear, physical and geometric analyzes in the studies of the structural systems and their members modeling the effects of plastification.

III. ATTRIBUTES NECESSARY FOR THE STUDY OF PLATIFICATION -SECOND ORDER EFFECTS.
The study of plastification in steel elements should be done by accounting for second order effects, such as loss of physical capacity of steel sheets (inertia, area, thermal expansion, etc.), and changes in geometry due to the effects of forces. These changes during the action of forces must be inserted into the model. The following are the items that should be observed in the modeling:  Initial imperfections due to the curvature of the bars, frames and columns out of alignment, displacement of the bars.  Residual tensions due to manufacturing and assembly processes -Welding action.  Connection types: flexible, rigid, semi-rigid.  Types of cross sections: symmetrical, nonsymmetric, open or closed profile.  Effects of loading: dynamic, variable, repetitive due to construction stages, etc.  P- moment: second-order moments due to axial force acting through displacements associated with member chord rotation.  P- moment: second-order moments due to axial force acting through displacements associated with member curvature bending. The structural theory used in this work is based on the hypothesis attributed to Bernoulli-Euler, which states that: "The cross-sections flat and orthogonal to the axis of the bar remain flat, indeformable and orthogonal to the axis after deformation." The displacements uc and vc of a section point in the corrotational system (xc , yc) are then determined by:

IV. FORMULATION
Stiffiness module or angular coefficient or slope of the strainstress curve

VI.
EXEMPLES A static foundation pile test was carried out in the city of Rio de Janeiro in 2011 in which the reaction beam was a W1000x217 (ASTM A36, fy = 250MPa) with 5 meters in length. The test load was 1697kN and so it was done. As a research objective to plasticize the bar, the load was increased to 2001 kN where from this point the lateral buckling mechanism started and the test was stopped. This reaction system (W1000x217) is studied in four different models: 1    Solving the problem up to the maximum load and the maximum stresses at the top and bottom of the beam are shown, however the stresses went beyond the ultimate tensile stress 550MPa.