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Buckling curves in the plastic domain
Source publication
In this paper the phenomenon of instability of frames in elasto-plastic domain was investigated. Numerical analysis was performed by the finite element method. Stiffness matrices were derived using the trigonometric shape functions related to exact solution of the differential equation of bending according to the second order theory. When the buckl...
Contexts in source publication
Context 1
... (3) is given by hyperbola function and it is valid until the critical stress is less than a proportionality limit, as it is shown in Figure 1. When the critical stress is exceeded, the member is buckling in the plastic range. ...
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Citations
... In the usual approaches based on the FEM, the solutions of the differential Equation (4) can be written as cubic polynomials, suitable for linear static analysis since they are derived from the solution of the differential equation of bending of a beam according to the linear theory. However, the outcome of such investigations showed [40] that significant errors for P cr might be obtained if an insufficient number of finite elements are used. In that case, it is always necessary to control how many finite elements are needed for a convergent solution. ...
... So, an essential aspect of this research was devoted to the investigation of suitable numerical methods to obtain the solution of the corresponding transcendental stability equation. These solutions were implemented in a self-developed computer program [40], representing this paper's one of the most important contributions. ...
... Column length is denoted by l, I is the moment of inertia, А is the cross-sectional area, and σ y is the yield stress. The stiffness matrix of the member that is clamped at one and hinged at the other end (so-called type "g") is given by Ćorić [40]. When the element is subjected to a tensile load, stiffness matrices have a similar form; only the hyperbolic functions are used instead of the trigonometric one. ...
This paper considers the phenomenon of the instability of steel plane frame structures in the elastic–plastic domain. The numerical analysis uses finite element method, where the corresponding stiffness matrices are based upon the trigonometric and hyperbolic interpolation functions of normal forces. The tangent modulus concept is applied when buckling occurs in the plastic range. Thus, the stiffness matrices for nonlinear material behavior are also derived. The procedure for determining effective length factors of compressed columns, which implies a global stability analysis of entire frames, is established too. It means that the proposed approach is based on the assumption that the collapse of the structure occurs when the most loaded columns reach their stability limit. So, the presented procedure enables the calculation of the real critical load of plane frame structures in the elastic–plastic domain and determines the corresponding effective length factors.
... Above that point it is inelastic with gradually decreasing resistance, measured by the tangent modulus E t . The theory postulates that, for an ideally straight column with an elastic critical stress greater than σ p , bifurcation of equilibrium can occur and the column will start to buckle at the load [8] ...
This paper presents the procedure for stability analysis of frames in elastic-plastic domain using the concept of the tangent modulus. When the buckling of structure occurs in plastic domain, it is necessary to replace the constant modulus of elasticity E with the tangent modulus Et. Tangent modulus is stress dependent function and takes into account the changes of the member stiffness in the inelastic range. Formulation of the corresponding stiffness matrices is based upon the solution of the equation of bending of the beam according to the second order theory. Numerical analysis was performed using the code ALIN, developed in the C++ programming language
Certain concrete structures during their service life are exposed to variable repeated loads with significant magnitude and duration. Typical examples are bridges, parking garages and storage buildings where besides permanent, variable loads can also affect the long-term concrete behavior. Currently, this concrete phenomenon to creep under variable loads is well-recognized in the codes and considered through the so-called quasi-permanent load. However, the creep and the recovery property under these load types are still far from clear.
This paper is concerned with a study of the effects of variable repeated stresses on the creep and creep recovery of concrete. For that purpose, two separate experiments were performed in which concrete specimens were exposed to time-variable uniaxial compressive stresses. The first experiment aims at assessing the influence of different service stress levels at loading (30% and 45% of fc) as well as different level of unloading (full and partial unloading). The second one focusses on the influence of different drying conditions of the specimens (sealed and unsealed condition).
The results indicate that regardless of the stress level, the creep becomes fully recoverable after a sufficient number of loading and unloading cycles. On the other hand, the drying conditions show remarkable influence on the irreversible proportion of the creep in each loading cycle. Moreover, the absolute value of the creep recovery seems unaffected by the hygral exchange conditions of the specimens.
The obtained results demonstrate that the creep behavior under repeating stresses in a large scale differs from the ones under just sustained stresses.
