Keywords: time-dependent, reinforced concrete, non-linear analysis, plane-beam.

The current state of computer technology and programs enables solving extensive statically and dynamically loaded structures, while taking into account the effects of material, geometric and structural non-linearity including consideration of the rheological properties of materials. To model structures from composite materials, special elements were and are being generated for the finite element method, which have the ability to include many effects important for the quality both of the design and evaluation of complex structures.

Reinforced and prestressed concrete can be assumed to be materials for which the non-linear material models of concrete, reinforcement and tendons are valid, as well as the distinct characteristics of concrete in compression and tension, the change of stress in tendons as a result of structure deformation, etc. The necessity of carrying out material non-linear analyses of building structures is due to these factors. The behaviour of structures in the serviceability state is among other things affected by the rheological effects and also by the construction procedure.

The paper presents a method and computational program for the time-dependent and material non-linear analysis of concrete plane frame structures. The computational method is based on a layered approach and uses material models, which are based on the theory of plasticity and fracture mechanics, and rheological effects, which are based on the viskoelastic theory. For the analysis, the ANSYS computational system with the user BEAM element is used.

For solving materially non-linear problems encountered while modelling the load-bearing elements of structures, three basic approaches can be generally applied: the integral, layered and cell approach. The computational method, which is found in the paper, is based on the layered approach.

When solving materially non-linear problems, it is necessary to define a model for the material characteristics and demonstrate their non-linear character, as well as possible unloading, reloading etc. Generally, two basic types of material models can be used: material models based on plasticity and material models based on the principles of fracture mechanics. As above mention for analysis with user beam element is possible used both groups of material models.

Rheological properties of concrete (creep and shrinkage) are dependent on the duration time of the loading effect. The viskoelastic theory is used for description of rheological effects. In order to respect rheological effects in analysing the construction, it is necessary to apply the method of time-discretization combined with the finite element method. In this method the state of stress is assumed to be constant in the selected time intervals. The changes are taking place only at the discrete time nodes. Here the stress and displacement fields are determined using the finite element method.

For solving time-dependent and materially non-linear analysis of concrete structures the ANSYS computational system with the user BEAM element is used. The user BEAM element, which is derived in [1], is a straight, three-node, 2D (plane XZ) finite beam element with eccentrically connected end nodes referential to the nodes of the finite element method , which are placed on the reference axis, Figure 110.1. The interior node lies at the centre of the beam element. The element allows the continuous deformation compatibility. This means that in cases where more than one beam element is placed between two nodes on the reference axis, those elements have a continuous deformation process. The advantage of this beam element is the individual modelling of a concrete cross-section, reinforcement and tendons. The user BEAM element takes into account the work done by the normal forces, the bending moments, and even the shear forces on the element deformation. This element can be used for modelling of a variety of load-bearing elements (beams, columns, reinforcement, tendons, etc.), which can generally be made of various materials (concrete, reinforcement, tendons, ceramics etc.).

1

Pencik, J., "Materially Non-Linear Analysis of Concrete Plane Frame Structures", PhD Thesis, Brno University of Technology, Brno, May, 2001.

2

Bathe, K.J., Jürgen, K., "Finite Element Procedures in Engineering Analysis", Prentice-Hall Inc., 1982, ISBN 0-13-317305-4.

3

ANSYS Theory Reference release 5.5, Ansys, Inc., SAS IP, Inc., Houston, September 1998.

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