A method for constructing a finite element model for the calculation of reinforced concrete bending beam in the theory of deformation model.

A.A. Suvorov, Scientific Consultant Ph.D. V.G. Murashkin.

FGFEI «Samara State University of Architecture and Civil Engineering»

Abstract. The technique of creating a plane finite element model for the calculation of reinforced concrete beam bending it in the theory of deformation model. The calculation is in the nonlinear formulation is taken into account creep of concrete and building load in walking-iterative design process calculations. Performed simulations of crack and the final state of the beam in a deformed state within is based on a flat bend.

Key words: deformation model, flat bend, nonlinear analysis, creep of concrete stress-strain diagram, function curvature.

Simulation of beam produced in the PC "Lira" version 9.6, which realized the possibility of a nonlinear calculation taking into account the creep of concrete according to the method of Eurocode 2 [1]. The problem of modeling has solved in flat system «XOZ» elements such as beam-wall.

Fig. 1.0. Finite element model of reinforced concrete beam in the plane problem PC "Lira".

As seen in Figure 1.0, the beam was modeled in a longitudinal section with dimensions corresponding to the actual dimensions of the structure, namely the section height - 220 mm; section width - 120 mm; beam length - 1500 mm. Model beam consists of four blocks: concrete beam body disposed above the reinforcing bar, the contact area around the reinforcing rod, the rod itself valves Æ20The protective layer of the concrete bottom. Load and communication have attached according to the design scheme design.

The finite element mesh has created from flat finite element (FE) beam-type wall to simulate plane stress. Geometric dimensions TBE selected so that, firstly, the cross section corresponds to a cross section model of the actual sample, secondly, has provided acceptable precise position (height) of the crack tip, as well as the ability to analyze the stress-strain state of the concrete in the zone his contact with the valve.

Concrete is modeled from physically nonlinear finite element rectangular plane problem number 221 5 mm along the axis «Z», and 10 mm along the axis "X" with the task of stiffness characteristics for concrete class B30 (type "TA" - natural hardening). The width of the data elements in the space for concrete, located above and below the rebar is the real width of the beam section.

Contact zone reinforced concrete is modeled by three thin layers of a thickness of 1 mm and a width of 10 mm TBE. The first (internal to the rebar) layer is modeled physically nonlinear finite element rectangular plane problem number 281 (ground) with the task of further traction, angle of internal friction, limiting tensile strength for concrete contact zone. The second and third (external to the rebar) layers are physically non-linear finite element rectangular plane problem number 221 with the characteristics of the material according to CE concrete. The width of the contact zone is modeled equal - semi perimeter corresponding reinforcing bar in order to get the shear stresses corresponding to the actual contact surface. The presence or absence of coupling is modeled respectively the presence or absence of elements adjacent directly, facility to the reinforcing rod. When you reach the contact tangential stresses the limits that have been taken to be 2R_bt, interaction with concrete reinforcement is modeled as follows. Adjacent to the reinforcing bar element in which the shear stresses have reached the limit values destroyed, and to the reinforcement and concrete are applied opposing force equal:

(1.0)

where lk- length of the finite element.

The body of the valve has created by physically nonlinear finite element rectangular plane problem number 221 with the dimensions of 20 mm along the axis «Z», and 10 mm along the axis "X" with the task of reinforcement stiffness characteristics for class A400. Deformation law has adopted for the main concrete and concrete contact zone under number 21 - Exponential (standard strength) (Fig. 1.1.). For valves - 11th exponential law of deformation with the task to design resistance strength of the steel [2] (Fig. 1.2.). In a further menu (Figure 1.3) for the stiffening of concrete parameters are set taking into account creep, calculated by the algorithm in the environment «Mathcad» according to block coefficient calculation creep in the Annex to Eurocode 2 [1].

Cracks are modeled jointing nodes in the development of normal cracks. A method of modeling crack conducted according to the calculation of crack opening width [1] and their development is in accordance with the position of the main areas of tensile stresses that can more accurately simulate the stress state of the concrete at the crack tip and to determine its depth.

For inclusion in the work of these laws, nonlinear deformation produces a nonlinear load. In the nonlinear static load, uploading has used in accordance with the design scheme design. The number of steps of the load has selected independently. In the appropriate boxes on settlement, periods creep of concrete specified n-th day since the control of the load. The number of iterations - 300 [4].

When loading the beam is considered appropriate n-th time period to attend the element creep of concrete. In one of the sections where tensile stresses ultimate tensile concrete in bending, reaching values of 1,75 R_bt, is formed crack normal process of development which, in accordance with the vertical trajectory of principal tensile stress is simulated serial jointing nodes of the finite element from the lower edge of the side of the compressed zone. Allowable precision overlay cracks according to calculations by Eurocode 2 was established and modeled on the sites of the principal stresses. The position of the crack tip height section is set such that the principal tensile stresses at the crack tip were equal or close to R_bt. After determining the position of the crack tip is analyzed magnitude of tangential stresses in the contact area and the elements (adjacent to the reinforcing bar), in which the voltage reaches the limit (2R_bt), are eliminated, and the interaction of reinforcement and concrete is simulated as mentioned above, the application of oppositely directed efforts N_t. At the same time, as the destroyed adjacent to the valve CE, controlled the main tensile stresses at the crack tip and, if necessary, adjusted her position. Set out the process of development of the crack, flowing at a constant load, corresponding to the moment of its formation, continues as long as the shear stresses in the contact zone and the normal stresses at the crack tip will no longer exceed 2Rbt and R_bt respectively [3].

As determined by the point of zero relative displacements reinforcement and concrete, and adjusted its displacement. Moving the contact layer of concrete and reinforcement at zero mutual displacement together, which allows its location to correct the error, since it may be between the member nodes.

REFERENCES

1. BRITISH STANDARDS INSTITUTION. BS EN 1992-1-1, Eurocode 2: Design of concrete structures. General rules and rules for building. BSI, 2004.

2. SP 63.13330.2012. Concrete and reinforced concrete structures. The main provisions. The updated edition of SNIP 52-01-2003. Moscow, 2012.

3. A.A. Prokopovych Bending resistance of reinforced concrete structures with different conditions clutch armature with concrete. Samara, illegal armed groups "SMS", 2000.

4. V.G. Murashkin, D.A. Panfilov, A.A. Suvorov. Modelling of reinforced concrete beam finite element method taking into account the creep of concrete / Tradition and Innovation in Building and Architecture: Materials 70th Anniversary All-Russian Scientific and Technical Conference on the results of R & D 2012 - Samara, 2013 - p. 307-308 - Part2