Calculation of composite elements of slabs in buildings, structures and fragments of spans of bridges

. The calculation consists of two stages. The first one begins with the definition of their class, bearing capacity at temperature of 20 °C, according to EN 1992-1-1. At the second stage, the calculation at high temperatures shall be carried out in accordance with Eurocode 4 part 1-2. Comparison of the “stress-strain” diagram of concrete of class 30 under compression and temperature of 20 °C in two formulas showed their difference. That is, the designers do not have the opportunity to continue the calculation of diagrams at different heating temperatures. There was a need to improve the mathematical model of the “stress-strain” ratio of concrete high temperatures, clarification of the criteria of the bearing capacity of concrete in calculation of the fire resistance of composite structures in EN 1994-1-2:2005. In this paper, the method of determination of 1, cu   developed has allowed, based on the energy approach, to formulate the corrected dependence of the limit deformation on temperature, dependence of the maximum deformation on temperature, and the value of the parameters of the “stress-strain” diagram. According to these data, using the formulas of the first stage, the “stress-strain” diagrams of the concrete of class 30 are calculated at the compression and heating according to


Improvement of mathematical model of deformation diagram of compressed concrete of steel-and-reinforced concrete structures under heating
The paper [1] describes defects in the strength and deformation properties of concrete at higher temperatures that are given in EN 1994-1-2:2005 Eurocode 4, which during harmonization were included in DSTU-N-P B В.2.6-159:2010. The method of determination of the specified diagrams " , " for the design of steel reinforced concrete structures under the fire conditions was developed. The values of the parameters of the diagram for concrete based on silicate filler at higher temperatures were specified, and the mathematical model of the "stress-strain" ratio of the concrete at compression and higher temperatures was refined. Despite such a significant refinement of the mathematical model of the "stress-strain" diagram of concrete under compression and higher temperatures, designers do not have sufficient information to calculate the fire resistance of the structure.
The calculation of elements of reinforced concrete and composite structures consists of two stages. The first stage begins with determination of their bearing capacity at a normal temperature of 20 °C, that is, when using Eurocode 2 EN 1992-1-1:2005 [2] or DBN V.2.6-98:2009 [3]. These standards propose to use two equations to describe the relationship between c  and c  for short-term axial load. Equation (1) deformations at maximum loads according to table 1 and equation (2) in the form of a quintal polynomial, which is based on the results of numerous experimental researches of the State Research Institute of Building Structures, the statistical processing of which allowed to propose a more complete normative basis: For both formulas, use limits were defined: where 1 cu  -nominal boundary deformations of concrete. The paper [1] also shows that graphs practically coincide on the ascending branch according to DBN and EN92-1-1.  cm E   , complete "strain-deformation" diagram of concrete at a temperature of 20 °C shall be determined by the formula (1).

Analysis of recent research
In the course of the study [4], a method for determination of the criterion of concrete bearing capacity 1, Is is shown that these diagrams are obtained on special presses equipped with a heating device and a servo-control of pressure in the press cylinder, which allows passing through the descending branch practically zero stress. In this case, the branch descending to zero is no longer the area of deformation of the integral concrete sample, but the area of deformation of individual parts of the fragmented concrete. So, the values of deformations in columns 4 and 7 of  (4), it is possible to vary only the value of compressive strength c f , therefore these diagrams, even on the ascending branch, incorrectly represent the actual properties of the physical nonlinearity. Fig. 1 shows a "stress-strain" diagram of concrete of class 30 under the formula (1) in comparison with the formula (4).  [7], [8] harmonized with EN 1994-1-2:2005 [6] are also found.
So, it is necessary to improve the mathematical model of the "stress-strain" ratio of concrete under compression and elevated temperatures, refinement of the criteria of the bearing capacity of concrete when calculating the fire resistance of composite structures in EN 1994-1-2:2005.

Results of theoretical studies
Section 3 of the standard [5] states that the strength and mechanical properties of concrete at higher temperatures can be determined from the stress-strain dependencies given in EN 1992-1-2 [7].
In fact, the deformations 1, c   given in Table 3.1 are taken to be the same for all classes of concrete, including for silicate (column 4) and carbonate (column 7) fillers. So, depending on the class of concrete in formula (4), it is possible to vary only the value of compressive strength c f , therefore these diagrams, even on the ascending branch, incorrectly represent the actual properties of the physical nonlinearity.
Eurocode EN 1992-1-2:2004 is definitely the leading normative document in the theory of concrete, reinforced concrete and composite structures, their fire resistance, and is based on high-level experiments, with new test devices, which allowed the implementation of progressive nonlinear computational models.
At the same time, the main results of the conducted studies are not consistent with the basic Eurocode 2 EN 1992-1-1:2005 [2]: Design of reinforced concrete structures -Part 1-1: General norms and rules for structures, that is shown, for example, by comparing deformation diagrams at a temperature of 20 °C and other parameters.
The correction in the indicated tables and the method for determination 1, cu   on the basis of the energy approach [10] have made it possible to formulate the corrected dependence of the limit deformation on temperature (Fig. 2), the dependence of the maximum deformation on temperature (Fig. 3) and Table 3 -Value of the parameters of the "stress-strain" diagram. According to these data, using the formula (1), the "stress-strain" diagrams of concrete of class 30 were calculated under compression and heating according to EN 1992-1-2:2004 (Fig. 3).    [3]. These standards propose to use two equations to describe the relationship between c  and c  for short-term axial load. Equation (1), which is used in Eurocode 2 EN 1992-1-1:2005 [2], and equation (2) in the form of quintal polynomial, which is based on the results of numerous experimental researches of the National State Institute of Concrete Structures (NSICS), the statistical processing of which allowed to offer a more complete normative base.
3. In the course of the study [4], a method for determination of the criterion of concrete bearing capacity