Computer simulation of load-bearing elements and junction units in the calculation scheme of multistory frame buildings

. In the last three decades, preference was given to the construction of monolithic buildings, but the construction of multistory frame buildings from prefabricated concrete is very relevant at the present stage. Therefore, there is a need to revise the normative base for the design of prefabricated housing construction, including the revision of standards for certain types of prefabricated reinforced concrete structures. Such work is currently being carried out taking into account the use of modern building materials, new technologies for the production of prefabricated structures and the erection of prefabricated buildings, as well as taking into account the widespread use of computer design methods in design practice. The Code of Rules for the design of multistory frame buildings in prefabricated concrete SP 356.1325800 was developed as an extension of the Code of Rules for the design of reinforced concrete structures SP 63.13330. The article reviews the normative and technical literature on the computer simulation of load-bearing elements and junction units of the calculation scheme of multistory frame buildings. The means of the LIRA software package for computer simulation are considered and a quantitative assessment of the stiffness of the connection in the hinged joint of the crossbar with the column, as well as a flat model for assessing the stress distribution in the cantilever of this joint, is proposed.


Introduction
Multistory frame buildings built from prefabricated reinforced concrete continue to be in demand and are actively used in industrial and civil construction.
During the period of predominant development of prefabricated reinforced concrete in domestic construction, load-bearing elements and their junction units were developed within the framework of various standard series and standards, as well as unified frames for multi-storey buildings [1].The last three decades have been marked by the priority construction of monolithic buildings, which has led to a reduction in the construction of prefabricated buildings and, accordingly, has suspended the wide development of the constructive and normative base of their design.
As shown in [2,3], the current task is to update the normative base for the design of prefabricated multistory frame buildings.For this purpose, the Code of Rules 356.1325800.2017(Reinforced concrete frame structures of precast multistory buildings.Design rules) was issued.However, it is also required to revise the standards for certain types of prefabricated reinforced concrete structures, the design of which was carried out according to currently canceled normative documents, due to the emergence of new building materials, in the conditions of using a different technology for the production of prefabricated structures.The need to rework building codes is also explained by the emergence of new design solutions for the load-bearing elements of the prefabricated frame and their junction units.
An essential point of the modern design of multistory frame buildings built from prefabricated reinforced concrete is the widespread use of numerical design methods, which made it possible to calculate the bearing structural system of the building in a spatial setting, taking into account its joint work with the base, and also, if necessary (for buildings of classes KS-2, KS -3 with a massive crowd of people) -calculate buildings for progressive collapse.
It should be noted that when performing the reconstruction of multistory buildings erected from prefabricated reinforced concrete in previous construction periods, one also has to deal with a discrepancy between modern normative requirements for the design of reinforced concrete structures and the normative requirements that were previously imposed on them [4].
Taking into account the above, it is relevant to consider the currently used load-bearing elements of multistory frame buildings and their junction units, their classification, the features of their computer simulation in the calculation scheme.

Materials, methods and research results
The research material was the scientific and technical literature in the field of designing multi-storey frame buildings built from prefabricated reinforced concrete.During the research, the following methods were applied: study, generalization, comparison, analysis, concretization, problem setting, forecasting.
The design of prefabricated reinforced concrete structures made of heavy, fine-grained and lightweight structural concrete, which are used in the construction of buildings with a height of not more than 75 meters, is regulated by the Code of Rules 356.1325800.2017.
Depending on the type of junctions of crossbars with columns for a prefabricated multistorey frame beam structural system with transverse and longitudinal frames of the spatial frame of the building, the Code of Rules 356.1325800.2017establishes three structural schemes: tied, frame-tied and frame.

Design scheme Type of joints of transverse frame
Type of joints of longitudinal frame tied hinged joints hinged joints frame-tied rigid joints hinged joints frame rigid joints rigid joints During computer simulation in SP LIRA-SAPR the spatial calculation scheme of a multi-storey frame building erected from prefabricated concrete, the junctions of frame crossbars with columns are automatically set rigid [5].
To replace rigid joints with hinged ones, it is necessary to install hinges with zero rigidity at the ends of the rod-crossbars.For hinges, it is also possible to set stiffness other than zero values, which, in turn, determines the values of the span and support moments in the crossbars [6].
Fig. 1a shows the junction of the crossbar with the column.The value of the moment on the crossbar support is determined by the bearing capacity of the connecting plate [7].
Fig. 1b shows a graph linking the values of the support moment with the assigned stiffness of the hinge in the junction of the crossbar with the column of the spatial calculation scheme of the structural system of the building.At present, when using software systems for engineering calculations, a characteristic feature is the computer simulation of calculation schemes for prefabricated multi-storey frame buildings, during which the description of the stiffness of the joints of the bearing elements is performed.In addition to computer simulation of the junctions of crossbars with columns, it is also necessary to describe the joints of floor slabs when they rest on the crossbars.
They can be represented by vertical joints of the ends of floor slabs with crossbars and horizontal joints of floor slabs with supporting platforms of the crossbar.In the calculations, it is also necessary to take into account the work of the longitudinal joints between the floor slabs.Recommendations for determining the stiffness of the joints are given in the Code of Rules 356.1325800.2017.
To simulate the elastic connection between the joints of crossbars and floor slabs using the SP LIRA-SAPR, you can use the finite element FE55, setting the linear stiffness of the ties along (around) the global axes.Computer simulation of the elastic connection between the joints of the crossbars and floor slabs can also be carried out by combining the displacements of the junction units of floor slabs and crossbars in the required directions.The results of comparative computer calculations of the spatial frame with various options for modeling the connections between the elements of the calculation scheme are given in [8].The use of finite elements KE55 is recognized as optimal for modeling the elastic connection between the junction units of crossbars and floor slabs.
Ribbed and multi-hollow floor slabs with double-sided support on crossbars of transverse frames are used in tied and frame-tied schemes of multistory frame buildings.Inter-column and edge floor slabs act as a crossbar of the longitudinal frames of the spatial design scheme.The rest of the floor area is filled with ordinary slabs.
In the frame calculation scheme, crossbars rigidly mated with columns are part of the longitudinal and transverse frames, which makes it possible to use for solid floor slabs supported on crossbars along the contour.
Columns of prefabricated multistory frame buildings usually have joints along the height of the building.Prefabricated fragments of columns can be located within one to three floors.For columns in multistory buildings, modern building codes call for rigid joints as the main option.
For multistory buildings with a tied structural scheme, when stiffening diaphragms work to percept of horizontal loads, and a small vertical load is transferred to the columns, hinged joints can be used.Thus, in computer calculations of multistory buildings, it may be necessary to simulate hinged joints of rods-columns of the design scheme.
The hinged joint was used before, but found limited use.A new constructive solution of the hinged joint is considered in [9].It consists in the fact that when organizing a hinged joint, the adjacent ends of the prefabricated fragments of the columns must have spherical end surfaces.For easy centering when making a joint, as well as for the perception of a possible horizontal displacement of adjacent fragments, a pin was installed in the center of one prefabricated fragment, which was inserted into a tube embedded in the end face of another joined prefabricated column fragment.Some other options of design solutions for the hinged joint are given in [9].
It is shown in [8] that in the calculation scheme for rods-column, in order to take into account the possible horizontal displacements in the seams of concreting, hinged joints should be installed in these places.For these hinged joints, the horizontal stiffness component must be specified.It is determined depending on the type of expected technological defects in the seams of concreting.
It was shown in [8] that in the calculation scheme for rods-column, in order to take into account possible horizontal displacements in the seams of concreting, hinged joints should be installed in these places.For these hinged joints, the horizontal stiffness component must be specified.It is determined depending on the type of expected technological defects in the seams of concreting.
To improve the efficiency of calculations of prefabricated multistory frame buildings for progressive destruction, performed using software systems, it is recommended in [10] to perform sequential removal of individual load-bearing structures of the building frame, taking into account the coefficient of significance of the structure, which will provoke the process of progressive destruction.The improvement of load-bearing structural elements of a multistory frame building can be based on the use of computer simulation.Fig. 2 shows the constructive solution of the cantilever of the column (a) and its computer simulation as a flat element (b).The distribution of the main tensile forces is shown, in the direction of which the rods of the longitudinal and transverse reinforcement of the console are installed.

Conclusions
The tools of computer simulation, including those offered in the LIRA software package, allow creating spatial calculation models for engineering calculations in accordance with the requirements of the Code of Rules SP 356.1325800.2017for the design of multistory frame buildings in prefabricated concrete.At the same time, an important feature of creating a spatial design scheme is taking into account the stiffness of the joints of prefabricated elements, which requires a preliminary quantitative assessment of the stiffness of the joints.The appointment of rational reinforcement of reinforced concrete structures of a building should be based on knowledge of the distribution of stresses in the calculated building structure.This work was financially supported by the Ministry of Science and Higher Education of Russian Federation (grant # 075-15-2021-686).Tests were carried out using research equipment of The Head Regional Shared Research Facilities of the Moscow State University of Civil Engineering

Fig. 1 .
Fig. 1.Hinged junction of the crossbar with the column, having a set stiffness: a -diagram of the constructive solution of the node, b -graph of the dependence of the stiffness of the junction and the support moment in the crossbar

Fig. 2 .
Fig. 2. Structural solution (a) and distribution of the main tensile forces (b) in the cantilever of the column of a multistory frame building