Pachmurin O.R.   Mikhaylov V.S.   Khamgushkeev M.S.  

Impact of genetically nonlinear application of external loads on the fundamental vibration modes and stress-strain state of reinforced concrete frame buildings on elastic foundation

Reporter: Khamgushkeev M.S.

When designing multi-storey reinforced concrete frame buildings, two complex tasks arise. The issue of the first task is related to the need to ensure sufficient rigidity of the building for its comfortable and safe exploitation. The first problem is solved by correct location in the floor plan and the selection of the cross section of the diaphragm. The quality of such a layout of the stiffening parameters of the building can be checked by performing a modal analysis of the design model. At the same time, a second problem arise, for the solution of which it is necessary to take into accounting the genetic nonlinearity of statically indeterminable systems, which are multi-storey reinforced concrete frame buildings. Accounting of the loading history is significant in buildings with a significant proportion of their own weight of structures in the total combination of effects. As an example of the incorrect layout of the rigidity of a high-rise building framework, the authors cite the consequences in an emergency seventeen-story residential building in Kemerovo, and on its basis demonstrate the influence of genetically non-linear effects on the  fundamental tone, and the stress-strain state of the structures on a rigid and compliant base.

Quite often, design errors are made in connection with the placement of stiffness diaphragms in the building plan based on expert judgment. At the same time, the layout of the stiffness diaphragms of buildings with a typical planning solution with allowable deformations calculated by means of statistical decisions is very convenient. The number and gabarits of the cross section of the diaphragms are selected for flexural rigidity and for allowable horizontal deflections for multi-storey buildings. Despite the recommendations of the maximum removal of stiffness diaphragms from the center of torsion on the floor plan, for their best placement on the floor plan, the torsional rigidity of the diaphragms should be refined with a applicability tolerance of the flat section hypothesis for the preliminary enlarged solution of the layout problem.

The quality of preliminary layout based on the static solution of the problem can be improved by additional verification the dynamic characteristics of the multi-storey reinforced concrete frame. The basic tone of the oscillations depends on the mass distribution and the rigidity of the structure, which can be represented as the simplest console problem with a plane section of complex shape. In this case, the availability of information about flexural and torsional stiffness allows you to  estimate the expected main period of natural oscillations. Despite the convenience of an analytical solution only for simple single-mass systems, this approach allows one to compare the period of natural oscillations when taking into account flexural or torsional stiffness to ensure that the first two basic forms of natural vibrations of the system are flexural and the third form as a torsional. This requirement, according to the Set of Rules 14.13330.2018 “Construction in seismic areas”, makes it possible to classify a building as a simple form taking into account of seismic effects only in two directions, but it is of a recommendatory nature. For example, in contrast of our standards in the seismic standards of the Republic of Kazakhstan and the People’s Republic of China, there is an official requirement to ensure a flexural the first two basic forms of natural vibrations.

After completing the pre-layout of the diaphragms of the rigidity of the frame buildings, taking into account the allowable deflections and ensuring the first two bending forms of natural oscillations, As well as dynamic comfort, at which the maximum acceleration of the building floor should not exceed the allowable value, the authors recommend performing a modal analysis in the SCAD design complex. The results of the calculation of the spatial dynamic model of the building will have a higher degree of reliability, in contrast to the analytical calculations of the enlarged characteristics of the building as for a single-mass console task. In addition, the main period of natural oscillations of the computational scheme calculated in modal analysis is recommended by the authors to be compared with the intervals of the pitch values of multi-storey buildings that are observed according to the results of seismic monitoring, which are given in addition  GOST R 54859-2011 "Determining the parameters of the fundamental tone of natural oscillations". It is necessary to take into account the fact that in order to increase the reliability of the fundamental tone calculated by the finite element method of the building oscillations, it is necessary to take into account the flexibility of base.

The second part of the study is based on a comparative analysis of the stress-strain state of a multi-storey reinforced concrete frame for the results of a linear and genetically non-linear calculation of a reinforced concrete frame building. Design schemes are compared on a rigid basis, on a flexible basis of constant stiffness, on a compliant basis of variable stiffness, which takes into account the dynamic modulus of elasticity of the soil at the last loading stage at the time of application of dynamic effects.

Thus, based on the results of a numerical-analytical study, the authors demonstrate the high importance of taking into account the stages of construction and the history of changes in the stiffness parameters of the design scheme in the design of multi-storey reinforced concrete frame buildings. The reflected methodology of the preliminary layout of the framework, which is necessary for the qualitative research, can be useful, including for classic linear calculations of buildings and structures, in which the value of the own weight of structures does not have a decisive effect in total combinations of effects.

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