Investigation of the stress-strain state of hybrid timber-reinforced concrete multi-storey buildings

Problem statement. The use of timber in multi-storey buildings is a promising direction in terms of reducing the impact of the construction industry on the environment. Hybrid buildings represent a rational combination of timber as the main structural material and reinforced concrete for spatial stability providing. At present time there are no recommendations for the choice of structural system of multi-storey hybrid buildings, the issues of joint work and stressstrain state of load-bearing structures of timber and reinforced concrete in the spatial system of multi-storey buildings are insufficiently studied. The article is devoted to the analysis of the stress-strain state of hybrid timber-reinforced concrete multi-storey buildings. In the study, the number of storeys of the building was accepted of 5, 10 and 15 floors. The type of the joints between of the load-bearing structures and the method of ensuring spatial rigidity, namely the number and location of the shear walls and the rigidity core, were varied. For each option, a spatial finite element model was compiled and a static load analysis was performed in accordance with the requirements of current design standards. Results and conclusion. The data on the magnitude of the horizontal displacements of the upper part of the building, as well as the maximum values of the forces from adverse combinations of loads, were obtained. The analysis of the stability of the building and the bearing capacity of timber columns were performed. Based on the results obtained, the recommendations are proposed for choosing a structural scheme, a method for ensuring the spatial rigidity of a building, as well as assigning cross-sectional dimensions at the initial stage of the design of a hybrid timber-reinforced concrete multi-storey building.


Ключевые слова: гибридные здания; древесина; железобетон; напряженно-деформированное состояние;
Вісник Придніпровської державної академії будівництва та архітектури, 2020, № 5 (269-270) ISSN 2312-2676 перемещения Introduction.The traditional construction industry has a negative impact on the environment in ways (greenhouse gas emissions, waste accumulation, the use of nonrenewable resources, etc.).Timber has several advantages in terms of sustainable development and circular economy.Awareness of global environmental problems and the search for ways to solve them contributed to the emergence of innovative solutions based on timber as a structural building material.
Currently, new solutions are being developed for hybrid structures for the construction of both multi-story and high-rise buildings, in which timber is the main structural material (up to 80%), and reinforced concrete or steel is used to increase resistance to external loads.The following projects can be cited as examples: LifeCycle Tower ONE, Panorama Giustinelli, Cenni di Cambiamento, Murray Grove, Origine Condos, Brock Commons etc. [1−5].In research [6], the authors substantiate the use of the developed hybrid system for buildings with a height of 10...30 floors.Structural system consists mainly of timber elements that are used to arrange the central core and stiffness diaphragms, ceilings, load-bearing walls and columns.Analyzing the above projects, it can be concluded that the spatial rigidity is achieved due to the regular location of the load-bearing structures in the plan and in the height of the building, as well as symmetrically located in the plan of the shear walls and the rigidity core.
Despite the growing popularity of multistorey buildings with a hybrid structure, comprehensive regulatory and technical documentation for the calculation and design of this type of building currently does not exist.It is necessary to develop scientifically based recommendations for choosing the structural system of the building at the initial stage of design, preliminary assignment of geometric parameters and strength characteristics of the material of the load-bearing structures.
The purpose of this study is to analyze the stress-strain state of hybrid timber-reinforced concrete multi-storey buildings depending on the number of storeys and the method of providing the spatial rigidity.
Materials and methods.For the analysis of the stress-strain state of multi-storey buildings of a hybrid structure, a prototype building was chosen.The spacing of frames was adopted of 5 m in both directions.The number of floors was varied of 5, 10, and 15 storey.The storey height for all options was 3 m.Thereby the height of the buildings was 15, 30 and 45 m, respectively.Two types of joints between horizontal and vertical load-bearing elements were consideredhinge and rigid.To ensure the spatial rigidity of the building, the use of vertical shear walls and a rigidity core were considered.Layout schemes for each option are shown on Figure 1.The beams and columns of glued laminated timber and the shear walls and rigidity core of reinforced concrete were adopted as load bearing elements.The physical and mechanical characteristics of materials and the parameters of the cross section of the structural elements of the building are shown in Table 1.An analysis of the stress-strain state in accordance with the requirements of the current design standards was carried out for the adopted options of the building.Loads on building elements were determined in accordance with the requirements of [7].The design value of the selfweight of the floor and floor coverings was taken 1.5 kN/m 2 , the imposed load on the floor elements -1.95 kN/m 2 (as for a residential building), and the snow load -1.6 kN/m 2 (for wind load zone III according to Ukrainian wind map).The design values of the wind load on the vertical frames considering the spacing of 5 m are presented in Table 2.A diagram of the variation of wind load depending on height is shown on Fig. 2.

Fig. 2. A diagram of the variation of wind load depending on height
For each variant of the building, a 3D finite element model was compiled using LIRA-SAPR commercial software.Beams and columns were modelled with elements of the FE 10 type (universal spatial rod FE).The diaphragms and stiffness core were set by elements of type FE 41 (universal rectangular FE shell).The following loads were applied to the elements of the model in accordance with the determined load values: 1 -self-weight of the construction elements (permanent action); 2 -imposed on the floor structure (variable); 3 -snow load; 4 -wind load.The models obtained are illustrated on the 5 storey building variant in Figure 3. Results and discussion.As a result of the static calculation of spatial models, data were obtained on the values of the horizontal displacements of the upper part, i.e. the deviation of the building from the vertical axis.The values obtained were used to assess the spatial stability of the building.The maximum allowable horizontal displacements of the upper part of the multi-storey building according to [8] are f u = h/500 (where h is the total height of the building).Therefore for the variants considered this value is limited to 30 mm for 5 storey; 60 mm for 10 storey and 90 mm for 15 storey.
Diagrams of horizontal displacements caused by the wind load along the height of the building are shown on Figure 4.
Maximum values of internal forces caused by unfavorable load combinations were obtained for each variant of buildings.Using these data, the analysis of the load-bearing capacity (strength and stability) was performed for timber columns as the most loaded elements.The maximum values of internal forces and loadbearing capacity utilization rate of timber columns are presented in Table 3 and on Figure 5.
The data obtained on the horizontal displacements of the considered building types indicate that spatial rigidity is provided: -for 5 and 10-storey buildings for all variants, except for the hinge joints of frame elements without additional measures for spatial rigidity providing; -for a 15-storey building for rigid joints of frame elements and for hinge joints of elements with a rigidity core.It should be noted that in the case of four stiffness diaphragms, horizontal displacements of the upper point of the building are approximately equal to the maximum allowable values.According to the results of the analysis of the load-bearing capacity utilization rate of the columns, it was found that the accepted dimensions of the cross sections of the columns provide load-bearing capacity in accordance with the requirements of current regulatory documents.The exception is the 5-story building with hinge joints (utilization rate 1.96), as well as a 10-story building with rigid joints between elements (utilization rate 1.11).
Thus, at the initial stage of the design of a hybrid timber-reinforced concrete multi-storey building, the following structural schemes can be recommended.For a 5-storey building it is possible to use rigid type of joint, as well as hinge but with the application of shear walls or a rigidity core; the dimensions of the cross-section of the columns should be assigned at least 250x250 mm.For a 10-story building the dimensions of the cross-section of the columns 300x300 mm and a scheme with hinge type of joints with a shear walls or rigidity core should be adopted.For a 15-story building, the crosssectional dimensions of the columns should be taken at least 400x400 mm, as well as a scheme with rigid of frame elements or hinge joints in combination with a stiffness core is recommended.
Conclusions.The analysis of the stress-strain state of hybrid timber-reinforced concrete multi-storey buildings depending on the number of storeys and the method of ensuring spatial rigidity in accordance with the requirements of current standards has been performed.The buildings of 5, 10 and 15 storey with rigid and hinge type of joints between frame elements, as well as different modes of spatial stiffness providing (various configuration of shear walls and rigidity core) were considered.3D finite-element model for each type of buildings were developed using available commercial software.As a result of the static calculation of the models, data were obtained on the values of the horizontal displacements of the upper part of the building, as well as the maximum values of internal forces caused by unfavorable load combinations.Using these data, an analysis of the spatial stability of the building and the load-bearing capacity of timber columns as the most loaded elements was performed.
Based on the results obtained, recommendations were proposed for choosing a structural scheme, a method for providing the spatial rigidity of a building, as well as assigning cross-sectional dimensions at the initial stage of the design of a hybrid timber-reinforced concrete multi-storey building.

Fig. 3 .
Fig. 3. Diagrams of horizontal displacements caused by the wind load along the height of the building: a) for a 5-story building; b) for a 10-story building; c) for a 15-story building: 1 -hinge joints without rigidity elements; 2 -rigid joints without rigidity elements; 3 -hinge joint + 2 shear walls; 4 − hinge joint + 4 shear walls; 5 − hinge joint + rigidity core

Table 1
Physical and mechanical characteristics of materials and parameters of the cross section of the structural elements

Table 2
The design values of the wind load

Table 3
Maximum values of internal forces and load-bearing capacity utilization rate of timber columns