Study of the features of the work of concrete-steel composite beams in buildings with a steel frame

. Concrete-steel composite structures are unique structures that combine the advantages of both steel and concrete. Their application is especially relevant in cases where construction objects need to withstand high loads with small cross-sectional dimensions. Thanks to the factory production of most of the elements and easy installation, it is possible to significantly reduce construction times. The main areas of application are high-rise construction, industrial construction, and bridge construction. The main task in the design of concrete-steel composite structures is to take into account the joint work of a reinforced concrete slab and steel beams, i.e. correct modeling of the structure when using calculation systems. This article explores various options for setting the numerical model of a concrete-steel composite beams using the example of one floor of a high-rise building, evaluates their reliability and compliance with the actual behavior of the structure. In conclusion, recommendations are offered on the numerical modeling of concrete-steel composite beams for calculation using the finite element method.


Introduction
In the construction and reconstruction of industrial and civil buildings, concrete-steel composite beams are widely used [1][2][3][4][5][6][7][8].Steel concrete composite beams consists of a steel beam over which a reinforced concrete slab is cast with shear connectors.The main types of concrete-steel composite structures include: composite slabs, which are typically constructed from reinforced concrete cast on top of profiled steel decking, composite beams, which could be constructed as downstand beams or shallow floors, composite columns, etc.A large number of experimental [9][10][11][12][13][14][15] and numerical [16][17][18][19][20] studies are devoted to the operation of concrete-steel composite structures.The article analyzes various options for finite element models of a concrete-steel composite beams formed by a monolithic reinforced concrete slab and steel beams.

Methods
The design model of the concrete-steel composite beams consists of the main and secondary steel beams and a reinforced concrete slab made along the upper flanges of the main and secondary beams.The main beams are rigidly fixed between the reinforced concrete stiffening shaft and inclined columns (elements of the diagonal mesh shell).The secondary beams hinged on the main beams.The considered model works as a concretesteel composite structure and makes it possible to rationally use the properties of concrete and steel.The calculation takes into account permanent loads (self-weight of structures and a multi-layer flooring structure) and short-term loads (uniformly distributed load on floor slabs for service premises) in accordance with SP 20.13330.2016"Loads and Impacts".The design was calculated using the Lira SOFT ver.10.8 computer complex.
The steel frame of the building is made of steel of strength classes C390 and C345.The main beams are made of rolled I-beam 70Sh4 (C390), the secondary beams are made of rolled I-beam 40Sh2 (C345), the diagonal mesh shell is made of pipes 1620x34, 1020x34, 720x34, 530x30 (C390).The main beams are located along the radii of the floor, the total number of main beams on each floor is 40 pcs.Step of secondary beams 4.4 m.Reinforced concrete slab is 200 mm thick, made of concrete class B25.
The following variants of the finite element model of concrete-steel composite beams are considered:  1 variant.Modeling of a concrete-steel composite structure with a bar elements (main and secondary steel beams) and shell elements (reinforced concrete slab).The slab and beams are connected by highly rigid rods, the length of which is equal to the distance between the centers of gravity of the I-beams and the reinforced concrete slab.The general view of the computational model and its fragments are shown in fig. 1 and 2.  2 variant.The model is similar to variant 1, but above the main and secondary steel beams, at the junction of the slab to the stiffening core and the contour beams, expansion joints are arranged in order to reduce tensile forces in the slab.To reduce the forces in individual structures and prevent the formation of cracks in them, expansion joints are arranged.In the design scheme, this design is modeled by FE 56 -a single-node finite element that describes an elastic connection.For this type of FE, the necessary parameters are the stiffness per unit length in the X, Y, Z, UX, UY, UZ directions.An isotropic elastic bond is assumed, while the linear stiffness in the X, Y, Z directions was taken to be 50 MN/m (as for rubber materials), and for the angular stiffnesses in the UX, UY, UZ directions, zero was taken.In variants 1 and 2 of the design scheme, the concrete of the entire slab has a long-term modulus of elasticity: E b,t =8571 MPa.
 3 variant.Modeling of a steel-reinforced concrete slab using a slab of variable stiffness and bar elements that take into account additional reinforcement of the slab in areas of high tensile forces.In order to perceive tensile forces in the reinforced concrete floor slab above the main beams and at the junction of the slab to the stiffening core and the contour beam, rod elements are introduced into the design scheme in tension zones.Assuming that the concrete in the tensile zone is not included in the tensile work due to the formation of cracks, in the finite elements located in the tensile zone, the modulus of elasticity of the material is significantly reduced, which makes it possible to exclude the concrete of these zones from the tensile work and ensure the transfer of tensile forces only by reinforcing these areas.The value of the reduced modulus of elasticity of concrete in the tension zone is 0.0003-0.3% of E b (initial modulus of elasticity in compression and tension).Fig. 3a shows the location of elements that simulate reinforcement in tension zones, fig.3b -sections  The cross-sectional area of the reinforcement is determined on the basis of preliminary calculations for the forces in the tension zone of the slab and is 16.084 cm 2 /m for the reinforcement of class A500.

Results
The calculation of the first version of the concrete-steel composite structure showed that in the finite elements simulating the concrete slab in the areas above the flanges of the main beams in the places of their rigid attachment to the stiffener and columns, significant tensile longitudinal forces occur.The results are shown in fig. 4. Therefore, the inclusion of concrete in tension zones in the finite element model does not correspond to the actual operation of the slab, in which cracks appear in the tension zone, and these sections should be excluded from the model, which will lead to a redistribution of forces in the system.
The results of the calculation of the second variant in the construction of expansion joints are shown in fig. 5.The introduction of single-node finite elements of an elastic connection into the design scheme, taking into account the presence of expansion joints, made it possible to reduce the values of tensile stresses in the slab by several times.The tensile stresses in the slab in this variant do not exceed the concrete tensile strength R bt : N x = 0,163 MPa < R bt = 1,05 MPa.Thus, when installing expansion joints, the strength of the floor slab is ensured.However, the introduction of expansion joints in the design, located along the axes of the beams, does not effectively ensure the joint operation of the slab and steel beams.Expansion joints are located above the beams, where stud bolts are welded to the upper flanges of the beams.The expansion joint violates the integrity of the slab, excludes the reliable interaction of the slab with stud bolts and does not impede the transfer of shear forces.With this in mind, a floor slab with expansion joints cannot work together with beams, even in the presence of stud bolts, like a concrete-steel composite structure.In the presence of expansion joints, the floor slab does not form a hard floor disk and complicates the transfer of horizontal forces to the reinforced concrete stiffener.
The calculation results of the third variant of the finite element model are shown in fig.6 Fig. 6.Principal normal stresses ϭ 1 in the slab (model variant No. 3) In accordance with the calculation performed, the tensile stresses arising in the slab in the slab are 0.834 MPa, which is less than the tensile strength of the concrete of the slab (1.05 MPa).The forces in the bars simulating reinforcement amounted to 130.5 kN/m.The required cross-sectional area when using A500 class reinforcement was 14.76 cm 2 /m.With this in mind, the reinforcement of the stretched zones of the slab is carried out with class A500 rods with a diameter of 14 mm with a step of 100 mm, the cross-sectional area of the reinforcement is 15.39 cm 2 /m.The length of reinforcement anchoring in the concrete of the slab outside the tension zone is set according to the method of SP 63.13330.2018and is l an = 580 mm.The total length of the rods, taking into account their work in the tension zone in the supporting sections of the slab and the anchoring length, will be 2.2-2.4 m.

Discussion
The conducted numerical calculations made it possible to establish the stress-strain state of the concrete-steel composite beams, depending on different methods of finite element modeling of the concrete-steel composite structure.Correct modeling of a concrete-steel composite structure allows obtaining reliable displacements and forces in the calculation of multi-storey buildings with a steel frame and concrete-steel composite slabs.The analysis of the obtained results showed that in the first variant of the simulation, the stresses arising in the slab in some areas exceed the tensile strength of the slab concrete.The introduction of expansion joints into the structure in accordance with the second modeling variant leads to a disruption in the joint work of the reinforced concrete floor with steel beams.Therefore, the use of the first two variants of calculation models for the calculation of concrete-steel composite beams is not correct.The third variant most accurately simulates the joint work of a monolithic slab and steel beams.The installation of additional reinforcement in the tension zone makes it possible to significantly reduce the values of tensile stresses arising in the slab above the main beams when the slab and beams are reliably included in the joint operation.
Based on a comparison of the results of calculations of the first and third variants, it can be noted that along with the longitudinal forces in the reinforced concrete slab, the longitudinal forces in the main beams also change.With the introduction of additional reinforcement with anchoring into the slab, the longitudinal force in the main beams in the area of the supports decreased several times.At the same time, the longitudinal forces at the attachment points of the secondary beams to the main beams increased.Longitudinal forces on beam supports are, kN: -main beams, 1 var.: -927.67;-main beams 3 var.: -226.18;-secondary beams 1 var.: -201.44;-secondary beams 3 var.: -630.45.
Thus, the modeling of the concrete-steel composite beams according to the third option makes it possible to exclude the appearance of cracks in the floor slab, correctly determine the forces at the junctions of the main beams to the stiffener, columns and contour beams, as well as at the attachment points of the secondary beams to the main ones.

Conclusions
1.The inclusion of a floor slab with a constant modulus of elasticity over the entire floor area in the finite element model does not provide the correct calculation of the concrete-steel composite beams due to the development of unacceptable tensile forces in the floor slab.2. The device of expansion joints in the stretched areas of the floor slab allows several times to reduce the value of tensile forces, however, at the same time, steel beams and a reinforced concrete slab stop working together.3. Additional reinforcement of the stretched zones of a concrete slab with a simultaneous decrease in the concrete elasticity modulus in these zones to a value of 0.0033…0.33%from the initial concrete elasticity modulus is an effective measure to eliminate large tensile forces in the slab and ensure the performance of steel-reinforced concrete floors and allows you to reliably determine the stressdeformed state of the floor.
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 . 2023 Fig. 2 .
Fig. 1.General view of the finite element model of concrete-steel composite structure

Fig. 3 .
Fig. 3. 3 variant of numerical model with additional reinforcement above the main beams, above the secondary beams along the stiffening core and external contour beams.a) bar elements simulating reinforcement in tensioned zones of the slab; b) reinforced concrete floor slab (areas highlighted in green with a long-term modulus of elasticity E b,t =8,571 MPa; in red -with a reduced modulus of elasticity E b,red =0.001 MPa).

Fig. 4 .
Fig. 4. Principal normal stresses ϭ 1 in the slab (model variant No. 1) The obtained results indicate that the strength condition in the stretched zones of the plate is not fulfilled.Stresses in concrete exceed the design tensile strength of concrete: N x = 3,21 MPa > R bt = 1,05 MPa.