Finite element analysis on composite steel-concrete shear walls with centered and staggered openings

Present paper presents a comparative study made on the seismic performance of composite steel-concrete shear walls with rectangular openings, by performing numerical analyses using ATENA 3D software. Two specimens were designed at a reduced scale 1:3 having similar arrangements in the cross-section and the same geometry. First element was conceived with centered openings while the second one was designed with staggered openings. Steel connectors disposed as horizontal stiffeners were used to design and to assure the full connection between the structural steel profiles embedded in the edges and the concrete core. The openings that were considered on each story of the walls, were having the dimension of a common architectural door. A part of the results recorded from the experimental tests were used to calibrate the numerical models. This study aims to establish the seismic performance and to investigate the influence of the openings and the geometric position on the overall seismic behavior of the composite shear walls. Key parameters which describe the seismic performance of structural elements such: bearing capacity, deformation capacity, stiffness degradation, cracks and strain development are compared between the specimens and discussed. The results showed that different arrangements of the openings could significantly modify or increase the seismic performance of the composite structural walls.


Introduction
Composite steel-concrete walls are frequently met in case of low to high-rise buildings to brace the structures against seismic activity.In general, the composite walls are made from a rectangular concrete web panel reinforced by a series of hot-rolled or welded structural steel profiles.These profiles could be partially or totally embedded in the cross-section, the connection with the concrete web panel being assured by steel connectors [1].Many times, due to architectural reasons, structural walls need to be conceived with different types of openings such as doors or windows, to assure the building functionality.In most of the cases, the openings are geometrically aligned but sometimes staggered openings are required on the height of the walls (figure 1).In other cases, due to functional modifications of the existing buildings, new openings are needed to be cut out into the structural walls, to assure the ventilation or heating services paths.The openings could significantly modify the seismic behavior of structural walls and have to be considered in the design process of the structures [2], [3].In the literature the subject related to the seismic behavior of composite steel-concrete shear walls with centered or staggered openings is not thoroughly investigated, additional investigations and analytical or numerical studies are needed to extend the knowledge and the existing database of such structural elements.To investigate the influence of the geometrical position of openings on the seismic behavior of composite steel-concrete shear walls, a comparative study made on two specimens designed at a reduced scale 1:3 is presented in this paper, as part of a large theoretical and experimental study that is in progress now.The present study is based on the numerical results recorded using the non-linear structural analysis software ATENA 3D Engineering.The seismic performance of one composite steel-concrete shear wall with centered openings CSRCW-21-CO and one with staggered openings CSRCW-21-SO is investigated and the results are compared in terms of: load bearing capacity, deformation capacity, lateral stiffness degradation, cracks, and strain development.Also, the boundary conditions and material laws used to calibrate the numerical models with the experimental results are described in this article.

Details of the designed specimens
The investigated specimens present partially I-shaped steel profiles embedded in the edges and measure three meters height, one meter in width and one hundred millimeters in thickness, being designed at a reduced scale 1:3 to simulate the first three storeys of an element part of a lateral resisting system.The core of the walls was encased into a rectangular reinforced concrete block of foundation which measure 1,50 m in length, 400 mm in height and 350 mm width.The CSRCW-21-CO specimen has centered aligned door openings (which measure at the reduced scale 300x700 mm equivalent to real dimensions of 900x2100 mm) while in the case of the CSRCW-21-SO specimen, the openings were moved eccentrically left-right on the height of the wall, from the vertical axis to the edges by 95 mm (figure 2 The structural I-shaped steel profiles embedded in the edges were manufactured using 5,65 mm welded steel plates.The composite connection between the reinforced concrete web panel of the walls and the structural steel profiles was designed as full connection.The connection was assured by a series of steel plates perforated by two circular holes, through which two longitudinal bars were passing as can be seen in figure 3. Hot-rolled steel bars with 8 mm diameter were used to reinforce the concrete web panel of both specimens.The shear capacity of the vertical piers was increased using enclosed stirrups which were welded to the steel profiles on the edges and were spaced at every 60 mm on the height of the walls.The specimens were constructed with a U-shaped steel profile on the top to assure a more uniform distribution of the local stresses induced by the vertical load.More details about walls detailing are described in [4].

Numerical analysis
The geometry of the composite walls was defined and modeled using 3D volume elements called macroelements.The contact between each macroelement was assumed to be perfectly rigid.Eight macroelements were used to model the overall geometry of the walls.The 3D solid tetra elements with six nodes of integration and 80 mm size were used to assure the FE mesh of the models.To prevent stress concentrations at the points where horizontal and vertical external forces were applied, two 30 mm thick metal plates were defined.A surface spring was attached on the bottom side of the walls beam foundation to simulate the surface support generated by the lab foundation (figure 4).The spring was set as infinite rigid in compression and inactive in taking the negative translations (simulating a rocking foundation) effect produced by the overturning bending moment at the base of the walls.The negative translations were prevented by the secondary surface spring attached on the top part of the beam foundation edges, simulating the axial stiffness of the local steel anchoring rods.
-9999999.0The rebars embedded in concrete were modeled using truss linear discrete elements with two integration nodes, each bar being modeled individually.All the stirrups were modeled using four lines with four integration nodes, being completely closed neglecting the hooks.All the reinforcement bars were modelled with an assumption of perfect bond to concrete macroelements.The SBETA (StahlBETonAnalyse) CC3DNonLinCementitious2 material model was used to calibrate the nonlinear behavior of concrete in tension and compression, based on the recommendations from other researches [5]- [8].All the nonlinear concrete parameters were automatically calculated by the software using the mean cubic strength of concrete determined experimentally.The 3D Steel Bilinear Von Mises material model which incorporate the Von Mises failure criterions was applied to simulate the behavior of steel in compression and tension from the steel profiles partially embedded in the edges.The following parameters were considered in the simulation: yield limit σ y =445 MPa; hardening modulus H=2100 MPa; elastic modulus E=210000 MPa and Poisson's ratio μ=0.3.In case of steel reinforcements, the CCReinforcement multilinear plastic stress-strain constitutive model was used to cover the behavior in tension and compression.The buckling of longitudinal bars in compression was not considered in this study.In figure 5 and figure 6 are presented the numerical models defined for both specimens.

Envelope curves
The numerical analyses were performed using the displacement control mode (pushover analysis).A constant vertical load of 100 kN was applied on both specimens during the numerical analysis, simulating the gravitational load.The experimental hysteretic curve of the CSRCW-21-CO specimen was used to calibrate and to compare the results of the numerical models [4].The envelope curves of both analyzed specimens are presented in figure 7.In case of the CSRCW-21-CO specimen, the envelope curve obtained numerically is quite similar with the experimental hysteretic curve.Also, the brittle failure mode characterized by the sudden degradation of the horizontal force is recorded by the approached numerical model.The maximum load bearing capacity recorded experimentally was F exp =266 kN while numerically F num =263.9 kN.It can be said that the numerical approaches considered for the numerical models could be used for further investigations of such walls.By modifying the position of the openings, the seismic behavior of CSRCW-21-SO specimen is not significantly changed.The load bearing capacity of the specimen and the lateral stiffness is quite close with those recorded by the CSRCW-21-CO specimen, but the failure mode is triggered in a different way.The composite wall with staggered openings CSRCW-21-SO has an improved deformation and stresses redistribution capacity in comparison with composite wall with regular openings CSRCW-21-CO. -

Lateral stiffness degradation
The lateral stiffness of the walls (figure 8) was evaluated as the ratio between the lateral force F (kN) and the top lateral displacement (∆).The behavior of both specimens is quite similar until the failure occur, but the initial stiffnesses in the first step of loading recorded are different.The shear wall CSRCW-21-SO recorded a greater initial stiffness K=48,59 kN/mm while element with centered openings CSRCW-21-CO K=33,04 kN/mm, a difference about 30%.This aspect may be the result to the fact that, in case of the CSRCW-21-SO composite wall the coupling beams became shorter after changing of openings position and therefore the deformed length was reduced and due to a better confinement assured by the enclosed stirrups.Other aspects can be related to the vertical piers, that had an local alternate increased cross-section with an enhanced moment of inertia, that contributed on the increasing of the wall lateral stiffness.In figure 9 are shown for comparative study the trajectories of the compressed concrete strain for both analyzed specimens.These trajectories are marked with blue color on the concrete web panel.It can be seen that for the CSRCW-21-CO wall the most damaged parts are the coupling beams.The vertical piers developed a high state of stresses just over the encasement level in the beam foundation.In case of the wall with staggered openings, this situation is slightly modified due to different openings arrangement.The compression stresses in concrete are more accentuated at the level of first coupling beam in time that for the second beam these trajectories are more widespread.Similar tensile stresses are developed in steel profiles partially embedded in the edges in case of both specimens, but the composite wall with staggered openings developed a larger state of tensile stresses in steel reinforcements as can be seen in figure 10.The composite wall CSRCW-21-SO will develop a higher capacity to dissipate the hysteretic energy due to larger plastic deformations in reinforcements and will experience a more stable seismic behavior in comparison with the composite wall with regular openings.In case of CSRCW-21-CO specimen the concrete in the coupling beams will be crushed or damaged almost simultaneously in the same time due to the uniform state of stresses recorded as is stated in figure 9.

Cracks analysis
By analyzing the cracks distribution of the composite walls (figure 11), it can be observed that the CSRCW-21-SO specimen with staggered openings presents a different crack distribution in comparison with the composite wall with regular openings.In case of CSRCW-21-CO both coupling beams are intersected by inclined shear cracks when the total drift reached only 0,25% from the total height.In case of CSRCW-21-SO specimen, these cracks occur only on the horizontal beam from the second level, in time that the first beam from the first level is intersected only by bending cracks propagated from the coupling beam edges.This mode of cracking may suggest an improved lateral stiffness of the composite wall with staggered openings.

Conclusions
This paper presents the results of a comparative study made on the seismic behavior of composite steel-concrete walls with rectangular openings, by performing a series of numerical analyses.Two walls with centered and staggered openings were analyzed and their seismic performance in terms of load bearing capacity, lateral stiffness degradation, deformation capacity and cracks distribution were compared and discussed during the chapters.To validate the numerical models, the experimental curve of the CSRCW-21-CO specimen was used.By analyzing the results, the following conclusions can be drawn from the present study: -The numerical approaches considered to simulate the seismic performance of composite steelconcrete shear walls with staggered and regular openings using ATENA 3D Engineering are in a good agreement with the results recorded by the experimental tests; -The composite wall with staggered openings CSRCW-21-SO developed a higher initial stiffness, with more than 30% in comparison with the composite wall with regular openings CSRCW-21-CO; -The specimen CSRCW-21-SO will dissipate a higher rate of the seismic energy due to larger plastic deformations developed in steel reinforcements and will experience a more stable seismic behavior in comparison with the composite wall with regular openings CSRCW-21-CO; -The sequence of the occurrence and cracks distribution in case of the CSRCW-21-SO specimen is quite different in comparison with the composite wall with central openings CSRCW-21-CO;

Figure 2 .
Figure 2. The geometry and reinforcements of the investigated specimens

Figure 3 .
Figure 3. Details of composite connection between steel profiles and reinforced concrete core

Figure 4 .
Figure 4. Modeling of the walls boundary conditions

Figure 7 .
Figure 7. Envelope curves of the investigated composite walls

Figure 11 .
Figure 11.Cracks development on the concrete web panel

Table 1 .
Mechanical parameters of steel