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Figure 1. Database analysis: a) wall density in the two mains directions; b) slenderness ratios. Subsequently, 18 linear numerical models of representative buildings from the database were constructed, anc ypical values of variables such as the axial load ratio (ALR), the ratio between the bending moment and shear (M/V), the fundamental period, aspect ratio, and the interstory and roof drift were identified, among others (Ortega et al. 2019). From this analysis, three representative 5-, 8- and 12-story buildings were selected and labeled E1, E2, and E3, respectively. Nonlinear numerical models were constructed for these buildings and adjusted in two ways. At a globa evel, the models were adjusted based on the experimental results from an ambient vibration test in one of the buildings analyzed in this study. This test made it possible to assess the actual dynamic properties and to adjust the numerica model by varying the parameters related to the degree of cracking in the structure, which were extrapolated to the othe wo buildings. At a local level, the models were adjusted to simulate the inelastic response of the walls of the building: using the modeling and calibration parameters determined for the numerical model of isolated walls based on the hysteretic response measured in the experimental tests. = . iw ae ig: * ee we i i a ns x: a mice ‘ies

Figure 1 Database analysis: a) wall density in the two mains directions; b) slenderness ratios. Subsequently, 18 linear numerical models of representative buildings from the database were constructed, anc ypical values of variables such as the axial load ratio (ALR), the ratio between the bending moment and shear (M/V), the fundamental period, aspect ratio, and the interstory and roof drift were identified, among others (Ortega et al. 2019). From this analysis, three representative 5-, 8- and 12-story buildings were selected and labeled E1, E2, and E3, respectively. Nonlinear numerical models were constructed for these buildings and adjusted in two ways. At a globa evel, the models were adjusted based on the experimental results from an ambient vibration test in one of the buildings analyzed in this study. This test made it possible to assess the actual dynamic properties and to adjust the numerica model by varying the parameters related to the degree of cracking in the structure, which were extrapolated to the othe wo buildings. At a local level, the models were adjusted to simulate the inelastic response of the walls of the building: using the modeling and calibration parameters determined for the numerical model of isolated walls based on the hysteretic response measured in the experimental tests. = . iw ae ig: * ee we i i a ns x: a mice ‘ies

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Graphical abstract ) Latin American Journal of Solids and Structures. ISSN 1679-7825. Copyright © 2021. This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Graphical abstract ) Latin American Journal of Solids and Structures. ISSN 1679-7825. Copyright © 2021. This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The hysteretic performance was modeled using the pivot hysteresis model, which was proposed by Doweel et al. (1998), and is recommended for reinforced concrete members (CSI, 2017). This model can simulate the pinching effect, control stiffness degradation, and enable the application of non-symmetry in hysteretic loops. The behavior of this model is based on the fact that the loading and unloading directions are directed toward specific points, which are termed pivot points, in the force-deformation plane.
The hysteretic performance was modeled using the pivot hysteresis model, which was proposed by Doweel et al. (1998), and is recommended for reinforced concrete members (CSI, 2017). This model can simulate the pinching effect, control stiffness degradation, and enable the application of non-symmetry in hysteretic loops. The behavior of this model is based on the fact that the loading and unloading directions are directed toward specific points, which are termed pivot points, in the force-deformation plane.
Figure 2. Representation of concrete and reinforcement steel layers in a Shell Layered element (Lu et al., 2014). In numerical models, the stress-strain curves of conventional concrete and ductile reinforcement steel were definec using models developed by Mander et al. (1988) and Park and Paulay (1975), respectively. The stress-strain curve o nonductile WWM was calculated using equation (1), which was proposed by Mirza and Mac-Gregor (1981). In isolatec walls, the mechanical properties of the materials were defined according to laboratory reports. In the models of the buildings, the stress-strain curves of unconfined concrete and reinforcement steel were constructed using the parameters shown in Table 1. The elastic modulus of concrete, E,, was estimated to be 3900 vf’. (MPa).
Figure 2. Representation of concrete and reinforcement steel layers in a Shell Layered element (Lu et al., 2014). In numerical models, the stress-strain curves of conventional concrete and ductile reinforcement steel were definec using models developed by Mander et al. (1988) and Park and Paulay (1975), respectively. The stress-strain curve o nonductile WWM was calculated using equation (1), which was proposed by Mirza and Mac-Gregor (1981). In isolatec walls, the mechanical properties of the materials were defined according to laboratory reports. In the models of the buildings, the stress-strain curves of unconfined concrete and reinforcement steel were constructed using the parameters shown in Table 1. The elastic modulus of concrete, E,, was estimated to be 3900 vf’. (MPa).
Note: N: number of stories, tw: wall thickness, H: total height, hw: interstory height, A: floor area, Dx, Dy: wall density in the X- and Y-directions Table 2. Properties of the TRCW buildings.
Note: N: number of stories, tw: wall thickness, H: total height, hw: interstory height, A: floor area, Dx, Dy: wall density in the X- and Y-directions Table 2. Properties of the TRCW buildings.
Figure 3. Comparison of the numerical and experimental responses of wall M1R10: a) hysteresis curve; b) stiffness degradation and cumulative dissipated energy.
Figure 3. Comparison of the numerical and experimental responses of wall M1R10: a) hysteresis curve; b) stiffness degradation and cumulative dissipated energy.
Figure 4. Numerical models and plan view of the buildings, a) E1, b) E2 and c) E3.
Figure 4. Numerical models and plan view of the buildings, a) E1, b) E2 and c) E3.
Figure 5. Experimental vibration test: a) instrumented building, b) triaxial accelerometer. The ambient vibration test was performed in building E2 (Figure 5a) to adjust its numerical model and to determine the global parameters for adjusting the models of the other buildings, E2 and E3. The test consisted of acquiring accelerations due to ambient vibration at relevant points of the structure. For this purpose, uniaxial and triaxial sensors were used (Figure 5b), and readings were taken on the sixth and eighth story of the building.
Figure 5. Experimental vibration test: a) instrumented building, b) triaxial accelerometer. The ambient vibration test was performed in building E2 (Figure 5a) to adjust its numerical model and to determine the global parameters for adjusting the models of the other buildings, E2 and E3. The test consisted of acquiring accelerations due to ambient vibration at relevant points of the structure. For this purpose, uniaxial and triaxial sensors were used (Figure 5b), and readings were taken on the sixth and eighth story of the building.
Table 3. Experimental fundamental periods. The numerical model of the building was adjusted by modifying the parameters that control the inelastic response of the walls and the level of cracking in the walls and beams. The process was performed using an application programming interface (API) between the programs MATLAB and ETABS, which facilitated the variation in these parameters within reasonable ranges. The cracking levels assessed after adjusting the model were approximately 50% for walls and 35% for beams. Table 4 summarizes the results from the adjustment of the model of building E2 regarding the fundamental period, T. The nonlinear behavior, modeled with the Shell Layered element, was only implemented in the walls of the lower third of the building, assuming a linear behavior in the two upper thirds. These parameters were used in the models of buildings E1 and E3.
Table 3. Experimental fundamental periods. The numerical model of the building was adjusted by modifying the parameters that control the inelastic response of the walls and the level of cracking in the walls and beams. The process was performed using an application programming interface (API) between the programs MATLAB and ETABS, which facilitated the variation in these parameters within reasonable ranges. The cracking levels assessed after adjusting the model were approximately 50% for walls and 35% for beams. Table 4 summarizes the results from the adjustment of the model of building E2 regarding the fundamental period, T. The nonlinear behavior, modeled with the Shell Layered element, was only implemented in the walls of the lower third of the building, assuming a linear behavior in the two upper thirds. These parameters were used in the models of buildings E1 and E3.
Table 4. Comparison of experimental and analytical fundamental periods of the adjusted and unadjusted models.
Table 4. Comparison of experimental and analytical fundamental periods of the adjusted and unadjusted models.
Figure 6. Identification of the natural frequency for the first two mode vibration of building E2.
Figure 6. Identification of the natural frequency for the first two mode vibration of building E2.
Table 5. Seismic vulnerability indices according to NSR-10. A more detailed analysis showed that in building E2, the ten walls with an OSlgenpinc value higher than 1.0 are the longest walls of the seismic resistance system, are mainly concentrated at the core and ends of the building and are oriented in the direction with the lowest wall density. For building E3, most walls with a bending index higher than 1 (i.e 40%) are located at the ends of the building and oriented in the y-direction, which is the most critical direction due tc the discontinuity of the floor diaphragm. In building E1, the maximum values also occurred in the longest walls, but the, did not reach values higher than 1.
Table 5. Seismic vulnerability indices according to NSR-10. A more detailed analysis showed that in building E2, the ten walls with an OSlgenpinc value higher than 1.0 are the longest walls of the seismic resistance system, are mainly concentrated at the core and ends of the building and are oriented in the direction with the lowest wall density. For building E3, most walls with a bending index higher than 1 (i.e 40%) are located at the ends of the building and oriented in the y-direction, which is the most critical direction due tc the discontinuity of the floor diaphragm. In building E1, the maximum values also occurred in the longest walls, but the, did not reach values higher than 1.
Figure 7. Story drifts: a) earthquake in the x-direction, b) earthquake in the y-direction. direction was more affected by the discontinuity in the floor diaphragm. The 5- and 8-story buildings E1 and E2 showed maximum drifts of 0.09 and 0.47%, respectively, in the directions with the lowest wall density.
Figure 7. Story drifts: a) earthquake in the x-direction, b) earthquake in the y-direction. direction was more affected by the discontinuity in the floor diaphragm. The 5- and 8-story buildings E1 and E2 showed maximum drifts of 0.09 and 0.47%, respectively, in the directions with the lowest wall density.
Figure 8. Seismic vulnerability indices of the buildings according to NSR-10.
Figure 8. Seismic vulnerability indices of the buildings according to NSR-10.
Figure 9. Response spectra of earthquakes scaled to the design spectrum for building E1. Table 6. Properties of seismic signals.
Figure 9. Response spectra of earthquakes scaled to the design spectrum for building E1. Table 6. Properties of seismic signals.
Table 7. Parameters and acceptance criteria for seismic performance assessment of TRCW buildings. Note: * Lp = 0.5lw, ** Lp = 2.5tw. Where Lp: plastic hinge length, tw: wall thickness, and lw: wall length. The acceptance criterion of the first parameter (1), rotation at the base of the walls, was taken from ASCE/SEI 41-01 (2007) for walls with axial load ratios (ALR) lower than 0.10, a mean maximum shear force lower than or equal to 0.02 MPa and walls without confined boundary elements according to ACI 318 (2014). According to Elwood etal. (2007), the experimental results of Hidalgo et al. (2002), EERI/PEER (2006), and Wallace et al. (2006) showed that the criteria of thi he most recent versions, are conservative for walls with well-confined special boundary elements Therefore, they could be used for this type of thin wall. In addition, these walls meet the condition of absence of confinex s because a thickness lower than or equal to 150 mm does not guarantee adequate concrete confinemen (Arteta, 2015). The plastic hinge was evaluated according to ASCE/SEI 41, at a wall height equal to 0.5 times its length ani standard, un boundary ele at a height o like men f2.5 imes the wal & Bonett, 2020; Ortega et al., 2 was proposed by buildings with wa TRCWsS tests CEER 2018). T limit values thickness, in line with the hinge length experimentally reported in thin wall tests (Blando: 021). For the parameter story drift, two acceptance criteria were taken (2 and 3). The firs Gonzales and Lopez-Almansa (2012), according to a numerical evaluation of the seismic behavior o Is of limited d according to the rupture strain taken as the Story dri uctility in Peru. The second was taken according to the experimental response assessed i Rosso et al. 2015, Blandon et al. 2018, Bland6n & Bonett 2020, Carrillo & Alcocer 2012, Ortega et al. 2021, an hese studies suggest that a story drift of 0.5% could be a limit of good behavior for this structural system. Th for strains in ducti e reinforcement (4) and meshes (5), for the life safety performance level, were define proposed by Arroyo et al. (2021) for these materials. The limit for the sixth parameter wa heoretical ultimate compressive strain of unconfined concrete. fts were assessed for each accelerogram. The plastic hinge rotation and the compressive strain of concrete at thi a a ees, a ees ee Se mt eemessts—i(itstsH ge ne ee. The building performance was assessed regarding local and global damage quantification parameters, such as strains in concrete and reinforcing steel, plastic hinge rotation at the base of the walls, and story drift. The proposed acceptance criteria (C), which are based on the experimental performance of concrete walls, are shown in Table 7. This analysis was performed for the life safety performance level because the seismic demand (D) was defined concerning the design spectrum of NSR-10, with a return period of 475 years.
Table 7. Parameters and acceptance criteria for seismic performance assessment of TRCW buildings. Note: * Lp = 0.5lw, ** Lp = 2.5tw. Where Lp: plastic hinge length, tw: wall thickness, and lw: wall length. The acceptance criterion of the first parameter (1), rotation at the base of the walls, was taken from ASCE/SEI 41-01 (2007) for walls with axial load ratios (ALR) lower than 0.10, a mean maximum shear force lower than or equal to 0.02 MPa and walls without confined boundary elements according to ACI 318 (2014). According to Elwood etal. (2007), the experimental results of Hidalgo et al. (2002), EERI/PEER (2006), and Wallace et al. (2006) showed that the criteria of thi he most recent versions, are conservative for walls with well-confined special boundary elements Therefore, they could be used for this type of thin wall. In addition, these walls meet the condition of absence of confinex s because a thickness lower than or equal to 150 mm does not guarantee adequate concrete confinemen (Arteta, 2015). The plastic hinge was evaluated according to ASCE/SEI 41, at a wall height equal to 0.5 times its length ani standard, un boundary ele at a height o like men f2.5 imes the wal & Bonett, 2020; Ortega et al., 2 was proposed by buildings with wa TRCWsS tests CEER 2018). T limit values thickness, in line with the hinge length experimentally reported in thin wall tests (Blando: 021). For the parameter story drift, two acceptance criteria were taken (2 and 3). The firs Gonzales and Lopez-Almansa (2012), according to a numerical evaluation of the seismic behavior o Is of limited d according to the rupture strain taken as the Story dri uctility in Peru. The second was taken according to the experimental response assessed i Rosso et al. 2015, Blandon et al. 2018, Bland6n & Bonett 2020, Carrillo & Alcocer 2012, Ortega et al. 2021, an hese studies suggest that a story drift of 0.5% could be a limit of good behavior for this structural system. Th for strains in ducti e reinforcement (4) and meshes (5), for the life safety performance level, were define proposed by Arroyo et al. (2021) for these materials. The limit for the sixth parameter wa heoretical ultimate compressive strain of unconfined concrete. fts were assessed for each accelerogram. The plastic hinge rotation and the compressive strain of concrete at thi a a ees, a ees ee Se mt eemessts—i(itstsH ge ne ee. The building performance was assessed regarding local and global damage quantification parameters, such as strains in concrete and reinforcing steel, plastic hinge rotation at the base of the walls, and story drift. The proposed acceptance criteria (C), which are based on the experimental performance of concrete walls, are shown in Table 7. This analysis was performed for the life safety performance level because the seismic demand (D) was defined concerning the design spectrum of NSR-10, with a return period of 475 years.
Figure 10. Seismic performance assessment of building E1: a) D/C ratio; b) critical walls.
Figure 10. Seismic performance assessment of building E1: a) D/C ratio; b) critical walls.
Figure 11. Seismic performance assessment of building E2: a) D/C ratio; b) critical walls.
Figure 11. Seismic performance assessment of building E2: a) D/C ratio; b) critical walls.
Figure 12. Seismic performance assessment of building E3: a) D/C ratio; b) critical walls.
Figure 12. Seismic performance assessment of building E3: a) D/C ratio; b) critical walls.
Figure 13. Parametric analysis variables: a) Study variables; b) Location of response parameters. nas, ina region between tne dase and up [0 a Ne lgnt OF 2.5 times the wali thickness, aS snown In Figure L5b. ROOT ariit wa xpressed as t The yield he percentage ratio in percent between the displacement at the top of the wall and the total height (6./Hw) and rupture strains of the bars were taken as 0.002 and 0.06, respectively, according to the rupture limi roposed by CEER (2018). For the electro-welded reinforcement, the yield and rupture strains were taken as 0.0025 anc .015, respec ively. The first plastic hinge of the wall was assumed at the instant in which the reinforcing steel, at th dges, reached a strain equal to twice the yield strain (CEER, 2018). The ultimate compressive strain of unconfinec oncrete was established as 0.004. Limit drifts of 0.5, 1, and 1.43% are indicated in the wall capacity curves as a reference 1 this study, apacity does he failure state is defined for the instant in which a 20% drop in lateral resistance occurs. Since this loss o not occur in all curves, two criteria were defined to establish an ultimate damage state close to failure hat is, when the strain in the bars exceeds the breaking limit or when the crushing of the concrete begins. From thes« vents, the capacity curve of the walls was differentiated with more subdued color. 6.3 Results of parametric analysis
Figure 13. Parametric analysis variables: a) Study variables; b) Location of response parameters. nas, ina region between tne dase and up [0 a Ne lgnt OF 2.5 times the wali thickness, aS snown In Figure L5b. ROOT ariit wa xpressed as t The yield he percentage ratio in percent between the displacement at the top of the wall and the total height (6./Hw) and rupture strains of the bars were taken as 0.002 and 0.06, respectively, according to the rupture limi roposed by CEER (2018). For the electro-welded reinforcement, the yield and rupture strains were taken as 0.0025 anc .015, respec ively. The first plastic hinge of the wall was assumed at the instant in which the reinforcing steel, at th dges, reached a strain equal to twice the yield strain (CEER, 2018). The ultimate compressive strain of unconfinec oncrete was established as 0.004. Limit drifts of 0.5, 1, and 1.43% are indicated in the wall capacity curves as a reference 1 this study, apacity does he failure state is defined for the instant in which a 20% drop in lateral resistance occurs. Since this loss o not occur in all curves, two criteria were defined to establish an ultimate damage state close to failure hat is, when the strain in the bars exceeds the breaking limit or when the crushing of the concrete begins. From thes« vents, the capacity curve of the walls was differentiated with more subdued color. 6.3 Results of parametric analysis
Figure 15. Linear and statistical analysis of the 18 MDCR buildings: a) ratio between roof drift and maximum story drift; b) aspect ratio.
Figure 15. Linear and statistical analysis of the 18 MDCR buildings: a) ratio between roof drift and maximum story drift; b) aspect ratio.
Figure 16. Capacity curves as a function of thickness. The longitudinal reinforcement ratio in the edges has an important influence on the ductility of the walls, as shown in Figure 14. It is evident that an increase in the longitudinal reinforcement ratio at the edges increases the lateral resistance, the displacement capacity and causes the ultimate deformation of the materials to be reached for larger roof drifts. Regarding the thickness, it influences exclusively the lateral load capacity, and the stiffness of the walls, as shown in Figure 16. This is without considering other effects such as out-of-plane slenderness. Figure 16 shows, in more detail, the capacity curves for a 4 m long wall, with a 2% longitudinal reinforcement ratio at the edges, for the evaluated heights of 5, 10, and 15 stories. In this wall, although the variation between the evaluated thicknesses is small (80 to 150 mm), it is observed that the damage states occur for similar drift levels between one thickness and another.
Figure 16. Capacity curves as a function of thickness. The longitudinal reinforcement ratio in the edges has an important influence on the ductility of the walls, as shown in Figure 14. It is evident that an increase in the longitudinal reinforcement ratio at the edges increases the lateral resistance, the displacement capacity and causes the ultimate deformation of the materials to be reached for larger roof drifts. Regarding the thickness, it influences exclusively the lateral load capacity, and the stiffness of the walls, as shown in Figure 16. This is without considering other effects such as out-of-plane slenderness. Figure 16 shows, in more detail, the capacity curves for a 4 m long wall, with a 2% longitudinal reinforcement ratio at the edges, for the evaluated heights of 5, 10, and 15 stories. In this wall, although the variation between the evaluated thicknesses is small (80 to 150 mm), it is observed that the damage states occur for similar drift levels between one thickness and another.
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