Influence of slab structure on the behavioral analysis of hybrid outrigger system

Outriggers are internal structural systems used to enhance the stiffness and strength of high‐rise structures. This research investigates the efficacy of a hybrid outrigger system (HOS) which consists of one conventional and one virtual outrigger at two distinct floor levels in high‐rise RCC buildings. A non‐dimensional quantity, ϒ, defined as the relative stiffness ratio between the core and the diaphragm is used to describe variations in the stiffness of the building's core, stiffness of floor diaphragm, breadth, and height of the structure, in the behavioral analysis of the HOS. To investigate the efficacy and optimum locations of the hybrid outriggers, static and dynamic analysis are carried out on models with four‐story heights of 140, 210, 280, and 350 m under static wind loading, uniform wind loading, equivalent static earthquake loading, and dynamic earthquake loading. Results are assessed based on the responses from roof displacement (Disptop), base bending moment, roof acceleration (Acctop), fundamental period, and absolute maximum inter‐story drift ratio (ISDabs.max). Based on the minimum responses of the aforementioned dependent parameters under wind and earthquake excitations, the corresponding optimum locations of hybrid outriggers are investigated. To investigate the impact of the slab on the functionality of the HOS, the behavior of shell stress variation in the tension and compression side of the slab at the outrigger floor level and the force transmission through the column at the outrigger level is analyzed. Also, the optimum location of the hybrid outriggers based on the ideal performance index (IdealPI) is investigated. IdealPI is defined as a parameter that considers the combined response of Disptop, Acctop, and ISDabs.max and the criteria required for the structure under wind and seismic loads. From the behavioral analysis results, it is found that an increase in the stiffness of the slab showed an improved performance of the HOS compared to an increase in the stiffness of the core, and HOS performance can be maximized by increasing both thickness of the slab and outrigger arm length. The findings of the optimum location analysis could serve as a guide for structural engineers when selecting suitable positions for hybrid outriggers in high‐rise structures.


| INTRODUCTION
Outrigger structures are often considered as efficient lateral load-resisting systems which can effectively reduce the lateral deformations in tall structures.They can be divided into two categories based on connectivity: conventional outriggers (COs) and virtual outriggers (VOs).2][3][4] As the outrigger arms span the width of the building, the floor in the CO level cannot be used for habitation.To eliminate this space constraint at the outrigger level, VOs were introduced. 5VO concept has an indirect connection between the core and external columns and the transmission of forces happens via floor diaphragms. 5Due to the CO's direct force transmission through the outrigger arms, it offers a better reduction in lateral deformation compared to the VO. 5,6Thus, a novel concept termed hybrid outrigger system (HOS) is framed in this study which considers the enhanced load reduction capacity of COs and the space efficacy provided by VOs.A HOS is termed as an outrigger system having one CO and one VO at two distinct floor levels.Figure 1  space obstruction brought on by the outrigger arms, thus making the system cost-effective in terms of usable floor area for the occupants.However, when comparing a HOS's performance to a CO, the CO would be more efficient regarding its lateral deformation resistance capacity.
However, the lateral load resistance of a HOS can be improved by redesigning the dimensions of the structural components while taking concrete volume optimization into account.To avoid the intricate connection details between steel or composite outriggers and concrete core, 7 this study explores a concrete core and concrete outrigger system.
Even while outrigger systems appear to be advantageous for high-rise buildings, passive control using passive damper, and resilience evaluation may still be helpful in the modern world.Takewaki and Akehashi in their paper had presented a detailed review on non-linear models with and without passive dampers under earthquake (EQ) loading 8 and also presented an optimization method for the design of viscous dampers. 9Passive viscous dampers largely improve resilience and decrease uncertainty concerning the manpower to repair the components. 10If an optimum damping design is provided in outriggers, its effectiveness in controlling lateral deformations and acceleration could be enhanced.2][13] Also, studies on damped outrigger systems, and combined conventional damped outriggers and negative stiffness damped outriggers were performed using stochastic optimization procedures to explore the optimal configurations of damped outriggers. 14,157][18][19][20][21][22][23] Typically, the outrigger is placed in the plant/machine rooms, but this makes the outrigger extremely unyielding and expensive, so an optimum position study needs to be performed and the positioning of outriggers is greatly influenced by the parameters stated above.5][26][27][28][29][30] Eom et al. 7 in their paper suggested that observing the axial forces on the column above and below the outrigger helps in evaluating the force transmission in outriggers.Hoenderkamp 24 and Huang et al. 31 suggested that analysis of the behavior of the outrigger floor slabs is frequently disregarded, and in their paper, they considered the slab behavioral analysis at outrigger level as it is through the slab the shear force from EQ is transferred.Thus, the influence of slab on the behavioral analysis of a HOS is a significant factor that needs to be considered.
Therefore, in this study, the influence of the floor diaphragm on the behavior of HOS is investigated.The behavioral analysis of the HOS is performed for variation in stiffness of core, stiffness of the floor diaphragm, width, and height of the building.These independent factors are represented in the form of a non-dimensional factor termed Υ considered as the ratio of relative stiffness of the core to relative stiffness of the diaphragm.For each variation in Υ, the outrigger positions are varied along the building height and the optimum position of outriggers is investigated for each loading condition by taking responses from roof displacement, roof acceleration, fundamental period, inter-story drift ratio, and base bending moment.Static and dynamic analysis is performed for four-story heights of 140, 210, 280, and 350 m having 40, 60, 80, and 100 stories, respectively, under static wind loading, uniform wind loading, equivalent static EQ loading, and dynamic EQ load.For the purpose of analyzing the force transfer mechanism in slabs at the outrigger level, the column axial forces below and above the outrigger floor are observed, and the shell stress at the outrigger level in both the tension and compression side of the slab is observed to examine the influence of slab on the performance of HOS.Shell stresses are the direct stress acting on the tension and compression phase of the slab in both the x and y directions.Also, the optimum position for the hybrid outrigger is determined using an ideal performance index criterion that takes into account the combined responses of the dependent parameters and the requirements for a building under wind and EQ excitation.

| Parameter definitions
As in Nair, 5 the core moment transfer at the VO level takes place through the floor diaphragms located above and below the outrigger level and so this study considers the performance of the floor diaphragm and its influence on the behavior of HOS.A non-dimensional parameter termed Υ is introduced which takes into account the relative stiffness ratio between the core and diaphragm.The expression for evaluating Υ is given in Equation (1).
where E is the elastic modulus of concrete, w is the building width, H is the building's total height, I dia is the moment of inertia of the diaphragm slab, and I core is the core moment of inertia.The thickness of the slab is varied from 180 to 720 mm, and the bending stiffness in the horizontal plane is evaluated for each variation.Table 1 gives the assumed practical variables for evaluating Υ values used in the parametric analysis for four building heights having 40, 60, 80, and 100 stories.The typical slab thickness is considered as 180 mm, and the thickness of slab (tk slab ) connecting the outrigger level is increased from single fold to four-fold to analyze the performance of increased slab thickness variation on the outrigger behavior.The building width w is varied from 35,000 to 50,000 mm in 5000 mm increments, and the ratio of floor area to core wall area is kept constant except in cases where the variation study in core thickness (tk core ) and w is performed.The width of the core wall is kept at 18 m in all the models and only its thickness is varied.The outrigger thickness of 800 mm and square column size of 3200 mm are assumed for all the models to maintain uniformity in the performance comparison study.

| Relative outrigger positions
For each variation in the 12 Υ values of Table 1, the location of the outrigger is moved along the height of the building as per their relative position.Table 2 gives the floor positions for both CO and VO, and their corresponding relative height for the considered 40-, 60-, 80-, and 100-story models.In HOS for 40-story models, where two techniques are used, a preliminary investigation is done to determine the interval between the VO and CO.In the first technical approach, the CO is maintained at the mid-height story, and starting from the fifth story, the VO is varied along the height of the building at fixed intervals and also vice versa positioning (VO maintained at the mid-height story, and CO is varied along the height of the building) is evaluated.In the second approach, maintaining the interval between the VO and CO as H/3, where H is the total building height, the outriggers are moved along the height of the building, initially with CO below the VO and later with VO below the CO.The second method led to a superior reduction in the lateral response of the structure assessed based on base bending moment, roof displacement and absolute maximum inter-story drift ratio, according to the preliminary analytical findings.
Consequently, an interval of H/3 is maintained between the VO and CO in HOS when varying them along the height of the building.The analysis findings from the preliminary investigation are not presented in this manuscript due to the briefness of the content.From Table 2, the abbreviations marked in italics have the CO placed below the VO level and vice versa positioning for the other relative height positions marked in bold.A sample floor plan and 3-D view for Υ 60 = 0.207 (7-60) is shown in Figure 2 where t o and l o are the thickness of outrigger and length of the outrigger arm respectively.Figure 3 shows the elevation view for three models in 40 stories and a model in 60 stories for a better understanding of the relative outrigger position and change in the outrigger position along the height.

| Loading details
The studied models are analyzed in a finite element software, ETABS with symmetry along both the x and y axis, and the elastic modulus of concrete is calculated for a concrete compressive strength of 60 MPa.The typical story height assumed is 3.5 m and loadings are assigned based on IS codes.A super dead load having 1.5 kN/m 2 and a live load of 3.5 kN/m 2 are assigned on the slabs, and a live load of 1.5 kN/m 2 is assigned on the roof. 32,33The slab thickness below and above the CO and VO are modeled as shell-thin elements and it is varied from 180 to 720 mm in 180 mm increments with other slabs having a typical thickness of 180 mm.Each model is subjected to static wind and equivalent static EQ loading as per IS codes, uniform wind load and dynamic EQ loading.A wind speed of 44 m/s and seismic zone of 0.16-III corresponding to Mumbai location is assumed as per IS 875-3 34 and IS 1893, 35 respectively.
A windward load of 2 kN/m 2 and a leeward load of 1 kN/m 2 is distributed uniformly along the building height. 17,18,36,37For performing dynamic analysis using time history analysis, the peak ground acceleration (PGA) from known EQs are selected on the basis of their EQ frequency T A B L E 2 Relative outrigger positions for 40-, 60-, 80-, and 100-story models.and magnitude content, and spectrum matching is performed to stimulate the design event by matching the functions to a target response spectrum with soil type 2 and 0.05 damping ratio.Detailed explanations of loadings are given in John and Kamath. 38Figure 4 shows the time history curve of selected EQs matched to the target response spectrum.The ground motions selected are El Centro Array #9-Imperial Valley-02-1940 with a PGA of À0.28 g along x axis and À0.21 g along y axis, El Centro Array #5-Imperial Valley-06-1979 having a PGA of À0.51 and À0.38 g along x and y axes, respectively, and Golden Gate Park, 1957-San Francisco with PGA of À0.068 and À0.095 g along x and y axes, respectively.

| Analytical procedure
For investigating the influence of slabs on the behavior of HOS, parameters that could influence the slab performance, namely, stiffness of core, stiffness of slab, and width of the building, are altered through the range shown in Table 1 for models having 40, 60, 80, and 100 stories.The outrigger positions are varied along the building height as per Table 2, and a total of 504 models are modeled in ETABS software.The load and model details assigned are given under Section 2.3.The column axial forces below and above the outrigger floor are observed for analyzing the force transfer mechanism in slabs at the outrigger level, and the shell stress at the outrigger level in both tension and compression side of the slab is observed to study the influence of slab on the performance of HOS.The influence of increase in core thickness, length of outrigger arm, and slab thickness on the performance of the HOS is assessed based on the results from base bending moment, roof acceleration, roof displacement, fundamental period, and absolute maximum inter-story drift.From this parametric analysis, the optimum position of hybrid outriggers corresponding to each load and Υ value for the considered dependent parameters are evaluated.When the outrigger level is varied along the building height, for each loading condition, the position that constituted the maximum reduction in the values of each dependent parameter when comparing the results to the control model, which is the one with the core wall alone, is selected as their corresponding optimum position.A performance index criterion is formulated considering the combined responses of dependent parameters and the optimum hybrid outrigger position based on that is also portrayed.A detailed review of the results is given in Section 3.

| Force transfer mechanism in outrigger level
Axial forces in the columns can be considered a significant factor that can be used for assessing the stress concentration and shear lag phenomenon in the structure. 39To evaluate the force transfer through the slabs at the outrigger level, the axial forces in the column are observed in this study.Nair 5 in his paper commented that for a VO, the core moment is resisted by the floor slabs located below and above the outrigger level, and therefore, the slabs play a vital role in the case of VO as it helps in the indirect transfer of forces.To study the significance of axial force at the VO level, the column forces at a particular location of the outrigger are observed for Υ values in Sl.No. 9-12 in Table 1 for   Also, it can be observed that the column axial forces for the CO model (Figure 5b) are less compared to the VO at the same level which shows the effectiveness of outrigger arms of CO in reducing the lateral deformation of the building.When observing the axial forces at the outrigger level in Figure 5c-f which is for various slab thicknesses, it is noticed that the axial forces tended to reduce from 1520 to 1438 kN with an increase in slab thickness from 180 to 720 mm, which reflects the effectiveness in reducing the lateral deformation of the structure when slab thickness is increased.Similar changes can be observed in the intermediate columns as well.The above representation in Figure 5 is for 60-story models, a similar trend in pattern is observed in 40-, 80-, and 100-story models as well.Table 3 gives the column axial forces in corner column C15 at 28 th , 35 th , 52 nd , and 68 th floor level for 40-, 60-, 80-, and 100-story models, respectively, corresponding to various Υ values taken for studying the outrigger behavior based on increased slab thickness.The column axial forces at the outrigger level are marked in bold for reference.
Due to brevity of content, for each story height, only one floor level which is almost at the mid-height is chosen.The trend in pattern which is explained above for Figure 5 can be observed for the model results in Table 3 as well.
As suggested by Kamgar and Rahgozar 40 in their paper, the axial force in a column depends on the displacement of columns in the axial direction, the stiffness of the column and the outrigger position.Thus, the change in the outrigger position will create a variation in the axial column forces which can be observed in Figures 6 and 7. From Figures 6 and 7, it is seen that as the outrigger position moved upwards the column axial

| Behavior of slab located at outrigger level
The slab structure transfers the horizontal shear force from the EQ; thus, the behavioral analysis of the slab at the outrigger level is a significant study that needs to be performed.For the behavioral analysis, the maximum shell stress at the tension and compression side of the slab located at the outrigger level is noted in 40-, 60-, 80-, and 100-story models under equivalent static EQ loading.The shell stress in the x direction is termed S11, and the shell stress in the y direction is termed S22.The maximum shell stress acting along S11 tension and compression side is considered for the analysis.Figure 8 gives a sample diagram for tension and compression slab stress S11 at the VO level for various positions of the outrigger having CO below VO in 40-story models under equivalent static EQ loading in the x direction for Υ = 0.31.
For analyzing the shell stress at the outrigger level, the maximum value of shell stress S11 at tension and compression phase is observed for each model of 40, 60, 80, and 100 stories under equivalent static EQ load in the x direction for Υ values which considered the outrigger behavioral study for increase in slab thickness (Sl.No. 9-12 from Table 1).The shell stresses vibrational study for Υ values 0.62, 0.31, 0.21, and 0.15 is portrayed in Figure 9.The six groups of bars represent the six outrigger positions (three with CO below VO and three vice versa) in 40-story models, and the bars with aligned lines represent the VO position.From the study, it is observed that at the same outrigger position, the maximum shell stress for VO is greater than the CO value, and when the slab thickness is increased from 180 to 720 mm (Υ value 0.62 to 0.15), the increase in maximum shell stress for CO is more significant when compared to the values of VO.Also, when the HOS is moved upwards along the height of the building, always the bottom outrigger (CO or VO) has an increase in maximum shear stress and the top outrigger has a decrease in the maximum shell stress at various outrigger positions.A similar pattern trend is also observed in other models having 60, 80, and 100 stories under the same conditions.This study reflects the importance of shell stress analysis in HOSs and further analysis on the same for other loading conditions is under study.

| Behavior of HOS for variation in Υ values corresponding to each dependent parameter
On varying the Υ values over the specific range mentioned in Table 1, the performance of the outrigger is studied for variation in tk core , w, and tk slab .This is done for equivalent static EQ loads, static wind loads, uniform wind loads along windward and leeward sides, and also for dynamic EQ loads.The performance of HOS is assessed based on the responses from base bending moment, roof acceleration, roof displacement and absolute maximum inter-story drift.The results from these dependent parameters for models with HOS are compared to the model with a core F I G U R E 6 Axial force in corner column (C15) and intermediate column (C17) for various outrigger positions having CO below the VO in Υ = 0.413.
wall alone which is the control model.From the results it is found that the outrigger can give supplementary stiffness to the structure and to quantify the values, percentage reduction is calculated for each loading corresponding to each dependent parameter at each outrigger location.
The position which gives the maximum percentage reduction is noted as the optimum position and the results on that are given under Section 3.5.
Table 4 gives the percentage reduction values for the corresponding dependent factors when Υ is varied under static wind loading.
When the percentage reduction values in static EQ loading results are considered, the percentage values of static wind are 1.5% to 3% more for 40-story models, 1% to 2% more for 60-story models, 1% to 2.5% more for 80-story models, and 0.5% to 2% more for 100-story models which can infer that the hybrid outriggers are better in controlling the wind loads than the EQ loads.The percentage reduction values under uniform wind loads are almost similar to the results in Table 4, but in a few cases, 1% to 2% additional reduction is observed for 40-story models, and reduction values are lessened by 0.5% to 1% for 60-and 80-story models and lessened by 0.2% to 0.5% for 100-story models.For dynamic loading, there is a percentage reduction in the values of the dependent parameters, but it varied over a range of 25% to 38% for all the loadings in 40-story models, 13% to 34% for 60-story models, 10% to 30% for 80-story models, and 4% to 28% for 100-story models depending to the PGA of the EQ and outrigger position due to randomness in the ground motion.
From Table 4, it can be observed that the percentage reduction values decrease as the structural height of the model is increased and that can be because of the additional lateral deformation as the weight and height of the structure increase.Additional seismic weight on the structure can amplify the acceleration magnitude response, but peak acceleration response showed a reduction compared to the control model (model without outriggers) for dynamic EQ loads when the outriggers are placed towards the roof and also for wind loads because of the reduction in roof displacement as peak acceleration as per equation in IS 875-Part 3 34 is directly proportional to displacement.
The values of percentage drop in Acc top seemed to be less in all of the model instances taken into consideration in this study compared with the other dependent variables in Table 4, which can be due to increased stiffness and elastic responses when outriggers are installed.The maximum increase in percentage reduction in the results happened for an increase in building width which in turn increased the length of the outrigger arm.The percentage decrease values of dependent components increased by around 10% to 20% when the building width w is raised from 35 to F I U R E 9 Variation maximum shell stress S11 at tension and compression phase for 40-story models at various outrigger positions for static EQ load in the x direction.

T A B L E 4
The percentage reduction values for the corresponding dependent parameters when Υ is varied under static wind loading.
50 m, except in the case of BM @base where the percentage reduction grew only from 4% to 10%.Thus, an increase in the length of the outrigger arm can enhance the stiffness of the structure offering a better reduction in the lateral deformations compared to the values when tk core and tk slab are increased.The percentage reduction values grew only by 1% to 3% when tk core and tk slab are increased, and the reduction offered by tk slab increase is better when compared to the increment in tk core .From this, it can be observed that variation in slab thickness plays a significant effect on the behavioral analysis of HOS.
3.4 | Behavior of HOS for variation in Υ values based on the fundamental period of the structure The fundamental period of the model is a significant factor that needs to be considered as it is related to the location of the outrigger and its stiffness.Additional stiffness in the building can cause a reduction in the fundamental period and that's an important factor which needs to be considered for the resident's comfort in a high-rise structure. 19,41Figures 10-13 give a graphical representation of the fundamental period of the structure for various Υ values considered as per Table 1 in 40-, 60-, 80-, and 100-story models, respectively.From the figures, it can be observed I G U R E 1 0 Fundamental period variation for various Υ values considered in 40-story models at each outrigger position.
F I G U R 1 Fundamental period variation for various Υ values considered in 60-store models at each outrigger position.
that the fundamental period of the structure with the outrigger is less than the control model, and at different locations of the outrigger the fundamental period varies.In all the models, a U-shaped pattern is seen which infers that as the location of the outrigger is moved upwards, at a particular location, the fundamental period is the least which can be termed as the optimum outrigger location based on the fundamental period, and above that position, the fundamental period tends to increase again.In all the cases, it's observed that in models with outriggers, the fundamental period is the highest when the outriggers are positioned towards the roof similar to the past results, 19,25,41 and as the height of the structure increases, the fundamental period value also increased due to increased lateral deformations and loads acting on the buildings.Also, there is a significant decrease in the fundamental period for 40-and 60-story models when compared to 80 and 100 stories which infers that the HOS shows better supplementary stiffness in tall buildings compared to super tall buildings.The variation in the fundamental period is not that significant in the case where tk slab is incremented, but for an increase in tk core and w, significant variation is visible.
3.5 | Study on the optimum location for a HOS

| Optimum position of HOS when the significant factor considered is the base bending moment
The HOS reduces the lateral deformation of the building by resisting the bending moment at the base.Figure 14 gives the graphical representation of the optimum position in the HOS for various Υ values considered for the study as in Table 1.The optimum position is the same regardless Fundamental period variation for various Υ values considered in 80-story models at each outrigger position.
F I G E 3 Fundamental period variation for various Υ values considered in 100-story models at each outrigger position.
of the change in tk core , w, and tk slab for all the loading conditions in this study.In all the cases, the optimum position is obtained towards the base of the structure (1-40, 1-60, 1-80, and 1-100) with the CO position located below the VO level, and this can be because the CO provides better stiffness compared to VO and when it is positioned near the base, the resisting moment at the base can be brought down effectively.Previous studies 19,42 performed with CO alone in the structure had similar results to this.

| Optimum position of HOS when the significant factor considered is top displacement
The displacement at the roof is one of the critical factors that need to be addressed while designing high-rise structures.For obtaining the optimum location when Disp top is considered as the critical factor, the position that gives the maximum reduction in displacement at the roof level is evaluated for each variation in Υ as in Table 1 when the outrigger is varied along the structural height of the building as per the positions given in Table 2 under various loads considered.Figure 15 gives the optimum positions for various Υ values under each load when Disp top is factor in 40-, 60-, 80-, and 100-story models.The optimum positions for dynamic loads varied due to randomness in the ground motions and in all the cases, positions having VO below the CO gives a better performance, and the position of CO and VO varied between 0.48 to 0.98 and 0.15 to 0.65, respectively, when considering all four heights.
Even though the Disp top responses are different for static wind and uniform wind loads, they share the same optimum locations with VO over CO giving better results.For static EQ loads, the optimum position remained unvaried for 40-and 60-story models, but there is a shift in position for an increase in w for 80-story models and for tk core increase when 100-story models are considered, but all the cases gives better results when CO is positioned above VO.

| Optimum position of HOS when the significant factor considered is absolute maximum inter-story drift
The inter-story drift ratio is a very significant response quantity and gives an indication of the structural performance of the building especially under EQ excitations.In this study, when the outriggers are varied along the building height as per Table 2, the position that gives a maximum reduction in the absolute value of the maximum inter-story drift ratio is selected as its optimum position.Figure 16 gives optimum locations for various Υ values under each load when ISD abs.max is the critical factor in 40-, 60-, 80-, and 100-story models.The optimum location for dynamic loads varied in each case, but the position with CO over VO gives better results in all the cases, and the optimum position of CO ranged from 0.42 to 0.92 and VO from 0.08 to 0.58 considering all the model heights.The ISD abs.max responses are different for both static wind and uniform wind loads, but they share the same optimum locations with VO over CO giving better results as obtained in the case of Disp top .For static EQ loads, 40-, 60-, and 80-story models have a better performance when CO is located below the VO, but the optimum position swapped with CO Optimum position for various values when BM @base is the critical factor in 40-, 60-, 80-, and 100-story models under all the loads considered.
over VO in 100-story models.The optimum position remained unvaried for 40-and 60-story models, but there is a shift in position for an increase in w for 100-story models and tk core increase in 80-story models for equivalent static EQ loads.

| Optimum position of HOS when the significant factor considered is roof acceleration
The acceleration at the top is another critical factor that needs to be addressed in tall buildings as it's important for the comfort of humans in the upper stories of the buildings.The Acc top for wind loads has been taken from IS 875-3, 34 and for dynamic loads values from the software are Optimum positions for various Υ values under each load when Disp top is the critical factor in 40-, 60-, 80-, and 100-story models.
considered.For static and uniform wind loads, the optimum position obtained is the same, but the responses are varying, and the position with CO over VO is performing better in 40-story models and position with VO over CO in 60-, 80-, and 100-story models.For dynamic EQ loads, the position with CO over VO gives better performance in all the cases, and the optimum location of CO ranged from 0.53 to 0.98 and of VO from 0.19 to 0.65 considering all four heights.Figure 17 gives the optimum positions for various Υ values under each load when Acc top is the critical factor in 40-, 60-, 80-, and 100-story models.
F I G U R E 1 6 Optimum positions for various Υ values under each load when ISD abs.max is the critical factor in 40-, 60-, 80-, and 100-story models.

| Optimum position of HOS based on ideal performance index
In previous literature reviews, the dependent parameters are considered individually to study the optimum location of the HOS.In this study, after individual parameter analysis for optimum positions, a study has been conducted to analyze the optimum position considering the combined response of the dependent parameters, namely, Disp top , Acc top , and ISD abs.max .The procedural steps for evaluating the optimum position based on PI are explained in detail in John and Kamath. 38The equations for evaluating the performance index for wind and EQ load are given in Equations ( 2) and (3), respectively.
Optimum positions for various Υ values under each load when Acc top is the critical factor in 40-, 60-, 80-, and 100-story models.
requirements for a building under wind and EQ excitation.For finding the Ideal PI , the results of PI wind and PI EQ are considered.From Equation ( 2) and ( 3), the range of PI wind can vary from 0 to 3 and of PI EQ from 0 to 2. From these findings, the stiffness % for wind and EQ loads can be calculated from Equations ( 4) and ( 5), respectively.
For instance, if the performance index value for wind is calculated and obtained as 0, it implies that the lateral deformations are not there and the building is 100% stiff, and this can be quantitatively calculated from Equation (4).Further, the ratio of stiffness PI wind to stiffness PI EQ is calculated once the results are obtained, and the optimum position is selected as the one that gives the highest ratio among them.This is performed for each Υ value under each load and outrigger location.
On considering a particular Υ value, the highest value in the ratio of stiffness PI wind to stiffness PI EQ infers that the stiffness offered by PI wind is the largest and of PI EQ is the lowest.This ratio having the highest value among the other ratios can be considered the optimum position based on Ideal PI .Tables 7 and 8 gives a sample calculation for Υ = 0.809 in 40-story models for the calculation of Ideal PI for uniform wind loading and dynamic EQ Imperial Valley-02, #9 in X, respectively.Based on Equations ( 2) to ( 5), the values are calculated, and largest ratio among the stiffness PI wind /stiffness PI EQ is selected as the optimum position and is marked in bold.It can be observed that the bolded stiffness PI wind is the largest among the values in Table 7 and bolded stiffness PI EQ is the lowest among them in The stiffness PI wind /stiffness PI EQ in Table 7 and Table 8 is obtained by taking the ratios of the corresponding values of stiffness PIwind in Table 7 to the corresponding values of Stiffness PIEQ in Table 8.
static and dynamic EQ loads).For all the load cases, the position with CO below the VO gives better performance, and for dynamic loads, the position varied randomly with the range of CO from 0.19 to 0.58 and of VO from 0.52 to 0.92.

| CONCLUSION
This study analyzes the influence of floor diaphragms on the behavior of HOS.The behavioral analysis of the HOS is performed for variation in stiffness of core, stiffness of floor diaphragm, width, and height of the building, and the results are formulated based on the responses from roof displacement, roof acceleration, fundamental period, base bending moment, and inter-story drift ratio.From the findings of the analysis, the following conclusions are drawn: 1. On analyzing the column axial forces, the difference in column forces in control model is not that significant when compared to the axial forces at the outrigger level which infers that a part of the moment resisted in the core is being transferred to the column through the belt walls, and the axial forces at outrigger level are tending to reduce with increase in slab thickness.
2. On analyzing the shell stress on slabs, comparing values at the same outrigger position, the maximum shell stress for the VO is greater than the CO, and the increase in maximum shell stress with an increase in slab thickness is more significant for the CO when compared to the values of the VO.
3. An increase in tk slab can improve the performance of a HOS when compared to tk core .The impact can also be maximized by increasing the tk slab and outrigger arm length.On accounting for the fundamental period of the structure, they have the maximum values when the outriggers are positioned towards the roof, and the variation in the fundamental period is not that significant in the case where tk slab is incremented.
4. For maximum reduction in base bending moment, the optimum position is obtained towards the base of the structure with the CO position located below the VO level.When the PI criterion is accounted for, the optimal location of the CO and VO varied from 0.53 to 0.7 and 0.19 to 0.37, respectively, for equivalent static EQ loads, and from 0.25 to 0.42 and 0.58 0.75, respectively, for wind loads.For dynamic loads, VO's optimal locations ranged from 0.06 to 0.55 and CO's from 0.4 to 0.88 when all models are taken into consideration.
5. When Ideal PI is considered, the optimal locations of CO and VO varied from 0.25 to 0.45 and 0.58 to 0.78, respectively, for PI wind /PI static EQ , and from 0.19 to 0.58 and 0.52 to 0.92, respectively, for PI wind /PI TH .
depicts a 2-D representation of HOS.According to prior reviews in the literature, research into concrete outrigger systems was mostly focused on COs, outriggers with belt truss/wall, VOs, outriggers with dampers, and facade riggers.The study of CO and VO in the same structure, which serves as a HOS, is under-explored in the literature.The VO's indirect force transfer mechanism lessens the moments created in the core and removes the F I G U R E 1 Illustration of hybrid outrigger system in a 40-story model.

F I G U R E 2
Plan at conventional outrigger floor level and hybrid outrigger system's 3-D view for Υ 60 = 0.207.F I G U R E 3 Elevation view for various outrigger positions in 40-and 60-story models.
40, 60, 80, and 100 stories under wind loads in the x direction.For the pictorial representation of the axial forces, outrigger level 2-60 having VO at 35th story is observed for Υ values 0.413, 0.207, 0.138, and 0.103 corresponding to 60-story models under wind loads in the x direction.The difference in the axial forces at the story above (36th story) and the story below (34th story) is quantitatively observed for analyzing the force transfer.

Figure 5
Figure5gives a pictorial representation of the axial forces acting in the columns connected above and below the outrigger level.For the comparison of axial forces at the VO level, axial forces at the same story level for the CO and control model are portrayed in Figure5.From Figure5, it can be observed that the difference in column forces in control model is not that significant when compared to the axial forces at the outrigger

5
Representation of column axial forces above and below the outrigger level (35th story) for 60-story models.forces reduced and is the least for the outrigger positions near to the roof which can be because the outrigger near to the ground can create an additional resistance moment in the core which can generate increased force in the corner and intermediate columns.Thus, this change in the axial force at different positions can create a change in the aggregate value of axial force in a structure and an optimum position evaluation based on the aggregate value of axial force is under study.
Axial force in corner column (C15) and intermediate column (C17) for various outrigger positions having VO below the CO in Υ = 0.413.F I G U R E 8 Tension and compression slab stress S11 at the virtual outrigger level for various positions of outrigger having CO below VO in 40-story models under static earthquake loading in x direction Υ = 0.31.

F I G U R E 1 9
Optimum positions for various Υ values under each load based on Ideal PI in 40-, 60-, 80-, and 100-story models.
Assumed design variables for evaluating Υ values.
Table 8 leaving the control model.Figure19gives the optimum positions for various Υ values under each load based on Ideal PI in 40-, 60-, 80-, and 100-story models.As both static wind and uniform loads are considered in this study, the PI STATIC WIND to each EQ load and PI UNF WIND to each EQ load are calculated.Except in the case of PI UNF WIND /PI S- TATIC EQ optimum position values in 60 stories, others have a similar optimum position for both PI UNF WIND /PI EQ and PI STATIC WIND /PI EQ (both T A B L E 7 Sample calculation of uniform wind load PI UNF WIND for Υ = 0.809 for 40-story models.The stiffness PI wind /stiffness PI EQ in Table7and Table8is obtained by taking the ratios of the corresponding values of stiffness PIwind in Table7to the corresponding values of Stiffness PIEQ in Table8.T A B L E 8 Sample calculation of dynamic EQ Imperial Valley-02, #9 in X for Υ = 0.809 for 40-story models.