An investigation on optimal outrigger locations for hybrid outrigger system under wind and earthquake excitation

Outriggers are considered as an effective system to alleviate the responses caused due to the lateral loads on high rise buildings. The concept of hybrid outrigger system which has a conventional and a virtual outrigger at different levels has been proposed. This study analyzes the static and dynamic behaviour of hybrid outrigger system based on stiffness of core, stiffness of outrigger beam and belt wall, length of the outrigger arm, and height of the building as varying parameters, and investigated on optimal positions of hybrid outrigger system under wind and earthquake loads. The dynamic behaviour was evaluated using nonlinear time history analysis, and the static wind and earthquake response using Indian Standard codes. Analytical models of 40, 60 and 80 storeys having building heights of 140 m, 210 m and 280 m, respectively were considered for the parametric study. The optimal positions for hybrid outrigger system were obtained based on the response from absolute maximum inter storey drift ratio (ISDmax), roof displacement (disproof), roof acceleration (accroof) and base bending moment. A performance index criterion was introduced which was utilized to obtain the optimal position of the hybrid outrigger system considering the combined effect of ISDmax, accroof and disproof under each load. The study concludes with a flowchart giving the preliminary recommendations for choosing the optimal position of hybrid outrigger system.


Introduction
Outrigger structures are used in high rise buildings since decades as a lateral load resisting member. The significance of outrigger system has emerged rapidly due to its ability to enhance the behavioural performance of the building under wind and earthquake excitation. The conventional outriggers which are restrained to the peripheral columns and core, try to counter the rotation of the core on application of lateral excitations and hence reduces the deformation and moments acting in the core (Smith & Salim, 1981). The overall persuasion is to increase the effective depth of the structure on bending of core wall, thus, generating tensile and compressive forces on the columns which can create a couple that reduces the effective bending moment in the core (Smith & Coull, 1991;Smith & Salim, 1983;Taranath, 2006). Thus, the outrigger system enhances the stiffness of the structure which can effectively reduce the inter storey drift ratio, acceleration if an optimal damping design is proposed and roof displacement as well (Huang & Takeuchi, 2017).
The outrigger system can be classified as conventional and virtual outriggers based on their direct and indirect connection between core wall and peripheral columns. The conventional outriggers which have direct connection between core wall and columns can cause space obstruction at the outrigger level and difficulties in the architectural planning. Thus, as an alternative to overcome such difficulties, virtual outriggers were developed which transfer moments indirectly through floor diaphragms (Nair, 1998). The semi rigid floor diaphragms transfer the equivalent horizontal couple from the core to the vertical belt wall/truss which converts it into vertical couple and is transferred to the columns. This action reduces the bending moment in the core by generating tensile and compressive forces on the columns (Horton, 2000;Nair, 1998). The installation of virtual outriggers can eliminate the problems caused due to space hindrance by conventional outrigger arms, thus, utilizing that floor for occupants which makes it more cost effective. As conventional outriggers are directly connected to the core, the effectiveness of it in resisting lateral loads are better when compared to virtual outriggers (Bayati et al., 2008;Nair, 1998). Thus, taking both the effectiveness and space obstruction into consideration, a new lateral load resisting system termed hybrid outrigger system, which contain one conventional and one virtual outrigger at different levels, is proposed in this study. A 77-storey structure in Kuala Lumpur named Plaza Rakyat Tower can be given as an example for hybrid outrigger system (Baker et al., 2013). Commonly, we have noticed that steel or composite construction is used in outrigger and belt structures, and reinforced concrete construction in the core wall. This form of connection can increase the time of construction period and make the connection detailing complicated (Eom et al., 2019). This can be avoided by using concrete construction for both core wall and outrigger systems, thus, eliminating the complicated connection details and minimising the cost and intervention between construction procedure (Eom et al., 2019).
Installing the outriggers at their optimal position rather than keeping the outrigger at plant rooms can reduce the stiffness of core and outrigger systems, which can further reduce the overall cost of construction (Xing et al., 2021). Therefore, in this study, the efficacy of a concrete hybrid outrigger system for various parameters and the optimal hybrid outrigger system location under wind and earthquake excitations is studied. Figure 1 shows the pictorial representation of hybrid outrigger system and its force transfer mechanisms.
Behavioural analysis of conventional outriggers considered influence of optimal locations and, variation in elemental stiffness of core and outriggers on vibration period, base moment, and drift under triangular and uniform loadings (Wu & Li, 2003). The study (Wu & Li, 2003) reported that the optimal position differs with the type of loading. Behavioural analysis of facade-riggers considered axial stiffness of the columns, bending stiffness of core walls, bending and racking shear stiffnesses of the facade riggers, bending and shear stiffness of floor structures (Hoenderkamp, 2009;Hoenderkamp & Snijder, 2000Hoenderkamp et al., 2012). The studies (Hoenderkamp, 2009;Hoenderkamp & Snijder, 2000Hoenderkamp et al., 2012;Wu & Li, 2003) reported that the considered parameters and loadings greatly influenced the behaviour and position of outriggers. Several studies considered inter storey drift, displacement, base bending moment, base shear, axial forces in core and columns, vibration period, frequency, acceleration, energy dissipation and mass/weight as the dependent parameters for analysing the optimal location outrigger (Chen & Zhang, 2018;Hoenderkamp, 2008;Fig. 1 Pictorial representation of hybrid outrigger system and its force transfer mechanisms Moghadam et al., 2015;Park et al., 2016;Patil & Sangle, 2016;Po, 2001;Tan et al., 2015;Zhao & Jiang, 2014). The studies reported that the optimal position of outrigger varies with the dependent parameter. It was suggested that placing the outrigger between 0.5 and 0.8 was efficient in resisting the inter storey drift and displacement (Chen & Zhang, 2018;Hoenderkamp, 2008), placing the outriggers near the base was efficient in resisting the base bending moment (Park et al., 2016), and placing the outrigger at higher levels was efficient in reducing acceleration (Moghadam et al., 2015) and for greater energy dissipation in case of dampers (Tan et al., 2015).
Based on the above literature review, a study has been conducted for analysing the behaviour of hybrid outrigger system. In this study, the static and dynamic behaviour of hybrid outrigger system were analysed based on stiffness of core, stiffness of outrigger beam and belt wall, length of the outrigger arm, and height of the building as varying parameters and investigated on optimal positions of hybrid outrigger system under wind and earthquake loads. A nondimensional parameter termed β considered as the stiffness ratio between core and outrigger was used to represent the independent parameters stated above. The dynamic Earthquake response of the models was studied using fast nonlinear time history analysis, and the static wind and earthquake response using Indian Standard codes. The optimal position of hybrid outrigger system was evaluated based on the results from absolute maximum inter storey drift ratio (ISD max ), roof displacement (disp roof ), roof acceleration (acc roof ) and base bending moment (BM base ). A detailed procedure for the parametric analysis is given in "Procedure for Parametric analysis". A performance criterion termed as Performance Index (PI) was established to evaluate the optimal position of hybrid outrigger system considering the combined effect of ISD max , acc roof and disp roof under each load. This study concludes with a design flowchart which could serve as preliminary recommendations for choosing the optimal position of hybrid outrigger system.

Parametric definitions
The parameters which could influence the performance of hybrid outrigger system were identified as stiffness of core, stiffness of outrigger beam and belt wall, length of the outrigger arm, the height and width of the building. The above parameters were represented in the form of a nondimensional parameter termed β which was considered as the stiffness ratio between core and outrigger (Smith & Coull, 1991). The expression is given in Eq. (1) where E is the modulus of elasticity of concrete,I core is the moment of inertia of core, I o is the moment of inertia of the outrigger, d is the width of the building and H is the height of the building. As the hybrid outrigger system consist of one conventional outrigger (CO) and one virtual outrigger (VO), two β values were formulated (β CO and β VO ) as the moment of inertia of both were calculated differently. The values for I core and I conv were calculated based on Eq. (2) and (3) (Park et al., 2016) and I virt based on Eq. (4).
where b is the breadth of the core wall, t core the thickness of the core, I conv the moment of inertia of conventional outrigger, I virt the moment of inertia of virtual outrigger, t o the thickness of outrigger, h is the height of the storey and A slab is the area of the slab. For the parametric analysis, 12 β values were generated by varying the thickness of core, outrigger thickness and the width of the building over a specific range. Building width d was varied from 35 to 50 m in 5 m increment and outrigger thickness t o from 500 to 950 mm in 150 mm increment. For uniformity, the core wall breadth b was assumed to be fixed at 18 m for all the models and t core was varied proportionally keeping the ratio of floor area to core wall area a constant. But the ratio can't be a constant in cases where the variation effect of t core and d is being studied (6)(7)(8). Practical values for thickness of core and outrigger were assumed and used in the calculation of β values. Table 1 shows the design variables used for formulating the values of β CO and β VO .

Assumptions used in analysis
The analysis was based on certain assumptions (Smith & Coull, 1991) (a) The structure was assumed to be linearly elastic (b) In the columns only axial forces were induced (c) The connection between the core and outrigger was rigid and the core was attached rigidly to the foundation (d) Uniform sectional property was assumed throughout the core, outriggers, and the columns.

Outrigger positions
A preliminary analysis was conducted in choosing the interval between the conventional and virtual outrigger in hybrid outrigger system for 40 storey models where, two approaches were followed. The first approach had virtual outrigger fixed at mid-height storey and the conventional outrigger was varied along the building height at regular intervals starting from the 5th storey and vice versa (with conventional outrigger fixed at the mid-height storey and varying the virtual outrigger along the building height).
In the second approach, the conventional and virtual outrigger was varied along the building height keeping the interval between them as H/3, initially with conventional outrigger below the virtual outrigger and later with virtual outrigger below the conventional outrigger. According to the preliminary analytical findings, the second method resulted in a better reduction in the values for the lateral response from roof displacement, base bending moment, and absolute maximum inter storey drift ratio. The results from the second approach were agreeing to the past research results (Chen & Zhang, 2018;Moon, 2016;Patil & Sangle, 2016;Samarakkody et al., 2017;Smith & Coull, 1991). Therefore, the positions of conventional and virtual outrigger in hybrid outrigger system were varied along the building height keeping interval H/3. Due to brevity of content the results of preliminary study is not included in this manuscript. Table 2 gives the relative positions for the hybrid outrigger system in the studied 40,60 and 80 storey models. In 40 storey models, 6 positions of hybrid outrigger system were chosen. In that, the first three set (1-40-sq-β, 2-40-sq-β, 3-40-sq-β) have CO below the VO and in the next three sets (4-40-sq-β, 5-40-sq-β, 6-40-sq-β) have VO below the CO. Similarly, 60 and 80 storey models have 8 and 10 positions, respectively for hybrid outrigger system where the first four sets in 60 storey and five sets in 80 storey models represent CO below VO and the remaining sets represent VO below CO. The positions having virtual outrigger below the conventional outrigger are marked in italics under Table 2.
Figure 2(a) shows the floor plan at the conventional outrigger level and Fig. 2(b) shows the 3-D view for β CO -40 = 128.7 and corresponding β VO -40 = 6.9 with outrigger position at 2-40-sq-β and the benchmark model for it. The benchmark model is one without outriggers and with a core wall of 18 m wide. In this study, the models for each β value was compared with its corresponding benchmark model to analyse the performance of hybrid outrigger system. In Fig. 2(a), l o represent the length of the outrigger arm which was varied from 8.5 m to 16 m in 2.5 m increment to study the effect of length of outrigger arm on outrigger behaviour. Figure 3 shows the floor plan at conventional outrigger level for β CO -40 = 226.3 and corresponding β VO -40 = 6.9 for a better understanding of the variation of l o .

Model details
The models considered were symmetrical along x and y axis, and the storey height and compressive strength of concrete was assumed to be 3.5 m and 60 MPa, respectively. The dead and live loads were assigned as per IS codes (1987b; IS, 1987a) with live load as 3.5 kN/m 2 , live load in roof as 1.5 kN/m 2 and super dead load as 1.5 kN/ m 2 . The typical slab thickness was assumed as 160 mm and as 250 mm in the mechanical floors due to heavier impact loads (Baker et al., 2013;Khan & Gore, 2018;Mousleh & Batikha, 2020). The analysis was performed in a finite element software, ETABS. The core wall and outriggers were designed as wall elements with modelling type as shell thin. The slabs were defined as shell thin elements, and beam and columns as frame elements. For slabs connecting the virtual outrigger, semi-rigid diaphragms were assigned to simulate actual inplane stiffness properties and force transfer through slabs   and beams connecting to the virtual outrigger walls. The frame elements were designed to carry the gravity loads and the beam and column size was 1 m x 1 m and 2.5 m × 2.5 m, respectively for all the models to keep the mass source constant. The typical slab thickness for benchmark model is 160 mm, and the frame elements' size and loading distribution are the same as for other models.

Static and dynamic analysis
All the models underwent static wind and earthquake analysis, uniform wind analysis and dynamic earthquake analysis. The building was assumed to be in Mumbai, so the corresponding wind speed and seismic zone was chosen as 44 m/s and 0.16 -III, respectively (IS, , 2016. The soil type was assumed as type 2-medium soil and building importance factor and response reduction factor were chosen as 1 and 5, respectively (IS, 2016). These factors were defined in ETABS software for carrying out the static wind and earthquake analysis. For the uniform wind loads, a windward uniform load of 2 kN/m 2 and a leeward uniform load of 1 kN/m 2 , chosen from past research (Hoenderkamp & Bakker, 2003;Hoenderkamp & Snijder, 2000Kim et al., 2020), were defined in both x and y directions. The uniform loads were converted to point loads taking the area of distribution around each joint and they were assigned as joint loads in ETABS software. Dynamic analysis was carried out using time history method of analysis by taking Peak Ground Acceleration (PGA) from known Earthquakes. Time history analysis is used for describing the real time behaviour of a structure during an earthquake as it considers the non-linear properties of the structure. It analyses the dynamic response of the structure at each time increment when the base of the structure is subjected to a particular ground motion. Ground motions were selected based on their frequency content (FC) and magnitude classification. Ground motions corresponding to low, intermediate, and high frequency class and with magnitude classification as major, strong, and moderate were chosen. To stimulate the design event, spectrum matching was adopted and the maximum response from the ground motions were selected to analyse the building performance (IS, 2017). Figure 4 shows response spectra of time history cases matched to target response spectrum of the site considered. The ground motions selected were Imperial Valley-02, 5/19/1940-El Centro Array #9 of magnitude 6.95 and PGA of − 0.28 g in x direction (Intermediate FC) and − 0.21 g in Array #5 of magnitude 6.53 and PGA of − 0.51 g in x direction (Intermediate FC) and − 0.38 g in y direction (Low FC), San Francisco-Golden Gate Park,1957 earthquake of magnitude 5.28 with PGA of − 0.068 g in x direction (High FC) and PGA of − 0.095 g in y direction (High FC). Fast nonlinear analysis (FNA) is often recommended over direct integration methods because of its efficient formulation. Time history FNA was adopted for the dynamic analysis and the functions were matched to the target response spectrum having damping ratio 0.05 in soil type 2 and seismic zone 3.

Procedure for parametric analysis
Parametric analysis mainly involves analysing the behaviour of the selected models for various parameters considered. In this study, the behaviour of hybrid outrigger system was analysed based on certain parameters and from the analysis results, the optimal position of the hybrid outrigger system was obtained. The independent parameters considered were the stiffness of core, stiffness of outrigger beam and belt wall, length of the outrigger arm, and the height of the building. These independent parameters were combined to from a non-dimensional parameter β. The independent parameters as defined in "Parametric definitions" were varied over a specific range as given in Table 1 for all the three heights of 140 m, 210 m and 280 m. For each variation of β value, the position of hybrid outrigger system was varied along the height of the building as per their relative height positions as given in Table 2. For these variations, the behaviour of hybrid outrigger system was analysed under various loads as defined in "Static and dynamic analysis". All the 324 models were analysed in ETABS software. The behaviour of hybrid outrigger system was evaluated based on the roof displacement (disp roof ), roof acceleration (acc roof ), base bending moment (BM base ) and absolute maximum inter storey drift ratio (ISD max ) which were considered as the dependent parameters in this study. A preliminary analysis was done for hybrid outrigger system which showed the efficiency of using hybrid outrigger system over conventional and virtual outriggers (John & Kamath, 2022). From those preliminary analysis results, need for a detailed analysis of hybrid outrigger system was required to authenticate its efficiency.
To evaluate the optimal position of hybrid outrigger system the following procedure was adopted. For each β value, the hybrid outrigger system position was varied along the building height and the position which gave the maximum reduction in disp roof , acc roof , BM base and ISD max under each load was evaluated for all the three building heights and was considered as the optimal hybrid outrigger system position. Once the optimal position for each dependent parameter was obtained, a performance index (PI) was formulated to evaluate the optimal position considering the dependent parameters disp roof , acc roof and ISD max together. For calculating the PI, the limit for roof displacement, roof acceleration and absolute maximum inter storey drift ratio for wind and earthquake (EQ) loads were selected as per Indian Standards. The procedure for fixing PI is explained in detail under "Optimal positions of hybrid outrigger system using Performance Index (PI)". The study concludes with the design guidelines flowchart which can serve as a base for the preliminary recommendations of hybrid outrigger system positions.

Analysis results
The models with outriggers installed showed a good reduction in disp roof , acc roof , BM base and ISD max when compared to the benchmark model which indicate that the outriggers can provide supplementary stiffness to the building. Conclusions drawn for various independent parameters are as follows: (i) For β values which compare the outrigger behaviour based on increase in core thickness ( t core ) : when the core thickness was increased, the disp roof , acc roof and ISD max for the benchmark model showed reduction in its values for all three building heights. When hybrid outrigger system was installed, for wind loads, there was a percentage reduction of almost 15-19% in terms of ISD max and disp roof , 11-12% for acc roof and 22-26% for BM base in 40 storey models when compared to the benchmark model. For 60 storey models, ISD max and disp roof reduced by 10.5-12%, acc roof by 5.8-6.5% and BM base by 21-27%. For 80 storey models, ISD max and disp roof reduced by 8.5-10%, acc roof by 3.5-4% and BM base by 22-31%. When the earthquake loads were compared, the effect of outriggers were slightly seen to reduce. The above percentage reduction values were almost reduced by 2-3% for 40 storey models and 1.5-2% for 60 and 80 storey models when disp roof , ISD max and BM base was compared to the benchmark model. The lower limit in the percentage reduction value is for the lowest t core and the upper limit is for the highest t core value. when the length of outrigger arm was increased the disp roof , acc roof and ISD max for the benchmark model showed a rise in its values for all three building heights. When hybrid outrigger system was installed, for wind loads, there was a percentage reduction of almost 18-36% in terms of ISD max and disp roof , 12-26% for acc roof and 25-34% for BM base in 40 storey models when compared to the benchmark model. For 60 storey models, ISD max reduced by 12.2-32.5%, disp roof reduced by 10.8-31.8%, acc roof by 5.5-18.5% and BM base by 25.8% -35.4%. For 80 storey models, ISD max and disp roof reduced by 8.4-24%, acc roof by 3.4-11.4% and BM base by 29.5% -37%. When the earthquake loads were compared, the effect of outriggers were slightly seen to reduce. The above percentage reduction values were almost reduced by 2% -3% for 40 storey models and 1.5-2% for 60 and 80 storey models when disp roof , ISD max and BM base was compared. The lower limit in the percentage reduction value is for the lowest l o and the upper limit is for the highest l o . . When the earthquake loads were compared, the effect of outriggers were slightly seen to reduce. The above percentage reduction values were almost reduced by 1-2% for all building heights when disp roof , ISD max and BM base was compared. The lower limit in the percentage reduction value is for the lowest t o and the upper limit is for the highest t o .
From the above percentage values, it is noticed that, as the height of the building increased from 40 to 80 storey, the percentage reduction for disp roof , acc roof and ISD max has reduced but has increased for BM base . When outriggers are installed, there was a reduction in the time period in all the locations when compared to the time period of the benchmark model. A sample modal analysis results for β CO -60 = 150.9 and corresponding β VO -60 = 4.6 is given in the Table 3 and Fig. 5 shows its pictorial representation. Also, the first three mode shapes showing centre of mass displacement in diaphragm 1 for modal analysis results of the same model is shown in Fig. 6. Observing the percentage reduction values of the dependent parameters, reduction in acc roof was less compared to other dependent parameters which can be due to increased stiffness and elastic responses. From the above values it can be inferred that the hybrid outrigger system is more effective in reducing the wind loads when compared to the earthquake loads. On comparing the effect of independent parameters t core , l o and t o on the behaviour of outrigger, increase in l o gave the best performance. It is noticeable that, when l o was increased from 35 to 50 m, there was a rise of 10-20% in the percentage reduction values of the dependent parameters but, only 2-4% rise in the percentage reduction values when t core and t o was increased. Thus, the length of the outrigger arm has maximum effect on the behaviour of outrigger performance when compared to the thickness of core and outrigger. Table 4 shows the percentage reduction for various β values considered in studying the increase in length of outrigger arm under static wind loads for 40 storey models and the values showing maximum percentage reduction is marked in bold. Similarly, percentage reduction values for all β values in Table 1 were tabulated for 40, 60 and 80 storey models corresponding to each dependent parameter and loads considered. From those tables, the position of hybrid outrigger system which showed maximum reduction in the corresponding values of disp roof , ISD max , acc roof and BM base were noted as the optimal position.
The optimal position of hybrid outrigger system for each dependent parameter is shown below from Figs. 7,8,9,10. The x axis shows the β variation and y axis shows the optimal position of hybrid outrigger system. The β CO is marked in x axis to show the distribution as few values of β VO remain unchanged in cases where the t core is unvaried.
Under dynamic earthquake loads, the position of hybrid outrigger system was varying due to the random nature of its ground motions but for all the cases the position with Fig. 6 The Centre of mass displacement diagrams for diaphragm 1 in mode shapes 1, 2 and 3 for modal analysis results for β CO -60 = 150.9 and corresponding β VO -60 = 4.6 along x axis

Optimal position of hybrid outrigger system when absolute maximum inter-storey drift ratio is the critical factor
Inter-story drift ratio is one of the significant factor for controlling the design of tall structures compared to top drift (Chen & Zhang, 2018;Patil & Sangle, 2016). Placing the outrigger at the position where the inter storey drift is critical can mitigate the response caused due to it. From the results of wind loads, it was noticed that for 40 storey models the optimal position of hybrid outrigger system were near to the base with VO below the CO giving better results, but for 60 and 80 storey models the position was towards the mid-height with CO below the VO giving better results. The shift in the position of conventional and virtual outrigger as the height increased can be due to adverse effect caused by the heavier mass at the top. From the results of static earthquake loads, it was noticed that for 40 storey models the optimal position of hybrid outrigger system were near to the roof with CO below the VO giving better results, but for 60 and 80 storey models the position was almost towards the mid-height with VO below the CO giving better results. Similar results of wind loads were obtained in past research Moon, 2016). Also, it was noted that regardless of increase in core thickness or outrigger thickness or length of outrigger arm, the optimal position of hybrid outrigger system remained unchanged for 40 and 60 storey models under both wind and static EQ loads. In 80 storey models, under wind loads, the optimal position of hybrid outrigger system remained unchanged with increase in core thickness and outrigger thickness, but, shifted downwards from 4-80-sq-β to 3-80-sq-β with increase in length of outrigger arm and in the case of static EQ loads, optimal position shifted upwards from 7-80-sq-β to 8-80-sq-β with increase in core thickness and remained unchanged for increase in outrigger thickness and outrigger arm length. For dynamic loads, when interstorey drift ratio was the critical factor, the position of conventional outrigger approximately varied from 0.4 to 0.75 and the position of virtual outrigger varied from 0.08-0.42 for all the models with exceptions in very few cases which can be due to its random nature. Figure 7 shows the distribution of optimal positions for maximum reduction in ISD max in 40,60 and 80 storey models for various β values as in Table 1.

Optimal position of hybrid outrigger system when displacement is the critical factor
Usually in structures the horizontal deflections are considered either using roof drift or inter storey drift. Controlling the response due to the roof displacement is also a critical factor in tall structures as its widely dependent on the building height and stiffness of the core and outrigger (Gerasimidis et al., 2009;Park et al., 2016;Radu et al., 2014). From the results of wind loads, it was noticed that the optimal position of hybrid outrigger system was almost same as obtained in the case of ISD max results. From the results of static earthquake loads, it was noticed that for 40, 60 and 80 storey model the optimal position was almost towards the mid-height with VO below CO giving better results. Similar results were obtained in past research (Chen & Zhang, 2018;Hoenderkamp, 2008;Lin et al., 2019). Also, it was noted that the optimal position of hybrid outrigger system remained unchanged for all storey heights under static EQ loads and for 80 storey models under wind loads, regardless of increase in core thickness or outrigger thickness or length of outrigger arm. Under wind loads, for 40 storey models, the optimal position remained unchanged with increase in core thickness and outrigger thickness but shifted upwards from 4-40-sq-β to 5-40-sq-β with increase in length of outrigger arm, and for 60 storey models, the position shifted upwards from 2-60-sq-β to 3-60-sq-β with increase in core thickness and length of outrigger arm but remained unchanged with increase in outrigger thickness.
For dynamic loads, when roof displacement was the critical factor, the position of conventional outrigger approximately varied from 0.4 to 0.95 and the position of virtual outrigger varied from 0.06 to 0.42 for all the models with exceptions in very few cases. Figure 8 shows the distribution of optimal positions for maximum reduction in disp roof in 40,60 and 80 storey models for various β values as in Table 1.

Optimal position of hybrid outrigger system when acceleration is the critical factor
Acceleration is one of the dominant factors in tall buildings which can affect the human sensation to vibrational motion. Thus, placing the outrigger at the position where the response due to acceleration is critical can reduce the perception to motion. The peak acceleration for wind loads were calculated as per IS code (IS, 2015) and for dynamic loads results from ETABS software was considered. From the results of wind loads it was noticed that for 40, 60 and 80 storey models, placing the hybrid outrigger system near to the roof with CO below VO gave maximum reduction in acc roof . Similar results were obtained in past research (Huang & Takeuchi, 2017). Also, it was noted that the optimal position of hybrid outrigger system remained unchanged for 40 and 60 storey models regardless of increase in core thickness or outrigger thickness or length of outrigger arm, and in 80 storey models the position remained unchanged at 5-80-sq-β with increase in core thickness and at 4-80sq-β with increase in length of outrigger arm and outrigger thickness.
For dynamic loads, when peak acceleration was the critical factor, the position of conventional outrigger approximately varied from 0.45 to 0.95 and the position of virtual outrigger varied from 0.25 to 0.62 for all the models with exceptions in very few cases. Figure 9 shows the distribution of optimal positions for maximum reduction in acc roof in 40,60 and 80 storey models for various β values as in Table 1.

Optimal position of hybrid outrigger system when base bending moment is the critical factor
Installation of outriggers on a structure make it more stiff by applying a resisting moment at the outrigger level, thus, reducing the base bending moment. It was seen that positioning of outriggers near to the base can reduce the base bending moment effectively than placing in the upper storeys of the structure (Wu & Li, 2003). When the hybrid outrigger system was varied along the building height, it was found that the maximum reduction in BM base was when the outrigger was near to the base (1-40-sq-β, 1-60sq-β, 1-80-sq-β) for all the chosen loads and β values. It was also noted that for maximum reduction in BM base , the position with CO below the VO gave better results and the position remained same regardless of increase in core thickness or outrigger thickness or length of outrigger arm. The obtained values were close to the optimal values received for conventional outriggers from the past research (Lee et al., 2008;Wu & Li, 2003;Zeidabadi et al., 2004). Figure 10 shows the distribution of optimal positions for maximum reduction in BM base in 40,60 and 80 storey models for various β values as in Table 1.

Comparison of optimal position for wind and static earthquake loads
On examining the optimal position of hybrid outrigger system for maximum reduction in ISD max and disp roof under wind and static earthquake loads, it was noticed that, for 40 storey models the optimal position for earthquake loads were above wind loads position but as the height increased, there was a swap in its position. For 60 and 80 storey models the optimal position for wind loads were above the position of earthquake loads which can be due to greater response caused due to wind loads with increase in height. Similar results were obtained in past research (Xing et al., 2021). Figures 11 and 12 shows the optimal position for maximum reduction in ISD max and disp roof in 40,60 and 80 storey models under wind and static earthquake loads.

Optimal positions of hybrid outrigger system using performance index (PI)
In this study, a performance criterion was fixed which considered the combined response of all the dependent parameters and was termed as Performance Index (PI). The aim was to get an optimal position for the hybrid outrigger system considering the effect of ISD max , acc roof and disp roof under each load. The procedure for fixing the PI is as follows:   Table 1, the values of ISD max , acc roof and disp roof corresponding to each outrigger position as per Table 2, was noted. b) A performance limit was fixed for each parameter as per IS codes. Under wind loads, the limit for displacement at top was fixed as H/500, where H is the total height of the building (IS, 2000), the limit for roof acceleration was fixed as 250 mm/s 2 (IS, 2017), and for absolute maximum inter-storey drift ratio as 1/400 . Under earthquake loads, the limit for displacement at top was fixed to H/500, where H is the total height of the building (Husain et al., 2021;Lin et al., 2019) and for absolute maximum inter-storey drift ratio as 1/250 (IS, 2017). c) Once the limit was set, the values of ISD max , acc roof and disp roof was divided by its corresponding limit. This was done for each β value, at each outrigger level. Then, the PI for wind and earthquake loads were calculated based on Eqs. 5 and 6, respectively. Once the PI values were calculated, the position having the least PI was considered as the optimal position. Table 5 gives a sample calculation of PI wind for β CO -60 = 150.9 and corresponding β VO -60 = 4.6. The relative positions marked in italics has virtual outrigger below the conventional outrigger. From Table 5, the PI wind for benchmark model is seen maximum compared to the other values, which shows the efficiency of using an outrigger system. The optimal position for outrigger was chosen as the one which gives the minimum value for PI wind . Therefore, in Table 5 the relative outrigger position at 0.417 and 0.750 marked in bold is chosen as the optimal position. Figure 13 shows the distribution of PI wind corresponding to its relative outrigger position, for the values given in Table 5. Similar calculation was done for other β values for all the three building heights under each load. Figure 14 shows the distribution of optimal positions of hybrid outrigger system based on performance index study under each load for all the β values considered.
From the results of wind loads, the optimal position of hybrid outrigger system was almost towards the mid-height with CO below the VO giving better results. For static earthquake loads, the optimal position of hybrid outrigger system was towards the roof with CO below VO giving better results in 40 storey models, but, for 60 and 80 storey models the optimal position shifted almost to mid-height with CO over VO giving better results. Also, it was noted that the optimal position of hybrid outrigger system remained unchanged under static EQ loads for all storey heights and under wind loads for 40 and 60 storey models, regardless of increase in core thickness or outrigger thickness or length (5) PI wind = ISD max ISD max limit + disp roof disp roof limit + acc roof acc roof limit (6) PI EQ = ISD max ISD max limit + disp roof disp roof limit  . 13 Distribution of PI wind corresponding to its relative outrigger position for the values in Table 5 of outrigger arm. In 80 storey models under wind loads, the optimal position of hybrid outrigger system remained constant at 4-80-sq-β and 3-80-sq-β with increase in core thickness and outrigger thickness, respectively but shifted downwards from 4 to 80-sq-β to 3-80-sq-β when the length of outrigger arm was increased. For dynamic earthquake loads the position of hybrid outrigger system were varying due to the random nature of its ground motions but for all

Preliminary design recommendations
Selecting the suitable outrigger positions is one of the main agenda for design practises as they show maximum effect on overall performance of the structure. Based on the results obtained through the static and dynamic analysis, a design flowchart was produced and is given in Fig. 15. The performance of the hybrid outrigger system can be maximised by increasing the outrigger thickness and length of outrigger arm. Once the height and the width of the building is fixed, the size of the main load bearing elements need to be evaluated based on the load demands and this leads to the determination of β value. When the β value is fixed, the optimal position for the hybrid outrigger system can be determined. It's necessary to place the outrigger at their optimal position because it can reduce the size demands of the core and outrigger dimensions. The usual practice is to keep the outrigger at the plant room or mechanical floors, but this leads to a very stiff outrigger which makes it expensive. Thus, placing the outrigger at their optimal position is significant and if that floor can be used for occupancy it can be made more beneficial and economical, which is possible in the virtual outrigger level of hybrid outrigger system. The results from Figs. 7,8,9,10. and 14 which gives the optimal position for hybrid outrigger for various β values is condensed in Fig. 15 to create a design flowchart which can serve as preliminary recommendations for choosing the optimal position of hybrid outrigger system.

Conclusion
This study analysed the static and dynamic behaviour of hybrid outrigger system based on stiffness of core, stiffness of outrigger beam and belt wall, length of the outrigger arm, and height of the building. The optimal positions for hybrid  Fig. 15 Flowchart of preliminary recommendations for choosing the optimal position of hybrid outrigger system outrigger system under wind and earthquake loads were obtained based on the response from absolute maximum inter storey drift ratio, roof displacement, roof acceleration and base bending moment. The following conclusions were drawn from the analysis results: • The length of the outrigger arm gave maximum effect on the behaviour of hybrid outrigger system performance when compared to the thickness of core and outrigger which suggest that the outrigger stiffness can be maximised by increasing its arm length. • For wind and EQ loads, the value of BM base was best reduced when the hybrid outrigger system was positioned near to the base with conventional and virtual outrigger in the range of 0.06-0.13 and 0.4-0.46, respectively. For wind loads, maximum reduction in the response due to acceleration is when the hybrid outrigger system was positioned near to the roof with conventional and virtual outrigger in the range of 0.44-0.63 and 0.77-0.96 respectively, and for dynamic EQ loads in the range of 0.45-0.95 and 0.25-0.62, respectively. • For wind loads, the value of ISD max and disp roof was best reduced when the hybrid outrigger system was positioned near to the base with conventional and virtual outrigger in the range of 0.45-0.7 and 0.12-0.37, respectively for 40 storey models, and for 60 and 80 storey models in the range of 0.25-0.44 and 0.58-0.77, respectively. In static EQ loads, ISD max and disp roof was best reduced when the hybrid outrigger system was positioned near to the mid height with conventional and virtual outrigger in the range of 0.53-0.7 and 0.19-0.37 respectively, and for dynamic EQ loads in the range of 0.4-0.95 and 0.06-0.42, respectively. • For wind loads, when performance index was considered, the optimal position of hybrid outrigger system was near to the mid-height with conventional and virtual outrigger in the range of 0.31-0.625 and 0.65-0.96, respectively. For static EQ loads, the optimal position of conventional and virtual outrigger was obtained at 0.63 and 0.96, respectively for 40 storey models, and in the range of 0.53-0.58 and 0.19-0.28, respectively for 60 and 80 storey models. For dynamic EQ loads, the optimal position of conventional and virtual outrigger was obtained in the range of 0.4-0.95 and 0.06-0.42, respectively.