Static Analysis of Tall Buildings with Combined System of Framed Tube, Shear Core, Outrigger and Belt Truss

Seyed Mozafar Davari, Mohsen Malekinejad, Reza Rahgozar Ph.D. Candidate, Civil Engineering Department, Sirjan Branch, Islamic Azad University, Sirjan, Iran sm_davari@iauk.ac.ir Assistant Professor, Civil Engineering Department, Sirjan Branch, Islamic Azad University, Sirjan, Iran Young Researchers and Elite Club, Sirjan Branch, Islamic Azad University, Sirjan, Iran. m.malekinejad@iausirjan.ac.ir Professor, Civil Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran rahgozar@uk.ac.ir


I. INTRODUCTION
In recent years, in Iran, as in other countries, tall buildings construction in cities has been taken into account in the context of population based on policies and land shortages. Today, construction is taking place for taller buildings, especially in major cities, and one of the most important issues in tall structures is choosing the suitable structural form sustaining of lateral loads. The susceptibility of tall structures to lateral loads is far greater than gravity loads and if the height of the structure increased, the conventional methods for resisting these structures are not enough. One of the most applied structural systems for tall structures is outrigger and belt truss in tall structures to reduce structure deformations and resistance to lateral loads. Outrigger and belt truss connects external columns to the inner shear core. As a result, the set of external columns and outrigger resists against the shear core rotation, reducing the lateral deformations and reducing the momentum on the structure's bottom. Addition to columns at end of the outriggers, usually other peripheral columns are also used to fix the outriggers. This type of structural form is outrigger and belt truss [1].Several methods have been proposed for analysing framed tubes. Coull and Bose presented a method based on theory of elasticity. In this method, the structure is modelled as equivalent orthotropic plates, and the equilibrium and compatibility equations are satisfied in the equivalent structure [2]. Coull and Ahmed presented a method for obtaining deflection of the framed tube [3]. Using equivalent orthotropic plates, energy relations and the relations of the theory of elasticity. Kwan provided equations for determining the stress in the columns, as well as obtaining lateral displacements of framed tube structure [4]. Connor and Pouangare proposed a five-member vertical method in which the structure is equated to vertical beams and vertical plates. By calculating the shear and bending stiffness of the members, relations are obtained for stresses in the columns [5]. Another way to improve the behaviour of framed tube is to add internal framed tubes to the original structure. In this case, distribution of stress and displacement can be significantly adjusted. Also, several other methods for analysing framed tubes have been presented by researchers such as Paulino [6], Mahjoub et al. [7]. Kamgar and Rahgozar studied vibration of tall structures using analytical methods [8]. Jahanshahi and Rahgozar determined the best position of a belt in a combined framed tube system using energy method [9]. Malekinejad and Rahgozar investigated free vibration analysis of tall structures that has a framed tube system [10]. In addition, Ramezani et al. conducted their research on analysis of non-uniform tall building structures considering axial force effects [11]. Tavakoli et al. evaluated the soil-structure interaction of outrigger-belt truss system of high-rise structures under seismic demand criteria [12]. Kim et al. studied optimization usage of outriggers in tall buildings in order to diminish lateral displacement and di erential axial shortening [13].A dimensionless formula has been developed for flexural stiffness of tall buildings with objective of optimization problem by Alavi et al. in 2017 [14]. Kamgar [14] umns, and ot usually d in initial following outriggers orm along TRUSS ement and core. As a the lateral and shear effects of uniformly Given 3, this mo Assum Where as: And: The ab according without As can be seen, considering original coordinates at support, 0 0   and the relation x M as shown inFig. 2 is: Consequently, usingEquation (6): As a result: Equation (10) can also be written as follows: In above relation,q is the intensity of the lateral load, Mis moment at x point, E is modulus of elasticity of the braced shear core, I is moment of inertia of the structure, A is cross section of the peripheral columns in the structure, L is height of the structure, and d is distance between outer columns and K is calculated from Equation (4).
Displacement is also obtained according to superposition principle, including displacement due to loading of the structure, 1 ( ) y x , and displacement due to the presence of a spring, 2 ( ) y x , which are calculated according to the following relations.
And finally, total displacement is equal to:

IV. MODELLING OF RIGID OUTRIGGER AND BELT TRUSS SYSTEM BASED ON TIMOSHENKO'S THEORY
In the previous section, using Euler-Bernoulli method, displacement of the structure can be calculated at any desired point, but in this method, the shear effect is ignored. However, in Timoshenko's beam theory, effects of shear are taken into account and the relations are modified as follows.
To calculate x  as shown in Fig. 4, using superposition principle, x  will be equal to the sum of 1 x  from the concentrated lateral load without spring, and 2 x  resulting from the moment,M, due to the spring and 3 x  resulting from the shear effects: , we have: oulli's theory, ,k, is used, as: Using above relationship: By integrating the above relation, results: Given the boundary conditions: As a result: Equation (38) represents the relation In order to obtain the displacement, displacement caused by the loading of the structure 1 ( ) y x is due to presence of a spring 2 ( ) y x and the displacement caused by the shear effect, 3 ( ) y x , according to the superposition principle, we have: Displacement due to presence of a spring is in accordance with Equation (13), and the displacement due to loading of the structure and the shear effect is obtained in accordance with Equation (38).

V. SOFTWARE ACHIEVEMENTS AND NUMERICAL REVIEWS
In this section, in order to investigate accuracy and efficiency of the proposed method, static analysis of tall buildings with a system of framed tube, shear core, outrigger and belt truss with symmetric plan was performed. The building is a 40-story concrete building modeled with SAP2000 software. All beams, columns, outrigger and belt truss have a value of 0.8( ) 0.8( ) m m  . Height of the floors is 3 m, thickness of the slab is 0.25 m, and distance from the center to center of columns is 2.5 m. Modulus of elasticity and shear modulus are 20 GPa and 8 GPa, respectively. Shear core dimensions are equal to 5( ) 5( ) m m  and thickness of shear wall is equal to 0.25 m. The structure is subject to a uniformly distributed lateral load with intensity120 KN/m [4]. Fig. 9 and Fig. 10 presents model of the structure, which has been modeled in SAP2000.
In Fig  Bernoulli  method   Displacement at different location of heights of building based on Euler-Bernoulli method, in which shear effects has been is neglected, is very different from the proposed method (Timoshenko's beam theory). In this method, the shear effects are considered that the analysis results are much closer to reality

VI. CONCLUSION
The proposed model for static analysis of tall structures with symmetrical plan produces acceptable results. In particular, in the initial design stage, this method can provide a proper prediction of behavior of the structure and, based on it, obtains a basic design for the structure. Although the results obtained from the analytical method are different from those obtained by computer analysis, but the accuracy of the results can be increased by knowing the reasons for this phenomenon and fixing it. The main reasons for the discrepancy between results including the shear lag effect, the nature of the proposed method is based on the continuous model, while the actual structure has discrete elements. The combined system of framed tube consisting of periphery beams and columns is simplified with the simple model of the equivalent box section. In addition, the combined system of outrigger and belt truss and periphery columns has been replaced with a concentrated spring. The flexural stiffness of the outrigger and belt truss is assumed to be rigid, whereas it is not the same in real constructions.However, if the revised Timoshenko's theory has been used to analysis the structure, more accurate result will be concluded.