Analysis of outrigger numbers and locations in outrigger braced structures using a multiobjective genetic algorithm

Due to its advantages, the outrigger braced system has been employed in high‐rise structures for the last 3 decades. It is evident that the numbers and locations of outriggers in this system have a crucial impact on the performance of high‐rise buildings. In this paper, a multiobjective genetic algorithm (MGA) is applied to an existing mathematical model of outrigger braced structures and a practical project to achieve Pareto optimal solutions, which treat the top drift and core base moment of a high‐rise building as 2 trade‐off objective functions. MATLAB was employed to explore a multiobjective automatic optimization procedure for the optimal design of outrigger numbers and locations under wind load. In this research, various schemes for the preliminary stages of design can be obtained using MGA. This allows designers and clients easily to compare the performance of structural systems with different numbers of outriggers in different locations. In addition, design results based on MGA offer many other benefits, such as diversity, flexible options for designers, and active client participation.     

An inter‐story drift‐based parameter analysis of the optimal location of outriggers in tall buildings

Outriggers are usually added in structural systems of tall buildings to collaborate central shear walls with peripheral columns. With outriggers, the structural overturning moment can be balanced, and the inter‐story drift can be controlled under horizontal loads. Therefore, the optimal location of outriggers plays a very important role in controlling the behavior of the whole building. Existing research has focused on the optimal position of outriggers on the base of the structural roof deflection. In the engineering practice, however, inter‐story drift is the most important target to control the design of tall building structures. This paper investigates the theoretical method of inter‐story drift‐based optimal location of outriggers. A Matlab program is written to perform the parameter analysis of optimal location of outriggers. Take a 240‐m tall building for a target building, the optimal location of one to three sets of outriggers under wind and earthquakes is obtained and can be utilized for the structural preliminary design of tall buildings. Copyright © 2015 John Wiley & Sons, Ltd.     

A general solution for performance evaluation of a tall building with multiple damped and undamped outriggers

This paper presents a general solution for performance evaluation of a tall building with multiple damped and undamped outriggers. First, general rotational stiffness (GRS) is proposed to model an outrigger that consists of the stiffness of perimeter columns and an outrigger connection and the damping of dampers in an outrigger. By utilizing the dynamic stiffness method, the GRS can be represented by complex stiffness in an outrigger element. To analyze the dynamic characteristics of a tall building with multiple outriggers, a dynamic transcendental equation is obtained from the combination of the GRS and dynamic stiffness method. The structural responses can be calculated through the Fourier transform based on this equation. Moreover, the GRS can also be blended into a finite element (FE) model to generate an augmented state‐space equation for the analysis of the dynamic characteristics and structural responses. Applications to various outriggers are illustrated. In the numerical analysis, good agreements are found between the GRS and the FE that validates the proposed method, and the performances of various outrigger systems are evaluated parametrically. As the results of a tall building with multiple damped or undamped outriggers, the proposed method is capable of providing an optimally parametric design with respect to the position of outriggers, damping, and core‐to‐column and core‐to‐outrigger stiffness ratio. Copyright © 2015 John Wiley & Sons, Ltd.     

Shear wall with outrigger trusses on wall and column foundations

A graphical method of analysis is presented for preliminary design of outrigger truss‐braced high‐rise shear wall structures with non‐fixed foundation conditions subject to horizontal loading. The method requires the calculation of six structural parameters: bending stiffness for the shear wall, bending and racking shear stiffnesses for the outrigger, an overall bending stiffness contribution from the exterior columns, and rotational stiffnesses for the shear wall and column foundations. The method of analysis employs a simple procedure for obtaining the optimum location of the outrigger up the height of the structure and a rapid assessment of the influence of the individual structural elements on the lateral deflections and bending moments of the high‐rise structure. It is concluded that all six stiffnesses should be included in the preliminary analysis of a proposed tall building structure as the optimum location of the outrigger as well as the reductions in horizontal deformations and internal forces in the structure can be significantly influenced by all the structural components. Copyright © 2004 John Wiley & Sons, Ltd.     

An analytical model for high‐rise wall‐frame structures with outriggers

In this paper, the governing equations of wall‐frame structures with outriggers are formulated through the continuum approach and the whole structure is idealized as a shear–flexural cantilever with rotational springs. The effect of shear deformation and flexural deformation of the wall‐frame and outrigger trusses are considered and incorporated in the formulation of the governing equations. A displacement‐based one‐dimensional finite element model is developed to predict lateral drift of a wall‐frame with outriggers under horizontal loads. Numerical static results are obtained and compared with previously available results and the values obtained from the finite element package MIDAS. The proposed method is found to be simple and efficient, and provides reasonably accurate results in the early design stage of tall building structures. Copyright © 2007 John Wiley & Sons, Ltd.     

Parameter study of framed‐tube structures with outriggers using genetic algorithm

In this paper, the analysis of optimal locations of framed‐tube structures with outriggers is conducted with the uniform and nonuniform core and peripheral columns using genetic algorithm, aiming to minimize the interstory drift. Also, comparison and difference of the results between the uniform and nonuniform structures are carried out and discussed. Besides, several parameters which influence the behavior of the structure are identified and analyzed, such as different objective functions, segments of outriggers, thickness of core wall, stiffness of outriggers, and grade of concrete strength. In addition, a Matlab program is written to perform the parameter analysis of optimal location of outriggers. Take a 260‐m high‐rise building as a target building, the optimal locations of one to two sets of outriggers subjected to three kinds of horizontal loadings (uniform, parabolic, and triangular) are obtained and can be utilized for the structural preliminary design of tall buildings.     

Distribution of strong earthquake input energy in tall buildings equipped with damped outriggers

The seismic design of optimal damped outrigger structures relies on the assumption that most of the input energy will be absorbed by the dampers, whilst the rest of the structure remains elastic. When subjected to strong earthquakes, nevertheless, the building structure may exhibit plastic hinges before the dampers begin to work. In order to determine to which extent the use of viscously damped outriggers would avoid damage, both the host structure's hysteretic behaviour and the dampers' performance need to be evaluated in parallel. This article provides a parametric study on the factors that influence the distribution of seismic energy in tall buildings equipped with damped outriggers: First, the influence of outrigger's location, damping coefficients, and rigidity ratios core‐to‐outrigger and core‐to‐column in the seismic performance of a 60‐story building with conventional and with damped outriggers is studied. In parallel, nonlinear behaviour of the outrigger with and without viscous dampers is examined under small, moderate, strong, and severe long‐period earthquakes to assess the hysteretic energy distribution through the core and outriggers. The results show that, as the ground motion becomes stronger, viscous dampers effectively reduce the potential of damage in the structure if compared to conventional outriggers. However, the use of dampers cannot entirely prevent damage under critical excitations.     

An analytical approach to free vibration analysis of multi‐outrigger–belt truss‐reinforced tall buildings

This paper deals with a new and simple mathematical model that may be used to determine natural frequencies and mode shapes of a multistory building that consists of a framed tube, a shear core and multi‐outrigger–belt trusses. The effect of outrigger–belt truss and shear core on a framed tube was modeled as a concentrated moment placed at outrigger–belt truss location, which acted in opposite direction of the rotation created by lateral loads. The analysis is based on a continuum approach, in which a tall building structure may be replaced by an idealized cantilevered beam to model the building's structural characteristics. Energy method and Hamilton's principle have been used to develop the governing equations. After applying separation of variables method to time and space variables, the resulting eigensystem was solved to obtain the building's natural modes and frequencies of vibration. A computer program has been developed in MATLAB (Mathworks Inc., CA, USA) environment, and a numerical example has been solved to demonstrate the accuracy of this method. Results obtained from the proposed mathematical model give a good understanding of a structure's dynamic characteristics. The method is simple to use yet reasonably accurate and hence suitable for quick evaluations during preliminary design stages. Copyright © 2011 John Wiley & Sons, Ltd.     

Simultaneous size and topology optimization of 3D outrigger‐braced tall buildings with inclined belt truss using genetic algorithm

To investigate the optimum location of the outrigger system, a metaheuristic‐based size and topology optimization of the outrigger‐braced tall buildings is carried out by various three‐dimensional structural frames with different shapes of belt trusses. By considering the elastic behavior, the whole elements of the structural models such as beams, columns, core, and trusses are optimized simultaneously in conjunction with the location of the outrigger. Furthermore, to reach more optimality, several novel types of belt truss are proposed having inclined and inverse‐inclined belt trusses with better structural and architectural features and optimum performance in comparison with the horizontal one. Different models with 25 to 40 stories having various span numbers are optimized using the genetic algorithm, and the results are compared with each other. In the modeling process, the exact wind load distribution is applied to the structure based on the ASCE7‐16 rather than the uniform or triangular ones. According to the results, the optimum cross‐sectional size and outrigger locations of different models are obtained, and it is indicated that the proposed novel belt trusses are optimal solution for the problem.     

Geometric nonlinear analysis of tall building structures with outriggers

In this paper, the geometric nonlinear behavior of wall‐frame tall building structures is analyzed. The governing equations of the wall‐frame systems with outrigger trusses are formulated through the continuum approach, and the whole structure is idealized as a shear‐flexural cantilever with rotational spring. The effect of shear and flexural deformation of the wall frame and outrigger trusses are considered and incorporated in the formulation of the governing equations. Geometric nonlinearity in the sense of von Karman is included in the formulation, and Newton–Raphson iterative method is employed to solve the nonlinear equations. A displacement‐based one‐dimensional nonlinear finite element model is developed. Numerical results for wall frame and mega‐column structures with outriggers are obtained and compared with the finite element package MIDAS. The proposed method is found to be simple and efficient, providing reasonably accurate results in early design stages of tall building structures. Copyright © 2011 John Wiley & Sons, Ltd.     

高层建筑结构腰架最佳位置研究

根据一种新的更接近实际情况的计算模型，即考虑梁柱节点为刚性节点，采用广义连续化方法，探讨各种结构参数对腰架最优位置的影响，以及顶部侧移减小和基底弯矩减小的腰架最优位置和数量。     

Outrigger system analysis and design under time‐dependent actions for super‐tall steel buildings

The outrigger system has been widely adopted as an efficient structural lateral‐load resisting system for super‐tall buildings in recent years. Although the outrigger system has many structural advantages, it has a significant defect due to differential shortening, which cannot be neglected. Due to the shrinkage and creep of concrete, as well as the differential settlement of foundation, the shortening of the structural member is an important time‐dependent issue, which leads to additional forces in the outriggers after the lock‐in of the outriggers. As a result, it will increase the size of the structural member cross section in the design. In a real project, engineers can delay the lock‐in time of the outrigger system to release the additional forces caused by the differential shortening during the construction phase. The time‐dependent actions, such as the column shortening and the differential settlement of the foundation, were estimated. A mega frame steel structure was employed to illustrate the analysis and design of the outrigger under the time‐dependent actions. Furthermore, a simple optimal method, considering the structural stability and overall stiffness, was proposed to optimize the construction sequence of the outrigger system.     

伸臂特性对框-筒结构中加强层力学性能的影响

本文根据伸臂结构的简化模型和伸臂与外框柱的变形协调条件,考虑伸臂的实际刚度,导出伸臂对核心墙的附加力矩,求得结构顶点侧移。对伸臂位置及刚度变化引起的侧移变化与内力突变进行了分析,结合工程分析结果对高层建筑加强层设计提出了一些参考意见。     

Fragility assessment of an outrigger structure system based on energy method

Fragility curves development in structures has always been a focus of research interest among structural and earthquake engineers for which the maximum story drift is usually considered as the engineering demand parameter (EDP) known as the conventional approach. This paper aims at calculating the fragility curves of a tall building with outrigger braced system by considering the plastic strain energy as the EDP and compare it with the conventional approach. In addition, the effect of optimizing the position of outriggers on the exceedance probability of the structure under near- and far-fault seismic loadings is investigated in this paper. Fragility curves of this structure in four performance levels including immediate occupancy (IO), life safety (LS), collapse prevention (CP), and instability is extracted based on the conventional method. The fragility curves for the aforementioned performance levels are also extracted based on the plastic strain energy and compared with the conventional approach. The results have demonstrated that optimizing the location of the bracing system would lower the exceedance probability of the structure. Moreover, the exceedance probability of the investigated building with outrigger braced system under far-fault records in various levels is more than that of near-fault records. It is also concluded that the conventional approach would lead to more conservative results compared with the energy approach.     

Optimal vertical configuration of combined energy dissipation outriggers

The damped outrigger system emerged as an improvement of the conventional outriggers with the aim to provide supplemental damping and to contribute to the vibration control in super tall buildings where this system is usually applied. In addition to viscous dampers (VDs), buckling‐restrained braces (BRBs) have also been employed as energy dissipating members in outriggers. Nevertheless, the combined use of outriggers with VDs and BRBs in the same structure has not yet been studied. Such combination can contribute to achieve an effective multiperformance design of super tall buildings. This paper presents a study whose main objective was to determine the optimal vertical combination of two types of energy dissipation outriggers to control the seismic responses of a 9‐zone super tall model structure. Outriggers with VDs (OVDs) and outriggers with BRBs (OBRBs) were placed at the different zones of the structure considering all the possible combinations and in configurations of up to four outriggers. The effects of these combinations on the seismic performance of the structure were studied through parametric analysis and optimization methods. This form of the outrigger system is defined in this paper as combined energy dissipation outrigger system. The results indicate that when two energy dissipation outriggers are used, the combination of OBRB plus OVD shows superior seismic performance compared with other double‐outrigger configurations. In addition, the results show that the locations of OVDs and OBRBs play an important role in the structure behavior; it was found that it is more beneficial to place OBRBs above OVDs.     

Torsional analysis of multi‐storey building structures under horizontal load

New closed‐form formulae are presented for the torsional analysis of asymmetrical multi‐storey buildings braced by moment‐resisting (and/or braced) frames, (coupled) shear walls and cores. The analysis is based on an analogy between the bending and torsion of structural systems. A closed‐form solution is presented for the rotation of the building. The torsional behaviour is defined by three distinctive phenomena: warping torsion, Saint‐Venant torsion and the interaction between the two basic modes. Accordingly, the formula for the maximum rotation of the building consists of three parts: the warping rotation is characterized by the warping stiffness of the bracing system, St Venant rotation is associated with the St Venant stiffness of the building and the third part is responsible for the interaction. It is demonstrated that the interaction between the warping and St Venant modes is always beneficial, as it reduces the rotation of the structure. It is shown how the proposed formula for torsion can be used for the determination of the maximum deflection of multi‐storey asymmetrical building structures. The results of a comprehensive accuracy analysis demonstrate the validity of the method. A worked example is given to show the ease of use of the procedure. Copyright © 2010 John Wiley & Sons, Ltd.     

Simplified analysis of asymmetric high‐rise structures with cores

A simplified elastic hand‐method of analysis for asymmetric multi‐bent structures with cores subjected to horizontal loading is presented. The structures may consist of combinations of framed structures such as coupled walls, rigid frames and braced frames with planar and non‐planar shear walls. Results for structures that are uniform with height compare closely with results from stiffness matrix analyses. The method is developed from coupled‐wall deflection theory which is expressed in non‐dimensional structural parameters. It accounts for bending deformations in all individual members, axial deformations in the vertical members as well as torsion and warping in nonplanar walls. A closed solution of coupled differential equations for deflection and rotation gives the deflected shape along the height of the building from which all internal forces can be obtained. The proposed method of analysis offers a relatively simple and rapid means of comparing the deformations and internal forces of different stability systems for a proposed tall building in the preliminary stages of the design. The derivation of equations for analysis shown in this paper are for unisymmetric stability systems only, but the method is also applicable to general asymmetric structures with cores. Copyright © 2002 John Wiley & Sons, Ltd.     

Analysis of outrigger‐braced reinforced concrete supertall buildings: Core‐supported and tube‐in‐tube lateral systems

This study is primarily focused on the approximate analysis of reinforced concrete outriggers which are commonly used in the design and construction of supertall buildings subject to distributed horizontal loads. Existing global analysis formulae that provide preliminary results for lateral deflections and moments are reviewed for two lateral load resisting systems, namely, core‐supported‐with‐outrigger (CSOR) system and less frequent tube‐in‐tube‐with‐outrigger (TTOR) system. These formulae are only applicable for CSOR and neglect the reverse rotation of the outrigger actually suffered due to the propping action from the outer columns and give rather high predictions of the deflections compared with advanced numerical finite element (FE) models. An improved model is proposed which overcomes this issue and provides more consistent results to FE predictions. The same can also be extended to TTOR. Several case studies are investigated to verify the accuracy of the proposed methodologies. The global analysis is followed by the local analysis of reinforced concrete outrigger beams using strut‐and‐tie modelling and non‐linear FE analysis to obtain optimized reinforcement layouts (reduction of quantities of reinforcement). The results highlight the different challenges in detailing such structural members which are heavily loaded (high congestion of reinforcement), and the behaviour at failure can be brittle.     

Strength demand of dual‐purpose outrigger system for reducing lateral displacement and differential axial shortening in a tall building

Certain maximum lateral displacement (LAT) and differential axial shortening (DAS) values can lead to the deterioration of the serviceability of a structure. Previous studies indicated that an outrigger system can be used to control both the DAS and the LAT in a tall building. In order to enhance the applicability of the dual‐purpose outrigger system, the amount of stress developed on the outrigger due to the reductions of the LAT and DAS should be determined. Therefore, in this study, the stresses due to the LAT and DAS were analyzed in terms of the reduction ratio of the LAT and DAS, and the absolute sum of stresses, which was the strength demand of the outrigger, was evaluated as well. To identify the parameters affecting the additional stress of the outrigger, analytic equations were proposed to predict the additional shear force acting on the outrigger due to DAS reduction. A finite‐element analysis was performed to quantitatively identify the reduction ratio of the LAT and DAS as well as the resulting stress by changing four parameters: the stiffness, location, number, and connection time of outriggers. The results demonstrated that the stress of the dual‐purpose outrigger can be minimized by adjusting the design parameters.     

Seismic assessment of RC core‐wall building capable of three plastic hinges with outrigger

In a core‐wall structure with buckling restrained braces (BRB) outrigger, locations of the plastic hinges are influenced by the outrigger action. Therefore, the designer should consider the issue and use suitable details in the plastic hinge area. The essential questions that arise here are the plastic hinge location and the design moment demand used for design of this kind of structure. In this paper, responses of the core‐wall buildings with BRB outrigger designed by using the traditional response spectrum analysis procedure are assessed by implementing the nonlinear time history analysis. The result demonstrates that the plasticity can extend over anywhere within the core‐walls specially, at the base and above or below the outrigger levels. Formation of three plastic hinges in the core‐wall is recognized suitable for the system. To control the plasticity extension in the core‐wall, it is recommended that a new modal combination method be applied to calculate the moment strength of the three plastic hinges over the height. A capacity design concept is used to design other regions of the core‐wall where the plasticity does not extend to. The proposed procedure improves behavior of the system by restricting the plasticity extension to the predefined plastic hinge regions. Copyright © 2016 John Wiley & Sons, Ltd.