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.     

Effect of axial deformation on vibration of tall buildings

In this paper, the governing equations of a frame‐core wall building are formulated through the continuum approach and the whole structure is idealized as a shear–flexural cantilever. The effect of axial deformation in the frame is considered and incorporated in the formulation of the governing equations. The Bubnov–Galerkin method is used to transform the governing differential equations into a set of algebraic equations. Numerical examples are solved and the results compared with the values obtained from the finite element package ‘ETABS’. The study indicates that the effect of axial deformation should be considered especially for tall and/or slender buildings. The proposed method is simple and efficient, provides reasonably accurate results and can be easily implemented on any personal computer. Copyright © 2001 John Wiley & Sons, Ltd.     

The effects of axial deformation and axial force on vibration characteristics of tall buildings

A tall building comprising frames and shear walls coupled together is idealized as a shear–flexure cantilever through the continuum approach. The effects of axial deformation as well as axial force in the frames are considered and incorporated in the formulation of the governing equations. Numerical examples are solved through the Galerkin method and the results compared with finite element solutions. The study indicates that the effect of axial deformation in the frame should be considered for tall and/or slender buildings while the effect of axial force in the column should be included for buildings with soft‐storeys resulting from the termination of core walls in the lower portion of the building. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance analysis of rocking shear wall‐frame structure

Incorporating the shear deformation effect of the shear wall and the restrained moment effect of the link beam, a continuum model is presented to conduct the preliminary analysis of the rocking shear wall‐frame structure. It can be applicable to fixed/hinged systems with link beams fixed/hinged at the ends and to clamped/rocking shear wall‐frame structures with clamped/rocking shear wall at the base. Its comprehension can improve the accuracy and integrality of the analytical theory for shear wall‐frame structures. Analytical solutions to three loading scenarios are derived and make manual computation possible. A finite element with the analytical solutions as the shape functions is presented. This formulation is convenient to analyze the stepped shear wall‐frame structures with variable cross sections along the height and under complicated loads. The frequency equations and mode shapes are also derived. Numerical examples demonstrate the accuracy and excellent predictions of the present model and the finite element formulation.     

Structural performance of multi‐outrigger‐braced tall buildings

The optimum designs of multi‐outriggers in tall building structures are presented and discussed in this paper, through the analysis of structural performance of outrigger‐braced frame‐core structures. The influences of the locations of outriggers and the variations of structural element stiffness on the base moment in core, top drift and fundamental vibration period of such tall building structures are analysed in detail. A non‐linear optimum design procedure for reducing the base moment in the core is presented based on the penalty function method. The computer programs are developed on the basis of the proposed methods for analysing the behaviour and optimum design of multi‐outrigger structures. A series of figures presented in this paper can be used for the design purposes of outrigger‐braced tall building structures. Copyright © 2003 John Wiley & Sons, Ltd.     

Exact method of analysis of shear lag in framed tube structures

Framed tube structures are particularly suitable for tall buildings. Owing to flexural and shear flexibilities of the frame members, the overall bending of the frame is complicated by the occurance of shear lag. The shear lag phenomenon in framed‐tube structures under lateral loads is explained in the literature, but explanation of its origin and comprehensive studies of it is lacking. In this paper an analogy between the shear lag behaviour of a cantilever box representing a uniform framed‐tube building is used for exact analysis of stress and displacement components of perimeter columns. The coefficients of the power series used for the governing equilibrium and compatibility equations are functions of the height and width of the frame panels. Numerical examples are given to demonstrate the accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Modelling shear–flexure interaction in equivalent frame models of slender reinforced concrete walls

Quasi‐static cyclic tests on reinforced concrete (RC) walls have shown that shear deformations can constitute a significant ratio of the total deformations when the wall is loaded beyond the elastic regime. For slender RC walls that form a stable flexural mechanism, the ratio of shear to flexural deformations remains approximately constant over the entire range of imposed displacement ductilities. This paper proposes a method for incorporating shear‐flexure interaction effects in equivalent frame models of slender RC walls by coupling the shear force‐shear strain relationship to the curvature and axial strain in the member. The suggested methodology is incorporated in a finite element consisting of two interacting spread inelasticity sub‐elements representing flexural and shear response, respectively. The element is implemented in the general finite element code IDARC and validated against experimental results of RC cantilever walls. In a second step, it is applied in inelastic static and dynamic analyses of tall wall and wall‐frame systems. It is shown that ignoring shear‐flexure interaction may lead to erroneous predictions in particular of local ductility and storey drift demands. Copyright © 2013 John Wiley & Sons, Ltd.     

Seismic behavior of tall buildings using steel–concrete composite columns and shear walls

For the seismic design of tall building structures, the behavior under severe earthquakes should be carefully considered and the upper limit of inter‐story deformations are often defined by the design codes. To improve the performance of structures under severe earthquakes, composite structural members, including steel reinforced column and steel plate reinforced shear wall, are often adopted. In the present work, the seismic behavior of tall buildings using steel–concrete composite columns and shear walls is investigated numerically. Fiber beam–column element models and multilayer shell models are adopted to establish the finite element model of structure, and the material nonlinearities are described by the plasticity and damage models. The accuracy of the developed models is verified by the experimental results of a single shear wall. Systematic numerical simulations are performed for the tall building structures subjected to different earthquakes. The comparative study indicates that the nonlinear redistribution of internal forces plays a very important role for the performance of tall buildings under severe earthquakes.     

双筒剪力墙结构动态特性分析

某电信枢纽工程主体建筑为双筒剪力墙高层建筑，根据结构特点，采用有限元法对该结构进行有限元离散，框架中的梁，柱采用空间梁单元模拟，筒体，剪力墙，楼板和屋盖采用薄板单元进行离散，探讨了整体结构动力分析模型和按对称和反对称边界条件取一半结构进行动态特性计算的差异，并与结构设计软件TBSA的计算结果进行了对比，得出一些有益的结论，可供该类型结构抗震设计与动力计算参考。     

天津现代城酒店塔楼及裙房抗震设计研究

天津现代城酒店塔楼建筑高度209m,建筑要求高度56m、平面长度65m的裙房结构和塔楼结构连为一体,中间不设置防震缝。酒店塔楼采用带加强层的钢筋混凝土框架-核心筒结构体系,为超B级高度超限高层。结构低区外框柱为型钢混凝土柱,核心筒低区采用了钢板混凝土组合剪力墙和带钢斜撑混凝土剪力墙。核心筒高宽比为20,因此为提高刚度设置两道加强层。中部设置伸臂桁架和环带桁架,建筑对与伸臂桁架相连的框架柱截面控制极严,因此伸臂桁架腹杆选用屈曲约束支撑;裙房部位为提高刚度,在不能设置剪力墙且抗侧支撑竖向不连续的情况下设置了屈曲约束支撑。高区设置环带桁架作为加强层,结构底部存在斜撑转换和搭接柱转换。系统介绍了该工程的结构体系特点、抗震性能化设计原则和方法、整体计算结果、罕遇地震作用下的弹塑性时程分析结果以及地基基础的设计。     

A generalized method for estimating drifts and drift components of tall buildings under lateral loading

A generalized method for estimating the drifts of tall buildings composed of planar moment‐resisting frames and coupled shear walls under lateral loading is presented. This method establishes the stiffness equations at the story levels by assuming that all the nodes in the same floor of a planar lateral‐force‐resisting unit have an identical lateral displacement, an identical rotation component due to the axial deformations of the columns, and an identical rotation component due to the flexural and shear deformations of the beams. By adopting this simplification, the story drifts contributed by different types of deformations, namely, the axial deformations of the columns or wall piers, the flexural and shear deformations of the beams, and the double‐curvature bending and shear deformations of the columns or wall piers, can be identified. In the formulation of the stiffness matrix, the P‐Delta effects were also incorporated. Through comparisons between the lateral displacements and story drifts computed using the proposed method and those computed using the structural analysis software Midas/Gen, the proposed method is proved to have high accuracy in estimating the drifts of tall building structures.     

超高层建筑伸臂桁架“延迟连接”技术在沈阳恒隆广场主塔楼施工中的应用

在水平荷载起控制作用的超高层建筑中,设置伸臂桁架可以提高结构的整体工作性能,从而提高结构的抗侧刚度,控制结构的顶部位移,降低核心筒所承担的倾覆力矩。但是,伸臂桁架在施工阶段,由于内外筒施工不同步,结构布置不对等原因,会导致施工过程中内、外筒的变形存在一定差异,如果盲目施工,将会造成在伸臂桁架内部过早产生较大应力,导致结构成形后整体受力状况与原结构设计模型不符。通过研究,提出一种超高层伸臂桁架"延迟连接"的施工技术。该方法在沈阳恒隆广场主塔楼施工应用的情况表明,可有效解决外框与芯筒不均衡变形导致的伸臂桁架应力过大的问题,确保了伸臂桁架施工和使用阶段的结构性能。     

Progressive collapse resisting capacity of building structures with outrigger trusses

In this paper, the progressive collapse potential of building structures with core and outrigger trusses were evaluated using nonlinear static and dynamic analyses. To this end 36‐storey analysis model structures composed of RC core walls and perimeter frames connected by outrigger trusses at the top were prepared. The static pushdown analysis of the structure with mega‐columns and outrigger trusses showed that the maximum strength reached only about 20% of the load specified in the US General Services Administration guideline when a mega‐column in the first storey was removed. According to dynamic analysis results, the vertical displacement monotonically increased until collapse as a result of buckling of some of outrigger truss members. However the structure with outrigger and belt trusses remained stable after a perimeter column was removed. The stability of the structure with mega‐columns and outrigger trusses could be achieved by redesigning it with additional belt trusses or with moment connections in interior or exterior frames. Based on the analysis results it was concluded that the dynamic amplification factor of 2.0 recommended in the guidelines provided reasonably conservative results. Copyright © 2010 John Wiley & Sons, Ltd.     

Shaking table test and seismic behavior of Ningbo Hengda Tower

A super tall building named Ningbo Hengda Tower is located in Ningbo City, China. It has 91 stories with a total height of 450 m. The structure system of the building consists of three parts, that is, the reinforced concrete core, the outer frame system, and the outrigger trusses connecting the core wall and outer frame. The unique outer frame system is spindle shaped with oblique columns. The outrigger trusses are located at three different levels above the ground, thus strengthening the building and creating irregularities in the stiffness of the structure along the building height. Great challenges are existed in seismic design and analysis of the building. Shaking table test was carried out for a 1/40 scaled model of the building under a series of different base excitations with increasing amplitudes. The dynamic properties, seismic responses, and failure mechanism of the structure are investigated. Test results show that the structure behaved well under designed level earthquakes. The weak points of the structure are identified based on visible damage of the tested model, and some suggestions are made for the improvement of the seismic behavior of the building. It is suggested that measures be taken to improve the ductility of the building from floor 71 to floor 79 and the adjacent floors.     

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.     

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.     

广义位移的有限条法及其在高层建筑结构分析中的应用

本文提出了广义位移的有限条方法,用于分析物理特性沿高度突变的高层建筑构。该法消除了经典有限条方法分析此类结构的缺陷,即截面应力在刚度突变处不连续,致使靠近突变截面一定范围内的应力收敛到不正确的结果。本文对这种非均匀的高层建筑平面结构在T-300微型机上进行了实例分析,算例包括实体剪力墙、联肢墙、框剪结构。此法同样适用于分析均匀高层结构。     

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.     

Nonlinear seismic assessment of irregular coupled wall systems using high‐performance fiber‐reinforced cement composites

Reinforced concrete coupled wall systems that consist of multiple shear walls linked by coupling beams are known to be very effective for resisting lateral loads in high‐rise buildings. As to improving the seismic capacity of coupled wall systems, high‐performance fiber‐reinforced cement composites (HPFRCCs) have been recently considered. These materials are characterized by tension strain‐hardening behavior that can improve the ductility and toughness of structures subjected to reversed cyclic loading. In this study, nonlinear finite element analyses were conducted to investigate the effects of HPFRCCs on the seismic behavior of irregular tall buildings with coupled wall systems. The coupling beams were modeled using moment hinge elements, and the structural walls were modeled using fiber elements. Comparisons between analysis and test results of coupled wall specimens with and without HPFRCCs indicate that the modeling methods used well predict both the overall and local behaviors. The responses of a 56‐story irregular tall building with coupled walls are discussed with focus on the effects of HPFRCCs. It is noted that the use of HPFRCCs in coupling beams and structural walls of one‐fourth height from the base greatly affects the failure mode. For irregular tall buildings, nonlinear response history analysis indicates higher mode effects are critical.     

Efficient structural analysis of wall–frame structures

In this study, an efficient analytical model for the dynamic analysis of tall buildings with a shear wall–frame structural system has been proposed. A shear wall–frame structural system usually consists of a core wall showing flexural behavior and a frame presenting shear behavior. Therefore, the deformed shape of the shear wall–frame structural system is shown by the combination of flexural mode and shear mode. To consider this characteristic in developing an efficient analytical model, the effect of shear wall and frame on the dynamic behavior of a tall building with a dual system has been separately investigated. In order to consider the effect of the shear wall in the frame model without shear wall, a rigid body was used instead of the shear wall. Each equivalent model for the separated shear wall part and frame part has been independently developed, and two equivalent models were then combined to create an efficient analytical model for tall buildings with a shear wall–frame structural system. In order to verify the efficiency and accuracy of the proposed method, time history analyses of tall buildings with a shear wall–frame system were performed. With analytical results, it has been confirmed that the proposed method can provide accurate results with significantly reduced computational time and memory. Copyright © 2013 John Wiley & Sons, Ltd.