Coupled‐two‐beam discrete model for dynamic analysis of tall buildings with tuned mass dampers including soil–structure interaction

An equivalent coupled‐two‐beam discrete model is developed for time‐domain dynamic analysis of high‐rise buildings with flexible base and carrying any number of tuned mass dampers (TMDs). The equivalent model consists of a flexural cantilever beam and a shear cantilever beam connected in parallel by a finite number of axially rigid members that allows the consideration of intermediate modes of lateral deformation. The equivalent model is applied to a shear wall–frame building located in the Valley of Mexico, where the effects of soil–structure interaction (SSI) are important. The effects of SSI and TMDs on the dynamic properties of the shear wall–frame building are shown considering four types of soil (hard rock, dense soil, stiff soil, and soft soil) and two passive damping systems: a single TMD on its top (1‐TMD) and five uniformly distributed TMDs (5‐TMD). The results showed a great effectiveness of the TMDs to reduce the lateral seismic response and along‐wind response of the shear wall–frame building for all types of soils. Generally speaking, the dynamic response increases as the flexibility of the foundation increases.     

Estimation of floor acceleration demands in high‐rise buildings during earthquakes

A simplified method to estimate lateral acceleration demands in high‐rise buildings subjected to earthquakes is presented. In the proposed method acceleration demands are obtained by approximating the dynamic characteristics of the building with those of a continuous model consisting of a combination of a flexural cantilever beam and a shear cantilever beam. Closed‐form solutions for mode shapes, period ratios and modal participation factors for the first six modes of vibration are presented. The method is evaluated by comparing peak floor acceleration demands and acceleration time histories computed with the proposed method to those recorded during earthquakes in six instrumented high‐rise buildings. A comparison of floor spectra computed with the approximate method and spectra computed with recorded motions is also presented. Results indicate that the proposed method produces relatively good results with a very small computational effort and requires only a small amount of information about the building. Variations of accelerations demands along the height are closely examined in each building for each component. It is shown that the variation of acceleration demands along the height of high‐rise buildings can differ significantly from that currently recommended in US seismic provisions for anchoring building nonstructural components. Copyright © 2005 John Wiley & Sons, Ltd.     

Approximate analysis of tall buildings using sandwich beam models with variable cross‐section

In this paper an approximate method is carried out for determining the natural periods of multistory buildings subjected to earthquake. The building resists lateral forces through a combination of lateral resisting systems. These systems could be replaced by a cantilever Timoshenko or a sandwich beam with varying cross‐section that characterizes three kinds of stiffnesses: the global bending stiffness, the local bending stiffness and the shear stiffness. Using appropriate transformations, the differential equations for flexural and shear free vibration of a cantilever beam with variably distributed mass and stiffness are reduced to Bessel's equations and ordinary differential equations. The frequency equations can be solved by selecting suitable expressions such as exponential and power functions for stiffness and mass distribution along the height of the building. The calculated frequencies are combined appropriately by using approximate methods. Based on the fact that shear and bending deformations are all considered, the free vibration frequency of the structure could be calculated. The capability and accuracy of the proposed method are demonstrated by a numerical example in which finite element results are compared with the proposed methodology and other approximate methods. Copyright © 2007 John Wiley & Sons, Ltd.     

Towards optimal design of high‐rise building tube systems

The primary objectives of this study are to investigate effects of varying design parameters on the tube action and shear lag behaviour of a typical reinforced concrete frame‐wall tube building, and propose optimal design approaches for similar tube structures. A parametric study was conducted with selected key design variables on the performance of a 55‐storey hotel building planned in New York City. The lateral force resistance of the case study building is primarily exerted by exterior shear walls in one direction and by exterior moment frames in the other direction, enhanced by the tube action credited to the connection of the walls and the frames. The design variables considered for the parametric study include the column depth, beam depth, column width and beam width of the moment frames. The performance of each model was assessed in terms of overall and critical (maximum) storey drifts, force distributions between various lateral force‐resisting members and shear lag behaviour. Overall, the effects of the column depth (column dimension parallel to the frame direction) on the tube action and shear lag behaviour were more prominent than the other member dimensions. Copyright © 2010 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.     

Probabilistic updating of fishbone model for assessing seismic damage to beam–column connections in steel moment‐resisting frames

This article presents a probabilistic method of updating fishbone models for assessing seismic damage on beam–column connections in steel moment‐resisting frames. Fishbone models enable explicitly identifying the rotational stiffness of beams, which is not possible with a shear building model commonly used in Bayesian model updating approaches. Necessary formulations to utilize fishbone models for model updating with measured floor accelerations under small‐amplitude loadings including ambient excitations were first formulated. To accommodate the incompleteness of modal data to update unknown parameters of fishbone models, that is, the stiffness of rotational springs, a hierarchical Bayesian model updating algorithm is implemented. Seismic damage of beam–column connections are estimated by making a comparison of the identified rotational stiffness of springs in the fishbone models before and after earthquakes. The effectiveness of the proposed method is first examined with numerical simulations using a 10‐story building model. Then, the applicability to realistic beam damage, that is, not artificially introduced, is evaluated through a full‐scale steel frame test at the E‐Defense shaking table facility. The article also discusses coefficients of variation of the identified stiffness and influence of modeling error on estimation of realistic damage to check the credibility of the method for real‐life applications.     

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.     

Proposed robust tuned mass damper for response mitigation in buildings exposed to multidirectional wind

The most common device for control of tall buildings under wind loads is the tuned mass damper (TMD). However, during their lifetimes, high‐rise and slender buildings may experience natural frequency changes under wind speed, ambient temperatures and relative humidity variations, among other factors, which make the TMD design challenging. In this paper, a proposed approach for the design of robust TMDs is presented and investigated. The approach accounts for structural uncertainties, optimization objectives and input excitation (wind or earthquake). For the use of TMDs in buildings, practical design parameters can be different from the optimum ones. Nevertheless, predetermined optimal parameters for a primary structure with uncertainties are useful to attain design robustness. To illustrate the applicability of the proposed approach, an example of a very slender building with uncertain natural frequencies is presented. The building represents a case study of an engineered design that is instructive. Basically, due to its geometry, the building behaves differently in one lateral direction (cantilever building) than the other (shear building). The proposed approach shows its robustness and effectiveness in reducing the response of tall buildings under multidirectional wind loads. In addition, linear‐quadratic Gaussian and fuzzy logic controllers enhanced the performance of the TMD. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic P‐Δ effects for multistorey steel columns in long‐span tube‐in‐tube tall buildings

An Euler–Bernoulli beam–column model is employed to investigate the dynamic P‐Δ effects of steel columns located at the external tube of a long‐span tube‐in‐tube tall building. A steel column with multistorey lateral open‐web beam supports is modelled as a beam–column element supported by elastic springs, from which a governing partial differential equation is established for the vibration of the column subjected to an axial compression force, lateral beam forces and base excitations. The problem is solved by a modal superposition method for both transient and steady‐state solutions. A numerical example is illustrated and the results indicate that the secondary moment of a steel column induced from dynamic multistorey P‐Δ effects is essential and should not be ignored in a practical design. The influences of the factors including flexural rigidity of the column, axial stiffness of the open‐web beams and the magnitude of the compressive axial force are discussed. Copyright © 2005 John Wiley & Sons, Ltd.     

中高层混合结构弹塑性变形简化计算方法

将中高层混合结构简化为一竖向弯曲梁与一竖向剪切梁,考虑其协同工作,并考虑重力二阶效应的影响。分别采用弹性设计反应谱和增大系数方法计算结构弹性位移和弹塑性位移,进而计算结构在多遇地震下的弹性位移以及罕遇地震下的弹塑性位移。对一20层混合结构算例进行分析,结果显示:采用该方法计算所得地震作用下的横向变形同"精确"分析方法所得的结果很相近,满足结构初步设计阶段要求。     

Practical modelling of high‐rise dual systems with reinforced concrete slab‐column frames

This paper discusses practical modelling issues pertinent to the design of an irregularly shaped reinforced concrete (RC) high‐rise building currently under development in New York City. The structure analysed consists of a 60‐storey residential tower and a 25‐storey hotel building structurally connected to each other. For the seismic force resistance, a dual system combining ordinary RC shear walls and intermediate slab–column moment frames was used at the upper portion, while a building frame system of ordinary RC shear walls was used at the lower portion of the structure. A variety of models were used to simulate the behaviour of various elements of the structure, with special attention given to overall systemic effects of different member stiffnesses considered to account for distinct stress levels under service and ultimate loads. The models used for slab–column frames and shear walls were verified by comparing with other available models or laboratory tests. The in‐plane flexibility of floor diaphragms at the interface between the two substructures with different geometries was simulated to identify the most critical wind conditions for each structural member. Finally, building dynamic analyses were performed to demonstrate the modelling issues to be considered for the lateral force design of irregular high‐rise buildings. Copyright © 2009 John Wiley & Sons, Ltd.     

The effect of roof systems on seismic performance of reinforced concrete frame‐bent main building of large‐scale thermal power plant

The roof systems of turbine hall in large‐scale thermal power plant are often simulated by approximate rigid beam model. Wenchuan earthquake again revealed the frequent destruction of these roof systems. In this study, three kinds of general roof systems as space grid, trapezoid steel roof truss and reinforced concrete (RC) mansard roof truss were considered. Also, the numerical model of RC frame‐bent main building in large‐scale thermal power plant was established. Seismic performance of main building was compared with approximate rigid beam model, and the damage mechanism of roof systems was also investigated. The results indicate that the response calculation of frame part by rigid beam model is feasible, and roof systems give most contribution to the response of bent part. After considering roof systems, overall collaborative performance is enhanced, but bent part is still unable to become a second defence part after shear walls fail. The torsional irregularity of roof systems is very serious, and more attentions should be paid to the bearing shear failure of space grid and components strength failure of RC roof systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Identification of the mode shapes of spatial tall multi‐storey buildings due to earthquakes: the new ‘modal time‐histories’ method

In the present article, a new method is presented which attempts to identify the dynamic characteristics (eigen frequencies, eigen periods, mode shapes and modal damping ratios) of spatial asymmetric tall multi‐storey buildings through measured seismic responses (accelerations). This new method is entitled ‘method of modal time‐histories’, because its main target is to identify the modal time‐histories of accelerations that are obtained by accelerograms recorded on the points of buildings where suitable accelerometers have been installed. In the case of an earthquake, the multi‐channel local network of accelerometers records the time‐histories of the accelerations of the building. In addition, in order to have a successful outcome, the instrumentation form of the multi‐channel local network on the building can potentially play the most important role. This paper, first, presents a relevant mathematical analysis that is adapted to the instrumentation form applied to the multi‐storey buildings and, second, outlines the new method, which consists of nine steps. Finally, in order to illustrate the theory, a suitable numerical example of an instrumented asymmetric five‐storey r/c building that has been oscillated by a weak earthquake is also provided. On the one hand, the identification of the dynamic characteristics of spatial asymmetric buildings contributes to the removal of the uncertainties of building models in order to perform advanced non‐linear analyses about inherent building seismic capacity. On the other hand, this method supports the simple monitoring of a building's ‘structural integrity’. Copyright © 2010 John Wiley & Sons, Ltd.     

Reduced‐basis stiffness inversion of a structure–foundation system via component‐mode synthesis

The purpose of this paper is to propose a new formulation for incremental reduced‐basis stiffness inversion via component‐mode synthesis. An elastically supported shear building model is taken as an example of an assemblage of substructures. The superstructure, the swaying spring and the rocking spring are regarded as ­the constituent substructures. The story stiffnesses of the superstructure are expressed in terms of linear combinations of several stiffness basis distributions. Eigenmodes of a fixed‐base shear beam model having a uniform cross‐section combined with rigid modes due to swaying and rocking displacements of the foundation ­are adopted as component modes for an overall model. It is shown that inverse use of the component‐mode synthesis technique in an incremental inverse problem enables the development of an efficient computational procedure for finding stiffness parameters in the design problem. An approximate expression for the seismic response to stationary random excitations is also presented for the reduced model. The validity of the proposed method is demonstrated through several elastically supported shear building models. Copyright © 2000 John Wiley & Sons, Ltd.     

Comparative experimental study of full‐scale H‐subframe using a new industrialized building system and monolithic reinforced concrete beam‐to‐column connection

Industrialized building system (IBS) is a construction process that uses techniques, products, components or building systems that involve prefabricated components and on‐site installation. The structural behaviour of a prefabricated frame structure is widely affected by the specifications of the beam‐to‐column connection. The understanding on the real behaviour of a connection can be assessed by conducting full‐scale experimental tests. In this study, a new IBS hybrid steel–concrete connection in a full‐scale H‐subframe under monotonic loading is investigated. This innovative connection system, consists of precast concrete beam‐and‐column elements with embedded steel end connectors, is patented as Smart IBS. This paper reports the testing procedures and results of this semi‐rigid IBS beam‐to‐column connection to obtain the important attributes of the connection as well as its comparison with monolithic cast‐in‐place reinforced concrete model. The height of both H‐subframes is 3.3 m while the free length of the beam is 3.2 m. The incremental loads were applied as two point loads in one‐third and two‐third of the beam length. The characteristic relationships of the connection such as load to mid‐span deflection, strength, stiffness, ductility, failure modes and crack patterns are studied and compared between both structural systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Optimal drift design model for multi‐story buildings subjected to dynamic lateral forces

An optimal drift design model for a linear multi‐story building structure under dynamic lateral forces is presented. The drift design model is formulated into a minimum weight design problem subjected to constraints on stresses, the displacement at the top of a building, and inter‐story drift. The optimal drift design model consists of three main components: an optimizer, a response spectrum analysis module, and a sensitivity analysis module. Using a small example, the validation of the proposed model has been tested by a comparison of optimal solutions. Then, the performance of the optimal drift design model is demonstrated by application to three steel frame structures including a 40‐story building. Various structural responses including lateral displacement and inter‐story drift distributions along the height of the structure at the initial and final design stages are presented in figures and tables. Time‐consuming trial‐and‐error processes related to drift control of a tall building subjected to lateral loads is avoided by the proposed optimal drift design method. Copyright © 2003 John Wiley & Sons, Ltd.     

Interaction‐based design tables for transfer beams supporting in‐plane loaded shear walls

The analysis and behaviour of transfer beams that support in‐plane loaded shear walls have been receiving added emphasis owing to their importance in connection with the design of tall buildings. In this paper, analysis and structural behaviour of transfer beams supporting in‐plane loaded shear walls are presented, where emphasis is placed on the interaction between the transfer beam and the supported shear wall. The interaction effect is shown to cause significant stress re‐distributions both in the transfer beam and in the shear wall within an interactive zone. Parameters that significantly influence the structural behaviour and force transfer mechanism are also highlighted. Based on finite element analysis, interaction‐based design tables are constructed and presented for the design of the transfer beam–shear wall system, which is represented by an equivalent portal frame. The design tables have been shown to provide practising engineers a very simple and efficient, yet accurate, means of analysis of the internal forces of the transfer beams and the support columns. Copyright © 2001 John Wiley & Sons, Ltd.     

A simple method for the deflection analysis of tall wall‐frame building structures under horizontal load

New closed‐form formulae are developed for the static deflection of symmetric multi‐storey buildings braced by moment‐resisting (and/or braced) frames, (coupled) shear walls and cores. The behaviour is characterized by shear, local bending and global bending, and corresponding stiffnesses. The analysis is based on that of a single moment‐resisting framework. A closed‐form solution is presented for the lateral deflection. The procedure is then extended to a system of frameworks, (coupled) shear walls and cores by creating an equivalent column which represents the whole structure. Another closed‐form solution is presented, this time for the deflection of the whole building. The deflection is defined by three distinctive parts: the bending deflection of the building, the shear part of the deflection and interaction between the bending and shear modes. It is shown that the interaction between the bending and shear modes is always beneficial as it reduces the deflection of the structure. According to a comprehensive accuracy analysis of 270 multi‐storey building structures with both reinforced concrete and steel bracing units and covering wide ranges of stiffness, the proposed closed‐form solution for the top deflection is simple and reliable: the average error of the formula was 4%. A worked example demonstrates the ease of use of the method. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic analysis of combined system of framed tube and shear walls by Galerkin method using B‐spline functions

In this article, dynamic parameters (natural frequencies and mode shapes) of tall buildings that consist of framed tube and shear walls are obtained using a simple approximate method. The three‐dimensional structure is replaced by an equivalent cantilever beam, considering both bending and shear deformations. On the basis of dynamic equilibrium, the governing differential equation of motion is obtained and converted to its corresponding weak form. B‐spline functions are then utilized to approximate the weak form and to obtain the final matrix form of the problem. Finally, by applying essential boundary conditions, the natural frequencies and corresponding mode shapes are calculated. To demonstrate the accuracy of the proposed method, numerical examples are solved, and the results are compared with those obtained from SAP2000 computer analysis. The results show that the proposed method is efficient and accurate enough to be used in preliminary design. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic performance of friction dampers using flexure of rc shear wall system

Shear wall systems in high‐rise apartments are governed by the flexural behaviour of members such as a cantilever beam. The installation of the damper‐brace system in a structure governed by flexural behaviour is not suitable. Because of the relatively high lateral stiffness of the shear wall, a load is not concentrated on the brace and the brace cannot perform the role of a damping device. In this paper, a friction damper that applies the flexibility of a shear wall is proposed in order to reduce the deformation of the structure. To evaluate the performance of the proposed friction damper, a nonlinear time history analysis is executed by the SeismoStruct analysis program, and a multiple vertical linear element model is used for simulating flexural behaviour of the shear wall. It is found that the control performance of the proposed friction damper is superior to that of a coupled wall with a rigid beam. In conclusion, this study verified that the optimal control performance of the proposed friction damper is equal to 45% of the maximum shear force induced in the middle floor beam with the rigid beam. Copyright © 2009 John Wiley & Sons, Ltd.