Analysis Of Tall Buildings Research Articles

Free vibration analysis of tall buildings with outrigger-belt truss system

In this paper a simple mathematical model is presented for estimating the natural frequencies and corresponding mode shapes of a tall building with outrigger-belt truss system. For this purposes an equivalent continuum system is analyzed in which a tall building structure is replaced by an idealized cantilever continuum beam representing the structural characteristics. The equivalent system is comprised of a cantilever shear beam in parallel to a cantilever flexural beam that is constrained by a rotational spring at outrigger-belt truss location. The mathematical modeling and the derivation of the equation of motion are given for the cantilevers with identically paralleled and rotational spring. The equation of motion and the associated boundary conditions are analytically obtained by using Hamilton\'s variational principle. After obtaining non-trivial solution of the eigensystem, the resulting is used to determine the natural frequencies and associated mode shapes of free vibration analysis. A numerical example for a 40 story tall building has been solved with proposed method and finite element method. The results of the proposed mathematical model have good adaptation with those obtained from finite element analysis. Proposed model is practically suitable for quick evaluations during the preliminary design stages.

Column shortening analysis of tall buildings with lumped construction sequences

SUMMARYAn analysis method with lumped construction sequences for the column shortening of tall buildings is proposed and its efficiency is investigated. The lumped model shows results that are close to the exact model in subsequent shortening as well as total shortening. Different arrangement methods for the lumped model are investigated. The size of the lumping is studied and 1/15 is recommended considering the efficiency of the lumped model. The lumped models can be used efficiently for the three‐dimensional analysis as well as for the plane frame analysis. The proposed method can be used more effectively at the design stage of tall buildings. Copyright © 2010 John Wiley & Sons, Ltd.

A global approach for three‐dimensional analysis of tall buildings

AbstractIn the literature, several approximate approaches have been proposed to analyse the lateral loading distribution of external loads in high‐rise buildings; in this paper, a general method is proposed for the analysis of the lateral loading distribution of three‐dimensional structures composed of any kind of bracings (frames, framed walls, shear walls, closed and/or open thin‐walled cores and tubes) under the customary assumption of floor slabs being undeformable in their planes. This general formulation allows analyses of high‐rise structures by taking into account the torsional rigidity of the elements composing the building without gross simplifications, even in the case of very complex shapes and with the contemporary presence of different kinds of bracing. The method is aimed at gaining an insight into the force flow in the structure, in order to understand how the building response is governed by decisive structural parameters and to compare preliminary calculations with other approaches such as the structural finite element analysis. Copyright © 2009 John Wiley & Sons, Ltd.

Analysis of Tall Buildings with Damped Outriggers

A novel damped outrigger system has been recently proposed for tall buildings, and is quite promising. To gain insight into the conceptual design of such systems, a simple beam-damper system model for a building with such dampers installed is developed and studied. A partial differential equation governing the motion is derived assuming a Bernoulli-Euler beam. A closed-form analytical solution is developed for vibration of the beam by analyzing the regions above and below the damper separately using separation of variables. By applying appropriate boundary conditions at the ends, a transcendental characteristic equation is obtained that governs the system's complex natural frequencies. An explicit form for the complex mode shape is determined for dynamic analysis. A numerical iteration scheme is adopted to solve the characteristic equation for the complex eigenvalues (i.e., the system modal frequencies and damping ratios). This solution was used to determine design curves for optimal damper position and size. For engineering convenience, empirical equations were provided by fitting numerical results. These equations include one for determining the optimal location of the damper for each mode, and two for determining the optimal damping coefficient of the damper, and for calculating the maximum modal damping ratio of the system while the beam vibrates in its first mode. Furthermore, relatively accurate approximations of the pseudoundamped natural frequency and damping ratio of the first mode were obtained using a Taylor expansion of the characteristic equation. All of the results obtained are nondimensionalized for convenience of analysis and application.

A simple mathematical model for approximate analysis of tall buildings

The focus of this article is to present a new and simple mathematical model that may be used to determine the optimum location of a belt truss reinforcing system on tall buildings such that the displacements due to lateral loadings would generate the least amounts of stress and strain in building’s structural members. The effect of belt truss and shear core on framed tube is modeled as a concentrated moment applied at belt truss location, this moment acts in a direction opposite to rotation created by lateral loads. The axial deformation functions for flange and web of the frames are considered to be cubic and quadratic functions respectively; developing their stress relations and minimizing the total potential energy of the structure with respect to the lateral deflection, rotation of the plane section, and unknown coefficients of shear lag, the mathematical model is developed. The proposed model shows a good understanding of structural behavior; easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stage which requires less time. Numerical examples are given to demonstrate the ease of application and accuracy of the proposed modeled.

Importance of Accurate Modeling Input and Assumptions in 3D Finite Element Analysis of Tall Buildings

With ever increasing land prices, design and construction of high-rise buildings are becoming very common. There is a trend among design Engineers to resort to 3D Finite Element Analysis (FEA) during the design of such high rise buildings. This is due to the fact that challenging architectural concepts, when combined with inherent complexities and scale of such projects, require the need of complex structural systems and components such as outriggers, transfer plates, etc. However incorrect modeling input and assumptions could lead to a situation where predictions made using such models may differ greatly from the actual behaviour. In this paper, the importance of accuracy in modeling FEA of high rise buildings is demonstrated through the use of a case study of a 34 storey hotel building with outriggers. The impact of modeling accuracy and assumptions on the predicted performance of the outrigger is also evaluated.

초고층 구조물의 지진해석을 위한 지진기록의 조정방법

최근 감쇠장치 등을 가진 초고층 건축물의 지진해석에 시간이력해석법이 자주 사용되고 있다. 지진기록은 구조물의 기본 진동주기를 T라 할 때 설계기준에서 요구하는 바와 같이 0.2T에서 1.5T 사이의 스펙트럼 값을 설계응답스펙트럼에 부합하게 조정되어 사용되고 있다. 설계기준에서 제시한 방법으로 조정할 경우 주기가 길어질수록 두 해석법 사이의 응답차이는 커지는 현상이 발생한다. 즉 설계기준에 의하여 조정된 지진기록을 사용하여 시간이력해석을 수행하면 밑면전단력 등은 비슷하지만 변위, 층간변위, 부재력 등은 적게 평가되는 현상이 발생하였다. 이들 결과에 밑면전단력 조정계수를 적용하면 응답이 더욱 작아지는 것을 확인하였다. 이에 본 연구에서는 인공지진을 만드는 데 어려움이 있는 엔지니어들을 위하여 기존 설계기준에 부합하는 지진기록 조정방법을 제시하였다. In recent years, time history analysis has been the method generally used for the seismic analysis of tall buildings with damping devices. When T is the natural period of the first vibration mode of the structure, the sum of the spectral acceleration of the earthquake ground motion is usually adjusted to that of the design response spectrum in the period ranging from 0.2T to 1.5T to meet the requirements of design code. However, when the ground motion is scaled according to the design code, the differences in the responses obtained by response spectrum analysis (RSA) and time history analysis (THA) of the structures increase as the natural period of the structure becomes longer. When time history analysis is performed by using ground accelerations that are scaled according to the design code, base shear is similar to that obtained from RSA, but other responses, such as displacements, drifts and member forces, are underestimated compared to RSA. If these results are adjusted by multiplying with the scale-up factor, the scaled responses become much smaller. Therefore, a scaling method of ground motions corresponding with the design code is proposed in this study, as a way of assisting structural engineers in generating artificial ground motions.

Lateral shear‐St. Venant torsion coupled vibration of asymmetric‐plan frame structures

AbstractFree vibration analysis is presented for asymmetric‐plan frame structures. Emphasis of the analysis is given to the lateral–torsional vibration of the structures, where lateral shear vibrations in two orthogonal directions are coupled with St. Venant torsion vibration. Based on the continuum approach in tall building analysis, the governing equation of coupled vibration of the problem is developed, and the corresponding eigenvalue equation is then derived. A theoretical method of solution is proposed to solve the eigenvalue problem and a general solution is given to determine the natural frequencies and associated mode shapes of the structure. By following the proposed calculation procedure, frequencies of the coupled vibration are quickly determined and the corresponding mode shapes can clearly be displayed. The numerical investigation pertaining to coupled vibration analysis of a general asymmetric‐plan frame building shows that the results from the proposed method and FEM analysis agree very well. Copyright © 2008 John Wiley & Sons, Ltd.

Ground motion issues for seismic analysis of tall buildings: a status report

AbstractThe Pacific Earthquake Engineering Research Center (PEER) is coordinating a major multidisciplinary programme, the Tall Buildings Initiative (TBI), to address critical technical issues related to the design and analysis of new tall buildings located in coastal California. The authors of this paper, listed alphabetically, are involved in various research studies related to ground motion modelling, selection, modification and simulation for analysis of tall buildings. This paper summarizes the scope and progress of ongoing activities related to ground motion issues for response history analysis of tall buildings. Copyright © 2007 John Wiley & Sons, Ltd.

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

AbstractIn 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.

Dynamic response and reliability analysis of tall buildings subject to wind loading

This paper explores the wind stochastic field from a new viewpoint of stochastic Fourier spectrum (SFS). The basic random parameters of the wind stochastic field, the roughness length z 0 and the mean wind velocity at 10 m height U 10, as well as their probability density functions (PDF), are obtained. It provides opportunities to use probability density evolution method (PDEM), which had been proved to be of high accuracy and efficiency, in computing the dynamic response and reliability of tall buildings subject to the wind loading. Principals and corresponding numerical solving algorithm of the PDEM are first presented. Then, the adopted model of the wind stochastic field is described briefly. The simulation method of the fluctuating wind velocity based on the SFS is introduced. Finally, as an example of the application of the PDEM, a 20-storey frame subject to wind loading is investigated in detail. The responses, including the mean value and the standard deviation, and the reliabilities of the frame are evaluated by the PDEM. The results demonstrate that the PDEM is applicable and efficient in the dynamic response and reliability analysis of wind-excited tall building.

Simplified dynamic inelastic analysis of tall buildings

Since the Kobe and Northridge earthquakes, static inelastic analysis has become an accepted and simple method for the seismic evaluation of high-rise buildings. In this method, the lateral load is monotonically increased with the same profile to find the ultimate capacity of the structure. Pushover analysis, however, has a limitation in the evaluation of a higher-mode dominant structure: for this reason, inelastic time history is used to compensate. In engineering practice, using inelastic time history analysis to evaluate the inelastic capacity of a building is impractical for tall buildings owing to the amount of computational time required and the difficulties in interpreting results. Therefore, a simplified inelastic analysis method is required for practical application. In the present paper, a simplified dynamic inelastic analysis (SDIA) method using elastic and inelastic response spectrums is introduced as a way to perform an inelastic analysis of a structure. The relative accuracy and efficiency of SDIA are explored by comparing the results with those of time history analysis software, DRAIN-2DX. The results of SDIA and DRAIN-2DX are almost identical, while with SDIA the computational time is dramatically reduced and time-consuming efforts interpreting results are saved.

Seismic random vibration analysis of tall buildings

A highly efficient random vibration algorithm, the pseudo-excitation method (PEM), is developed for the random vibration analysis of seismic responses of tall buildings. A 40-storey tall building and a 79-storey super tall building are considered in this paper to illustrate the application of the PEM in the seismic analysis of tall buildings under random seismic actions. The finite element model of the 79-storey building has 18 171 nodes, 23 976 three-dimensional beam elements, 6057 membrane elements and 40 837 degrees of freedom. Seismic random vibration analysis of such a complex three-dimensional model can hardly be found in the literature because of low computational efficiency of the conventional random vibration methods. By using the PEM, the power spectrum densities of the structural responses can be obtained in a convenient and efficient way. This algorithm is an accurate complete quadratic combination (CQC) method because the cross-correlation terms between different modes are considered. The computation results show that random vibration analysis of the super tall building with large numbers of degrees of freedom can be conducted conveniently by the PEM on an ordinary personal computer, since the algorithm makes the structural stationary random response analysis be reduced to the analysis of structural harmonic response. In addition, the effects of several factors such as frequency integration interval and integration region, foundation conditions, number of participant modes and duration of earthquake excitation on the seismic random responses of the two tall buildings are presented and discussed in detail.

A modified dynamic inelastic analysis of tall buildings considering changes of dynamic characteristics

Pushover analysis is commonly used to evaluate the inelastic ultimate capacity of structures. However, pushover analysis is carried out based on constant distributions throughout the incremental analysis, which cannot capture the variation in the acceleration profile due to inelastic behavior. For this reason, when plastic hinges form in structure, constant distributions of lateral forces cannot be used any longer. Conventional dynamic inelastic method by time-history analysis can be used for specific earthquakes to consider the changes in the distribution of lateral forces. This alternative approach, however, is not practical due to the volume of calculations required. In this study, MOdified Dynamic Inelastic Analysis (MODIA) is introduced to capture a distribution proportional to changing mode shapes affected by the change of stiffness. In this method, as a structure enters into the inelastic range, the distribution of lateral forces is changed according to the mode shapes of structure. The efficiency of the proposed method is verified by comparing the results from DRAIN. A 7-story moment resisting frame and a 36-story existing structure were analysed by both methods. The comparison showed a good agreement. The story shear–drift relationship, base shear, drift, ductility and overturning moment for the structures are also evaluated. Copyright © 1999 John Wiley & Sons, Ltd.

A modified dynamic inelastic analysis of tall buildings considering changes of dynamic characteristics

Pushover analysis is commonly used to evaluate the inelastic ultimate capacity of structures. However, pushover analysis is carried out based on constant distributions throughout the incremental analysis, which cannot capture the variation in the acceleration profile due to inelastic behavior. For this reason, when plastic hinges form in structure, constant distributions of lateral forces cannot be used any longer. Conventional dynamic inelastic method by time-history analysis can be used for specific earthquakes to consider the changes in the distribution of lateral forces. This alternative approach, however, is not practical due to the volume of calculations required. In this study, MOdified Dynamic Inelastic Analysis (MODIA) is introduced to capture a distribution proportional to changing mode shapes affected by the change of stiffness. In this method, as a structure enters into the inelastic range, the distribution of lateral forces is changed according to the mode shapes of structure. The efficiency of the proposed method is verified by comparing the results from DRAIN. A 7-story moment resisting frame and a 36-story existing structure were analysed by both methods. The comparison showed a good agreement. The story shear–drift relationship, base shear, drift, ductility and overturning moment for the structures are also evaluated. Copyright © 1999 John Wiley & Sons, Ltd.

Vibration analysis of tall buildings with narrow rectangular plane configuration

Vibration analysis of tall buildings with narrow rectangular plane configuration

Closure to “Dynamic Analysis of Tall Building Using Reduced‐Order Continuum Model” by Michael J. Chajes, Liyang Zhang, and James T. Kirby

Closure to “Dynamic Analysis of Tall Building Using Reduced‐Order Continuum Model” by Michael J. Chajes, Liyang Zhang, and James T. Kirby

Discussion: Dynamic Analysis of Tall Building Using Reduced-Order Continuum Model

Discussion: Dynamic Analysis of Tall Building Using Reduced-Order Continuum Model

Dynamic Analysis of Tall Building Using Reduced-Order Continuum Model

On Oct. 17, 1989, a tall, steel-framed, San Francisco office building with 47 above-grade stories was excited by the Loma Prieta earthquake. The building response was recorded by accelerometers maintained by the California Division of Mines and Geology Strong Motion Instrumentation Program. From the records, important characteristics of the building response can be identified. In this paper, a computationally efficient, approximate dynamic analysis of the building using a reduced-order continuum model is conducted. By making use of the repetitive nature of the lattice framing system, finite-element models generated using continuum methodology have significantly fewer degrees of freedom than models generated using classical discrete finite-element techniques. These reduced-order models can therefore lead to significant savings in the computational effort and cost typically associated with dynamic analyses of large structures. The vibrational characteristics of the continuum model, as well as the results of the dynamic analysis, are compared to the building’s recorded response. The continuum model is accurate in capturing the dominant periods of vibration as well as the time-history response and shows promise as a tool for preliminary design of large lattice structures.

Analysis of Free Vibrations of Tall Buildings

An analysis of free vibrations of tall buildings, such as frame, shear‐wall, and frame‐shear‐wall structures, is proposed and discussed in this paper. Frame buildings are treated as shear beams with varying cross sections, the solutions of mode shapes of such buildings are expressed in Bessel's functions, and the parameter of determining the fundamental period can be found from a figure provided in the paper. Based on the fact that the shear deformation and bending deformation are all considered for shear wall and frame‐shear‐wall structures, the formulas for calculating free vibrations of such structures are presented. It is very simple and convenient to apply these formulas to dynamic analysis of tall buildings. The measurement results and statistical analysis of frame, shear‐wall, and frame‐shear‐wall structures in sites, and three examples of determining free vibrations of structures are also given in this paper. The examples show that the effect of shear deformation on the first natural frequency is not significant, but the effect of that on higher natural frequencies may not be neglected.