剪力墙和薄壁开口截面作为支撑的高层建筑抗震计算的简化方法

对高度方向性能恒定,不对称的建筑结构,提出了近似的抗震分析手算方法。通过剪力墙和薄壁开口截面结构的结合,增加了建筑物的刚度。基于连续技术和达朗伯原理,推导了自由振动的控制方程和相应的特征值问题。应用伽辽金技术,提出了一个通用的方法对剪力墙和薄壁开口截面结构的耦合振动进行自由振动分析。     

Coupled flexural–torsional dynamic stiffness matrix of an elastically supported axially loaded beam with shear resistant in‐fill

The dynamic stiffness matrix of an axially loaded elastically supported uniform beam with doubly asymmetric cross‐section that exhibits coupling between flexural and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The beam comprises a thin‐walled outer section that encloses, and works compositely with, a core of shear resistant in‐fill material. The outer layer provides flexure, warping and Saint–Venant rigidity, while the inner layer provides both Saint–Venant and shear rigidity. A three‐parameter Winkler model is used to describe the distributed elastic support. Hamilton's principle is used to derive the partial differential equations governing the free vibration of the beam, together with the associated natural boundary conditions. This gives rise to three coupled equations that are subsequently combined into a single, 12th order, ordinary differential equation. Throughout the process, the uniform distribution of mass in the member is accounted for exactly and thus necessitates the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick–Williams algorithm, which enables the required natural frequencies to be converged upon to any required accuracy with the certain knowledge that none have been missed. Finally, in order to verify the accuracy of the presented theory, the numerical solutions are given and compared with the results that are available in the literature and finite element solutions using abaqus software. Copyright © 2014 John Wiley & Sons, Ltd.     

A global approach for three‐dimensional analysis of tall buildings

In 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.     

FE‐Methoden zur Bestimmung der Lage des Schubmittelpunktes dünnwandiger Querschnitte

Finite element methods for the shear centre determination of thin walled cross‐sections. The position of the shear centre can be determined using different conditions and methods respectively. The calculation for complex cross sections, which consist of many components or hollow parts, is very extensive. For that reason the application of the finite element method (FEM) is suitable. It is shown, that the calculations are similar to FEM‐investigations of beam structures.     

Eine Finite‐Elemente‐Lösung auf der Basis eines erweiterten eindimensionalen Querschnittselementes für die freie Torsion dünnwandiger prismatischer Stäbe

A finite element solution on the basis of an extended one‐dimensional cross‐section‐element for the Saint‐Venant torsion of thin‐walled prismatic beams. It is presented a finite element solution on basis of an extended one‐dimensional cross‐section‐element to the calculation of the warping function, the torsional properties and the shear stresses, dependent on it, for thin‐walled prismatic beams under Saint‐Venant torsion. The formulated finite two‐node‐element with six element degrees of freedom can capture through inclusion of the torsion around the element axis the linear term of the variance of warping function perpendicular to the element axis. Only the shear stresses of the ring shear flows in the closed section parts unchangeable over the wall thickness can be calculated with the simple two‐node‐element with two element degrees of freedom. The extended two‐node‐element supplies in addition also the shear stresses of the cut open cross‐section linearly changeable over the wall thickness.     

Berechnung dünnwandiger Stäbe mit offenem Querschnitt bei Beanspruchung durch Längskraft,zweiachsige Biegung und Torsion – ohne Bestimmung von Schwerpunkt,Schubmittelpunkt und Hauptachsen

Analysis of thin‐walled bars with open cross‐section loaded by normal force, biaxial bending and torsion without use of centroid, shear centre and principal axis. For a generally loaded prismatic bar an analysis is presented, where the relations between stress resultants and deformations are not normalized, but written in a coupled form. This means that any system of coordinates y, z in the section can be chosen and is then maintained for all calculations. On this basis the equation of transfer matrix is developed, which allows the calculation of all stress resultants and displacements for a beam with arbitrary support. Finally at any point of the sections normal and shear stresses can be determined.     

Analysis of flexural natural vibrations of thin‐walled box beams using higher order beam theory

In order to study the influence of high‐order shear deformations and shear lag on the dynamic characteristics of thin‐walled box beams (TWBBs), this paper takes the Hamilton principle as a basis to consider multiple factors such as high‐order shear deformations, shear lag, and cross section rotary inertia of the TWBBs. The vibration differential equations and natural boundary conditions of TWBBs are deduced. On the basis of eight examples of TWBBs with different boundary conditions and span–width ratios, analytical results of this paper are compared with those of the ANSYS finite element method. Both results are in good agreement with each other, and the validity of the calculation method is verified. The effects of higher order shear deformations and shear lag on natural vibration characteristics of TWBBs are analyzed. And some meaningful conclusions are drawn: This theory shows the capability to accurately describe both higher order deformations and shear lag; when the span–width ratio is small, neglecting higher order web deformations will produce a large calculation error; under the action of shear lag, the natural vibration frequency of TWBBs decreases greatly, which cannot be neglected; and both the high‐order shear deformations and shear lag effect increase with increasing mode order and increase with decreasing span–width ratio.     

Coupled vibration of tall building structures

Free vibration analysis is presented for general tall building structures, which may consist of any combination of frames, shear walls, structural cores and coupled walls. Emphasis of the analysis is placed on the coupled lateral–torsional vibration characteristic of the structures. Based on the continuum technique and D'Alembert's principle, the governing equation of free vibration and corresponding eigenvalue problem are derived. By applying the Galerkin technique, a generalized method of solution is proposed for the analysis of coupled vibration of general tall building structures. Based on the proposed method, a computation procedure is presented for predicting the natural frequencies and associated mode shapes of the structures in coupled vibration. Numerical investigation is conducted to validate the simplicity and accuracy of the proposed method. It has been shown that the proposed analysis provides an effective way, particularly at the preliminary design stage, for evaluating the vibration behaviour of tall buildings. Copyright © 2004 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.     

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.     

One‐dimensional finite element solution for non‐uniform tall building structures and loading

By using a one‐dimensional finite element numerical version based on the continuous medium technique, plane panels of variable geometry and loading are considered, in order to emphasize the capacity of a corresponding very simple computer code. Twin shear walls linked by lintel beams, with walls of lower storeys having bigger cross‐section than the next upper floors, are considered under variable horizontal wind loading through the building height. Afterwards, in that same panel, stronger discrete lintel beam is subsequently placed at each floor position. Results may show where is the optimum level to place those reinforcements in order to get, for example, the smaller top horizontal deflection. The second example considers the case of shear wall curtailment, in the frame shear wall association by pinned bars. Due to the individual behaviour of a single shear wall and of a single frame, it is possible (and real construction may permit that) to construct the wall up to a certain level, smaller than the building height, without having any significant change in the panel top displacement. By using the particular continuous medium finite element computer code, developed by the first author, it is possible to analyse several modelled structures, each having the curtailed wall at subsequent levels, from base to top, and to build an ‘influence line’ to find out the optimum curtailment level. Comparisons with the matrix discrete method and with analytical solutions were considered. Reference to free vibration solutions for such structures was also made. Copyright © 2008 John Wiley & Sons, Ltd.     

Interactive instabilities of thin‐walled laminated composite pultrusion box columns

The problem of interactive buckling and post‐buckling of intermediate length thin‐walled columns built of laminated plate elements subjected to compressive load has been proposed and solved analytically. Pultrusion columns have wide‐range applications in high‐rise building due to their low weight and high load carrying capacity. Classic stability theory and laminate theory were implemented to prove the existence of mixed‐mode buckling in thin‐walled pultrusion columns. Interactive stability modes can result in lower loading capacity of most compressive members and affects their post‐buckling behaviour in major proportions. Interactive buckling load analysis has been performed by means of a simplified theoretical model and verified by means of numerical analysis. The calculations were carried out for commonly used square section thin‐walled composite columns dimensions. The post‐buckling performance of selected sections has been investigated and an optimum layup configuration criterion for each section has been extracted according to pre‐ and post‐critical behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

Formänderungsgrößenverfahren mittig gedrückter dünnwandiger Stäbe mit einfach‐ und doppeltsymmetrischen offenen Querschnitten

Deformation method for centrically compressed thin‐walled bars with mono‐ and bisymmetrical open cross‐sections. In correspondence with the classic deformation method of warping torsion for thin‐walled bars [1], that method has been moved into the field of column stability. For the single cross‐sectional symmetry, the general solution of the fundamental system of equations has been found and its particular shapes for three basic kinds of column support presented. Thereby, the formulas or the boundary simplified for analysis of the bimoments have been settled. These relations have been simplified for the double cross‐sectional symmetry. An analysis of a bisymmetrical cross‐section has lead to the determination of the necessary boundary forces for the three kinds of column support considered. It has been shown that all the relations for torsion are similar to those for bending. A proposal for the calculations of the critical loads of torsional buckling in continuous columns has been formulated and a relevant numerical example given. The paper calls special attention to the related merits of Professor Kurt Klöppel , a graduate of the former Technischen Hochschule Danzig. Actually, already 100 years have passed since the foundation of TH Danzig. It is also the predecessor of the contemporary Politechnika Gdańska, with which the author is being connected since 1949.     

On the applicability of pushover analysis for seismic evaluation of medium‐ and high‐rise buildings

The assumption that the dynamic performance of structures is mainly determined from the corresponding single‐degree‐of‐freedom system in pushover analysis is generally valid for low‐rise structures, where the structural behaviour is dominated by the first vibration mode. However, higher modes of medium‐ and high‐rise structures will have significant effect on the dynamic characteristics. In this paper, the applicability of pushover analysis for seismic evaluation of medium‐to‐high‐rise shear‐wall structures is investigated. The displacements and internal forces of shear wall structures with different heights are determined by nonlinear response history analysis, where the shear walls are considered as multi‐degree‐of‐freedom systems and modelled by fibre elements. The results of the analysis are compared with those from the pushover procedure. It is shown that pushover analysis generally underestimates inter‐storey drifts and rotations, in particular those at upper storeys of buildings, and overestimates the peak roof displacement at inelastic deformation stage. It is shown that neglecting higher mode effects in the analysis will significantly underestimate the shear force and overturning moment. It is suggested that pushover analysis may not be suitable for analysing high‐rise shear‐wall or wall‐frame structures. New procedures of seismic evaluation for shear‐wall and wall‐frame structures based on nonlinear response history analysis should be developed. Copyright © 2009 John Wiley & Sons, Ltd.     

Ermittlung der Grenztragfähigkeit von Mehrschraubenverbindungen bei Normalkraft‐Biegemoment‐Interaktion

Determination of the ultimate bearing capacity of multi‐bolt connections with normal force – bending moment – interaction. This paper will present a general design method for single or multi‐bolt connections of beams with arbitrary thin‐walled cross sections, suitable for application in computer programs. The design method is based on the classical strain iteration algorithm for the determination of the stress distribution in cross sections. In this case, the ultimate capacity of bolted connections will be obtained using an iterative numerical determination of the elastic‐plastic stress distribution in the connection elements. The numerical method will be derived in two steps – the first step is the numerical determination of the stress distribution in the connection for a given combination of internal forces and the next step is the determination of the ultimate bearing capacity of the connection. Furthermore, an analytical design method for a multi‐bolt tube connection will be derived. Finally, results of numerical and analytical calculations will be compared with corresponding test results.     

A new approach for free vibration analysis of nonuniform tall building structures with axial force effects

Dynamic analysis of beam‐like structures is significantly important in modeling actual cases such as tall buildings and several other related applications as well. This article studies free vibration analysis of tall buildings with nonuniform cross‐section structures. A novel and simple approach is presented to solve natural frequencies of free vibration of cantilevered tall structures with variable flexural rigidity and mass densities. These systems could be replaced by a cantilever Timoshenko beam with varying cross‐sections. The governing partial differential equation for vibration of a nonuniform Timoshenko beam under variable axial loads is transformed with varying coefficients to its weak form of integral equations. Natural frequencies can be determined by requiring the resulting integral equation, which has a nontrivial solution. The presented method in this study has fast convergence. Including high accuracy for the obtained numerical results as well. Numerical examples including framed tube as well as tube‐in‐tube structures are carried out in the study and compared with available results in the literature, and also with the results obtained from finite element analysis in order to show the accuracy of the proposed method in the study. Obtained results indicate that the presented method in this study is powerful enough for the free vibration analysis of tall buildings.     

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.     

A simple model for assessing periods of vibration and modal response quantities in symmetrical buildings

A simple mathematical model is proposed for assessing periods of vibration and mode shapes of common cantilever bents used in concrete structures, such as shear walls, coupled walls, rigid frames and wall‐frame assemblies. The bent is treated as a continuum and the proposed model is based on the technique of decomposing a cantilever bent into two complementary subsystems (a flexural and a wall‐frame bent) and on the finding that the use of Dunkerley's formula for calculating natural frequencies yields reasonable results for the first three modes of vibration. The objective in proposing this model is to consider the effect of column axial shortenings in the analysis of structural bents. With this model any cantilever bent may be approximated by a simple incompressible shear–flexure system of equal flexural rigidity, but of equivalent modal shear rigidity. This approach has the advantage that the response of different structural bents may be combined in buildings composed of these bents in any arrangement. All bents are approximated by equivalent shear–flexure models and therefore the complete structure may be analysed by a simple methodology, which has been extensively used in the past. Particularly in symmetrical buildings, frequencies may be determined by a simple formula and modal response quantities by available design charts. A quick estimate of these quantities is of particular importance at the early stages of structural design, prior to a full dynamic analysis. In order to illustrate the application of the proposed model a symmetrical building of varying height, composed of different structural bents, is analysed and comparisons are made with more accurate results obtained by 3D computer dynamic analyses. Copyright © 2006 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.     

Finite element method for stability and free vibration analyses of non-prismatic thin-walled beams

In this paper, a numerical method is presented for the free vibration and stability analyses of tapered thin-walled beams with arbitrary open cross sections. The proposed method takes the flexural–torsional coupling effect of tapered thin-walled beams with arbitrary open cross sections into account. The total potential energy is derived for an elastic behavior from the strain energy, the kinetic energy and work of the loads applied on the cross section contour. Free vibration is considered in the presence of harmonic excitations. The effects of the initial stresses and load eccentricities are also considered in stability analysis. The governing equilibrium equations, motion equations and the associated boundary conditions are derived from the stationary condition. As in the presence of tapering, stiffness quantities are not constant; therefore, the power series approximation is used to solve the fourth-order differential equations. Displacement components and cross-section properties are expanded in terms of power series of a known degree. Then, the shape functions are obtained by deriving the deformation shape of tapered thin-walled member as power series form. Finally, stiffness and mass matrices are carried out by means of the principle of virtual work along the member׳s axis. In order to measure the accuracy and check the validity of this method, the natural frequencies and buckling loads of non-prismatic thin-walled beams with web and flange tapering and various boundary conditions are obtained and compared to the results of finite element analysis using Ansys software and those of other available numerical and analytical ones. It can be seen that the results of present study are in a good agreement with other available theoretical and analytical methods.