Biegedrillknickmomente und Eigenformen von Biegeträgern unter Berücksichtigung der Drehbettung

Critical bending moments and modal shapes for lateral torsional buckling of beams under consideration of torsional restraints. The design for lateral torsional buckling according to DIN 18800 and EC 3 is based on the elastic critical bending moment. Because of economical reasons it is favourably to consider the stabilizing effects of adjacent structural members. This paper is dealing with the determination of M_Ki considering the influence of torsional restraints. Beyond that one shows the corresponding modal shapes because they are necessary for the verifications considering equivalent geometrical imperfections. As alternative to computations by EDP programs for selected structural systems approximation formulae are indicated to enable the determination of M_Ki by means of manual calculation.     

Assessment of semi-rigid connections in steel structures by modal testing

In conventional design and analysis, the common assumption is that connections of steel frames are fully rigid or frictionless pinned. However, today, the accepted notion is that the connections of members of a steel structure exhibit semi-rigid characteristics. Semi-rigid connections as well as damage cause changes in the dynamic characteristics of the structures. This study presents an investigation into the determination of the quality of the semi-rigid connections when considering changes in dynamic characteristics of steel structures. The investigations involve three scaled models: columns with box cross-sections, columns with rectangular cross-sections, and a 2D frame. The investigation algorithm first calculates natural frequencies and mode shapes from theoretical modal analyses by assuming the supports and joint connections are fully rigid. Secondly, experimental measurements on the models are performed to obtain natural frequencies, mode shapes and modal damping ratios. Thirdly, to reduce differences between theoretical and experimental results, linear elastic rotational springs are used on supports and joint connections of the analytical model. Finally, the connection percentages of both support and beam-to-column connections are determined using an approach improved depending on the rotational spring stiffness.     

An alternative approach for assessing eccentricities in asymmetric multistory buildings. 1. Elastic systems

A simple hand method for assessing modal eccentricities of multistory structures with partial symmetry is presented. The concept of the modal center of rigidity is introduced and the determination of eccentricities of the first two modal shears is obtained by means of an equivalent one‐story eccentric system. The method is based on Southwell's formula for calculating a lower bound of the fundamental frequency and is applicable to uniform structures composed of different types of bents, such as walls, rigid frames, coupled walls and wall–frame assemblies. These structures do not belong to the special class of proportionate buildings for which dynamic properties can be accurately obtained by analyzing two simpler systems: a multistory torsionally uncoupled counterpart of the actual structure and an associated one‐story coupled system. The accuracy of the proposed method is illustrated in a parametric study that includes common types of mixed‐bent‐type multistory structures and comparisons are made with the results obtained by three‐dimensional dynamic analyses on discrete member models. Copyright © 2007 John Wiley & Sons, Ltd.     

Dynamic investigation of a two story-two span frame including semi-rigid Khorjini connections

In this paper, the free vibration analysis and determination of dynamic parameters of a two story-two span frame is investigated. The frame is consisted of two continuous beams and three columns, in which the middle connections of the continuous beams to the column are provided by means of semi-rigid Khorjini connections. The individual members of the frame are assumed to be governed by the transverse vibration theory of an Euler-Bernoulli beam and the semi-rigid Khorjini connections are modeled employing rotational springs. First of all, a closed-form solution is proposed and then, a numerical analysis is performed for some comparison and validation purposes. At the closed-form solution, some differential equations must be solved, and several boundary conditions should be satisfied. Herein, 40 boundary conditions should be provided. Afterward, the eigenvalues of the frame are obtained. These eigenvalues are also obtained using finite element method as a numerical analysis and it is observed that the results obtained by this approach are completely identical with the result of closed-form solution. Also, the eigenvalues and mode shapes of the frame for different values of the semi-rigid Khorjini connections stiffnesses are obtained and some comparisons are made.     

Seismic performance of Y‐type eccentrically braced frames combined with high‐strength steel based on performance‐based seismic design

In the Y‐type eccentrically braced frame structures, the links as fuses are generally located outside the beams; the links can be easily repairable or replaceable after earthquake without obvious damage in the slab and beam. The non‐dissipative member (beams, braces, and columns) in the Y‐type eccentrically braced frames are overestimated designed to ensure adequate plastic deformation of links with dissipating sufficient energy. However, the traditionally code design not only wastes steel but also limits the application of eccentrically braced frames. In this paper, Y‐type eccentrically braced steel frames with high‐strength steel is proposed; links and braces are fabricated with Q345 steel (the nominal yield stress is 345 MPa); the beams and columns are fabricated with high‐strength steel. The usage of high‐strength steel effectively decreases the cross sections of structural members as well as reduces the construction cost. The performance‐based seismic design of eccentrically braced frames was proposed to achieve the ideal failure mode and the same objective. Based on this method, four groups Y‐type eccentrically braced frames of 5‐story, 10‐story, 15‐story, and 20‐story models with ideal failure modes were designed, and each group includes Y‐type eccentrically braced frames with ordinary steel and Y‐type eccentrically braced frames with high‐strength steel. Nonlinear pushover and nonlinear dynamic analyses were performed on all prototypes, and the near‐fault and far‐fault ground motions are considered. The bearing capacity, lateral stiffness, story drift, link rotations, and failure modes were compared. The results indicated that Y‐type eccentrically braced frames with high‐strength steel have a similar bearing capacity to ordinary steel; however, the lateral stiffness of Y‐type eccentrically braced frames with high‐strength steel is smaller. Similar failure modes and story drift distribution of the prototype structures designed using the performance‐based seismic design method are performed under rare earthquake conditions.     

Dynamic characteristics and viscous dampers design for pile‐soil‐structure system

A series of large‐scale shaking table tests are conducted on tall buildings with and without energy dissipation devices on soft soils in pile group foundations, representing pile‐soil‐structure interaction (PSSI) system and the corresponding fixed‐base situations. The superstructure is a 12‐story reinforced concrete (RC) frame. The dynamic characteristics of the test models show that the frequencies decrease and the damping ratio increase in PSSI system by comparison with the fixed‐base structures. The mode shapes of PSSI system are different from that under fixed‐base condition, and the mode shapes of structure without dampers change greater than that with energy dissipation devices under various white noises. An improved method for structural dynamic characteristics, considering the impedance function of piles, is developed to address the issue of modal parameters with PSSI effect. In addition, the structural dynamic parameters of the large‐scale shaking table tests are identified using the modification method and other regulation methods, demonstrating that the improved approach is highly accurate and effective. Subsequently, a design procedure for viscous dampers of structures with PSSI effect is presented based on the dynamic characteristics of the system. Finally, the dynamic responses of the structure with viscous dampers in the practical engineering are decreased effectively, indicating the good performance of designed viscous dampers. The numerical results also show that the damping efficiency of interstory drift is larger than the acceleration and interstory shear force. Therefore, the improved modal parameters method, validated through a series large‐scale shaking table tests, is applicable for identifying dynamic characteristics of pile‐soil‐structure with energy dissipation devices system. The design procedure of viscous dampers, proved by a reinforced concrete frame structure located on a practical Shanghai soft site, can be employed to design the viscous dampers considering seismic PSSI effect.     

Wavelet‐Based Detection of Beam Cracks Using Modal Shape and Frequency Measurements

Abstract: When a structure is subjected to dynamic or static loads, cracks may develop and the modal shapes and frequencies of the cracked structure may change accordingly. Based on this, a new method is proposed to locate beam cracks and to estimate their depths. The fault‐induced modal shape and frequency changes of cracked structures are taken into account to construct a new hybrid crack detection method. The method includes two steps: crack localization and depth estimation. The locations of the cracks are determined by applying the wavelet transform to the modal shape. Using the measured natural frequencies as inputs, the depths of the cracks are estimated from a database established by wavelet finite element method. The effectiveness of the proposed hybrid two‐step method is demonstrated by numerical simulation and experimental investigation of a cantilever beam with two cracks. Our analyses also indicate that the proposed method performed reasonably well at certain level of noise.     

Blind Modal Identification in Frequency Domain Using Independent Component Analysis for High Damping Structures with Classical Damping

Output‐only modal identification methods are practical for large‐scale engineering. Recently, independent component analysis (ICA) which is one of the most popular techniques of blind source separation (BSS) has been used for output‐only modal identification to directly separate the modal responses and mode shapes from vibration responses. However, this method is only accurate for undamped or lightly damped structures. To improve the performance of ICA for high damping structures, this article presents an extended ICA‐based method called ICA‐F, which establishes a BSS model in frequency domain. First, the basic idea of BSS and ICA applied in modal identification is introduced in detail. The free vibration responses and the correlation functions of ambient responses can be cast into the frequency‐domain BSS framework just by mapping the time history responses to frequency domain through fast Fourier transform (FFT). Then, an ICA‐based method in frequency domain called ICA‐F is proposed to accurately extract mode shapes and modal responses for both light and high damping structures. A simulated 3 degree of freedom mass‐spring system and a 4‐story simulated benchmark model developed by the IASC‐ASCE Task Group in Health Monitoring are employed to verify the effectiveness of the proposed method. The results show that the proposed method can perform accurate modal identification for both light and high damping structures. Finally, the IASC‐ASCE experimental benchmark structure is also utilized to illustrate the proposed method applied to practical structure.     

Operational Modal Parameter Identification from Power Spectrum Density Transmissibility

Abstract: Operational modal analysis subjected to ambient or natural excitation under operational conditions has recently drawn great attention. In this article, the power spectrum density transmissibility (PSDT) is proposed to extract the operational modal parameters of a structure. It is proven that the PSDT is independent of the applied excitations and transferring outputs at the system poles. As a result, the modal frequencies and mode shapes can be extracted by combing the PSDTs with different transferring outputs instead of different load conditions where the outputs from only one load condition are needed. A five‐story shear building subjected to a set of uncorrelated forces at different floors is adopted to verify the property of PSDTs and illustrate the accuracy of the proposed method. Furthermore, a concrete‐filled steel tubular half‐through arch bridge tested in the field under operational conditions is used as a real case study. The identification results obtained from currently developed method have been compared with those extracted from peak‐picking method, stochastic subspace identification, and finite element analysis. It is demonstrated that the operational modal parameters identified by the current technique agree well with other independent methods. The real application to the field operational vibration measurements of a full‐sized bridge has shown that the proposed PSDTs are capable of identifying the operational modal parameters (natural frequencies and mode shapes) of a structure.     

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.     

Response surface‐based finite‐element model updating of a historic masonry minaret for operational modal analysis

This study aimed to use the response surface (RS) method for finite element (FE) model updating, using operational modal analysis (OMA). The RS method was utilized to achieve better agreement between the numerical and field‐measured structure response. The OMA technique for the field study was utilized to obtain modal parameters of the selected historic masonry minaret. The natural frequencies and mode shapes were experimentally determined by the enhanced frequency domain decomposition (EFDD) method. The optimum results between the experimental and numerical analyses were found by using the optimization method. The central composite design was used to construct the design of experiments, and the genetic aggregation approach was performed to generate the RS models. After obtaining the RS models, an attempt was made to converge the natural frequency values corresponding to the five‐mode shapes with the frequency values identified by the experimental analysis. ANSYS software was used to perform 3D finite element (FE) modeling of the historic masonry minaret and to numerically identify the natural frequencies and mode shapes of the minaret. The results of the experimental, initial, and updated FE model were compared with each other. Significant differences can be seen when comparing the experimental and analytical results with the initial conditions.     

Bemessung der Bügel,Querkraftzulagen und Schrägstäbe nach DIN 1045‐1 und nach EC2

Design of stirrups, shear assemblies and bent‐up bars after DIN 1045‐1 and after EC2. For members in normal strength normal concrete C20/25 up to C50/60 with shear reinforcement BSt 500 design diagrams are presented. These enable the determination of required stirrups, shear assemblies (without enclosing the longitudinal reinforcement) and bent‐up bars under 45°, in any combination. The bearing capacity of the compression struts can be verified and the shifting of the tension line determined too.     

Dynamische Verformungsmessungen an Eisenbahnbrücken mittels Mikrowelleninterferometrie

Dynamic measurements of railway bridge displacements through microwave interferometry – Part 1: measurement method The microwave interferometry is a rather new measuring technique, yet little‐known in civil engineering applications. It allows the non‐contact acquisition of structural displacements with accuracy in the sub‐millimetre range at a sampling rate of up to 4 kHz. The high sampling frequency allows also the caption of dynamic structural responses, which can be used for a straightforward determination of the main modal parameters of the structures (natural frequencies, damping ratios). Furthermore, the synchronous acquisition of the overall motion of the targeted object is possible due to a high range resolution, which facilitates a direct identification of modal shapes. This paper gives a short introduction of the measurement method and outlines its boundary conditions and limitations with respect to applications in railway bridge dynamics. The knowledge has been gained on the basis of comprehensive systematic experimental investigations performed within the frame of a cooperation project with the German Railways (Deutsche Bahn AG). As a result an evaluation matrix was created, which clearly illustrates the applicability of the microwave interferometry for different railway‐specific tasks. The second part will present selected results of microwave interferometry measurements of railway bridges in comparison to parallel conventional measurements and the corresponding numerical investigations, which were used for the validation of the measurement technique.     

粘滞阻尼减震结构振型分解法的研究

减震结构的分析方法之一是振型分解反应谱法。结构附加阻尼器之后，附加阻尼一般为非比例阻尼，并使振型复杂采用振型分解法求解会带来较大误差。通过计算结构的复数特征值和特征向量可以改善振型分解法。     

Modal Response‐Based Visual System Identification and Model Updating Methods for Building Structures

This article proposes a new system identification (SI) method using the modal responses obtained from the dynamic responses of a structure for estimating modal parameters. Since the proposed SI method visually extracts the mode shape of a structure through the plotting of modal responses based on measured data points, the complex calculation process for the correlation and the decomposition for vibration measurements required in SI methods can be avoided. Also, without dependence on configurations of SI methods inducing variations of modal parameters, mode shapes and modal damping ratios can be stably extracted through direct implementation of modal response. To verify the feasibility of the proposed method, the modal parameters of a shear frame were extracted from modal displacement data obtained from a vibration test, and the results were compared with those obtained from the existing frequency domain SI method. The proposed method introduces the maximum modal response ratio of each mode computed by modal displacement data, and from this, the contribution of each mode and each measured location to the overall structural response is indirectly evaluated. Moreover, this article proposes a model updating method establishing the error functions based on the differences between the analytical model and measurement for the natural frequencies and the modal responses reflecting both mode shape and modal contribution. The validity of the proposed method is verified through the response prediction and modal contributions of the models obtained from model updating based on dynamic displacement from a shaking table test for a shear‐type test frame.     

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.     

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.     

Zur Entwicklung der Steifigkeitsmatrizen für dünnwandige Stäbe

On the development of stiffness matrices for thin‐walled members. A glance into the early development of element stiffness matrices for thin‐walled members is given in the present paper and their most mature shapes are shown. Those shapes, the most general and later reduced to two particular forms, refer to the specifics of the classical Vlasov theory of thin‐walled bars [1] as well as to the Bornscheuer systematics of the cross‐sectional properties involved [2]. Appropriate modifications of the relevant matrices are performed and their coordinate system dependence is demonstrated.