Story Stiffness Research Articles

Identification of Tall Shear Buildings under Unknown Seismic Excitation with Limited Output Measurements

Due to the fact that some structural external excitations such as earthquakes and wind forces can not be accurately measured under actual operating conditions, it is necessary to investigate algorithms for structural identification under unknown earthquakes. In this paper, an algorithm based on the extended Kalman estimator approach is proposed for the identification of structural parameters and unknown excitation of tall shear-type buildings with only partial measurements of structural absolute acceleration responses. The equation of motion of a tall shear building under ground motion is established in the absolute co-ordinate system, in which the ground-motion input is applied to the 1st floor of the building as an unknown excitation. Based on substructure approach, the tall building is decomposed into substructures. For each substructure above the 1st floor, substructural relative responses and parameters are identified by extended Kalman estimator. For the substructure containing the 1st floor, it is proposed that substructural extended state vector is firstly identified by the extended Kalman estimator and the unknown excitation is subsequently estimated by least-squares estimation. Then, the 1st story stiffness is estimated based on structural eigenvalue equation and the expansion of the determinate of the structural eigen-matrix. The unknown ground motion is identified by the Newmark-β method. A numerical simulation example demonstrates the efficiency of the proposed algorithm.

Rationalization of Structural Stiffness of Offshore Platform with Rocking-Wall

This paper presents a new offshore platform with rocking wall structure, and studies how to use the material more adequately by varying offshore platforms story rigidity. The results show that the greater the story stiffness, the more it can give full play to the material properties, as well as to improve the seismic capacity.

A simple damper optimization algorithm for both target added damping ratio and interstorey drift ratio

A simple damper optimization method is proposed to find optimal damper allocation for shear buildings under both target added damping ratio and interstorey drift ratio (IDR). The damping coefficients of added dampers are considered as design variables. The cost, which is defined as the sum of damping coefficient of added dampers, is minimized under a target added damping ratio and the upper and the lower constraint of the design variables. In the first stage of proposed algorithm, Simulated Annealing, Nelder Mead and Differential Evolution numerical algorithms are used to solve the proposed optimization problem. The candidate optimal design obtained in the first stage is tested in terms of the IDRs using linear time history analyses for a design earthquake in the second stage. If all IDRs are below the allowable level, iteration of the algorithm is stopped; otherwise, the iteration continues increasing the target damping ratio. By this way, a structural response IDR is also taken into consideration using a snap-back test. In this study, the effects of the selection of upper limit for added dampers, the storey mass distribution and the storey stiffness distribution are all investigated in terms of damper distributions, cost function, added damping ratio and IDRs for 6-storey shear building models. The results of the proposed method are compared with two existing methods in the literature. Optimal designs are also compared with uniform designs according to both IDRs and added damping ratios. The numerical results show that the proposed damper optimization method is easy to apply and is efficient to find optimal damper distribution for a target damping ratio and allowable IDR value.

A simple damper optimization algorithm for both target addeddamping ratio and interstorey drift ratio

A simple damper optimization method is proposed to find optimal damper allocation for shear buildings under both target added damping ratio and interstorey drift ratio (IDR). The damping coefficients of added dampers are considered as design variables. The cost, which is defined as the sum of damping coefficient of added dampers, is minimized under a target added damping ratio and the upper and the lower constraint of the design variables. In the first stage of proposed algorithm, Simulated Annealing, Nelder Mead and Differential Evolution numerical algorithms are used to solve the proposed optimization problem. The candidate optimal design obtained in the first stage is tested in terms of the IDRs using linear time history analyses for a design earthquake in the second stage. If all IDRs are below the allowable level, iteration of the algorithm is stopped; otherwise, the iteration continues increasing the target damping ratio. By this way, a structural response IDR is also taken into consideration using a snap-back test. In this study, the effects of the selection of upper limit for added dampers, the storey mass distribution and the storey stiffness distribution are all investigated in terms of damper distributions, cost function, added damping ratio and IDRs for 6-storey shear building models. The results of the proposed method are compared with two existing methods in the literature. Optimal designs are also compared with uniform designs according to both IDRs and added damping ratios. The numerical results show that the proposed damper optimization method is easy to apply and is efficient to find optimal damper distribution for a target damping ratio and allowable IDR value.

Friction Pendulum System as a Retrofit Technique for Existing Reinforced Concrete Building

Friction pendulum system (FPS) is one of the most effective base isolation systems, which is widely used for seismic upgrading of existing buildings. FPS is almost always non-linear and often strongly non-linear, so a mechanical model of FPS bearing is of great importance in seismic analysis. In this paper, three different models of FPS bearing are described and a building severely damaged by the L’Aquila earthquake in 2009 is examined according to the latest Italian code. Then, a case study presenting briefly an innovative technique that is able to introduce base isolation on existing buildings is provided with reference to the use of FPS. Different kinds of analyses, including response spectrum analysis and linear and non-linear dynamic analyses, are performed under the life-safety limit state. Storey shear, inter-storey drift, effective stiffness and energy dissipation are the considered parameters to investigate the effectiveness of the retrofitting procedure and analysis techniques.

Analysis on Seismic Behavior of Structures Supported by Foundations with Different Locations

In order to know more about the seismic behavior of structures supported by foundations with different locations, using the elastic and static elastic-plastic analysis method, the research is respectively from the aspects of the distribution characteristic of elastic inter-story displacement angle, the distribution law of story shear, and the distribution characteristic of elastic-plastic displacement angle and the sequence of plastic hinges. In the end, it is got that the characteristics of force and deformation of structures supported by foundations with different locations. It is found that the position of weak story would change along with the change of story stiffness. In order to guarantee the structures supported by foundations with different locations to have good seismic behavior, it needs to take the necessary internal force adjust measures and details of seismic design.

Approximate methods to evaluate storey stiffness and interstory drift of RC buildings in seismic area

During preliminary design of a RC building located in a seismic area, having quick but reliable analytical measurement of interstory drifts and storey stiffnesses might be helpful in order to check the fulfillment of damage limit state and stiffness regularity in elevation required by seismic design codes. This paper presents two approximate methods, strongly interrelated each other, and addressed to achieve each of these two purposes for frame buildings. A brief description of some already existing methods addressed to the same aims is included to compare the main differences in terms of general approaches and assumptions. Both new approximate methods are then applied to 9 'ideal' frames and 2 'real' buildings designed according to the Italian seismic code. The results are compared with the 'exact' values obtained by the code-based standard calculation, performed via FEM models, showing a satisfactory range of accuracy. Compared with those by the other methods from literature, they indicate the proposed procedures lead to a better approximation of the objective structural parameters, especially for those buildings designed according to the modern 'capacity design' philosophy.

Influence of ground motion characteristics on drift demands in steel moment frames designed to Eurocode 8

This paper investigates the influence of the frequency content of ground motion, as well as the structural characteristics and level of inelasticity, on the global and inter-storey drift demands in frames designed to comply with Eurocode 8 provisions. To represent a wide range of structural characteristics, a suite of 39 steel moment frames is considered by varying the number of storeys, intensity of loading, performance requirements and compliance criteria. Extensive incremental dynamic analyses are carried out on the study frames using 72 far-field ground motion records, which are scaled to simulate four levels of behaviour factor. It is shown that the salient parameters that influence the global drift are the ratio of fundamental period to mean period and the behaviour factor. In addition to these, the relative storey stiffness ratio and the first-mode participation factor have a direct, though less influential, effect on the maximum inter-storey drifts. Based on the parametric assessments, regression models are proposed for predicting the global and storey drifts. Finally, the implications of the findings on the rules incorporated in European and United States design codes are highlighted and discussed.

Free vibration analysis of asymmetric shear wall-frame buildings using modified finite element-transfer matrix method

In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of 6x6 by transforming the obtained stiffness matrix. Thus, the dimension, which is 12nx12n in classical finite elements, is reduced to the dimension of 6x6. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

APPLICATION OF THE BASELINE STIFFNESS METHOD FOR DAMAGE DETECTION OF AN RC BUILDING WITHOUT BASELINE MODAL PARAMETERS UTILIZING THE INDEPENDENT COMPONENT ANALYSIS FOR MODAL EXTRACTION

In this paper, a damage detection study is presented for a seven-story concrete building. This structure was affected by the 1994 Northridge earthquake. Acceleration signals of the damaged system are processed utilizing both the Independent Component Analysis and the Frequency Domain Decomposition Method to extract modal parameters. Utilizing solely these parameters from the damaged structure and the approximate undamaged lateral stiffness of the first storey, a pre-damage state is determined. Damage assessment is achieved by the Baseline Stiffness Method and comparing the computed undamaged state of the building and the damaged one to detect loss of stiffness on each element of the structure. Advantages of the proposed methods are discussed to demonstrate the feasibility of the methodology to extract modal parameters and to identify structural damage in buildings without baseline modal information.

Seismic shear demands in multi-storey steel frames designed to Eurocode 8

This paper investigates the influence of the frequency content of ground motion, as well as structural parameters and the level of inelasticity, on the shear demands in frames designed to comply with Eurocode 8 provisions. The investigation of the shear demands focuses on both the base shear and individual storey shears. To represent a wide range of structural characteristics, 39 steel moment-resisting frames are designed and considered in the analyses. The mean period, Tm, is employed as a measure of the frequency content of ground motion. Seventy-two records are selected from a broad range of seismological scenarios and these records have mean periods ranging from 0.31 to 0.98s. Incremental dynamic analysis (IDA) is used to investigate the influence of various structural parameters for different levels of nonlinearity by scaling the ground motions in order to simulate four levels of the behaviour factor, q. The results of the parametric study demonstrate that the base shear is significantly influenced by the period ratio T1/Tm (i.e., the ratio of the fundamental period of the structure T1 and the mean period Tm of the motion), the behaviour factor, the plasticity resistance ratio and the relative storey stiffness ratio. On the other hand, storey shear demands are found to depend strongly upon the normalised height (i.e., the height to a given storey divided by the total height of the frame) in addition to the behaviour factor, period ratio and plasticity resistance ratio. Robust regression models are proposed for the prediction of these shear demands. Finally, the implications of the findings with reference to European seismic design procedures are explored.

Substructure Identification for Shear Structures with Nonstationary Structural Responses

AbstractIn previous studies by the authors, a substructure identification method for shear structures was proposed to identify all structural story stiffness and damping parameters from top to bottom inductively. In the method derivation, the structural responses were required to be wide sense stationary to convert structural dynamic equations to differential equations in the correlation functions of structural responses, which are used to formulate substructure identifications. In this paper, this method is extended to accommodate nonstationary structural responses. A different derivation procedure is adopted to formulate substructure identifications directly from the Fourier transform of the structural dynamic equations, resulting in a formulation nearly the same as its stationary response predecessor. An identification error analysis for the substructure identification method reveals how structural responses affect the identification accuracy. On the basis of this result, a smart reference selection ru...

모드형상을 이용한 전단형 건물의 손상 위치 추정

Damage location and extent could be detected by the inverse analysis on dynamic response of the damaged structure. In general, detection of damage location is possible by the observation of the mode shape difference between undamaged and damaged structure and assessment of stiffness reduction is possible by the observation of the natural frequency difference of them. The study on damage detection by the dynamic response in civil structures is reported enough and in practical use, but in building structures it is reported seldom due to several problems. The purpose of this study is to present the damage detection method on shear building structures by mode shape. The damage location index using 1st mode shape is observed theoretically to find out damage location. The damage detection method is applied to numerical analysis model such as MATLAB and MIDAS GENw for the verification. Finally the shaking table test on 3 story shear building is performed for the examination of the damage detection method. In shaking table results, as the story stiffness decrease by 25% the 1st mode frequency increase by 12%, and the damage location index represents minus at damaged story.

Ambient Vibration Testing for Story Stiffness Estimation of a Heritage Timber Building

This paper investigates dynamic characteristics of a historic wooden structure by ambient vibration testing, presenting a novel estimation methodology of story stiffness for the purpose of vibration-based structural health monitoring. As for the ambient vibration testing, measured structural responses are analyzed by two output-only system identification methods (i.e., frequency domain decomposition and stochastic subspace identification) to estimate modal parameters. The proposed methodology of story stiffness is estimation based on an eigenvalue problem derived from a vibratory rigid body model. Using the identified natural frequencies, the eigenvalue problem is efficiently solved and uniquely yields story stiffness. It is noteworthy that application of the proposed methodology is not necessarily confined to the wooden structure exampled in the paper.

The Overall Stability Calculation Method for Sway Frame

There are three levels in stability calculating for sway frame. The first level is the traditional effective length method. The second level is the effective length method considering interaction of columns in one story and the third level is the effective length method considering inter-story interaction. The traditional effective length method may lead to unsafe design. Using the concept of equivalent negative stiffness, story stiffness to negative stiffness ratio factor and story support factor were proposed. Through the story stiffness to negative stiffness ratio factor, the weak-story and the inter-story support relationship can be found. Then, a formula for calculating the elastic stability capacity of sway frame is proposed, by which the inter-column interaction and inter-story interaction can be considered, and the finite element buckling analysis for stability capacity can be avoided. Through the stability capacity, the column effective length can be calculated. The results show that this simple calculation method has good precision and accuracy, can be used for engineering design and theoretical calculations.

Free Vibration Analysis of Asymmetric-Plan Shear Wall and Core Buildings Using One-dimensional Finite Element

In this study, a method is presented for free vibration analysis of multi-storey asymmetric structures whose bearing system is composed of shear walls and cores. The multi-storey structure was modeled as an equivalent cantilever beam in the study. The equivalent cantilever beam in the method was divided into as many finite elements as the number of the storeys. In the study first of all, a differential equation belonging to the equivalent cantilever beam was written for ith storey by using the calculation model in the continuous system. Then, a stiffness matrix for ith storey was obtained using the solution of the written differential equation. The masses in the model were applied on the storey levels. Angular frequencies were obtained using the system mass matrix and system stiffness matrix formed by storey stiffness matrices. At the end of the study, a sample taken from literature was solved and the results were evaluated to test the convenience of the method.

An Introduction to the Methodology of Earthquake Resistant Structures of Uniform Response

Structures of Uniform Response are special earthquake resistant frames in which members of similar groups such as beams, columns and braces of similar nature share the same demand-capacity ratios regardless of their location within the group. The fundamental idea behind this presentation is that seismic structural response is largely a function of design and construction, rather than analysis. Both strength and stiffness are induced rather than investigated. Failure mechanisms and stability conditions are enforced rather than tested. Structures of Uniform Response are expected to sustain relatively large inelastic displacements during major earthquakes. A simple technique has been proposed to control and address the gradual softening of such structures due to local/partial instabilities and formation of plastic hinges. In structures of uniform response, the magnitude and shape of distribution of lateral forces affects the distribution of story stiffness in proportion with story moments, therefore affecting the dynamic behavior of the system as a whole. Simple closed form formulae describing the nonlinear behavior of moment frames of uniform response have been proposed. While the scope of this contribution is limited to moment frames, the proposed method can successfully be extended to all types of recognized earthquake resisting systems.

Structure Observation & Identification Considering Soil-Structure Interaction of Story Stiffness and Damping Ratio of 8-Story Steel Encased Reinforce Concrete Structure by Microtremor

In this article, the authors identify the one built in 1998, eight-story structure of steel reinforced concrete body dynamic parameters, and discussed the soil - structure interaction on the identification results.In this study, an 8 degrees of freedom analytical model and the impact analysis model of soil-structure interaction to be established; through the analysis of microseismic observations, using non-parametric (transfer function and Random Decrement method) and parameter techniques (off-line system identification method, ARX :Auto-Regression with eXtra input) to identify the structure of the natural frequency, damping ratio and the story stiffness. Finally, in considering the soil-structure interaction cases, structural parameters were identification and compared the results to confirm the impact of soil-structure interaction.

Study on Rational Ratios of Lateral Stiffness for Masonry Building with Frame Structure at First Two Stories

There are two typical seismic damage characteristics to the masonry building with frame shear wall structure at first two stories, and the lateral stiffness ratio of the third storey to the second storey is one of the key factors mostly affecting the seismic performance of this kind of building. However, some factors are not considered sufficiently in current Chinese seismic codes. According to the theory of performance-based seismic design, the seismic performance of this kind of structure is analyzed in this paper by taking time-history analysis on models which with different storey stiffness ratios. The results show that when the lateral stiffness ratio controlled in a reasonable range, the upper masonry deformation can be ensured in a range of elastic roughly, and the bottom frame can be guaranteed to have sufficient deformation and energy dissipation capacity. Finally, according to the seismic performance characteristics of masonry building with frame shear wall structure at first two stories, especially the characteristics under strong earthquakes, a method of simplified calculation model for the upper masonry is discussed in this paper.

Substructure identification for shear structures I: Substructure identification method

A substructure identification method for shear structures is proposed herein. A shear structure is partitioned into many simple substructures; an inductive identification procedure is derived to estimate the structural parameters from top to bottom. In each identification step, the dynamic equilibrium of a one-floor substructure is utilized to construct a substructure identification problem, estimating the story stiffness and damping coefficient. An identification error analysis for least-square error identification problems, based on the linearization of the least-square error problem, is proposed and applied to the substructure identification method. The results show that the identification errors are closely related to two important structural responses: the frequency response of the interstory acceleration of the identified story and the frequency response ratio between adjacent interstory accelerations. Further, these responses are critical to the substructure identification only near a certain frequency, the substructure natural frequency of the identified story substructure. The larger the first response is and/or the smaller the second response is, the more accurate the estimation results will be. A numerical example of a five-story shear structure is given to demonstrate the effectiveness of the proposed substructure identification method and to verify the identification error analysis results. From the results of the identification error analysis, a companion paper proposes a controlled substructure identification method, utilizing specially designed algorithms for structural control devices to change the two key structural responses that affect the identification accuracy, to improve the accuracy of the substructure identification. Copyright © 2012 John Wiley & Sons, Ltd.