Nonlinear Response Spectra Research Articles

Simplified seismic design approach for steel portal frame piers with hysteretic dampers

AbstractA simplified seismic design procedure for steel portal frame piers installed with hysteretic dampers is proposed, which falls into the scope of performance‐based design philosophy. The fundamental goal of this approach is to design a suite of hysteretic damping devices for existing and new bridge piers, which will assure a pre‐defined target performance against future severe earthquakes. The proposed procedure is applicable to multi‐degree‐of‐freedom systems, utilizing an equivalent single‐degree‐of‐freedom methodology with nonlinear response spectra (referred to as strength‐demanded spectra) and a set of formulae of close‐form expressions for the distribution of strength and stiffness produced in the structure by the designed hysteretic damping devices. As an illustrative example, the proposed procedure is applied to a design of a simple steel bridge pier of portal frame type with buckling‐restrained braces (one of several types of hysteretic dampers). For the steel portal frame piers, an attempt is made to utilize not only the displacement‐based index but also the strain‐based index as pre‐determined target performance at the beginning of design. To validate this procedure, dynamic inelastic time‐history analyses are performed using the general‐purpose finite element program ABAQUS. The results confirm that the proposed simplified design procedure attains the expected performance level as specified by both displacement‐based and strain‐based indices with sufficient accuracy. Copyright © 2006 John Wiley & Sons, Ltd.

기존 비선형약산법들의 신뢰성 개선을 위한 비선형직접스펙트럼법

This paper considers the nonlinear direct spectrum method to estimate seismic performance of mixed building structures without iterative computations, given dynamic property from stiffness skeleton curve and nonlinear pseudo acceleration and/or ductility ratio p from response spectrum. Nonlinear response history analysis has been performed and analysed with various earthquakes for evaluation of correctness and confidence of nonlinear direct spectrum method. The conclusions of this study are as follows; (1) Nonlinear direct spectrum method is considered as a practical method which is applicable to compute the structural initial elastic period and the yielding strength from stiffness skeleton owe and calculate the nonlinear maximum response of structure directly from nonlinear response spectrum. (2) The comparison of the analysis results from NDSM and NRHA showed that the average errors were less than 20% in about 3/4 of the analysis cases, and that the results obtained from NDSM turned out to be generally larger than those from NRHA.

Higher modes in simplified inelastic seismic analysis of single column bent viaducts

The influence of the higher modes and their consideration in the pushover analysis of reinforced concrete single column bent viaducts with different degree of irregularity is discussed. Typical multimode pushover-based methods (modal pushover analysis, modal adaptive non-linear static procedure and incremental response spectrum analysis) are addressed and compared with a single mode procedure (N2) and inelastic time history analysis. If in the transverse direction the substructure of the viaduct is flexible in comparison with the superstructure, the influence of higher modes is small (the structure is regular) and single mode procedure works well. This typically occurs when the columns are high or considerably damaged. Conversely, for the analysis of irregular structures having short and slightly damaged columns, the multimode methods are needed. In most cases, all the analysed multimode pushover-based methods have given the results comparable with time history analysis, with the exception of cases where torsional sensitivity is varying during the response. All the methods have limitations (discussed in detail in the paper), which should be fully recognized by the user. Copyright © 2005 John Wiley & Sons, Ltd.

Spectral story drift demand analysis for building structures during the 1999 Chi‐Chi Taiwan earthquake

The 921 Chi‐Chi earthquake caused a very significant number of building collapses and damage of various degrees. Many collapsed buildings had pedestrian corridors and open fronts on the ground floors. Using a modified modal participation factor and the generalized shape function computed from the nonlinear push over analysis, story drift demands imposed on soft first story building systems are studied in this paper. Generalized shape functions are constructed from the nonlinear static push over analysis of shear buildings having specific distributions of story stiffness and strength. Nonlinear response spectrum analyses were performed on the ground acceleration recorded from 51 sites located in the Taipei Basin and 62 sites in the Taichung Region. Analytical results indicate that soft first story buildings are likely to have story drift demands significantly greater than regular buildings of short fundamental period. Results of the nonlinear dynamic analysis of a 6‐story structure indicate that the maximum story drift demand can be satisfactorily predicted by the story spectral drift constructed from the generalized shape functions.

Displacement ductility demand spectra for the seismic evaluation of structures

One of the major concerns in the structural engineering practice is to assess the nonlinear response of new or existing structures for moderate or strong earthquake motions in a simple way. This can be done using what the author defines as displacement ductility demand spectrum (DDDS). This DDDS is a variation of the well-known nonlinear response spectrum for single degree of freedom (SDOF) systems with fixed displacement ductility demands. The proposed spectra and their applications for the seismic evaluation of structures are illustrated for different structural systems that the author has previously evaluated using other methods.

Effects of temperature on the nonlinear response function for two-dimensional vibrational spectroscopy

We investigate the effects of temperature on the nonlinear response functions associated with various two-dimensional vibrational spectroscopies. It turns out that the system–bath interaction plays an important role in determining the nature of the temperature-dependencies of the nonlinear response functions and spectra of the two-dimensional vibrational spectroscopy. For a model Hamiltonian, we present exact quantum-mechanical expressions for the nonlinear response functions of two-dimensional vibrational spectroscopies in both the time and frequency domains.

Stochastic models for simulation of strong ground motion in Iceland

AbstractTwo types of modelling approaches for simulating ground motion in Iceland are studied and compared. The first type of models, named discrete‐time series models (ARMA), are based solely on measured acceleration in earthquakes occurring in Iceland. The second type of models are based on a theoretical seismic source model called the extended Brune model. Based on measured acceleration in Iceland during the period 1986–1996, the parameters for the extended Brune models have been estimated. The seismic source models are presented here as ARMA models, which simplifies the simulation process. A single‐layer soil amplification model is used in conjunction with the extended Brune model to estimate local site amplification. Emphasis is put on the ground motion models representing the variability in the measured earthquakes, with respect to energy, duration and frequency content. Demonstration is made using these models for constructing linear and non‐linear probabilistic response spectra using a discretised version of the Bouc–Wen model for the hysteresis of the second‐order system. Copyright © 2001 John Wiley & Sons, Ltd.

Uniform Hazard Ground Motions for Mid-America Cities

For performance evaluation of buildings and structures, synthetic uniform hazard (10% and 2% in 50 years) ground motions are generated for Memphis, Tennessee, St. Louis, Missouri, and Carbondale, Illinois. The method of simulation is based on the latest regional seismic information and stochastic ground motion models. Both point-source model and finite-fault model are used and the effects of soil profile are considered. The emphasis is on treatment of uncertainty and efficiency in application to evaluation of structural performance in both the linear and nonlinear range. The results show that the uniform hazard response spectra calculated from the simulated motions are comparable to those corresponding to USGS hazard maps. The suites of ten ground motions selected to match the uniform hazard response spectra represent events of different magnitudes, distances, and attenuation. The median value of the structural response to the selected ground motions matches closely the uniform hazard linear and nonlinear response spectra based on nine thousand ground motions and has a coefficient of variation of less than 10%. The suites of uniform hazard ground motions therefore can be used in probabilistic performance evaluation with good accuracy and efficiency.

Passive Structural Control Strategies Using Seismic Steel Energy Dissipators

The force versus deformation relationships of a steel frame constructed with the proposed hysteretic energy dissipators (HED) are characterized by a tri-linear model indicating the distinct yielding of the HED and the frame. The optimal stiffness and strength ratios between the HED and the frame are recognized from parametric analysis of the nonlinear response spectra. A design algorithm is presented to illustrate the strategies incorporated into the design of frame buildings for seismic response control, particularly on the reduction of the inelastic deformational demands imposed on the beam-to-column connections of a six-story example steel moment frame.

Multimodal nonlinear spectral response of a beam with impact under random input

A linearization procedure for estimating the spectral response of a randomly excited beam—stop system is proposed. The elastic stop is replaced by a spring with a stiffness depending on the amplitude of the deflection at the impact location. The probability density function of the amplitude is obtained using the stochastic averaging principle. Next, an estimate of the nonlinear response spectrum is derived providing the expectation of the spectral density function of the random spring linear system with respect to the probability density function of the amplitude response (assumed to be a random variable). The efficiency of the method is checked by comparing results with those of numerical simulations.

Simplified Response-Spectrum Seismic Analysis of Nonlinear Structures

A method is presented for a simplified seismic analysis of nonlinear multidegree-of-freedom structures. The method represents an improvement over an earlier attempt to extend the use of the conventional response-spectrum method to nonlinear structures, and is also based on the use of a modal superposition in combination with nonlinear response spectra. It involves the computation of their natural frequencies and mode shapes on the basis of their initial elastic properties, the calculation of a yield deformation for each of their modes using formulas proposed here, and readings from a nonlinear response spectrum. The procedure is formulated for plane rigid frames, but limited to elastoplastic force-deformation behavior. Its application is illustrated by means of numerical examples with a three-story shear building and a six-story plane frame. In a comparison with solutions obtained with a step-by-step integration method, the proposed approximate method predicts the maximum displacements of these two structures with an average error of about 5%.

Developments in seismic structural analysis and design

After a brief overview of the world-wide state-of-practice in seismic design, nonlinear structural response spectra for strength, ductility and number of yield reversals as a function of building period and structure strength for several strong motion earthquakes are presented. Illustrations of three-dimensional mesh surfaces for the absolute seismic energy input and the dissipated hysteresis energy for selected earthquakes are given. These results are compared with conventionally evaluated elastic response spectra and code criteria. The issues of overstrength factors in the Mexico City code are then examined. The remainder of the paper is devoted to the description of a simple frictional energy dissipating connection. Its behaviour in cyclic tests and in shake table tests of a three-storey braced steel structure is illustrated.

Evaluation of Seismic Design Criteria for Highway Bridges

After an overview of the development of U.S. seismic design specifications for highway bridges an evaluation of current Caltrans and AASHTO seismic criteria is presented. Linear and nonlinear response spectra of ground motions recorded on different soil conditions in the Loma Prieta earthquake and other recent earthquakes are compared with code recommendations. Special emphasis is placed on how present design procedures reduce elastic forces to take into account the energy absorption capacity of the structure, and on the estimation of maximum inelastic deformations. Results indicate that current design recommendations may underestimate strength and deformation demands, particularly for short-period bridges and for bridges on soft soils. Finally, recommendations are made on how seismic design specifications may be improved.

Simplified approach for the seismic analysis of equipment attached to elastoplastic structures

Abstract A simple approximate procedure is presented to estimate the maximum response of equipment, piping, or any other light secondary system mounted on nonlinear structures subjected to earthquake ground motions. The procedure is based on the consideration of structure and equipment as an integrated combined system, and on a response spectrum method for the analysis of nonlinear multistory structures. It is formulated in terms of the initial dynamic properties of the independent structure and equipment components, and the nonlinear response spectrum of a specified earthquake ground motion. It may be applied to any linear multiple-degree-of-freedom secondary system connected at one or two arbitrary points of a multistory structure. It fully takes into account the interaction between primary and secondary systems and the nonclassical damping character of structure-equipment systems. It is restricted, however, to structures with elastoplastic load-deformation behavior and to those cases in which the mass of the secondary system is small in comparison with the mass of the structure. Its accuracy is evaluated by means of a comparative study with the numerical integration solutions of a number of idealized systems. In this comparative study, the proposed procedure estimates the numerical integration solutions with an average error of about 2%.

Structural Dynamics—Theory and Computations (2nd Ed.)

Part I: structures modelled as a single degree-of-freedom system undamped single degree-of-freedom system damped single degree-of-freedom system response of one-degree-of-freedom system to haarmonic loading response to general dynamic loading Fourier analysis and response in the frequency domain generalized co-ordinates and Rayleigh's method nonlinear structural response response spectra. Part II: structures modelled as shear buildings the multistory shear building free vibration of a shear building forced motion of shear buildings damped motion of shear buildings reduction of dynamic matrices. Part III: framed structures modeled as discrete multidegree-of-freedom systems dynamic analysis of beams dynamic analysis of plane frames dynamic anaylsis of grids three-dimensional frames dynamic analysis of trusses time history response of multidegree-of-freedom systems. Part IV: structures modelled with distributed properties dynamic analysis of systems with distributed properties discretization of continuous systems. Part V: introduction to finite element method dynamic analysis of plates dynamic analysis of shells dynamic analysis of three-dimensional solid structures. Part VI: random vibration. Part VII: earthquake engineering equivolent staic lateral force method - uniform Building Code 1994 dynamic method - uniform Building Code - 1994.

Development of non-linear floor response spectra

A computational scheme for the development of non-linear floor response spectra is presented. Results in the case of an assumed missile impact on a reactor building are shown. Expected reductions, with respect to the linear case, for seismic or missile impact excitations are discussed.

Fast computer calculation of ESR and nonlinear spin response spectra from the fast motion to the rigid lattice limits

Fast computer simulation of the electron spin resonance and adiabatic rapid passage spectra of spin labels characterized by rotational correlation times ranging from the fast motion to the rigid lattice limits is demonstrated. Calculations are based upon a modification of the stochastic Liouville equation for the density matrix which explicitly includes interaction of the spins with applied radiation and modulation fields. Several mathematical simplifications of previous calculations are demonstrated, permitting computation with core and CPU requirements compatible with small computers.