Computational Methods in Earthquake Engineering

The seismic response of inhomogeneous soils is explored analytically by means of one-dimensional viscoelastic wave propagation theory. The system under investigation comprises of a continuously inhomogeneous layer over a homogeneous one of higher stiffness. The excitation is specified at the bottom of the base layer in the form of vertically propagating harmonic S waves. Shear wave propagation velocity in the inhomogeneous layer is described by a generalized parabolic function, which allows modeling of soil having vanishing shear modulus at the ground surface. The problem is treated analytically leading to an exact solution of the Bessel type for the natural frequencies, mode shapes and base-to-surface response transfer function. The model is validated using available theoretical solutions and finite-element analyses. The exact analytical solution is compared with energy-based Rayleigh techniques and equivalent homogeneous soil approximations. The latter are defined by means of alternative definitions for the representative shear wave velocity in the inhomogeneous layer. Results are presented in the form of normalized graphs demonstrating the effect of salient model parameters such as layer thickness, impedance contrast between surface and base layer, surface-to-base shear wave velocity ratio in the inhomogeneous layer, rate of inhomogeneity and hysteretic damping ratio. Harmonic response of inhomogeneous soils with vanishing shear wave velocity near soil surface is explored by asymptotic analyses.

The Evripos bridge in central Greece, connects the island of Evia to the mainland. The cable-stayed section of the bridge is 395 m in length, with a central span of 215 m and side-spans of 90 m each. The deck, 13.5 m in width, is at 40 m above sea-level, suspended by cables from two, 90 m high pylons. A permanent accelerometer special array of 43 sensors was installed on the bridge in 1994 by the Institute of Engineering Seismology and Earthquake Engineering. Two triaxial sensors have been monitoring the free-field (near pier M4) and pier M5 base response on the mainland (Boeotean) coast and two others the respective locations (pier base M6 and free-field near pier M7) on the Euboean coast. Since then the bridge’s behavior to seismic excitations has been continuously monitored and investigated. From various earthquake events recorded at the site, it became obvious that the excitation at each of the aforementioned locations differs, with the lowest peak acceleration values observed at site M7 for all three components, independently of magnitude, azimuth and epicentral distance of the earthquake, a fact that can be attributed to local site conditions. In the present research effort, an investigation of the dynamic response of the Evripos bridge due to the asynchronous base excitations along its supports is carried out. Comparisons are made with the conventional design procedure of assuming a common (synchronous) base excitation at all supports and interesting conclusions are drawn regarding the impact of spatially variable ground motion on the seismic response of the particular bridge.

Beam-column elements with section resultant plasticity for the hysteretic behavior of the end plastic hinges are widely used for numerical simulations in earthquake engineering practice because of the good compromise between accuracy and computational cost. This chapter presents a three-dimensional inelastic beam-column element of this type with significant capabilities for the description of the global and local response of frames under monotonic and cyclic loads. In the proposed element the concept of generalized plasticity is extended to section resultants and element deformations and is used to describe the hysteretic behavior of the plastic hinges forming at the element ends. The element accounts for the interaction of the axial force with the bending moments about the principal section axes with suitably defined yield and limit surfaces that permit the description of the gradual yielding and the post-yield hardening behavior of the end sections. Comparisons of the hysteretic response of structural elements and small structural models between the proposed element and the more accurate, but computationally more expensive fiber section description of the cross section demonstrate the capabilities of the proposed model.

This paper presents a methodology for predicting the seismic peak response of vibratory single-degree-of-freedom (SDOF) nonstructural elements with simple measures. The non-structural elements may be attached to both elastic and ductile load-bearing frame structures. The methodology is based on modified modal superposition of floor response spectra for SDOF oscillators on SDOF supporting structures. Dynamic interaction between the substructures is considered, and thus, the peak response of moderately heavy nonstructural elements can be assessed. The presented results are based on numerical simulations involving 44 ground motion records of the ATC63 far-field set and subsequent statistical evaluation. For several example problems “exact” results are contrasted with outcomes of the proposed methodology. This comparison provides evidence that the proposed methodology delivers sufficient accurate predictions of the seismic peak response of simple vibration-prone nonstructural elements on ductile load-bearing structures.

This chapter discusses the effectiveness of simplified nonlinear models for seismic assessment of steel moment frames using single and multi-mode nonlinear static methods. It is demonstrated that the nonlinear static procedure (NSP) has much value in understanding important behavior characteristics that are not being explored in a nonlinear response history analysis (NRHA) in which engineers usually focus on a “blind” demand/capacity assessment rather than interpretation and visualization of the steel frame behavior. It is also shown that NSP procedures have many limitations for quantitative assessment of steel moment frame demands even for low-rise frames. The conclusion is that both NSP and NRHA have intrinsic value and that it is advisable to employ a combination of both to understand seismic performance of steel moment frames and to quantify important engineering demand parameters for these lateral resisting structural systems.

In this chapter, an efficient method for rapid preliminary assessment of the seismic vulnerability of reinforced concrete buildings is presented. The method determines the columns’ limiting shear resistance at the critical storey of the structure, by applying a strength assessment procedure associated with typical column details representative of the state of practice from the era of the building’s period of construction and evaluates the severity of seismic displacement demand and the maximum seismic acceleration that the building can sustain by applying a stiffness index assessment. For application of the method, only knowledge of the basic geometric and material properties of the building is required. The proposed method is applied for verification reasons to two reinforced concrete buildings that failed during the 1999 Athens earthquake. It is shown that the proposed method can be used as a diagnostic tool for identification of both the building’s fragility and the prevailing failure mechanism, allowing the engineers to immediately identify the most vulnerable buildings that are likely to collapse in a potentially strong earthquake, as well as to set objectives for their rehabilitation.

Shear walls play an important role to the seismic strength of modern seismic resistant structures. They are designed so that they have significant bending and shear strengths and ductility. However, existing structures have lightly reinforced shear walls. In most cases, especially under cycling loading, shear cracks appear, reducing the shear capacity of the wall. Here, a typical shear wall of an existing structure is examined in which it is assumed that a crack has been formed. For the modelling of the geometry of the crack a new approach is applied, using the notion of fractal geometry. The aim of the chapter is the estimation of the post-cracking strength of the wall, taking into account the geometry of the cracks and the mixed friction-plastification mechanisms that develop in the vicinity of the crack. Due to the significance of the crack geometry a multi-resolution analysis is performed. The materials (steel and concrete) are assumed to have elastic-plastic behaviour. For concrete both cracking and crushing are taken into account in an accurate manner. On the interface unilateral contact and friction conditions are assumed to hold. For every structure resulting for each resolution of the interface, a classical Euclidean problem is solved. The obtained results lead to interesting conclusions concerning the post-cracking strength of lightly reinforced shear walls.

The goal of this study is to investigate seismic behaviour of existing R/C buildings designed and constructed in accordance with standards that do not meet current seismic code requirements. In these structures, not only flexure, but also shear and bond-slip deformation mechanisms need to be considered, both separately and in combination. To serve this goal, a finite element model is developed for inelastic seismic analysis of complete planar R/C frames. The proposed finite element is able to capture gradual spread of inelastic flexural and shear deformations as well as their interaction in the end regions of R/C members. Additionally, it is capable of predicting shear failures caused by degradation of shear strength in the plastic hinges of R/C elements, as well as pullout failures caused by inadequate anchorage of the reinforcement in the joint regions. The finite element is fully implemented in the general inelastic finite element code IDARC2D and it is verified against experimental results involving individual column and plane frame specimens with non-ductile detailing. It is shown that, in all cases, satisfactory correlation is established between the model predictions and the experimental evidence. Finally, parametric studies are conducted to illustrate the significance of each deformation mechanism on the seismic response of the specimens under investigation. It is concluded, that all deformation mechanisms, as well as their interaction, should be taken into consideration in order to predict reliably seismic damage of R/C structures with substandard detailing.

Current state of practice for seismic design of basement walls is using the Mononobe-Okabe (M-O) method that is based on the Peak Ground Acceleration (PGA). The National Building Code of Canada (NBCC) has considerably changed the seismic hazard level from 10 % in 50 years in NBCC1995 to 2 % in 50 years in NBCC2010, which leads to doubling the PGA in Vancouver from 0.24g to 0.46g. The current design PGA leads to very large seismic forces that make the resulting basement walls very expensive. Because there is a little evidence of any significant damage to basement walls during major earthquakes, the Structural Engineers Association of British Columbia (SEABC) initiated a task force to review current seismic design procedures for deep basement walls. Presented in this paper are some preliminary results of the work conducted by this committee. A series of dynamic numerical analyses have been carried out on a typical basement wall designed using the M-O earth pressures with the NBCC1995 PGA for Vancouver. This wall is then subjected to three ground motions spectrally matched to the Uniform Hazard Spectrum prescribed by the NBCC2010 and the seismic performance of the wall under this level of demand has been presented and discussed. Particular attention has been given to the resulting drift ratio in the walls.

This chapter presents an assessment of the behavior of infilled framed structures. The feasibility of possible immediate implementation of some recent developments both in analysis and design of infilled frames for practical design is investigated. It is now widely recognized that masonry infill panels, used in reinforced concrete (R/C) frame structures, significantly enhance both the stiffness and the strength of the surrounding frame. However, their contribution is often not taken into account because of the lack of knowledge of the composite behavior of the surrounding frame and the infill panel. Currently, Seismic Design Guidelines contain provisions for the calculation of the stiffness of solid infilled frames mainly by modeling infill walls as “diagonal struts.” However, such provisions are not provided for infilled frames with openings. The present study, based on available finite element results, proposes analytical equation for obtaining the reduction factor, which is the ratio of the effective width of a diagonal strut representing a wall with an opening over that of the solid RC infilled frame. The validity of the proposed equations is demonstrated by comparing our results, against work done by various researchers.

As a common practice, restoration projects of ancient colonnades have to deal with joining together fragments of architectural members using threaded titanium bars (reinforcement) fixed into place with cement mortar. The basic criterion for the design of such connections is that, in case of a seismic event, the reinforcement should absorb the seismic energy and fail before the marble suffers any damage. For the dimensioning of these connections, the capacity design concept is usually implemented. In this chapter, the efficiency of the reinforcement of the connection calculated with this methodology is investigated for selected severe seismic excitations. The analyses were performed for two case studies with different geometries: a column of the Parthenon Pronaos and the Southern colonnade of the Ancient Agora of Kos in Greece. The induced forces were calculated using the distinct element method. The results show that the design is adequate, as the stresses induced to the reinforcement bars were always less than their ultimate strength and, in many cases, considerably less than their yield resistance as well.

Numerous structures exhibit rocking behavior during earthquakes and there is a continuing need to retrofit these structures to prevent collapse. The behavior of stand-alone rocking structures has been thoroughly investigated, but there are relatively few theoretical studies on the response of retrofitted rocking structures. In practice, despite the benefits of allowing rocking motion, rocking behavior is typically prevented instead of optimized. This study characterizes the fundamental behavior of damped rocking motion through analytical modeling. A single rocking block analytical model is utilized to determine the optimal viscous damping characteristics which exploit the beneficial aspects of rocking motion while dissipating energy and preventing overturning collapse. To clarify the benefits of damping, overturning envelopes for the damped rocking block are presented and compared with the pertinent envelopes of the free rocking block. Preliminary experimental work to verify analytical modeling is also presented. Finally, the same principles of controlling rocking behavior with damping are extended to a particular class of rocking problems, the dynamics of masonry arches. A pilot application of the proposed approach to masonry arches is presented.

A web-based methodology for the prediction of approximate IDA curves, which was recently developed within ICE4RISK project, and demonstrated with the web application (http://​ice4risk.​slo-projekt.​info/​WIDA), is briefly summarized in this chapter and its applicability is presented by means of an example of a four-storey wall-equivalent dual system. The proposed methodology consists of two independent processes. The result of the first process is a response database of the single-degree-of-freedom model, whereas the second process involves the prediction of approximate IDA curves from the response database by using n-dimensional linear interpolation. The web application utilizes a response database of IDA curves, which was calculated for thirty ground motion records and the discrete values of the six parameters, which describe the period, damping and the force-displacement relationship of a building’s pushover curve. The web application enables quadrilinear idealization of the pushover curve, including strength degradation. Structural collapse capacity can therefore also be estimated. Very good agreement between the computed and the approximated IDA curves was observed if the error is measured in terms of peak ground or spectral acceleration which caused selected limit state.

An improvement of codes’ bilinear fit for static pushover (SPO) curves is put forward aimed at decreasing the error introduced in the conventional SPO analysis by the piecewise linear fitting of the capacity curve. In the approach proposed herein, the error introduced by the bilinear fit of the force-deformation relationship is quantified by studying it at the single degree of freedom (SDOF) system level, away from any interference from multiple degree of freedom (MDOF) effects. Incremental Dynamic Analysis (IDA) is employed to enable a direct comparison of the actual curved backbones versus their piecewise linear approximations in terms of the spectral acceleration capacity for a continuum of limit-states, allowing an accurate interpretation of the results in terms of performance. A near-optimal elastic-plastic bilinear fit can be an enhanced solution to decrease systematically the error introduced in the SPO analysis if compared to the fit approaches provided by most codes. The main differences are (a) closely fitting the initial stiffness of the capacity curve and (b) matching the maximum strength value, rather than disregarding them in favor of balancing areas or energies. Employed together with selective area discrepancy minimization, this approach reduces the conservative bias observed for systems with highly curved force-deformation backbones.

The inelastic behavior of reinforced concrete structures subjected to a number of strong motion excitations of escalated Intensity Measure (IM) and monitoring of characteristic Engineering Demand Parameters (EDPs) of the structure for all these different instances is presented. This provides the necessary data to estimate the overall performance of a structure at a particular site of specified seismic hazard within the framework of Incremental Dynamic Analysis (IDA). In this, generation of data regarding capacity and demand evolves following a lognormal distribution while the corresponding cumulative distribution function is used to define the corresponding fragility curves. This analysis facilitates further the deduction of statistically sound estimates of the measured parameters. The hysteretic inelastic response of reinforced concrete members, i.e. beams and columns designed on the basis of Eurocodes is of primal importance. The Bouc-Wen model, as implemented in “Plastique” code, with parameters established based on existing experimental data, is considered implementing the IDA procedure. Through this modeling, a series of plane frames of different number of spans and stories designed in a similar manner is investigated. Also, the effect of some general design code provisions on collapse capacity of these frames, such as stiffness distribution along height and strong column-weak beam design principle are examined. Numerical results are presented and their corresponding fragility curves are derived. Interesting features are revealed, regarding the effect of alternative designs on collapse capacity, which often deviate from collapse predictions made using the static pushover analysis.

Most of the Italian school buildings were not designed according to seismic criteria and, therefore, they are vulnerable from a seismic point of view. A clear proof of this was the catastrophic collapse of the school at San Giuliano during the October 2002 earthquake: thirty people died, of which twenty seven were young students and one their teacher. After this seismic event, the process for identifying the most seismically vulnerable school buildings was started in Italy, with the final aim of improving their strength. Furthermore, several school buildings, mainly located in the historical town centre were damaged during the recent seismic event of L’Aquila (April 6, 2009), as reported by Salvatore et al. (Rapporto dei danni provocati dall’evento sismico del 6 aprile sugli edifici scolastici del centro storico de L’Aquila, http://​www.​reluis.​it). The proposed research work was driven by the idea of defining a methodology that implements an analysis in successive steps with an increasing level of detail. Only the buildings with seismic risk higher than a given threshold go through to the following phase, so that the number of buildings analysed decreases at each phase. The implemented procedure follows some well known works published in literature (Grant et al. 2007; Crowley et al. 2008). The definition of a prioritisation scheme of intervention is strictly due to the high number of school buildings (almost 50000) that cannot be deeply analysed considering the limited resources available. The school building location, the exposure data and seismic input information are implemented in a WebGIS platform through interactive maps and tabs. By means of the developed WebGIS tools, the seismic risk analyses of the school buildings are performed and the obtained results, in terms of maps and tables, are herein presented.

In this work the geometric nonlinear dynamic response of saddle-shaped cable nets subjected to uniform harmonic loads is investigated. The detection of nonlinear phenomena can be realised by numerous numerical nonlinear dynamic analyses leading to diagrams of response curves. This procedure demands much computational effort for different loading amplitudes, changing the frequencies by very small steps and taking into consideration initial conditions by means of nodal initial displacements and velocities. The number of such analyses can be significantly reduced by means of an analytical solution that can provide the necessary information about the conditions for which nonlinear resonances occur. To that effect, an equivalent SDOF model is set up, and its equation of motion is found to be similar to the one of the Duffing oscillator, for which analytical solutions under primary or secondary resonances can be found in the literature. The transformation of the MDOF cable net to the SDOF one is obtained by similarity relations. The comparison between the two models by means of the steady-state amplitude of the central node demonstrates that the behaviour of the SDOF model describes satisfactorily the one of the MDOF model, predicting the dominant nonlinear phenomena.

Wind excited vibrations of slender structures such as towers, masts or certain types of bridges can be reduced using passive or active vibration absorbers. If there is available only a limited vertical space to install such a device, a ball type of absorber can be recommended. In general, it is a semi-spherical horizontal dish in which a ball of a smaller diameter is rolling. Ratio of both diameters, mass of the rolling ball, quality of contact surfaces and other parameters should correspond with characteristics of the structure. The ball absorber is modelled as a holonomous system. Using Lagrange equations of the second type, governing non-linear differential system is derived. The solution procedure combines analytical and numerical processes. As the main tool for dynamic stability investigation the 2nd Lyapunov method is used. The function and effectiveness of the absorber identical with those installed at the existing TV towers was examined in the laboratory of the Institute of Theoretical and Applied Mechanics. The response spectrum demonstrates a strongly non-linear character of the absorber. The response amplitudes at the top of a TV tower with ball absorber were reduced to 15–40 % of their original values.

Nowadays, the use of seismic isolation within the Italian and European context is gaining more and more acknowledgement, thanks to the high level of protection from the earthquake damage which can be guaranteed. However, the installation of devices within complex structural systems may influence the actual response due to the random variation of the installation and operating conditions with respect to the theoretical model. It is then of paramount importance a proper assessment of the overall isolating system response, considering the variability of the construction conditions. The main objective of the present work is to study the response of a particular installation system for Double Curved Surface Sliders (DCSS) for buildings with large plan development in case of construction defects related to the non-perfect co-planarity of the devices. A case study is presented, in which the effects of randomly simulated construction defects are analyzed. Preliminary results showed that the simulated construction defects have only limited influence on the global hysteretic behaviour of the system and that the simultaneous loss of contact may occur only for a limited number of devices. On the other hand, the effects of the vertical and horizontal force redistribution may cause important increase of the actions locally induced in the base connecting slab and create an eccentricity of the resultant horizontal force.

Very often, especially in densely-resided areas and city centers, neighboring buildings are constructed very close to each other, without sufficient clearance between them. Thus, during strong earthquakes, structural poundings may occur between adjacent buildings due to deformations of their stories. Furthermore, in the case of seismically isolated buildings, pounding may occur with the surrounding moat wall due to insufficient seismic gap at the base of the building. The current study presents a simple but efficient methodology that can be used to numerically simulate the incorporation of rubber layers between neighboring structures with relatively narrow seismic gaps in order to act as collision bumpers and mitigate the detrimental effects of earthquake-induced poundings. The efficiency of this potential impact mitigation measure is parametrically investigated considering both cases of conventionally fixed-supported and seismically isolated buildings subjected to various earthquake excitations. The results indicate that under certain circumstances the incorporation of rubber bumpers in an excising seismic gap can reduce the amplifications of the peak responses of the structures due to pounding.

In this chapter, an efficient design methodology which sizes, tunes and allocates multiple tuned-mass dampers in 3D irregular structures is presented. The proposed methodology is based on an iterative analysis/redesign algorithm which, while using two steps in each iteration, allows obtaining a very efficient amount of added dampers’ mass while converging to an allowable response of the structure. This performance-based design methodology is simple, relies on analysis tools only, and is fast converging, all of which make it very attractive for practical use.

Three remarkable projects on retrofitting by base isolation of the existing buildings are described in the chapter. One of them is retrofitting of a 5-story stone apartment building in Armenia. The operation was made without resettlement of the occupants. World practice provides no similar precedent in retrofitting of apartment buildings. The other project is retrofitting of the 60 years old 3-story stone school building also in Armenia. This building has historical and architectural value. Unique operations which were carried out in order to install the isolation system within the basement of this building and to preserve its architectural appearance are described. The third project is development of the design on retrofitting by base isolation of the 180 years old historical building of the Iasi City Hall in Romania. The structural concept of retrofitting is described and detailed results of the earthquake response analysis for two cases, i.e. when the building is base isolated and when it has a fixed base, are given. For all three buildings comparative analyses of the cost of innovative base isolation retrofitting technology vs. the costs of the different methods of conventional retrofitting are carried out and presented.

Seismically isolated R/C bridges is the target of an expert system based on the current design provisions of Eurocode 8, Part 2, which aims to facilitate their preliminary design. The expert system and the developed software includes a series of checks provided by Eurocode 8 (Part 2), in order to ensure the satisfactory seismic “optimum” performance of the selected isolation scheme. In doing so, the software accesses a specially created database of the geometrical and mechanical characteristics of commercially available cylindrical or prismatic elastomeric bearings, that can be easily enriched by relevant data from laboratory tests on isolation devices. The basic assumption included in the software is modeling the seismic response of an isolated bridge as a S.D.O.F. system. The features of this expert system are presented and discussed. Moreover, results from a number of tests are also included, indicative of the quality control procedure, specified by International Standard ISO 22762-1 (2005).

The paper is devoted to new computational techniques in structural dynamics where one tries to study, model, analyse and optimise very complex phenomena, for which more precise scientific tools of the past were incapable of giving low cost and complete solution. Soft computing methods differ from conventional (hard) computing in that, unlike hard computing, they are tolerant of imprecision, uncertainty, partial truth and approximation. The paper deals with an application of the bio-inspired methods, like the evolutionary algorithms (EA), the artificial immune systems (AIS) and the particle swarm optimisers (PSO) to optimisation problems. Structures considered in this work are analysed by the finite element method (FEM) and the boundary element method (BEM). The bio-inspired methods are applied to optimise shape, topology and material properties of 3D structures modelled by the FEM and to optimise location of stiffeners in 2D reinforced plates modelled by the coupled BEM/FEM. The structures are optimised using the criteria dependent on frequency, displacements or stresses. Numerical examples demonstrate that the methods based on the soft computation are effective for solving computer aided optimal design problems.

Recent earthquakes, especially those in Chile (2010) and Christchurch (2011), have demonstrated the unexpected performance of buildings designed according modern seismic design codes. These incidents strengthen the cause for moving towards performance-based design codes rather than serviceability and strength design. This chapter deals with optimal design of RC frames, a widely used structural type around the world, considering both the initial cost and structural performance as problem objectives. Initial cost comprises the total cost of materials and workmanship for structural components, while structural performance is measured by a two-level approach. First, each design is checked for acceptability according to existing codes, and next performance is quantified in terms of maximum interstory drift obtained from nonlinear inelastic dynamic analysis. This multi-objective, multi-level approach allows one to investigate the implications of the selection of design parameters on the seismic performance while minimizing the initial cost and satisfying the design criteria. The results suggest that structural performance varies significantly within the acceptable limits of design codes and lower initial cost could be achieved for similar structural performance.

H-infinity controller design for linear systems is a difficult, nonconvex typically nonsmooth optimization problem when the controller is fixed to be of order less than the one of the open-loop plant, a requirement with some importance in embedded smart systems. In this paper we use a new Matlab package called HIFOO, aimed at solving fixed-order stabilization and local optimization problems; it is based on a new hybrid solution algorithm. The problem is to reduce the vibration of the smart system using H-infinity control and nonsmooth optimization.

Decision-making for infrastructure systems is a difficult task to perform because of the complexity and the variety of the types of risks that may occur in the different phases of the life-cycle of an infrastructure system. To overcome these difficulties a new methodology for a risk-based decision making for planning and operating infrastructure systems is proposed. This methodology integrates: (i) the variability of impact upon risk occurrence, (ii) the available risk-response strategies, and (iii) the preference of the decision maker over these strategies with regard to the criticality of the various impacts upon risk occurrence. The proposed methodology considers four risk-response strategies, namely: (a) acceptance, (b) mitigation, (c) transfer, and (d) avoidance. Three approaches are applied, in order to determine the preference margins between these strategies: (i) compliance with regulations and specifications, (ii) determination based on data elaboration, and (iii) subjective judgment. Once, the expected value of the impact upon risk occurrence is estimated, the decision maker is capable to decide for the respective risk-response. An application example is presented as a proof-of-concept of the proposed methodology.

Time history analysis is a broadly accepted versatile approach, for real seismic analyses. In the most general case, time history analysis is based, on time integration, for which, the computational cost might be intolerable. For reducing the computational cost, a technique is recently proposed, based on replacing the digitized excitations, with excitations, digitized, at larger steps. After several successful implementations, of the technique, arriving at a deeper insight, into the practical performance, is the objective, here. Attention is paid to the significant role of bridges, at major earthquakes, and, a multi-span concrete bridge, designed according to the existing codes, and later upgraded laterally, by nonlinear steel shear keys, is selected. By carrying out time integration analyses, against earthquakes in consistence with the design codes, it is demonstrated that: (a) implementation of the technique can be well effective in reducing the computational costs of real seismic analyses, (b) when the nonlinearities are not severe, the effect of nonlinearity on the performance is trivial, (c) the assumptions, essential, in order to implement the technique, can be simplified, for seismic analyses.