THREE DIMENSIONAL NONLINEAR BUILDING POUNDING WITH FRICTION DURING EARTHQUAKES

The three dimensional pounding phenomenon of two adjacent buildings during earthquakes with aligned rigid horizontal diaphragms is investigated for the linear and nonlinear structural response. The developed formulation takes into account three dimensional dynamic contact conditions for the velocities and accelerations based on the impulse-momentum relationship, using the coefficient of restitution e and the ratio μ, of tangential to normal impulses, which corresponds to the coefficient of friction under certain conditions. The contact points are determined geometrically from the displacements of the diaphragms' centre of mass. The results of the proposed formulation are compared with those obtained with the Lagrange multipliers approach. Test results are performed for two sets of multi-storey adjacent buildings subjected to real earth-quake motions with elastic and inelastic structural response.     

Nonlinear Static and Dynamic Behavior of a 16-Story Torsionally Sensitive Building Designed According to Eurocodes

A 16-story building under construction in Bucharest has been designed according to the provisions of EC2 and EC8, using elastic spectral modal analysis. Considering that the building is torsionally sensitive in the nonlinear range, it was further checked and verified using nonlinear dynamic and static procedures, using a detailed space-frame model. Specifically, time-history analysis for seven different excitations, as well as respective inelastic static analysis taking into account torsional effects were performed. The results are examined regarding structural (global) and member (local) response and various issues concerning the adequacy of the original elastic design and the applicability of advanced analysis methods are discussed.     

Simple Models for Inelastic Seismic Analysis of Asymmetric Multistory RC Buildings

A simple stick model is presented for the inelastic seismic analysis in 3D of two-way eccentric multistory RC buildings. It has 3 DoFs per floor, point hinges at the ends of the vertical elements connecting floors, elastic story stiffness derived from the corresponding story force-interstory deformation relations of the elastic 3D structure under inverted-triangular floor loading (by torques for torsional stiffness, by horizontal forces for the lateral ones), story yield forces derived from the total resistant shear of the story vertical elements, but no coupling between lateral and torsional inelasticity. It is evaluated on the basis of comparisons of response histories of floor displacements to those from full nonlinear models in 3D of four actual buildings. Alternative locations of the story vertical element with respect to the floor mass center are examined: (a) the floor “center of twist” of the elastic 3D building under inverted-triangular floor torques; (b) the story “effective center of rigidity,” through which application of inverted triangular lateral forces does not induce twisting of floors; (c) the centroid of the secant stiffness of the story vertical members at yielding and (d) the centroid of the lateral force resistance of story vertical elements. Among alternatives (a)–(d), the floor “center of twist” provides the best agreement with floor displacement response-histories from full 3D nonlinear models. This means that the static eccentricity that matters for torsional response may be taken as that of the floor “center of twist.” The center of resistance comes up as the second-best choice.     

DEVELOPMENT AND VERIFICATION OF A DISPLACEMENT-BASED ADAPTIVE PUSHOVER PROCEDURE

In this paper, an innovative displacement-based adaptive pushover procedure, whereby a set of laterally applied displacements, rather than forces, is monotonically applied to the structure, is presented. The integrity of the analysis algorithm is verified through an extensive comparative study involving static and dynamic nonlinear analysis of 12 rein-forced concrete buildings subjected to four diverse acceleration records. It is shown that the new approach manages to provide much improved response predictions, throughout the entire deformation range, in comparison to those obtained by force-based methods. In addition, the proposed algorithm proved to be numerically stable, even in the highly inelastic region, whereas the additional modelling and computational effort, with respect to conventional pushover procedures, is negligible. This novel adaptive pushover method is therefore shown to constitute an appealing displacement-based tool for structural assessment, fully in line with the recently introduced deformation- and performance-oriented trends in the field of earthquake engineering.     

Predicting the Seismic Response of Capacity-Designed Structures by Equivalent Linearization

An equivalent linearization procedure is developed for predicting the inelastic deformations and internal forces of capacity-designed structures under earthquake excitations. The procedure employs response spectrum analysis, and mainly consists of the construction of an equivalent linear system by reducing the stiffness of structural members that are expected to respond in the inelastic range. These members are well defined in structures designed with capacity principles. Maximum modal displacement demands of the equivalent linear system are determined either from the equal displacement rule, or from independent nonlinear response history analysis of SDOF systems representing inelastic modes.

Predictions obtained from the proposed equivalent linearization procedure are evaluated comparatively by using the results of nonlinear response history analysis as benchmark, linear elastic response spectrum analysis and conventional pushover analysis. The deformations and capacity controlled actions of a 12-story symmetrical plan concrete frame and a 6-story unsymmetrical plan concrete frame are obtained by each method under 96 strong ground motions. It is observed that the proposed procedure results in better accuracy in estimating the inelastic seismic displacement response parameters and capacity controlled forces than the other two approximate methods.     

EXTENSION OF EUROCODE 8 TORSIONAL PROVISIONS TO MULTI-STOREY BUILDINGS

A procedure is presented to extend the static torsional provisions of the Eurocode 8 (EC8) to asymmetrical multi-storey buildings. It is shown that even if the conditions in Annex A of EC8 are satisfied, the static torsional provision will not be effective to compensate for the effect of torsion unless the building possesses a minimum level of torsional stiffness. By means of examples, it is shown that this minimum torsional stiffness condition can be specified in the Code using the mean stiffness radius of gyration of the building calculated based on the proposed procedure as an index.     

Effect of AAC Infill Walls on Structural System Dynamics of a Concrete Building

The effect of autoclaved aerated concrete (AAC) infill walls on the structural system dynamics of a two-story reinforced concrete building is investigated using its finite element structural model, which is calibrated to simulate the acceleration-frequency response curves from its forced vibration test. The model incorporating the AAC infill walls by equivalent diagonal struts captures the increase in lateral stiffness of the building and the torsional motions induced due to the asymmetrically placed AAC infill walls. A higher strut width coefficient than in ASCE/SEI 41-06 is recommended to model the stiffness of the AAC infill walls in the elastic range.     

SEISMIC TORSIONAL EFFECTS ON DUCTILE STRUCTURAL WALL SYSTEMS

With a distinct design rather than analysis-oriented approach, some torsional phenomena, arising during the elasto-plastic seismic response of building structures, are addressed. It is postulated that existing code recommendations, expressed only in terms of the properties of elastic structures, are largely irrelevant when the design needs to be based on ductile system behaviour. Torsional restraint provided by elastic elements of a system, is claimed to be the desirable property controlling the amplification of inelastic translatory deformations of critical elements by storey twist. With the identification of the sources of inelastic element deformations, a simple behaviour-based design strategy is proposed. This should ensure that the displacement ductility demand, expected to be imposed on the system, does not result in deformations that, as a consequence of storey twist, may exceed the displacement ductility capacity of critical elements.     

Inelastic Displacement Ratios for Nonstructural Components Subjected to Floor Accelerations

This paper describes a study on the characterization of the Inelastic Displacement Ratios (IDRs) of inelastic acceleration-sensitive nonstructural components subjected to floor accelerations obtained from the linear analysis of multistory building structures under far-field ground accelerations. Several building models having different structural systems and a number of stories were considered. IDRs were obtained from the displacement response of elastic and inelastic single-degree-of-freedom systems subjected to floor accelerations. Similarities and differences between floor acceleration IDRs and ground acceleration IDRs were identified, and efforts were made to explain the differences. Finally, a predicting equation for floor acceleration IDRs is proposed and validated.     

Modernist Unreinforced Masonry (URM) Buildings of Barcelona: Seismic Vulnerability and Risk Assessment

The main objective of this work is to assess the vulnerability and seismic risk of typical existing modernist unreinforced masonry (URM) modernist buildings and aggregates situated in the Eixample district of Barcelona, part of the architectural heritage of the city. The context of the analysis is the methodology proposed by the Risk-UE project. The buildings are characterized by their capacity spectrum and the earthquake demand is defined by the 5% damped elastic response spectrum, considering deterministic and probabilistic earthquake scenarios. A discussion addresses the basis of the seismic damage states probabilities and the calculated damage index. An important research effort has been focused on the buildings modeling. All the architectural elements and their mechanical properties have been studied and evaluated accurately. It has been evidenced that a detailed and complete knowledge of all the structural elements existing in this type of buildings influence directly their behavior and hence the calculations and the results. The analysis of the isolated buildings and of the aggregate building has been performed for both mentioned seismic scenarios. Finally, a complete discussion of the results is included.     

Equivalent Damping in Support of Direct Displacement-Based Design

The concept of equivalent linearization of nonlinear system response as applied to direct displacement-based design is evaluated. Until now, Jacobsen's equivalent damping approach combined with the secant stiffness method has been adopted for the linearization process in direct displacement-based design. Four types of hysteretic models and a catalog of 100 ground motion records were considered. The evaluation process revealed significant errors in approximating maximum inelastic displacements due to overestimation of the equivalent damping values in the intermediate to long period range. Conversely, underestimation of the equivalent damping led to overestimation of displacements in the short period range, in particular for effective periods less than 0.4 seconds. The scatter in the results ranged between 20% and 40% as a function of ductility. New equivalent damping relations for four structural systems, based upon nonlinear system ductility and maximum displacement, are proposed. The accuracy of the new equivalent damping relations is assessed, yielding a significant reduction of the error in predicting inelastic displacements. Minimal improvement in the scatter of the results was achieved, however. While many significant studies have been conducted on equivalent damping over the last 40 years, this study has the following specific aims: (1) identify the scatter associated with Jacobsen's equivalent damping combined with the secant stiffness as utilized in Direct Displacement-Based Design; and (2) improve the accuracy of the Direct Displacement-Based Design approach by providing alternative equivalent damping expressions.     

Seismic Response of Base-Isolated Benchmark Building with Variable Sliding Isolators

The seismic response of base-isolated benchmark building with variable sliding isolators like variable friction pendulum system (VFPS), variable frequency pendulum isolator (VFPI), and variable curvature friction pendulum system (VCFPS), along with conventional friction pendulum system (FPS), was studied under the seven earthquakes. The earthquakes are applied bi-directionally in the horizontal plane ignoring vertical ground motion component. The shear type base-isolated benchmark building is modeled as three-dimensional linear elastic structure having three degrees of freedom at each floor level. Time domain dynamic analysis of the benchmark building was carried out with the help of constant average acceleration Newmark-Beta method and nonlinear isolation forces was taken care by fourth-order Runge-Kutta method. The base-isolated benchmark building is investigated for uniform isolation and hybrid isolation in combination with laminated rubber bearings through the performance criteria and time history response of important structural response parameters like floor accelerations, base displacement, etc. It is observed that variable sliding isolators performed better than conventional FPS due to their varying characteristic properties which enable them to alter the isolator forces depending upon their isolator displacements thus improves the performance of the structure. The VFPS efficiently controls large isolator displacements and VFPI and VCFPS improve super structural response on the cost of isolator displacement. It is also observed that the hybrid isolation is relatively better in comparison to the uniform isolation for the benchmark building.     

Shaking Table Testing of a Full-Scale Prefabricated Three-Story Timber-Frame Building

Shake table tests were carried out on a 7 m × 5 m three-story, timber light-frame building (7.5 m height) at the TreesLab laboratory (Eucentre) in Pavia. The aim of the research was to evaluate the seismic behavior of a typical Italian prefabricated timber building and to study the interaction between the individual structural components tested in quasi-static manner in a previous experimental study. The 1979 Montenegro Earthquake ground motion, recorded at the Ulcinj-Hotel Albatros station, was selected as the ground motion for seismic tests. The maximum peak ground acceleration was scaled to 0.07 g, 0.27 g, 0.5 g. 0.7 g, and 1 g in order to evaluate the building’s performance at different levels of seismic input. More than 100 instruments were used to monitor the behavior of the building during seismic tests measuring acceleration, displacement, and forces. The visual inspection shows that the building did not show any damage during all seismic tests. However the data analysis (dynamic identification, capacity spectrum, inter-story drift) confirm that during the 1.00 g test the structure went beyond its linear elastic limit. The results obtained from this experimental study suggest that the design hypotheses commonly adopted in practice for seismic analysis (e.g., in terms of force distributions between the walls, and also the behavior factor q) are not always consistent with the real behavior of timber frame multi-story buildings, and should be backed by more accurate knowledge of the contributions of the individual structural components.     

YIELDING OSCILLATOR UNDER TRIANGULAR GROUND ACCELERATION PULSE

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the'response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.     

Estimating the Higher-Mode Response of Ductile Structures

While the importance of higher-mode actions is appreciated within the engineering community, the affect that ductile nonlinear response has on higher-mode characteristics and the subsequent implications this has for design has received little attention. In this article, the manner in which the higher-mode response of frame-wall structures is affected by inelastic behavior is closely examined and a means of accounting for this in design is proposed. The work focuses firstly on the characteristics of the higher modes present at the development of peak response and then considers how these characteristics would affect the total forces in the building. The study utilizes a series of nonlinear time-history analyses of two different groups of RC frame-wall structures subject to a suite of real records. It is shown that a new modal analysis approach that incorporates transitory inelastic modal characteristics gives significantly improved predictions of peak base shear in frame-wall structures than more traditional modal analysis methods which use elastic higher-mode characteristics. The issues associated with the use of transitory inelastic modal characteristics are discussed and various challenges that would need addressing for the prediction of other response parameters and structural types are identified.     

A PROCEDURE FOR COMBINING VERTICAL AND HORIZONTAL SEISMIC ACTION EFFECTS

The vertical component of earthquake ground motion has generally been neglected in the earthquake-resistant design of structures. This is gradually changing due to the increase in near-source records obtained recently, coupled with field observations confirming the possible destructive effect of high vertical vibrations.

In this paper, simple procedures are suggested for assessing the significance of vertical ground motion, indicating when it should be included in the determination of seismic actions on buildings. Proposals are made for the calculation of elastic and inelastic vertical periods of vibration incorporating the effects of vertical and horizontal motion amplitude and the cross-coupling between the two vibration periods. Simplified analysis may then be used to evaluate realistic vertical forces by employing the vertical period of vibration with pertinent spectra without resorting to inelastic dynamic analysis.

Finally, a procedure is suggested for combining vertical and horizontal seismic action effects which accounts for the likelihood of coincidence, or otherwise, of peak response in the two directions.     

EVALUATION OF CONVENTIONAL AND ADAPTIVE PUSHOVER ANALYSIS II: COMPARATIVE RESULTS

In this paper, the methodology for evaluation of conventional and adaptive pushover analysis presented in a companion paper is applied to a set of eight different reinforced concrete buildings, covering various levels of irregularity in plan and elevation, structural ductility and directional effects. An extensive series of pushover analysis results, monitored on various levels is presented and compared to inelastic dynamic analysis under various strong motion records, using a new quantitative measure. It is concluded that advanced (adaptive) pushover analysis often gives results superior to those from conventional pushover. However, the consistency of the improvement is unreliable. It is also emphasised that global response parameter comparisons often give an incomplete and sometimes even misleading impression of the performance.     

Simulation of Shake Table Tests on Out-of-Plane Masonry Buildings. Part (I): Displacement-based Approach Using Simple Failure Mechanisms

ABSTRACT

A displacement-based (DB) assessment procedure was used to predict the results of shake table testing of two unreinforced masonry buildings, one made of clay bricks and the other of stone masonry. The simple buildings were subject to an acceleration history, with the maximum acceleration incrementally increased until a collapse mechanism formed. Using the test data, the accuracy and limitations of a displacement-based procedure to predict the maximum building displacements are studied. In particular, the displacement demand was calculated using the displacement response spectrum corresponding to the actual shake table earthquake motion that caused wall collapse (or near collapse). This approach was found to give displacements in reasonable agreement with the wall’s displacement capacity.     

Retrofit Design Methodology for Substandard R.C. Buildings with Torsional Sensitivity

Recent earthquakes have revealed the susceptibility of non-ductile reinforced concrete (R.C.) buildings with deficiencies related to stiffness and/or mass irregularities in plan and elevation. This paper proposes a design methodology for the seismic upgrading of rotationally sensitive substandard R.C. buildings. The methodology aims to first eliminate the effect of torsional coupling on modal periods and shapes and then modify the lateral response shape of the building in each direction so as to achieve an optimum distribution of interstory drift along the building height. A case study is used to illustrate practical application of the proposed methodology.