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.     

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.     

Comparison of Numerical and Experimental Seismic Responses of FREI-Supported Un-reinforced Brick Masonry Model Building

Comparative study of numerically and experimentally obtained seismic responses of un-reinforced masonry building supported on in-house designed un-bonded fibre reinforced elastomeric isolator (U-FREI) are presented in this article. The effectiveness of U-FREI is established very clearly in terms of controlled dynamic response of the model building. Experimental studies are carried out on a shake table with elaborate instrumentations for measurement of acceleration and displacements at different floor levels. Numerical study of the model building supported on U-FREI is carried out to compare the results with experimental investigation. Multi-linear pivot hysteretic plasticity model is used to simulate the behavior of FREI, while plate elements are used for brick-masonry walls. Experimentally obtained force-displacement curves of FREI are used for defining the properties of multi-linear model representing FREI. The dynamic responses obtained from the numerical studies are compared with those from experimental investigations. This study indicates that the seismic responses of building supported on U-FREI can be numerically evaluated with quite reasonable accuracy. A good numerical model can be judiciously used at the preliminary design stage, followed by actual testing and construction of the base isolated building.     

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 tests on a stone masonry building: modeling and identification of dynamic properties including soil-foundation-structure interaction

This article presents the identification of dynamic properties of a stone masonry building, followed by numerical simulation of its dynamic response accounting for soil-foundation-structure interaction. The first part regards numerical simulations of the earthquake response of a two-story building prototype with timber floors, made of three-leaf stone masonry without laces. This 1:2 scale prototype was tested on a shaking table in its as-built state and after strengthening, at the National Technical University of Athens. Afterward, the building prototype was modeled with flat shell elements and equivalent frames (common frames and macro-elements), for an investigation of its linear and nonlinear seismic response, assuming base fixity. Numerical results were compared to the experimental ones, which yielded conclusions on the considerations of each employed modeling strategy, as well as its efficiency and applicability. The second part considers the effect of soil-structure interaction using appropriately modified foundation stiffness values to account for the foundation soil flexibility. Comparison of the numerical results with and without SSI effects showed how the flexibility of the soil-foundation system and the soil-structure interaction modified the system’s modal characteristics and response within the elastic range, in terms of both seismic loads and deformations, and produced conclusions about its consequences on the overall structural stability.     

TORSIONAL EFFECTS IN THE PUSHOVER-BASED SEISMIC ANALYSIS OF BUILDINGS

The general trends of the inelastic behaviour of plan-asymmetric structures have been studied. Systems with structural elements in both orthogonal directions and bi-axial eccentricity were subjected to bi-directional excitation. Test examples include idealised single-storey and multi-storey models, and a three-storey building, for which test results are available. The response in terms of displacements was determined by nonlinear dynamic analyses. The main findings, limited to fairly regular and simple investigated buildings, are: (a) The amplification of displacements determined by elastic dynamic analysis can be used as a rough, and in the majority of cases conservative estimate in the inelastic range, (b) Any favourable torsional effect on the stiff side, which may arise from elastic analysis, may disappear in the inelastic range. These findings can be utilised in the approximate pushover-based seismic analysis of asymmetric buildings, e.g. in the N2 method. It is proposed that the results obtained by pushover analysis of a 3D structural model be combined with the results of a linear dynamic (spectral) analysis. The former results control the target displacements and the distribution of deformations along the height of the building, whereas the latter results define the torsional amplifications. The proposed approach is partly illustrated and evaluated by test examples.     

SLIDING MODE CONTROL OF BUILDING FRAMES UNDER RANDOM GROUND MOTION

A sliding mode control theory is presented to control the response of building frames to predominant frequency components of the random ground motions. The control algorithm is derived based on a sliding surface which is a function of a state vector containing the structural displacements and velocities and variables that dictate the predominant frequency components of the excitation. Three control mechanisms are employed to control the response of the building frame namely, (1) active mass damper (AMD) placed at the top storey of the building, (2) an actuator placed at a storey level and, (3) an actuator placed at a storey level along with a tuned mass damper (TMD) situated at the top storey level. Responses obtained by the proposed control strategy are compared with those obtained by the linear feedback and feedforward-feedback control strategies (conventional control strategies). Also, they are compared with those obtained by the sliding mode control strategy that considers in its state vector only structural displacements and velocities. It is shown that the proposed control strategy generally performs better than other control strategies in the higher range of control forces. For the lower range of control forces, conventional control strategies are more effective.     

Experimental Study of Large Area Suspended Ceilings

Damage of nonstructural components during past seismic events was shown to be not only a critical threat to life safety in extreme cases but also led to substantial reduction of functionality of buildings and other facilities. Because of the complex construction of nonstructural and architectural components, current standards provide only limited guidance for the seismic design. Suspended ceiling systems are among the less understood important nonstructural/architectural components in buildings for which design standards provide limited guidance. To understand the dynamic behavior of suspended ceiling systems, a series of full scale shake table tests of 20 ft × 53 ft and 20 ft × 20 ft ceiling systems were conducted at the Structural Engineering and Earthquake Simulation laboratory (SEESL) at University at Buffalo (UB). For the full scale dynamic testing, a new test frame providing a continuous suspended ceiling area of 1,060 ft² was constructed on the tandem shake tables and was equipped with an open-loop shake table compensation procedure. The combined designs of the physical frame and of the shake table motion controllers allowed simulating the required floor/roof motion according to ICC-ES AC156 standard at the roof of the test structure. Various test configurations were selected in order to determine the influence of different system conditions and the effects or efficiency of various protective systems required by the current standard ASTM E580 for seismic design. Based on the test data and the failure mechanisms observed, damage states are defined, and fragility curves are developed. The results of the fragility analysis show that a ceiling system becomes more vulnerable as (a) it is subjected to multi-directional input motions, (b) heavier tiles are installed, (c) the size of a ceiling area increases, and (d) lateral restraints are not installed. In addition, simplified numerical models that can capture the special behavior of ceiling systems are developed and presented in a companion paper. This paper presents the experimental study of large area suspended ceiling systems involving test setup and configurations, test motions generated by a unique control system, and basic lessons gained from the experiments.     

PROCEDURE AND SPECTRA FOR ANALYSIS OF RC STRUCTURES SUBJECTED TO STRONG VERTICAL EARTHQUAKE LOADS

Abstract

In view of the compendium of field evidence and supporting analysis work indicating the possible damaging effects of vertical earthquake ground motion, this paper addresses the problem of code-type vertical force calculation. In light of recent engineering seismology studies of the relationship between vertical and horizontal peak ground acceleration, the inadequacy of the 2/3-rule depicted by codes is highlighted. A simple piece-wise linear relationship is proposed and shown to represent existing strong-motion measurements adequately. Bilinear and inelastic spectra are derived and studied. It is demonstrated that net tensile forces and displacements may ensue, thus eroding the shear resistance of RC columns. A simple procedure is outlined whereby modal analysis may be employed to estimate conservatively vertical earthquake forces on buildings. Finally, areas of further exploration and refinement are identified.     

ANALYTICAL MODELLING OF THE SEISMIC BEHAVIOUR OF PRECAST CONCRETE FRAMES DESIGNED WITH DUCTILE CONNECTIONS

Pure precast beam-column systems incorporate unbonded reinforced at the critical sections, causing strain incompatibility between steel and concrete. As a result, classical section analysis method, well know for characterising monolithic concrete members, cannot be directly applicable to these systems. This paper provides a section analysis method suitable for precast members, incorporating, through an analogy with equivalent cast-in-place solution named “monolithic beam analogy”, an additional condition on the member global displacement. The proposed method was first validated with the experimental data from tests on beam-column Hybrid subassemblages. Using appropriate hysteresis rules and the response envelopes defined by the section analysis method, a prediction of the behaviour of the PRESSS test building was carried out. Satisfactory agreements obtained between the analytical and experimental results confirm the validity of the suggested methodology. Derivation of the method and experimental validation are herein presented.     

Results of a 60-Year Monitoring System for Santa Maria del Fiore Dome in Florence

This study aims to present the results of the historical and statistical analysis carried out on the monitoring systems that control one of the most studied domes in the world: Santa Maria del Fiore in Florence, Italy. An accurate analysis of the dome crack widths and of its global displacements (horizontal and vertical), both considering the historical data and more recent data, has allowed detection of the static movements developed in the monument over time as well as in context of their relationship to environmental and seismic phenomena. Thanks to the large amount of measured data (from 1955 to 2010), some previous conclusions on the dome damage trend are updated herein. Moreover, in light of the experimental results, some issues on the dome stability—as the principal hypotheses advanced during centuries about the main cause of Brunelleschi’s dome crack pattern—are reconsidered, including the horizontal thrusts due to the dome’s self-weight characterized by Viviani in 1695 and Chiarugi in 1985, the differential settlement of pillars detailed by Cecchini in 1698, Ximenes in 1757 and Borga in 1975 and the influence of temperature variations investigated by Nervi in 1934. The final aim of this study is to show the great utility of modern and historical monitoring in setting up a reliable forecasting model of the monument.     

Inelastic Displacement Response of RC Systems with Cyclic Deterioration—An Energy Approach

Inelastic displacements of reinforced concrete systems are investigated by employing an energy-based approach. A hysteresis model is developed that accounts for stiffness degradation, strength deterioration and pinching. The model is calibrated by using experimental data from literature. Inelastic displacement ratios are calculated under a specific set of ground motion records with long effective durations. The results reveal the importance of deteriorating behavior under long duration excitations, especially for short and medium period structures. The last part of the study is devoted to the introduction of a simple empirical relationship for estimating the inelastic displacement demands of degrading RC structural systems.     

Seismic Performance and Modeling of a Half-Scale Base-Isolated Wood Frame Building

The concept of base isolation is a century old, but application to civil engineering structures has only occurred over the last several decades. Application to light-frame wood buildings in North America has been virtually non existent with one notable exception. This article quantitatively examines issues associated with application of base isolation in light-frame wood building systems including: (1) constructability issues related to ensuring sufficient in-plane floor diaphragm stiffness to transfer shear from the superstructure to the isolation system; (2) evaluation of experimental seismic performance of a half-scale base-isolated light-frame wood building; and (3) development of a displacement–based seismic design method and numerical model and their comparison with experimental results. The results of the study demonstrate that friction pendulum system (FPS) bearings offer a technically viable passive seismic protection system for light-frame wood buildings in high seismic zones. Specifically, the amount and method of stiffening the floor diaphragm is not unreasonable, given that the inter-story drift and accelerations at the upper level of the tested building were very low, thus resulting in the expectation of virtually no structural, non structural, or contents damage in low-rise wood frame buildings. The nonlinear dynamic model was able to replicate both the isolation layer and superstructure movement with good accuracy. The displacement-based design method was proven to be a viable tool to estimate the inter-story drift of the superstructure. These tools further underscore the potential of applying base isolation systems for application to North America's largest building type.     

Distributed Tuned Mass Dampers for Multi-Mode Control of Benchmark Building under Seismic Excitations

The effectiveness of the multi-mode control of seismically excited building installed with distributed multiple tuned mass dampers (d-MTMDs) is investigated by comparing dynamic response with the other controllers, such as passive friction dampers, semi-active dampers, single tuned mass damper (STMD), and multiple tuned mass dampers (MTMDs-all.top), both installed at the top of the building, and arbitrarily distributed MTMDs (ad-MTMDs). It is concluded that the d-MTMDs exhibit improved performance as compared with the STMD, MTMDs-all.top, and ad-MTMDs. The d-MTMDs are also convenient to install owing to the reduced space requirements, being placed at various floors.     

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.     

CODE PROVISIONS AND ANALYTICAL MODELLING FOR THE IN-PLANE FLEXIBILITY OF FLOOR DIAPHRAGMS IN BUILDING STRUCTURES

In this paper a review of the provisions of some modern seismic codes for the analytical modelling of the floor diaphragm action is made and a methodology using simplified 2-D finite elements models for monolithic floors is suggested, taking into consideration the in-plane flexibility of them. The simplified models use the coarsest discretisation mesh possible, simply taking into account all the connection points of the vertical structural elements on the diaphragm of each storey. The efficiency of the proposed simplified F.E. models is tested with comparative response-spectrum dynamic analyses of various building structures with different plan shapes, according to EuroCode 8 [EC8, 1994]. The simplified models provided excellent results for the dynamic characteristics of the entire building and the stress state of the framing substructure and a fair estimation for the in-plane stresses of the floor diaphragms.     

FRAGILITY ASSESSMENT OF SLAB-COLUMN CONNECTIONS IN EXISTING NON-DUCTILE REINFORCED CONCRETE BUILDINGS

Fragility functions that estimate the probability of exceeding different levels of damage in slab-column connections of existing non-ductile reinforced concrete buildings subjected to earthquakes are presented. The proposed fragility functions are based on experimental data from 16 investigations conducted in the last 36 years that include a total of 82 specimens. Fragility functions corresponding to four damage states are presented as functions of the level of peak interstory drift imposed on the connection. For damage states involving punching shear failure and loss of vertical carrying capacity, the fragility functions are also a function of the vertical shear in the connection produced by gravity loads normalised by the nominal vertical shear strength in the absence of unbalanced moments. Two sources of uncertainty in the estimation of damage as a function of lateral deformation are studied and discussed. The first is the specimen-to-specimen variability of the drifts associated with a damage state, and the second the epistemic uncertainty arising from using small samples of experimental data and from interpreting the experimental results. For a given peak interstorey drift ratio, the proposed fragility curves permit the estimation of the probability of experiencing different levels of damage in slab-column connections.     

Analytical Collapse Study of Lightly Confined Reinforced Concrete Frames Subjected to Northridge Earthquake Ground Motions

Review of older non seismically detailed reinforced concrete building collapses shows that most collapses are triggered by failures in columns, beam-column joints, and slab-column connections. Using data from laboratory studies, failure models have previously been developed to estimate loading conditions that correspond to failure of column components. These failure models have been incorporated in nonlinear dynamic analysis software, enabling complete dynamic simulations of building response including component failure and the progression of collapse. A reinforced concrete frame analytical model incorporating column shear and axial failure elements was subjected to a suite of near-fault ground motions recorded during the 1994 Northridge earthquake. The results of this study show sensitivity of the frame response to ground motions recorded from the same earthquake, at sites of close proximity, and with similar soil conditions. This suggests that the variability of ground motion from site to site (so-called intra-event variability) plays an important role in determining which buildings will collapse in a given earthquake.     

Discrete Element Modeling of Groin Vault Displacement Capacity

Displacements experienced by many historic masonry structures concentrate at masonry joints and can be large before collapse is a concern, making modeling of stability using discrete element modeling (DEM) particularly suitable. In this study, masonry groin vault and arch models with several geometries were subjected to horizontal and vertical support displacements using DEM. Support movements were applied in a quasi-static manner to simulate the support settlement process. Displacements at collapse and at the point when the first block fell from the vault were recorded. Block separation and mechanisms were also noted during the simulations. A two-dimensional (2D) analytical model using thrust line analysis was developed to help evaluate the DEM results. In general, the displacements at first block fall were relatively large but significantly less than those at collapse. The groin vaults and arches exhibited significantly higher capacity to sustain vertical support displacement compared to horizontal displacements. For many geometries, the DEM collapse displacements of the groin vaults compared reasonably well to similar arches, indicating that the displacement capacity of groin vaults can be reasonably estimated using 2D simplifications. However, for certain geometries, three-dimensional effects were found to significantly affect displacement capacity.     

Notes on Some Examples of Church Architecture in Cornwall

A survey of the George Inn, with some references to the medieval cloth and wool trade, and an interpretation of the architectural evidence to show the various stages of building, the existing structure being of the late fourteenth century overlaid with many subsequent alterations. The upper floors were given their present jettied front c. 1500 when the building was extensively remodelled. The George was used both as an Inn and for storing and selling cloth at two important annual fairs held by the owners of the manor, the Carthusian Priory of Hinton Charterhouse. The George Inn stands on the south side of the former market place (called the Plain) in the centre of Norton St Philip, a small stone-built market town a few miles north-east of the Mendip Hills (ST 775 560). Norton lies on the route from Salisbury to Bristol and owes its former prosperity to the wool and cloth trade. The George itself is by far the largest secular building in the town and stands three storeys high, head and shoulders above its neighbours, at the cross-roads.