Seismic Evaluation of Tall Buildings Using a Simplified but Accurate Analysis Procedure

A simplified analysis procedure for evaluating the nonlinear seismic responses of tall reinforced concrete (RC) buildings is examined in this study. It is called the Uncoupled Modal Response History Analysis (UMRHA) procedure. It can be viewed as an extended version of the classical modal analysis procedure, where the nonlinear response of each vibration mode is first computed, and they are later on combined into the total response of the structure. The procedure requires the knowledge of the modal hysteretic behavior, which can be obtained from a cyclic modal pushover analysis. The responses of four tall buildings in Bangkok to distant large earthquakes are computed by this procedure and compared with those obtained from the Nonlinear Response History Analysis (NLRHA) procedure. These four buildings have different heights—varying from 20 to 44 stories, different configurations of floor plan, and different arrangement of RC walls. The comparison shows that the UMRHA procedure is able to accurately compute the story shears and story overturning moments, floor accelerations, and inter-story drifts of all these tall buildings. The required computational effort is also extremely low compared to that of the NLRHA procedure. Moreover, since the UMRHA procedure computes the response of each individual vibration mode, it provides more understanding and insight into the complex nonlinear seismic responses of these tall buildings.     

Seismic Analysis of Non Proportionally Damped Two-Way Asymmetric Elastic Buildings Under Bi-Directional Seismic Ground Motions

This study investigates the effectiveness of the modal analysis using three-degree-of freedom (3DOF) modal equations of motion to deal with the seismic analysis of two-way asymmetric elastic systems with supplemental damping. The 3DOF modal equations of motion possessing the non proportional damping property enable the two modal translations and one modal rotation to be non proportional in an elastic state. The simple approximation method is to use the single degree-of-freedom (SDOF) modal equations of motion, which are obtained by neglecting the off-diagonal elements of the transformed damping matrix. One, one-story and one, three-story non proportionally damped two-way asymmetric buildings under the excitation of bi-directional seismic ground motions are analyzed. The analytical results are obtained by using the proposed method, noted simple approximation method, and direct integration of the equation of motion. It is seen that the proposed method can significantly improve the accuracy of the analytical results compared with those obtained by using the simple approximation method. Moreover, the proposed method does not substantially increase the computational efforts.     

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.     

Approximate Methods for Estimating Hysteretic Energy Demand on Plan-Asymmetric Buildings

The first step in a hysteretic energy-based design approach of performance-based design is the estimation of hysteretic energy demand in the structure. A nonlinear response-history analysis of the multi-degree of freedom model gives an accurate estimation, but it is not suitable for adopting in design. Two alternative methods, based on the concepts of modal pushover analysis (MPA) and 2D-MPA, are proposed in this article for uniaxial plan-asymmetric structures. Application studies show that both methods are efficient. While the 2D-MPA-based method is more accurate, the MPA-based method is more suitable for design adoption. Significant conclusions are given for prospective application of these methods.     

A Single-Run Dynamic-Based Approach for Pushover Analysis of Structures Subjected to Near-Fault Pulse-Like Ground Motions

In this paper, a fairly effective procedure called dynamic load pattern (DLP), is proposed to account for the effects of near-fault ground motions in estimating the seismic demands of structures from pushover analyses. The seismic demands are obtained by enveloping the results of single-run conventional first-mode and single-run DLP pushover analyses. Improving the estimation of target displacement is another objective, implemented by performing response-spectrum analysis. Three special steel moment-resisting frames are considered and the seismic demands resulting from DLP are compared to those from the nonlinear time-history analysis as a benchmark solution, as well as to those predicted from modal pushover analysis.     

Seismic Assessment of the Bell Tower of Santa Maria Del Carmine: Problems and Solutions

A complete structural analysis of the bell tower of Santa Maria del Carmine in Naples (Italy) has been developed by using a 3D FE model based on the results of detailed experimental investigations in situ. Linear analysis for gravity loads, linear modal analysis, and nonlinear static analysis (Push Over) were carried out in order to assess the seismic capacity of the structure. A check of local out-of-plane failure mechanisms was also performed to verify if the structure is able to attain a global behavior. Problems and solutions related to the different methods are presented and discussed.     

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.     

Dynamic Analysis and Seismic Response of Planar Circular Arches with Variable Cross-Section

The aim of this paper is to investigate the dynamic response of planar circular arches with variable cross-section subjected to seismic ground motions. Arches have a wide range of application (e.g. bridges, roofs) thanks to their capacity to span large areas by resolving vertical actions into compressive stresses and confining tensile stresses. The full understanding of their dynamic response is a challenging technical and computational problem, especially when seismic loading is considered. For example, the assumption of axial inextensibility simplifies the differential equations but overestimates the vibration frequencies, especially those of shallow arches since axial forces are of paramount importance (as opposed to beams). In lieu of the above, our formulation incorporates the effect of axial extension, and the arches are modeled using a new generic curved beam model that includes both axial (tangential) and transverse (normal) to the arch centerline deformations, and is able to account for variable mass and stiffness properties, as well as elastic support or restraint. The resulting dynamic governing equations of the circular arch are formulated in terms of the displacements, and solved using an efficient integral equation method. Three circular arches with variable rectangular cross-section are analyzed in order to investigate their dynamic properties and seismic performance. Using both time history and modal analysis useful conclusions are drawn with regard to the contribution of each mode on the calculation of different response quantities.     

CORRESPONDENCE AND DISCRIMINANT ANALYSES OF SAND AND SAND TEMPER COMPOSITIONS,TONTO BASIN,ARIZONA*

Geologists use petrographic modal analysis to relate fluvial sand composition to source rock composition, thus establishing provenance. Archaeologists seeking to establish provenance of sand temper in pottery can use similar petrographic methods, but their finer scale of investigation requires more precise statistical tools than those employed by geologists. A quantitative method for performing that task is presented. It utilizes correspondence analysis and discriminant analysis of logratio transformed point‐count data to define petrofacies, or sand temper resource procurement zones. The procedure is illustrated with sand and sand‐tempered sherd samples collected from the Tonto Basin, central Arizona; temporal trends in utilitarian ceramic production c. AD 100–1350 are reviewed.     

Floor Response Spectra for Bare and Infilled Reinforced Concrete Frames

The objective of this article is to study the effects of structural nonlinear behavior on Floor Response Spectra (FRS) of existing reinforced concrete frames. This study examines how the FRS vary with the level of post-elastic behavior in buildings of different number of stories and masonry infill wall configurations. The effect of damping modeling assumptions is also investigated. Differences and similarities with findings from the literature are discussed. On the basis of the obtained results, a commentary on the adequacy of basic assumptions used in predictive equations proposed by different seismic codes is offered.     

COMPLEX MODE SUPERPOSITION ALGORITHM FOR SEISMIC RESPONSES OF NON-CLASSICALLY DAMPED LINEAR MDOF SYSTEM

This paper deals with a complex mode superposition method for the seismic responses of general multiple degrees of freedom (MDOF) discrete system with complex eigenvectors and eigenvalues. A delicate general solution, completely in real value form, for calculat-ing seismic time history response of the MDOF system which cannot be uncoupled by normal modes, is deduced based on the algorithms of the complex superposition method. This solution comprises of two parts which are in relation to the Duhamel integration to sine and cosine function respectively. The related term of the Duhamel integration to sine function is actually the displacement response of the oscillator with corresponding modal frequency and the damping ratio. The other can be transferred into a combina-tion of the displacement and velocity responses of the same oscillator. In order to meet the practical needs of seismic design based on code design spectra for various kinds of structures equipped by viscous dampers, the complex complete quadratic combination (CCQC) method is deduced following similar procedures such as the well-known CQC method, in which a new modal velocity correlation coefficient, together with a new modal displacement-velocity correlation coefficient are involved besides the modal displacement correlation coefficient in normal CQC formula. The new algorithm of CCQC is not only as concise as that of the normal CQC but also has explicit physical meaning. The results obtained from complex mode superposition approaches are discussed and verified in some examples through step by step integration computation under a prescribed earth-quake motion input. From these examplary analyses, it may be pointed that the CCQC algorithm normally yields conservative outcome and that the forced mode uncoupling approach has good approximation even the discussed examplary structures are strongly non-proportional.     

Seismic Vulnerability Analysis of RC Bridges Based on Kriging Model

This paper presents a Kriging model-based method for seismic vulnerability analysis of reinforced concrete (RC) bridges. It aims at reducing the computational effect when the Monte Carlo technique is used for establishing the structural vulnerability curves. The general procedure of the proposed method is put forward firstly. In the procedure, the uncertainties existing in the structures and ground motions are both taken into account, and the uniform design (UD) technique is adopted for generating the random samples. The reliability of the proposed method is demonstrated by the vulnerability analysis of an single degree of freedom (SDOF) system using the Latin hypercube simulation (LHS) method. Vulnerability analysis of an RC bridge system is then carried out using the proposed method. The vulnerability curves of the bridge obtained by the Kriging model-based method are compared with those obtained by the LHS method. Additionally, three simulation schemes adopting different UD tables are employed to investigate the convergence and stability of the proposed method. The results show that the proposed method used for the seismic vulnerability analysis of RC bridges can reduce the computational effort and time to a large extent without much compromise on the accuracy.     

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.     

Controlled Rocking CLT Walls for Buildings in Regions of Moderate Seismicity: Design Procedure and Numerical Collapse Assessment

Controlled rocking heavy timber walls are designed to rock on their foundations in response to earthquakes. For regions of moderate seismicity, it is proposed that this rocking behaviour can be adequately controlled using only post-tensioning, even with a large force-reduction factor and no supplemental energy dissipation. This article presents a force-based design procedure for controlled rocking cross-laminated timber walls without supplemental energy dissipation, including a method for estimating higher mode effects. Fragility analyses of three prototype walls demonstrate that the procedure can limit the probability of collapse to <10% during a maximum considered earthquake in a region of moderate seismicity.     

Completeness Verification of Complex Response Spectrum Method for Underdamped and Overdamped Multiple-Support Systems Regarding the Decoupled Damping as Mathematical Parameter without Physical Meaning

The completeness of the complex response spectrum method for both formally underdamped and overdamped modes is theoretically proved, and the physical meanings of the decoupled modes as well as involved parameters are recognized and clarified in this paper. For the system with relatively large non-classical damping, the eigenvalue pairs generated by the complex mode decomposition method are real and the so-called modal damping ratios are larger than unity. In this paper, we firstly clarified that the decoupled modes are virtual and the so-called modal frequency and damping ratio are mathematical parameters that have no physical meaning. Then, the completeness of the complex response spectrum method for both formally underdamped and overdamped modes is rigorously proved by allowing the “damping frequency” to be an imaginary number. For the virtually overdamped modes, Duhamel integral involved in the calculation for formally underdamped modes automatically convert to hyperbolic Duhamel integral. A numerical example taken from the published literature is given to verify this method. Structural responses for the system with coupled damping under multi-support seismic excitations are further analyzed and numerical results indicate the accuracy of complex response spectrum method.     

An Automatic Modal Identification Procedure for the Permanent Dynamic Monitoring of the Sanctuary of Vicoforte

ABSTRACT

The interest in automatic modal parameter extraction techniques has increased significantly in recent years because of the rising demand for Continuous Structural Health Monitoring (CSHM) of civil structures and infrastructures. The wider use of CSHM is related to its capability for early damage detection and therefore to its usefulness for planning maintenance and strengthening interventions. This article presents the main steps followed in creating a robust routine to run on an online basis the first-ever Continuous Vibration-Based Structural Health Monitoring (CVB-SHM) of a large masonry oval dome, i.e., the dome of the Regina Montis Regalis Basilica, also known as Sanctuary of Vicoforte. The procedure uses an output-only stochastic subspace identification method complemented by an automatic analysis applied to identification results, which are typically provided in terms of stabilization diagrams. In this study, the fully automatic procedure also includes a hierarchical clustering algorithm to separate authentic from spurious modes.     

The Baseline Stiffness Method for Damage Detection in Buildings Without Baseline Modal Parameters

A new method called the Baseline Stiffness Method (BSM), used to locate and quantify damage in buildings without baseline modal parameters (undamaged state), is presented. In order to determine this reference state, the BSM uses modal parameters from the damaged state of the building and the lateral stiffness matrix of the first story without damage. Afterwards, by means of an iterative process using singular value decomposition, location and severity of damage are obtained by comparing information about the damaged and non damaged states. Numerical and experimental examples are presented and discussed showing the advantages of the application of the proposed BSM.     

Considering Soil-Nonlinearity Effect on Seismic Performance Evaluation of Structures based on Pushover Analysis

According to the most of current seismic codes, nonlinear soil behavior is commonly ignored in seismic evaluation procedure of the structures. To contribute on this matter, a pushover analysis method incorporating the probabilistic seismic hazard analysis (PSHA) is proposed to evaluate the effect of nonlinear soil response on seismic performance of a structure. The PSHA outcomes considering soil nonlinearity effect is involved in the analysis procedures by modifying the site-specific response spectrum. Results showed that incorporation of nonlinear soil behavior leads to an increase in displacement demand of structures which should accurately be considered in seismic design/assessment procedure. Results of implemented procedure are confirmed with the estimated displacement demand including soil-structure interaction (SSI).     

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.     

Seismic Reliability Assessment of a High-Voltage Disconnect Switch Using an Effective Fragility Analysis

This article deals with evaluation of the seismic vulnerability of a high-voltage vertical disconnect switch, one of the most vulnerable elements of electric substations. The main objective of the research is to evaluate the seismic fragility of the apparatus using a new effective method. By combining standard reliability methods for time-invariant problems with the response surface technique, this original procedure called “EFA” (Effective Fragility Analysis) permits the evaluation of fragility curves using a very limited number of numerical simulations. On the basis of experimental tests, to determine the mechanical characteristics of the disconnect switch components (ceramic, joints, etc.) the fragility curves of the equipment analyzed are carried out. The results are discussed and compared with the results of Monte Carlo simulations, which confirm the reliability of the procedure.