Capacity Spectrum Method Research Articles

Seismic Assessment of R C C Frame Building using Pushover Analysis

India is a making country with an arrangement of structure practices and social and money related structure, which needs to build up its own special strategies for seismic danger appraisal. The latest decade has shown our lack in peril decline programs, during the couple of hurting seismic quakes. In view of this quake alone in India there was massive loss of life and property. After this troublesome adversity thought is by and by being given to the appraisal of the adequacy of solidarity in structures to contradict strong ground developments. After Bhuj seismic quake IS-1893 was revised and appropriated in the year 2002, going before this scene it was refreshed in 1984. The code was first conveyed in 1962 as ‘Recommendations for Earthquake Resistant Design of Structure’. The central reason behind the loss of life and property was inadequacy of learning of direct of structures during ground developments. The frailty of the structures against seismic development must be fundamentally inspected. The most preferred strategy for seismic evaluation is Inelastic static assessment or Pushover examination in view of its straightforwardness. Inelastic static examination frameworks join Capacity Spectrum Method, Displacement Coefficient Method and the Secant Method. In this examination we are looking over seismic execution of G+17 standard RCC structure. The structure has been surveyed using Pushover Analysis.

Comparison of traditional vs low-damage structural and non-structural building systems through a cost/performance-based evaluation

Innovative damage-mitigation technologies have been recently developed to improve the seismic performance of structural and non-structural elements. The combination of these solutions can lead to a high-performance and cost-efficient building system, capable of sustaining earthquakes with limited damage and reduced socio-economic losses. This article investigates the convenience of implementing damage-control solutions through a cost/performance-based evaluation of multi-story-reinforced concrete buildings, comprising alternative combinations of traditional vs low-damage technologies for both structural skeletons (frames, walls) and non-structural elements (heavy/light facades, heavy/light partitions, suspended ceilings). The significant benefits of the innovative systems are investigated through loss assessment studies, implemented using a practical approach based on numerical pushover analyses and the capacity spectrum method. The parametric analyses confirm that the integrated low-damage structural/non-structural system can lead to significant savings, in these specific cases, in the range of 150–300 €/m2 during the 50-year building-life and downtime reductions at ultimate limit state in the order of 2–7 months.

Evaluasi Perbandingan Kinerja Bangunan Momen Frame dengan Eccentrycally Brace Frame

Generally, earthquake resistant design is based on elastic structural analysis with load factor to simulate ultimate condition. Actually, behavior of collapse structures during earthquake is in-elastic. Evaluation to predict in-elastic condition of structures during earthquake is needed in order to guarantee that it can perform well during earthquake. Analysis and performance evaluation can be done with pushover analysis given in SAP2000, while evaluation of performance point must be determined manually with various methods (except for capacity spectrum method). Pushover analysis is a non linear static analysis as a behavior of structural failure due to earthquake, while performance point is structural maximum displacement during design earthquake.
 Study on steel frame 3D concludes that performance evaluation for pushover in longitudinal direction according to ATC-40 gives displacement target for moment frame building of 0.054 m, building with eccentrically braced frame (EBF): 0.022 m. Pushover in transverse direction according to ATC-40 gives displacement target for moment frame building of 0.022 m, building with EBF: 0.015 m. According to FEMA 356, displacement target in longitudinal direction for moment frame building: 0.0803 m, building with (EBF): 0.0728 m. For building with moment frame in transverse direction: 0.1183 m, building with (EBF): 0.0614 m.

A New Method for Drawing the Capacity Spectrum for Seismic Analysis and Structural Rehabilitation

A review of previous studies shows that there are two general views on how to determine demand in structures through incremental nonlinear static analysis. In the first view, multi-modal methods are used to determine demand in structures. In this view, the applied load pattern is applied to the structure according to the shape of each vibration mode, assuming that the structure deformation follows the shape of the vibration mode, the capacity spectrum is drawn and after determining the target displacement and the corresponding demand for each vibration mode, the final demand is determined by combination of response modes. In the second view, structural analysis is performed as a single run nonlinear static analysis and the effect of different vibration modes is shown in one load pattern. In this method, the load pattern that has somehow the effect of different modes is applied to the structure and the structure is analyzed under this load pattern. In the second view, due to the non-conformity of the structure deformation and the lateral load of a particular vibration mode of the structure, the conventional capacity spectrum method cannot be used. Therefore, the purpose of this paper is to propose a method for drawing the capacity spectrum and determining the target displacement in single run nonlinear static analysis for non-adaptive load patterns. After presenting the equations, three frames including 3-storey, 9-storey and 20-storey frames have been selected and the results of the proposed method have been evaluated along with modal pushover method and time history analysis for the frames. Comparison of the results of the proposed method and the modal pushover with the results of the nonlinear time history analysis shows that the proposed method is more efficient in determining the lateral displacement of the stories and roof than the conventional modal pushover method.

Seismic retrofit of structures using rotational friction dampers with restoring force

In this study, the seismic performance of a rotational friction damper with restoring force is presented. The torsional spring friction damper consists of rotational friction pads with the heavy duty torsional springs attached on both sides of the friction damper. An analytical model and a design procedure for the damper are developed using capacity spectrum method. A parametric study is carried out to investigate the influence of the torsional spring in the response of the structure when subjected to ground motions. The seismic performances of steel structures retrofitted with the torsional spring friction damper and conventional rotational friction dampers are evaluated using fragility analysis, which shows that the structure retrofitted with the torsional spring friction damper has the smallest probability of reaching the specific limit states.

A Proposal of Seismic Index for Existing Buildings in Indonesia using Pushover Analysis

Indonesia has often suffered major earthquake damage over the past 50 years. There are thousands of buildings in earthquake-prone regions that still need seismic evaluation and rehabilitation. One method of evaluating the seismic performance of an existing building is by assessing it using the Japanese seismic index for structures. A basic seismic index can be calculated based on the strength and ductility criteria. The strength and ductility performance of a structure can be obtained by pushing a building until it reaches its maximum deformation capacity. This paper describes a proposal to obtain a basic seismic index using pushover analysis. Its adjustment to determine a seismic demand index by considering seismic hazard in Indonesia was carried out using the capacity spectrum method. Two existing buildings in Indonesia were evaluated. The evaluation result indicated that both buildings were in safe condition. The proposal of the seismic index method can be useful in determining the performance index of existing structures. The ductility index can also be used to estimate the response modification factor of a structure.

SIMPLIFIED ANALYSIS OF BUILDING SEISMIC STABILITY USING PRINCIPLES OF SPECTRUM CAPACITY METHOD

According to the current DBN, it is possible to apply the nonlinear static analysis based on the load-bearing capacity spectrum method. This analysis is allocated by essential simplicity in comparison with the direct dynamic method and also possibility of application as its alternative, considering necessity of application of a direct dynamic method also for buildings (constructions) of the responsibility class SS2. At the same time the complete nonlinear static analysis is also enough complex and sensitive to possible errors in modelling, after all it needs creation of nonlinear model of entire building. Aggregate points of analysis on seismic influences by the spectral method and the nonlinear static analysis (on the basis of the method of bearing capacity spectrum) according to the current DBN allow to execute the last (nonlinear static analysis) with proved simplifications regarding creation of spectrum load-bearing capacity diagram for constructive system on the basis of results conditionally linear spectral analysis.

Seismic performance evaluation of RC frames with uniform infilled walls based on adaptive CMS

In the development of performance-based seismic engineering, the capacity spectrum method (CMS) has been widely used in seismic performance evaluation because of its merits of clarity in concept and simplicity in computation. The lateral force resistance of nonstructural components and the influence of bidirectional loading are usually neglected in current seismic performance evaluation. Three archetype reinforced concrete (RC) frames were designed according to current Chinese standards and three-dimensional finite element models accounting for infilled walls or not at different modeling fidelity levels were created. Influences of infilled walls and bidirectional loading on seismic performance of RC frames are studied by CMS based on adaptive Pushover analysis. Results show that uniform infilled walls significantly improve seismic performance of RC frames. The bearing capacity under bidirectional loading is less than that under unidirectional loading. And bidirectional loading makes influences of infilled walls become somewhat inefficient.

Development of Fragility Curves for Single-Column RC Italian Bridges Using Nonlinear Static Analysis

ABSTRACT The main objective of this study is to assess the accuracy and suitability of Nonlinear Static Procedures (NSPs) in the development of analytical damage fragility curves for seismic risk assessment of large portfolios of Reinforced Concrete (RC) bridges. Seven NSP approaches, from widely used single-mode conventional pushover-based approaches to the more rigorous multi-mode conventional or adaptive pushover-based procedures are implemented. By systematically comparing fragility curve estimations in terms of shape and accuracy in predicting mean annual rates of exceeding predefined damage limit states, results indicate that when bridges can be classified as higher mode sensitive, multi-mode-based approaches offer a powerful alternative to rigorous time history analysis. In particular, Generalized Pushover Analysis and Adaptive Capacity Spectrum methods offer a better performance with respect to other multi-mode alternatives. For first mode dominated bridges, with a classical first mode shape, the performance of all methods is similar. Single-mode based procedures present an acceptable alternative only in such particular cases, for which the N2 method represents a viable approach when compared to other single-mode or multi-mode procedures.

Direct Displacement Based Design and Capacity Spectrum Method for Special Moment Resisting Frame

In designing seismic-resistant buildings, it is commonly used Forced-Based Design method. The concept of the Force-Based Design (FBD) method is based on an elastic analysis of the structure and indirectly shows the performance level of the structure towards the effects of the seismic forces. Therefore, it is required an approach that capable of analyzing and evaluating the performance of the inelastic structural response; it is called Performance-Based Design method. This paper uses two methods of Performance-Based Design, there are Direct Displacement-Based Design and Capacity Spectrum Method, by using pushover analysis. The objectives of the research are to analyze and compare the performance level of the building in inelastic condition by using these two methods. The structural model reinforced concrete special moment frames. Seismic design code that used in this study is SNI 1726:2012. The reviewed parameter values are displacement and story drift values, estimated plastic hinge response, and performance level of the building from two methods. As the results, all the parameter values of DDBD analysis are more significant than CSM. DDBD produces the drift and displacement values of 0.668 m with the rebar ratio is more significant than 1.00. While, the CSM produces the drift and displacement values of 0.501 m with the rebar ratio of 1.00. The failure mechanism of both methods indicates the strong column weak beam where the beams should fail before the columns. The structure performance level which refers to ATC-40 indicate that both DDBD method and CSM method are in Damage Control level despite displacement target of the two methods are different which is DDBD produces displacement target of 0.376 m while CSM produces the value of 0.345 m.

Seismic retrofit of gravity load designed RC buildings using external steel concentric bracing systems

This paper discusses the seismic vulnerability of Reinforced Concrete (RC) buildings designed to gravity loads only, which are representative of the Italian building stock mainly erected between ‘70s and ‘80s, and investigates the use of external steel concentric bracing systems to upgrade their seismic performance. A case study building has been selected and designed according to the codes and the current practice in force at the time of construction. The seismic performance has been evaluated through the so-called N2 method in the format of the Capacity Spectrum Method applied to three different models of the building, namely bare frame, full infilled frame and pilotis frame, to highlight the role of the infill walls arrangement. The three models have been retrofitted with the external bracing systems designed with an adopted rational methodology. The external arrangement of the bracing systems has been chosen in order to both minimize the impact on the existing building and avoid the local interaction between the RC structural elements and the steel bracings, as well as the additional loads on the existing foundations. The results have shown the strong role of the infills in the structural behaviour of the existing building and the efficiency of the external steel bracing systems as retrofitting technique of existing RC buildings.

Seismic Risk Assessment Using Stochastic Nonlinear Models

The basic input when seismic risk is estimated in urban environments is the expected physical damage level of buildings. The vulnerability index and capacity spectrum-based methods are the tools that have been used most to estimate the probability of occurrence of this important variable. Although both methods provide adequate estimates, they involve simplifications that are no longer necessary, given the current capacity of computers. In this study, an advanced method is developed that avoids many of these simplifications. The method starts from current state-of-the-art approaches, but it incorporates non-linear dynamic analysis and a probabilistic focus. Thus, the method considers not only the nonlinear dynamic response of the structures, modeled as multi degree of freedom systems (MDoF), but also uncertainties related to the loads, the geometry of the buildings, the mechanical properties of the materials and the seismic action. Once the method has been developed, the buildings are subjected to earthquake records that are selected and scaled according to the seismic hazard of the site and considering the probabilistic nature of the seismic actions. The practical applications of the method are illustrated with a case study: framed reinforced concrete buildings that are typical of an important district, the Eixample, in Barcelona (Spain). The building typology and the district were chosen because the seismic risk in Barcelona has been thoroughly studied, so detailed information about buildings’ features, seismic hazard and expected risk is available. Hence, the current results can be compared with those obtained using simpler, less sophisticated methods. The main aspects of the method are presented and discussed first. Then, the case study is described and the results obtained with the capacity spectrum method are compared with the results using the approach presented here. The results at hand show reasonably good agreement with previous seismic damage and risk scenarios in Barcelona, but the new method provides richer, more detailed, more reliable information. This is particularly useful for seismic risk reduction, prevention and management, to move towards more resilient, sustainable cities.

Dissipation in sheathing-to-framing connections of light-frame timber shear walls under seismic loads

The present study is concerned with the seismic analysis and design of light-frame timber shear walls, with focus on the energy dissipation ensured by sheathing-to-framing connections under in-plane lateral loads. In this perspective, a suitable parametric finite element model for light-frame timber shear walls is first developed using the software OpenSees. By means of such model, the equivalent viscous damping of the wall is assessed numerically, together with the damping factor adopted within the capacity spectrum method. Furthermore, the optimal layouts of slender (1.2 m × 2.4 m/3.94 ft × 7.88 ft) and squat (2.4 m × 2.4 m/7.88 ft × 7.88 ft) light-frame timber shear walls are found by solving a multi-objective optimization problem in which racking capacity and total material cost are optimized simultaneously (this task is accomplished via simple enumeration because of the low cardinality of the design variables set). So doing, it is shown that the total material cost of the optimal (non-dominated) wall configurations has a strong influence on the racking capacity whereas it does not affect the equivalent viscous damping ratio, which remains almost constant. A novel simplified analytical procedure for predicting the capacity curve of light-frame timber shear walls is finally proposed.

A new structural health monitoring system for real-time evaluation of building damage

The author has developed a new method for evaluating the seismic performance of existing structures from measured accelerations based on the capacity spectrum method. This involves comparing the performance curve, which is the equivalent nonlinear behavior of a simplified single-degree-of-freedom system, and the demand curve, which is the relationship between the response acceleration and displacement spectra. Two telecommunication towers in Japan were instrumented in 2016, and their responses during several earthquakes have been recorded. This paper discusses the evaluation of damage during the two earthquakes. Moreover, parameters such as the predominant period and the required performance are discussed. The proposed system evaluated both towers as being “elastic.” The damping ratios of the towers are very low, which caused the oscillations to continue for more than 5 min after the mainshock of each earthquake because of long-period components of the seismic motion

EXPERIMENTAL STUDY ON THE DAMAGE CLASSIFICATION METHOD WITH THE PERFORMANCE CURVES OF R/C STRUCTURES DERIVED FROM RECORDED ACCELERATIONS

Once a catastrophic earthquake occurs, many buildings may be affected. Some buildings are severely damaged and may collapse during a following strong aftershock. It is needed to conduct a rapid inspection to evaluate the buildings in the affected area. “Manual for post-earthquake rehabilitation techniques for buildings (draft)” was developed in 1986 to evaluate the damage class of the buildings based on the visual observation. Recent earthquakes revealed that it becomes quite difficult to conduct visual inspection because structural members are covered by the finishings and many highrise buildings were constructed. The author has been conducting a series of research to develop a new method to evaluate the damage class with instrumented sensors based on the capacity spectrum method. The capacity curve is derived from the measured accelerations and displacements calculated from accelerations with double integral. The proposed system can predict the possible damage level during the maximum aftershock. However, the damage class according to the proposed system and to the guidelines based on the visual observation has not been compared. The earthquake insurance also conducts the visual investigation and evaluate the damage class to estimate the earthquake insurance premium. The damage class according to the earthquake insurance is also compared.

Threshold Determination Using Bi-hazard Fragility Curves for the Evaluation of Structural Health Monitoring of USHER Technology

Structural Health Monitoring (SHM) is not new in the field of structural engineering and its application goes from the monitoring to evaluation of bridges, dams, buildings, and other similar structures. As per National Structural Code of the Philippines (NSCP) Volume 1[1-4], the Implementing Rules of earthquake recording instrumentation of buildings has been continually advancing, but not in the case of bridges and dams. The objective of this paper is to apply the established sensor-driven accelerometer developed by USHER (Universal Structural Health Evaluation and Recording) system in the evaluation of Padre Jacinto Zamora Bridge in Manila; specifically, to determine the proper installation of the developed accelerometer in the identified critical parts of the bridge. SHM addresses the problem of structural integrity assessment and help in assuring repair cost to a minimal. SHM helps quantify the strength of a structure by identifying the damage. Often evaluations are made using visual inspection and by age consideration. Most of the time, the use of this type of evaluation tend to be expensive. Repairs are not directed to the damaged component alone but the whole structure. Hence, the expenditure expands. SHM with the application of Micro-Electro-Mechanical Sensors (MEMS) will allow gathering of data that can be converted in the form of the structure’s modal properties (i.e. natural frequency, mode shape, and damping ratio) [6, 7]. Structural health is then determined and be ready to compare it to the structural model simulation results. A method was developed to incorporate seismic fragility curves [5] to determine the thresholds for the evaluation of the structural health. Capacity spectrum method was utilized to derive the seismic fragility function. A Monte Carlo Simulation was used to derive the flood fragility curves.

A SIMPLIFIED ANALYTICAL PROCEDURE FOR SEISMIC ANALYSIS OF TIMBER LIGHT-FRAME SHEAR WALLS

The seismic performance of timber light-frame shear walls is investigated in this paper with a focus on energy dissipation and ductility ensured by sheathing-to-framing connections. An original parametric finite element model has been developed in order to perform sensitivity analyses. The model considers the design variables affecting the racking load-carrying capacity of the wall. These variables include aspect ratio (height-to-width ratio), fastener spacing, number of vertical studs and framing elements cross-section size. A failure criterion has been defined based on the observation of both the global behaviour of the wall and local behaviour of fasteners in order to identify the ultimate displacement of the wall. The equivalent viscous damping has been numerically assessed by estimating the damping factor which is in use in the capacity spectrum method. Finally, an in-depth analysis of the results obtained from the sensitivity analyses led to the development of a simplified analytical procedure which is able to predict the capacity curve of a timber light-frame shear wall.

Influence of Real Ground Motion Records in Performance Assessment of RC Buildings

Reinforced concrete frame buildings with Open Ground Story (OGS) are one of the most common building configurations in urban habitat. These configurations are known to be vulnerable to seismic excitations, primarily due to the sudden loss in strength in the ground story and differential stiffness distribution throughout the structure. The differential stiffness distribution is attributed primarily to the interaction of non-structural infill wall with the moment-resisting frame. Hence, the interaction of infill wall needs to be accounted in estimating the seismic vulnerability. Therefore, the present investigation is focused on understanding the impact of utilizing real ground motion records on the performance assessment of RC buildings with and without consideration of infill walls. Fragility curves were developed for low and mid-rise structural models using Capacity Spectrum Method (CSM) specified by ATC-40 and with Incremental Dynamic Analysis (IDA). CSM uses the response spectrum specified by the respective code, unlike IDA where an ensemble of spectrum compatible real ground motion accelerograms satisfying the necessary site conditions is used in assessing the performance. Further, significant variations observed in the developed fragility curves by CSM and IDA emphasizes the sensitivity of real ground motion data in performance assessment.

Comparative earthquake loss estimations for high-code buildings in Istanbul

The paper presents the probabilistic and scenario based earthquake loss estimations for the case that the hazard and building inventory inputs are kept the same whereas the damage functions as well as the seismic demand estimation method are changed in an earthquake loss model. Spectral acceleration-displacement based damage assessments by alternating damage functions and inelastic demand evaluation methods are performed for high-code buildings in Istanbul. The buildings are mid- and high-rise, reinforced concrete, moment-resisting frames that are assumed to be designed in accordance with the provisions of Turkish Earthquake Resistant Design Code (1998). Three damage models, i.e. structural capacity and fragility curves, are employed for each building class: Expert judgment based capacity and fragility functions; HAZUS's high-code seismic design level capacity and fragility functions; and Capacity and fragility functions derived based on nonlinear analyses of code complying RC frames. Inelastic spectral displacement demands are computed with three methods: Capacity Spectrum Method, Modified Acceleration-Displacement Response Spectrum Method, and Displacement Coefficient Method. Analyses are realized under site-specific ground motions based on a state-of-the-art hazard model for eight return periods ranging from 100 to 2475 years as well as for an Mw = 7.5 scenario earthquake. Probabilistic loss curves for each case are developed. Estimated average annual losses (AAL) and loss ratios (AALR) are compared. Grid and district based maps illustrating the spatial distributions of estimated long term average losses per year and the loss ratios are presented. The estimated annualized loss ratios at district level in the city are compared to the earthquake insurance premium rates.

Out-of-plane closed-form solution for the seismic assessment of unreinforced masonry schools in Nepal

Traditional unreinforced masonry (URM) constructions still represent an important part of the school building stock in several low-income countries including Nepal. Unfortunately, their intrinsic vulnerability impacts negatively on the resilience of cities and local communities. Observations after major seismic events have shown that the predominant mode of failure is the out-of-plane (OOP) of the weak and loosely connected perimeter masonry walls which typically leads to partial or global collapse. Starting from this evidence, a closed-form analytical approach is presented aimed at deriving the OOP force-displacement response of URM walls for different boundary conditions and vertical loads. The novel analytical solution is successfully validated with the results of seventeen OOP experimental tests on URM walls available in the literature. Then, referring to a case-study Nepalese school building, capacity curves of the constituting walls are derived and adopted for the vulnerability assessment of the structure through the Capacity Spectrum Method (CSM) where equivalent hysteretic damping is calibrated with available OOP shaking table test results. Lastly, PGA capacities for different damage states are successfully compared with median values from observational fragility curves.