An improved modal pushover analysis procedure for estimating seismic demands of structures

The pushover analysis （POA） procedure is difficult to apply to high-rise buildings, as it cannot account for the contributions of higher modes. To overcome this limitation, a modal pushover analysis （MPA） procedure was proposed by Chopra et al. （2001）. However, invariable lateral force distributions are still adopted in the MPA. In this paper, an improved MPA procedure is presented to estimate the seismic demands of structures, considering the redistribution of inertia forces after the structure yields. This improved procedure is verified with numerical examples of 5-, 9- and 22-story buildings. It is concluded that the improved MPA procedure is more accurate than either the POA procedure or MPA procedure. In addition, the proposed procedure avoids a large computational effort by adopting a two-phase lateral force distribution..

Lateral load pattern in pushover analysis

The seismic capacity curves of three types of buildings including frame,frame-shear wall and shear wall ob- tained by pushover analysis under different lateral load patterns are compared with those from nonlinear time history analy- sis.Based on the numerical results obtained a two-phase load pattern:an inverted triangle(first mode)load pattern until the base shear force reaches β times its maximum value,V_(max)followed by a(x/H)~α form,here β and α being some coeffi- cients depending on the type of the structures considered,is proposed in the paper,which can provide excellent approxima- tion of the seismic capacity curve for low-to-mid-rise shear type buildings.Furthermore,it is shown both the two-phase load pattern proposed and the invariant uniform pattern can be used for low-to-mid-rise shear-bending type and low-rise bending type of buildings.No suitable load patterns have been found for high-rise buildings.

Pushover analysis of reinforced concrete frames considering shear failure at beam-column joints

Since most current seismic capacity evaluations of reinforced concrete （RC） frame structures are implemented by either static pushover analysis （PA） or dynamic time history analysis, with diverse settings of the plastic hinges （PHs） on such main structural components as columns, beams and walls, the complex behavior of shear failure at beam-column joints （BCJs） during major earthquakes is commonly neglected. This study proposes new nonlinear PA procedures that consider shear failure at BCJs and seek to assess the actual damage to RC structures. Based on the specifications of FEMA-356, a simplified joint model composed of two nonlinear cross struts placed diagonally over the location of the plastic hinge is established, allowing a sophisticated PA to be performed. To verify the validity of this method, the analytical results for the capacity curves and the failure mechanism derived from three different full-size RC frames are compared with the experimental measurements. By considering shear failure at BCJs, the proposed nonlinear analytical procedures can be used to estimate the structural behavior of RC frames, including seismic capacity and the progressive failure sequence of joints, in a precise and effective manner.

Pushover analysis of asymmetric-plan buildings based on distribution of the combined modal story shear and torsional moment

A pushover procedure with a load pattern based on the height-wise distribution of the combined modal story shear and torsional moment is proposed to estimate the seismic response of 3D asymmetric-plan building frames. Contribution of the higher modes and torsional response of asymmetric-plan buildings are incorporated into the proposed load pattern. The proposed pushover method is a single-run procedure, which enables tracing the nonlinear response of the structure during the analysis and averts the elusiveness of conducting multiple pushover analyses. The proposed method has been used to estimate the response of two moment-resisting building frames with 9 and 20 stories. The obtained results indicate the appropriate accuracy and efficiency of the proposed procedure in estimating the trend of the drift profiles of the structures resulted from nonlinear time history analyses.

Nonlinear pushover analysis of infilled concrete frames

Six reinforced concrete frames with or without masonry infills were constructed and tested under horizontal cyclic loads. All six frames had identical details in which the transverse reinforcement in columns was provided by rectangular hoops that did not meet current ACI specifications for ductile frames. For comparison purposes, the columns in three of these frames were jacketed by carbon-fiber-reinforced-polymer （CFRP） sheets to avoid possible shear failure. A nonlinear pushover analysis, in which the force-deformation relationships of individual elements were developed based on ACI 318, FEMA 356, and Chen＇s model, was carried out for these frames and compared to test results. Both the failure mechanisms and impact of infills on the behaviors of these frames were examined in the study. Conclusions from the present analysis provide structural engineers with valuable information for evaluation and design of infilled concrete frame building structures.

Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects （PASSI） is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights （3, 9 and 20） including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis （NLhRHA） method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ＇Code for Seismic Design of Buildings. The feasibility of the proposed procedure is verified.

Evaluation of Regular Multistory Buildings Using IBC2009 Code and ESEE Regulations by Pushover Analysis Method

For structural design and assessment of reinforced concrete members, the nonlinear analysis has become an important tool. The purpose of the pushover analysis is to assess the structural performance by estimating the strength and deformation capacities using static, nonlinear analysis and comparing these capacities with the demands at the corresponding performance levels. This paper aims to compare the results given by IBC2009 code and ESEE regulations. In this paper, four RC frames having 5, 15, 20 and 30 storeys were designed for seismicity according to both the recently adopted seismic code in Abu Dhabi (IBC2009) and the ESEE regulations. A pushover analysis is carried out for these buildings using SAP2000 (Ver. 15) and the ultimate capacities of the buildings are established. The obtained pushover curves and plastic hinges distributions are used to compare between the IBC2009 code and ESEE regulations. The comparison showed that there was variation in the obtained results by the two codes and the buildings designed by IBC2009 code were more vulnerable.

Seismic Evaluation of Reinforced Concrete Frames in the Harsh Environment Using Pushover Analysis

The main objective of this paper is to evaluate the seismic response of buildings of typical reinforced concrete frames when concrete starts to deteriorate gradually and to make a comparison between the base shear and the displacement at different stages of earthquake loading. Typical 5, 15, 20 and 30-storey reinforced concrete frames have been designed for seismicity according to the recently adopted seismic code in Abu Dhabi, ACI 318-08/IBC 2009 code. A pushover analysis has been performed to these four buildings by using SAP 2000. Twenty-four models have been created (6 models for each building) by decreasing the concrete strength gradually from 4000 psi (281 kg/cm2) to 1500 psi (105 kg/cm2). This is to simulate the effect of harsh environment on the strength of concrete in existing buildings.

Nonlinear Pushover Analysis of the Influences on RC Footing for the External Elevator Well

In contemporary society, reducing carbon dioxide emissions and achieving sustainable development are paramount goals. One effective approach is to preserve existing RC (Reinforced Concrete) buildings rather than demolishing them for new construction. However, a significant challenge arises from the lack of elevator designs in many of these existing RC buildings. Adding an external elevator becomes crucial to solving accessibility issues, enhancing property value, and satisfying modern residential buildings using convenient requirements. However, the structural performance of external elevator wells remains understudied. This research is designed by the actual external elevator project into existing RC buildings in Jinzhong Rd, Shanghai City. Specifically, this research examines five different external elevator wells under nonlinear pushover analysis, each varying in the height of the RC (Reinforced Concrete) footing. By analyzing plastic hinge states, performance points, capacity curves, spectrum curves, layer displacement, and drift ratio, this research aims to provide a comprehensive understanding of how these structures of the external elevator well respond to seismic events. The findings are expected to serve as a valuable reference for future external elevator projects, ensuring the external elevator designs meet the seismic requirements. By emphasizing seismic resistance in the design phase, the research aims to enhance the overall safety and longevity of external elevator systems integrated into existing RC buildings.

Regularity classification and corresponding analysis method requirements of horizontally curved bridges with unequal pier heights

The seismic behavior of horizontally curved bridges,particularly with unequal height piers,is more complicated than that of straight bridges due to their geometric properties.In this study,the seismic responses of several horizontally curved single-column-bent viaducts with various degrees of curvature and different pier heights have been investigated,employing three different analysis approaches:namely,modal pushover analysis,uniform load method,and nonlinear time history analysis.Considering the investigated bridge configurations and utilizing the most common regularity indices,the results indicate that viaducts with 45-degree and 90-degree deck subtended angles can be categorized as regular and moderately irregular,respectively,while the bridges with 180-degree deck subtended angle are found to be highly irregular.Furthermore,the viaducts whose pier heights are asymmetric may be considered as irregular for almost all ranges of the deck subtended angles.The effects of higher transverse and longitudinal modes are discussed and the minimum analysis requirements are identified to assess the seismic response of such bridge configurations for design purposes.Although the Regularity Indices used here are useful tools to distinguish between regular and irregular bridges,further studies are needed to improve their reliability.

Aseismic Reliability Analysis Approach for Offshore Jacket Platform Structures

By means of nonlinear pushover collapse analysis approach, the aseismic reliability analyses of two offshore jacket platforms in the Bohai Gulf in China are studied according to their ocean location and environmental loadings there. On the basis of those analyses, an aseismic reliability analysis approach is presented. The results show that the aseismic reliability of those platforms is high. Also it is proved that this aseismic reliability analysis approach is simple, practical and reliable.

Seismic response of skewed RC box-girder bridges

It is critical to ensure the functionality of highway bridges after earthquakes to provide access to important facilities. Since the 1971 San Fernando earthquake, there has been a better understanding of the seismic performance of bridges. Nonetheless, there are no detailed guidelines addressing the performance of skewed highway bridges. Several parameters affect the response of skewed highway bridges under both service and seismic loads which makes their behavior complex. Therefore, there is a need for more research to study the effect of skew angle and other related factors on the performance of highway bridges. This paper examines the seismic performance of a three-span continuous concrete box girder bridge with skew angles from 0 to 60 degrees, analytically. Finite element （FE） and simplified beam-stick （BS） models of the bridge were developed using SAP2000. Different types of analysis were considered on both models such as： nonlinear static pushover, and linear and nonlinear time history analyses. A comparison was conducted between FE and BS, different skew angles, abutment support conditions, and time history and pushover analysis. It is shown that the BS model has the capability to capture the coupling due to skew and the significant modes for moderate skew angles. Boundary conditions and pushover load profile are determined to have a major effect on pushover analysis. Pushover analysis may be used to predict the maximum deformation and hinge formation adequately.

Multi-hazard performance assessment of a transfer-plate high-rise building

Many urban areas are located in regions of moderate seismicity and are subjected to strong wind. Buildings in these regions are often designed without seismic provisions. As a result, in the event of an earthquake, the potential for damage and loss of lives may not be known. In this paper, the performance of a typical high-rise building with a thick transfer plate （TP）, which is one type of building structure commonly found in Hong Kong, is assessed against both earthquake and wind hazards. Seismic- and wind-resistant performance objectives are first reviewed based on relevant codes and design guidelines for high-rise buildings. After a brief introduction of wind-resistant design of the building, various methodologies, including equivalent static load analysis （ESLA）, response spectrum analysis （RSA）, pushover analysis （POA）, linear and nonlinear time-history analysis （LTHA and NTHA）, are employed to assess the seismic performance of the building when subjected to frequent earthquakes, design based earthquakes and maximum credible earthquakes. The effects of design wind and seismic action with a common 50-year return period are also compared. The results indicate that most performance objectives can be satisfied by the building, but there are some objectives, such as inter-story drift ratio, that cannot be achieved when subjected to the frequent earthquakes. It is concluded that in addition to wind, seismic action may need to be explicitly considered in the design of buildings in regions of moderate seismicity.

Response reduction factor of irregular RC buildings in Kathmandu valley

Most current seismic design includes the nonlinear response of a structure through a response reduction factor （R）. This allows the designer to use a linear elastic force-based approach while accounting for nonlinear behavior and deformation limits. In fact, the response reduction factor is used in modem seismic codes to scale down the elastic response of a structure. This study focuses on estimating the actual ＇R＇ value for engineered design/construction of reinforced concrete （RC） buildings in Kathmandu valley. The ductility and overstrength of representative RC buildings in Kathmandu are investigated. Nonlinear pushover analysis was performed on structural models in order to evaluate the seismic performance of buildings. Twelve representative engineered irregular buildings with a variety of characteristics located in the Kathmandu valley were selected and studied. Furthermore, the effects of overstrength on the ductility factor, beam column capacity ratio on the building ductility, and load path on the response reduction factor, are examined. Finally, the results are further analyzed and compared with different structural parameters of the buildings.

A macro-level global seismic damage model considering higher modes

For modal pushover analysis procedures, the model proposed by Ghobarah et al. （called the G model hereafter, 1999） has been extended to account for the contributions of transient higher modes to global seismic damage of structures excited by strong ground motions. The proposed model has physically and perfectly bridged the G model and the final softening model proposed by DiPasquale and Cakmak （1988）. Modal damage indexes corresponding to all considered vibration modes are combined by the CQC rule or the SRSS rule. Incremental dynamic analysis （IDA） is performed on three example RC frames to validate the proposed model, and a comprehensive comparison is carried out. The demonstration indicates that the proposed model is easy to implement and reflects the influence of the transition in transient vibration periods and modes on structural damage evolution. Some limitations associated with the proposed model are also addressed. Further experimental validations are needed to improve the model in the future.

Performance-based concept on seismic evaluation of existing bridges

Conventional seismic evaluation of existing bridges explores the ability of a bridge to survive under significant earthquake excitations. This approach has several major drawbacks, such as only a single structural performance of near collapse is considered, and the simplified approach of adopting strength-based concept to indirectly estimate the nonlinear behavior of a structure lacks accuracy. As a result, performance-based concepts that include a wider variety of structural performance states of a given bridge excited by different levels of earthquake intensity is needed by the engineering community. This paper introduces an improved process for the seismic evaluation of existing bridges. The relationship between the overall structural performance and earthquakes with varying levels of peak ground acceleration （PGA） can successfully be linked. A universal perspective on the seismic evaluation of bridges over their entire life-cycle can be easily obtained to investigate multiple performance objectives. The accuracy of the proposed method, based on pushover analysis, is proven in a case study that compares the results from the proposed procedure with additional nonlinear time history analyses.

Seismic demand evaluation of medium ductility RC moment frames using nonlinear procedures

Performance-based earthquake engineering is a recent focus of research that has resulted in widely developed design methodologies due to its ability to realistically simulate structural response characteristics. Precise prediction of seismic demands is a key component of performance-based design methodologies. This paper presents a seismic demand evaluation of reinforced concrete moment frames with medium ductility. The accuracy of utilizing simplified nonlinear static analysis is assessed by comparison against the results of time history analysis on a number of frames. Displacement profiles, drift demand and maximum plastic rotation were computed to assess seismic demands. Estimated seismic demands were compared to acceptance criteria in FEMA 356. The results indicate that these frames have sufficient capacity to resist interstory drifts that are greater than the limit value.

A simplified methd of evaluating the seismic performance of buildings

This paper presents a simplified method of evaluating the seismic performance of buildings. The proposed method is based on the transformation of a multiple degree of freedom (MDOF) system to an equivalent single degree of freedom (SDOF) system using a simple and intuitive process. The proposed method is intended for evaluating the seismic performance of the buildings at the intermediate stages in design, while a rigorous method would be applied to the final design. The performance of the method is evaluated using a series of buildings which are assumed to be located in Victoria in western Canada, and designed based on the upcoming version of the National Building Code of Canada which is due to be published in 2005. To resist lateral loads, some of these buildings contain reinforced concrete moment resisting frames, while others contain reinforced concrete shear walls. Each building model has been subjected to a set of site-specific seismic spectrum compatible ground motion records, and the response has been determined using the proposed method and the general method for MDOF systems. The results from the study indicate that the proposed method can serve as a useful tool for evaluation of seismic performance of buildings, and carrying out performance based design.

Case study of seismic performance assessment of irregular RC buildings: hospital structure of Avezzano(L'Aquila, Italy)

Most published studies on inelastic earthquake response of non-symmetric buildings are based on simplified inelastic, highly idealized models, while general conclusions regarding the inelastic torsional response of multistory building are still lacking. This paper aims to provide a useful contribution in the study of the torsional response of real irregular buildings. To this aim, the manuscript reports the comprehensive study on the seismic vulnerability of an irregular RC building： the hospital building ofAvezzano （L＇Aquila Italy）. For this multi-story building, which is irregular in both plan and elevation, the application of nonlinear static evaluation procedures is by no means straightforward. The study proposes a nonlinear static procedure based on pushover analysis under the multimodal distribution of lateral loads and a capacity spectrum method. This pushover procedure accounts for mass distribution, higher modes contribution and mode-shapes correlation. Furthermore, due to its non-iterative feature, it avoids problems of non-convergence and multiple solutions of the conventional capacity spectrum method. Applied to a real case study, the procedure is used to investigate, in a 3D plan irregular building, the sensitivity of torsional inelastic response to lateral force distribution, higher modes contribution, accidental eccentricity and controlled point for monitoring the target displacement.

Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects

A modified energy-balance equation accounting for P-delta effects and hysteretic behavior of reinforced concrete members is derived. Reduced hysteretic properties of structural components due to combined stiffness and strength degradation and pinching effects, and hysteretic damping are taken into account in a simple manner by utilizing plastic energy and seismic input energy modification factors. Having a pre-selected yield mechanism, energy balance of structure in inelastic range is considered. P-delta effects are included in derived equation by adding the external work of gravity loads to the work of equivalent inertia forces and equating the total external work to the modified plastic energy. Earthquake energy input to multi degree of freedom（MDOF） system is approximated by using the modal energy-decomposition. Energybased base shear coefficients are verified by means of both pushover analysis and nonlinear time history（NLTH） analysis of several RC frames having different number of stories. NLTH analyses of frames are performed by using the time histories of ten scaled ground motions compatible with elastic design acceleration spectrum and fulfilling duration/amplitude related requirements of Turkish Seismic Design Code. The observed correlation between energy-based base shear force coefficients and the average base shear force coefficients of NLTH analyses provides a reasonable confidence in estimation of nonlinear base shear force capacity of frames by using the derived equation.