Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

Extended consecutive modal pushover procedure for estimating seismic responses of one-way asymmetric plan tall buildings considering soil-structure interaction

Performance based design becomes an effective method for estimating seismic demands of buildings. In asymmetric plan tall building the effects of higher modes and torsion are crucial. The consecutive modal pushover (CMP) procedure is one of the procedures that consider these effects. Also in previous studies the influence of soil-structure interaction (SSI) in pushover analysis is ignored. In this paper the CMP procedure is modified for one-way asymmetric plan mid and high-rise buildings considering SSI. The extended CMP (ECMP) procedure is proposed in order to overcome some limitations of the CMP procedure. In this regard, 10, 15 and 20 story buildings with asymmetric plan are studied considering SSI assuming three different soil conditions. Using nonlinear response history analysis under a set of bidirectional ground motion; the exact responses of these buildings are calculated. Then the ECMP procedure is evaluated by comparing the results of this procedure with nonlinear time history results as an exact solution as well as the modal pushover analysis procedure and FEMA 356 load patterns. The results demonstrate the accuracy of the ECMP procedure.     

The extended consecutive modal pushover procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings under influence of two horizontal components of ground motions

This paper aims to extend the consecutive modal pushover (CMP) procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings subjected to bi-directional seismic ground motions taking the effects of higher modes and torsion into account. Multi-stage and single-stage pushover analyses are carried out in both X and Y directions. Inelastic seismic responses obtained by multi-stage and single-stage pushover analyses for X and Y directions are combined using the SRSS combination scheme. The final seismic responses are determined by enveloping the combined results of multi-stage and single-stage pushover analyses. To evaluate the accuracy of the proposed procedure, it is applied to two-way unsymmetric-plan tall buildings which include torsionally stiff and torsionally flexible systems. The results derived from the CMP procedure are compared with those from nonlinear response history analysis (NL-RHA), as a benchmark solution. Moreover, the advantages of the proposed procedure are demonstrated by comparing the results derived from the CMP to those from pushover analysis with uniform and fundamental effective mode distributions. The proposed procedure is able to accurately predict amplification or de-amplification of the seismic displacements at the flexible and stiff edges of the two-way unsymmetric-plan tall buildings by considering the effects of higher modes and torsion. The extended CMP procedure can accurately estimate the peak inelastic responses, such as displacements and storey drifts. The CMP procedure features a higher potential in estimating plastic hinge rotations at both flexible and stiff sides of unsymmetric-plan tall buildings under bi-directional seismic excitation when compared to the uniform and fundamental effective mode force distributions.     

A fuzzy–random analysis model for seismic performance of framed structures incorporating structural and non‐structural damage

Past earthquake experiences indicate that most buildings designed in accordance with modern seismic design codes could survive moderate‐to‐strong earthquakes; however, the financial loss due to repairing cost and the subsequent business interruption can be unacceptable. Designing building structures to meet desired performance targets has become a clear direction in future seismic design practice. As a matter of fact, the performance of buildings is affected by structural as well as non‐structural components, and involves numerous uncertainties. Therefore, appropriate probabilistic approach taking into account structural and non‐structural damages is required. This paper presents a fuzzy–random model for the performance reliability analysis of RC framed structures considering both structural and non‐structural damages. The limit state for each performance level is defined as an interval of inter‐storey drift ratios concerning, respectively, the non‐structural and structural damage with a membership function, while the relative importance of the two aspects is reflected through the use of an appropriate cost function. To illustrate the methodology, herein the non‐structural damage is represented by infill masonry walls. The probabilistic drift limits for RC components and masonry walls from the associated studies are employed to facilitate the demonstration of the proposed model in an example case study. The results are compared with those obtained using classical reliability model based on single‐threshold performance definition. The proposed model provides a good basis for incorporating different aspects into the performance assessment of a building system. Copyright © 2005 John Wiley & Sons, Ltd.     

A probabilistic performance‐based approach for mitigating the seismic pounding risk between adjacent buildings

Existing design procedures for determining the separation distance between adjacent buildings subjected to seismic pounding risk are based on approximations of the buildings' peak relative displacement. These procedures are characterized by unknown safety levels and thus are not suitable for use within a performance‐based earthquake engineering framework. This paper introduces an innovative reliability‐based methodology for the design of the separation distance between adjacent buildings. The proposed methodology, which is naturally integrated into modern performance‐based design procedures, provides the value of the separation distance corresponding to a target probability of pounding during the design life of the buildings. It recasts the inverse reliability problem of the determination of the design separation distance as a zero‐finding problem and involves the use of analytical techniques in order to evaluate the statistics of the dynamic response of the buildings. Both uncertainty in the seismic intensity and record‐to‐record variability are taken into account. The proposed methodology is applied to several different buildings modeled as linear elastic single‐degree‐of‐freedom (SDOF) and multi‐degree‐of‐freedom (MDOF) systems, as well as SDOF nonlinear hysteretic systems. The design separation distances obtained are compared with the corresponding estimates that are based on several response combination rules suggested in the seismic design codes and in the literature. In contrast to current seismic code design procedures, the newly proposed methodology provides consistent safety levels for different building properties and different seismic hazard conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

A methodology for defining seismic scenario‐structure‐based limit state criteria for rc high‐rise wall buildings using net drift

As a result of population growth and consequent urbanization, the number of high‐rise buildings is rapidly growing worldwide resulting in increased exposure to multiple‐scenario earthquakes and associated risk. The wide range in frequency contents of possible strong ground motions can have an impact on the seismic response, vulnerability and limit states definitions of RC high‐rise wall structures. Motivated by the pressing need to derive more accurate fragility relations to be used in seismic risk assessment and mitigation of such structures, a methodology is proposed to obtain reliable, Seismic Scenario‐Structure‐Based (SSSB) definitions of limit state criteria. A 30‐story wall building, located in a multi‐seismic scenario study region, is utilized to illustrate the methodology. The building is designed following modern codes and then modeled using nonlinear fiber‐based approach. Uncertainty in ground motions is accounted for by the selection of forty real earthquake records representing two seismic scenarios. Seismic scenario‐based building local response at increasing earthquake intensities is mapped using Multi‐Record Incremental Dynamic Analyses (MRIDAs) with a new scalar intensity measure. Net Inter‐Story Drift (NISD) is selected as a global damage measure based on a parametric study involving seven buildings ranging from 20 to 50 stories. This damage measure is used to link local damage events, including shear, to global response under different seismic scenarios. While the study concludes by proposing SSSB limit state criteria for the sample building, the proposed methodology arrives at a reliable definition of limit state criteria for an inventory of RC high‐rise wall buildings under multiple earthquake scenarios. Copyright © 2016 John Wiley & Sons, Ltd.     

Building damage scenarios based on exploitation of Housner intensity derived from finite faults ground motion simulations

In this paper earthquake damage scenarios for residential buildings (about 4200 units) in Potenza (Southern Italy) have been estimated adopting a novel probabilistic approach that involves complex source models, site effects, building vulnerability assessment and damage estimation through Damage Probability Matrices. Several causative faults of single seismic events, with magnitude up to 7, are known to be close to the town. A seismic hazard approach based on finite faults ground motion simulation techniques has been used to identify the sources producing the maximum expected ground motion at Potenza and to generate a set of ground motion time histories to be adopted for building damage scenarios. Additionally, site effects, evaluated in a previous work through amplification factors of Housner intensity, have been combined with the bedrock values provided by hazard assessment. Furthermore, a new relationship between Housner and EMS-98 macroseismic intensity has been developed. This relationship has been used to convert the probability mass functions of Housner intensity obtained from synthetic seismograms amplified by the site effects coefficients into probability mass function of EMS-98 intensity. Finally, the Damage Probability Matrices have been applied to estimate the damage levels of the residential buildings located in the urban area of Potenza. The proposed methodology returns the full probabilistic distribution of expected damage, thus avoiding average damage index or uncertainties expressed in term of dispersion indexes.     

Performance-based methodology for assessing seismic vulnerability and capacity of buildings

This paper presents a performance-based methodology for the assessment of seismic vulnerability and capacity of buildings. The vulnerability assessment methodology is based on the HAZUS methodology and the improved capacity- demand-diagram method. The spectral displacement (Sd) of performance points on a capacity curve is used to estimate the damage level of a building. The relationship between Sd and peak ground acceleration (PGA) is established, and then a new vulnerability function is expressed in terms of PGA. Furthermore, the expected value of the seismic capacity index (SCev) is provided to estimate the seismic capacity of buildings based on the probability distribution of damage levels and the corresponding seismic capacity index. The results indicate that the proposed vulnerability methodology is able to assess seismic damage of a large number of building stock directly and quickly following an earthquake. The SCev provides an effective index to measure the seismic capacity of buildings and illustrate the relationship between the seismic capacity of buildings and seismic action. The estimated result is compared with damage surveys of the cities of Dujiangyan and Jiangyou in the M8.0 Wenchuan earthquake, revealing that the methodology is acceptable for seismic risk assessment and decision making. The primary reasons for discrepancies between the estimated results and the damage surveys are discussed.     

An alternative approach for the seismic rehabilitation of existing RC buildings using seismic isolation

Usually, buildings with seismic isolation are designed to comply with an operational building performance level after strong earthquakes. This approach, however, may limit the use of seismic isolation for the seismic rehabilitation of existing buildings with low lateral strength or substandard details, because it often requires invasive strengthening measures in the superstructure or the use of expensive custom‐made devices. In this paper, an alternative approach for the seismic rehabilitation of existing buildings with seismic isolation, based on the acceptance of limited plastic deformations in the superstructure under strong earthquakes, is proposed and then applied to a real case study, represented by a four‐storey RC frame building. Nonlinear response‐time histories analyses of an accurate model of the case‐study building are carried out to evaluate the seismic performances of the structure, comparing different rehabilitation strategies with and without seismic isolation. Initial costs of the intervention and possible (future) repair costs are then estimated. Based on the results of this study, values of the behavior factor (i.e. response modification factor) higher than those adopted in the current codes for base‐isolated buildings are tentatively proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

Modified consecutive modal pushover procedure for seismic investigation of one-way asymmetric-plan tall buildings

The effects of higher modes and torsion have a significant impact on the seismic responses of asymmetric-plan tall buildings.A consecutive modal pushover(CMP) procedure is one of the pushover methods that have been developed to consider these effects.The aim of this paper is to modify the(CMP) analysis procedure to estimate the seismic demands of one-way asymmetric-plan tall buildings with dual systems.An analysis of 10-,15-and 20-story asymmetric-plan buildings is carried out,and the results from the modified consecutive modal pushover(MCMP) procedure are compared with those obtained from the modal pushover analysis(MPA) procedure and the nonlinear time history analysis(NLTHA).The MCMP estimates of the seismic demands of one-way asymmetric-plan buildings demonstrate a reasonable accuracy,compared to the results obtained from the NLTHA.Furthermore,the accuracy of the MCMP procedure in the prediction of plastic hinge rotations is better than the MPA procedure.The new pushover procedure is also more accurate than the FEMA load distribution and the MPA procedure.     

Improved performance‐based seismic assessment of buildings by utilizing Bayesian statistics

This paper addresses two important issues of concern to practicing engineers and researchers alike in application of performance‐based seismic assessment (PBSA) methodology on buildings: (i) the number of ground motion records required to exercise PBSA—current practice (FEMA P‐58‐1) requires eleven or more pairs of motions for this purpose, and (ii) the time and effort associated with performing the number of nonlinear response history analyses required to exercise PBSA. We present a method for exercising of PBSA that employs classical linear modal analysis to develop a first estimate (i.e., a priori) of probability distribution of loss, followed by utilizing Bayesian statistics to update this estimate using estimates of loss obtained by utilizing a small number of nonlinear response history analyses of a detailed model of the building (i.e., posterior). The proposed technique is used to assess the distribution of monetary loss of two case studies, a 4‐story reinforced concrete moment‐resisting frame building and a 20‐story steel moment‐resisting frame building, both located in Los Angeles, for a ground motion hazard with 10% probability of exceedance in 50 years. The efficiency of the proposed PBSA method is demonstrated by showing the similarity between the distribution of monetary loss at each story of case study buildings obtained from the traditional/sophisticated PBSA methodology and the proposed PBSA method in this study. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance‐based seismic assessment of conventional and base‐isolated steel buildings including environmental impact and resilience

Sustainability and resilience are issues that are recognized worldwide, and increased attention should be placed on strategies to design and maintain infrastructure systems that are hazard resilient, damage tolerant, and sustainable. In this paper, a methodology to evaluate the seismic sustainability and resilience of both conventional and base‐isolated steel buildings is presented. Furthermore, the proposed approach is used to explore the difference between the performance associated with these buildings by considering the three pillars of sustainability: economic, social, and environmental. Sustainability and resilience are both considered to cover a comprehensive performance‐based assessment content. The uncertainties associated with performance and consequence evaluation of structural and non‐structural components are incorporated within the assessment process. The proposed performance‐based assessment approach is illustrated on conventional and base‐isolated steel buildings under given seismic scenarios. Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluation of ASCE 7 equations for designing acceleration‐sensitive nonstructural components using data from instrumented buildings

This study uses instrumented buildings and models of code‐based designed buildings to validate the results of previous studies that highlighted the need to revise the ASCE 7 F_p equation for designing nonstructural components (NSCs) through utilizing oversimplified linear and nonlinear models. The evaluation of floor response spectra of a large number of instrumented buildings illustrates that, unlike the ASCE 7 approach, the in‐structure and the component amplification factors are a function of the ratio of NSC period to the supporting building modal periods, the ground motion intensity, and the NSC location. It is also shown that the recorded ground motions at the base of instrumented buildings in most cases are significantly lower than design earthquake (DE) ground motions. Because ASCE 7 is meant to provide demands at a DE level, for a more reliable evaluation of the F_p equation, 2 representative archetype buildings are designed based on the ASCE 7‐16 seismic provisions and exposed to various ground motion intensity levels (including those consistent with the ones experienced by instrumented buildings and the DE). Simulation results of the archetype buildings, consistent with previous numerical studies, illustrate the tendency of the ASCE 7 in‐structure amplification factor, [1 + 2(z/h)] , to significantly overestimate demands at all floor levels and the ASCE 7 limit of to in many cases underestimate the calculated NSC amplification factors. Furthermore, the product of these 2 amplification factors (that represents the normalized peak NSC acceleration) in some cases exceeds the ASCE 7 equation by a factor up to 1.50.     

Effect of irregular structural configuration on floor acceleration demand in hill‐side buildings

A suite of reinforced‐concrete frame buildings located on hill sides, with 2 different structural configurations, viz step‐back and split‐foundation, are analyzed to study their floor response. Both step‐back and split‐foundation structural configurations lead to torsional effects in the direction across the slope due to the presence of shorter columns on the uphill side. Peak floor acceleration and floor response spectra are obtained at each storey's center of rigidity and at both its stiff and flexible edges. As reported in previous studies as well, it is observed that the floor response spectra are better correlated with the ground response spectrum. Therefore, the floor spectral amplification functions are obtained as the ratio of spectral ordinates at different floor levels to the one at the ground level. Peaks are observed in the spectral amplification functions corresponding to the first 2 modes in the upper portion of the hill‐side buildings, whereas a single peak corresponding to a specific kth mode of vibration is observed on the floors below the uppermost foundation level. Based on the numerical study for the step‐back and split‐foundation hill‐side buildings, simple floor spectral amplification functions are proposed and validated. The proposed spectral amplification functions take into account both the buildings' plan and elevation irregularities and can be used for seismic design of acceleration‐sensitive nonstructural components, given that the supporting structure's dynamic characteristics, torsional rotation, ground‐motion response spectrum, and location of the nonstructural components within the supporting structure are known, because current code models are actually not applicable to hill‐side buildings.     

The extended N2 method taking into account higher mode effects in elevation

The N2 method has been extended in order to take into account higher mode effects in elevation. The extension is based on the assumption that the structure remains in the elastic range when vibrating in higher modes. The seismic demand in terms of displacements and storey drifts can be obtained by enveloping the results of basic pushover analysis and the results of standard elastic modal analysis. The approach is consistent with the extended N2 method used for plan‐asymmetric buildings. The proposed procedure was applied to three variants of three steel frame buildings used in the SAC project. The structural response was investigated for two sets of ground motions. Different ground motion intensities were used in order to investigate the influence of the magnitude of plastic deformations. The N2 results were compared with the results of nonlinear response‐history analysis, two other pushover‐based methods (modal pushover analysis (MPA) and modified MPA (MMPA)), and pushover analysis without consideration of higher modes. It was found that a considerable influence of higher modes on storey drifts is present at the upper part of medium‐and high‐rise structures. This effect is the largest in the case of elastic behaviour and decreases with ground motion intensity. The higher mode effects also depend on the spectral shape. The approximate methods (extended N2, MPA and MMPA) are able to provide fair estimates of response in the case of the test examples. Accuracy decreases with the height of the building, and with the intensity of ground motion. The N2 results are generally conservative. Copyright © 2011 John Wiley & Sons, Ltd.     

On the design and seismic response of RC frame buildings designed with Eurocode 8

Performance-Based Seismic Design is now widely recognized as the pre-eminent seismic design and assessment methodology for building structures. In recognition of this, seismic codes may require that buildings achieve multiple performance objectives such as withstanding moderate, yet frequently occurring earthquakes with minimal structural and non-structural damage, while withstanding severe, but rare earthquakes without collapse and loss of life. These objectives are presumed to be satisfied by some codes if the force-based design procedures are followed. This paper investigates the efficacy of the Eurocode 8 force-based design provisions with respect to RC frame building design and expected seismic performance. Four, eight, and 16-storey moment frame buildings were designed and analyzed using the code modal response spectrum analysis provisions. Non-linear time-history analyses were subsequently performed to determine the simulated seismic response of the structures and to validate the Eurocode 8 force-based designs. The results indicate the design of flexural members in medium-to-long period structures is not significantly influenced by the choice of effective member stiffness; however, calculated interstorey drift demands are significantly affected. This finding was primarily attributed to the code’s enforcement of a minimum spectral ordinate on the design spectrum. Furthermore, design storey forces and interstorey drift demand estimates (and therefore damage), obtained by application of the code force-based design procedure varied substantially from those found through non-linear time-history analysis. Overall, the results suggest that though the Eurocode 8 may yield life-safe designs, the seismic performance of frame buildings of the same type and ductility class can be highly non-uniform.     

Seismic vulnerability evaluation of RC moment frame buildings in moderate seismic zones

A multi‐level seismic vulnerability assessment of reinforced concrete moment frame buildings located in moderate seismic zones (0.25g) is performed on a set of ductile versions of low‐ to mid‐rise two‐dimensional moment frames. The study is illustrated through application to comparative trial designs of two (4‐ and 8‐story) buildings adopting both space‐ and perimeter‐framed approaches. All frames are dimensioned as per the emerging version of the seismic design code in Egypt. These new seismic provisions are in line with current European norms for seismic design of buildings. Code‐compliant designs (CCD), as well as a proposed modified code design relaxing design drift demands for the investigated buildings, are examined to test their effectiveness and reliability. Applying nonlinear inelastic incremental dynamic analyses, fragility curves (FC) for the frames are developed corresponding to various code‐specified performance levels. Code preset lower and upper bounds on design acceleration and drift, respectively, are also addressed along with their implications, if imposed, on the frames seismic performance and vulnerability. Annual spectral acceleration hazard curves for the case study frames are also generated. Estimates for mean annual frequency (MAF) of exceeding various performance levels are then computed through an integration process of the data resulting from the FC with the site hazard curves. The study demonstrates that the proposed design procedure relaxing design drift demands delivers more economic building designs relative to CCDs, yet without risking the global safety of the structure. The relaxed design technique suggested herein, even though scoring higher, as expected by intuition, MAF of exceeding various code‐limiting performance levels expressed in terms of interstory drift ratios, still guarantees a reasonably acceptable actual margin against violating code limits for such levels. Copyright © 2010 John Wiley & Sons, Ltd.     

Earthquake‐induced loss assessment of steel frame buildings with special moment frames designed in highly seismic regions

This paper discusses an analytical study that quantifies the expected earthquake‐induced losses in typical office steel frame buildings designed with perimeter special moment frames in highly seismic regions. It is shown that for seismic events associated with low probabilities of occurrence, losses due to demolition and collapse may be significantly overestimated when the expected loss computations are based on analytical models that ignore the composite beam effects and the interior gravity framing system of a steel frame building. For frequently occurring seismic events building losses are dominated by non‐structural content repairs. In this case, the choice of the analytical model representation of the steel frame building becomes less important. Losses due to demolition and collapse in steel frame buildings with special moment frames designed with strong‐column/weak‐beam ratio larger than 2.0 are reduced by a factor of two compared with those in the same frames designed with a strong‐column/weak‐beam ratio larger than 1.0 as recommended in ANSI/AISC‐341‐10. The expected annual losses (EALs) of steel frame buildings with SMFs vary from 0.38% to 0.74% over the building life expectancy. The EALs are dominated by repairs of acceleration‐sensitive non‐structural content followed by repairs of drift‐sensitive non‐structural components. It is found that the effect of strong‐column/weak‐beam ratio on EALs is negligible. This is not the case when the present value of life‐cycle costs is selected as a loss‐metric. It is advisable to employ a combination of loss‐metrics to assess the earthquake‐induced losses in steel frame buildings with special moment frames depending on the seismic performance level of interest. Copyright © 2017 John Wiley & Sons, Ltd.     

Response spectrum techniques for asymmetric buildings

A scheme is proposed to calculate the effect of torsion on each lateral load resisting element of asymmetrical buildings in the context of the response spectrum technique. The scheme consists of: (i) Obtain the modal shear and torque on the building by the response spectrum technique, (ii) Compute the total modal shear forces on each frame by resolving the modal shear and torque on the building according to principles of structural mechanics. The shears on each frame due to the lateral load effect and torsional effect are combined algebraically, (iii) Obtain the total shear force on each frame by combining the total modal shears on that frame in a root sum square manner. Since the proper phase relationship between the lateral load effect and torsional effect is accounted for on a modal basis, it is believed that the proposed scheme provides a more realistic load estimate on the frames than the conventional approach. An example of a simplified mono-symmetrical frame structure is chosen to illustrate the accuracy of the proposed scheme, using dynamic time-history analysis as a standard for comparison.