Seismic Response Factors Research Articles

Developments in Quantifying the Response Factors Required for Linear Analytical and Seismic Design Procedures

Despite the recent initiatives and developments in building design provisions using performance-based design, practicing engineers frequently adopt force-based design approaches, irrespective of the structural system or building irregularity. Modern seismic building codes adopt the concept of simplifying the complex nonlinear response of a structure under seismic loading to an equivalent linear response through elastic analytical procedures using seismic design response factors. Nevertheless, code-recommended seismic design response factors may not result in a cost-effective design with a uniform margin of safety for different structural systems. Previous studies also adopted different methodologies for quantifying the seismic response factors. Hence, there is a pressing need for a comprehensive review covering the developments in quantifying these vital design factors. This paper presents a systematic review of the response factors used with linear analytical procedures recommended by modern building design provisions and the techniques employed in previous studies to evaluate these factors using SDOF and MDOF systems covering analytical, experimental and hybrid assessment approaches. Limitations and gaps identified from the previous studies indicated that most investigations focused on 2D analysis and regular low-rise buildings, while limited studies were directed to shear wall structures, considering mostly unidirectional seismic loading. This comparative review provides insights into previous studies’ methodologies and constraints and identifies the need for future research to calibrate seismic response factors to achieve more economical designs with consistent safety margins for different structural systems.

Seismic performance evaluation of eccentrically braced frames with long links using FEMA P695 methodology

Short links that primarily yield under shear are usually preferred in eccentrically braced frames (EBFs) due to their high rotation and energy dissipation capacities. Long links that yield under flexure can be used in cases where large openings are required for architectural reasons. Research conducted in the past showed that the seismic response factors recommended in ASCE7 result in designs with higher collapse probabilities than expected for EBFs with shear links. Long link behavior differs from the behavior of short links because the former is governed by flexure and subjected to significant amounts of strength and stiffness degradation. A numerical study was undertaken to evaluate the seismic response factors for EBFs with long links using FEMA P695 methodology. Twenty-four EBF archetypes were designed by considering the bay width, number of stories, the link length to bay width (e/L) ratio and column base condition as the variables. Performances of these archetypes were evaluated under maximum considered earthquake (MCE), and collapse level earthquake (CLE). The effects of degradation were studied by considering degrading and non-degrading responses separately. The results showed that strength and stiffness degradation increases the link rotation angle as much as 46 percent when compared with the non-degrading models. The recommended response factors were found to provide acceptable performance for e/L = 0.5, when 20% probability of collapse is considered under MCE level events. Remedial measures were investigated to achieve acceptable performance for collapse probability of 10% under MCE level events.

Unified calculation model for the longitudinal fundamental frequency of continuous rigid frame bridge

The frequencies formulas of the bridge are of great importance in the design process since these formulas provide insight dynamic characteristics of the structure, which guides the designers to parametric analyses and the layout of the bridge in conceptual or preliminary design. Continuous rigid frame bridge is popular in the mountainous area. Mostly, this type of bridge was simplified either as a girder or cantilever when calculating the frequency, however, studies showed that the different configuration of the bridge made the problem more complex, and there is no unified fundamental calculation pattern for this kind of bridge. In this study, an empirical frequency equation is proposed as a function of pier's height, stiffness of pier and the weight of the structure. A unified fundamental frequency formula is presented based on the energy principle, then the typical continuous rigid frame bridge is investigated by finite element method (FEM) to study the dynamic characteristics of the structure, and then several key parameters are investigated on the effect of structural frequency. These parameters include the number, position and stiffness of the tie beam. Nonlinear regression analyses are conducted with a comprehensive statistical study from plenty of engineering structures. Finally, the proposed frequency equation is validated by field test results. The results show that the fundamental frequency of the continuous rigid frame bridge increases more than 15% when the tie beams are set, and it increases with the stiffness ratio of tie beam to pier. The results also show that the presented unified fundamental frequency has an error of 4.6% compared with the measured results. The investigation can predicate the approximate longitudinal fundamental frequency of continuous ridged frame bridge, which can provide reference for the seismic response and dynamic impact factor design of the pier.

Improving the seismic behaviour of reinforced concrete moment resisting frames by means of SMA bars and ultra-high performance concrete

In the design of concrete buildings in seismic zones, ductility is normally used to reduce design efforts and as a form of energy dissipation. This implies structural damage to buildings in the form of interstorey drifts that need to be subsequently repaired or demolished.Twelve moment resisting frames (MRF) were designed with different geometrical configurations and new materials, and shape memory alloy bars and ultra-high performance concrete were used in the critical zones of the structure to improve their seismic behaviour. MRFs were subjected to a non-linear static pushover analysis and an incremental dynamic analysis to assess their behaviour. To do so, six real accelerograms were selected to study the response of the 12 MRFs, scaled at increasing peak ground acceleration (PGA). The base shear, the building’s overall plastic mechanism and the seismic response factors for the different geometrical and material combinations were analysed. The obtained values were compared with ASCE 7-05 and EC-8 proposals.It was concluded that the combination of shape memory alloys and ultra-high performance concrete allowed the behaviour factor to increase and residual drifts to decrease, which are advantages for both design and seismic behaviour.

Evaluation of seismic response factors for BRBFs using FEMA P695 methodology

This paper reports the details of a numerical study undertaken to evaluate seismic response factors for steel buckling-restrained braced frames (BRBFs) using the FEMA P695 methodology. In the United States, BRBFs are designed according to Minimum Design Loads for Buildings and Other Structures (ASCE 7) and the Seismic Provisions for Structural Steel Buildings (AISC 341). Twenty-four archetypes were designed according to the U.S. specifications and their behavior was assessed by making use of non-simulated collapse models. The interstory drift, brace axial strain and cumulative brace axial strain demands under collapse level ground motions were determined. The results obtained indicate that the current seismic response factors are adequate in terms of interstory drift and cumulative axial strain demands. On the other hand, large differences between the design level and collapse level axial strains were reported, which can result in undesirable brace behavior. Modified approaches were developed to estimate the axial strains for collapse level ground motions. These include a modification to the deflection amplification factor and a modification to the AISC 341 requirements for expected brace deformations. The archetypes were redesigned using the proposed modifications and reevaluated using the FEMA P695 methodology. The results indicate that the proposed modifications result in axial strain demands that are in close agreement with the calculated demands.

Dynamic behavior of upgraded rocking wall-moment frames using an extended coupled-two-beam model

Rocking wall-moment frames (RWMFs), which perform well in controlling the soft-story mechanism, can achieve an enhanced performance by substituting their pinned base by a variable base rotational constraint provided by replaceable self-centering and energy dissipation devices. Rather than experiencing damage inside the moment frames, those upgraded RWMFs show a high potential towards seismic resilience by transferring damage to the replaceable base rotational constraint. The effect of this rotational constraint and the stiffness ratio between the moment frame and rocking wall on the dynamic behavior of upgraded RWMFs is investigated with the aid of an extended coupled-two-beam model proposed in this paper. In this model, the rocking wall and moment frame are represented by a linked flexural beam and a shear beam, respectively. The model replaces the fixed base of the flexural beam by a rotational spring to take the variable base rotational constraint into account. Closed-form solutions for modal displacement shapes, modal drifts, modal shear force and modal moment are derived. The model is verified with finite element analysis, and modal contributions to seismic response and drift concentration factor demand under earthquakes are investigated. It is found that within identified ranges of the rotational constraint and the stiffness ratio between the moment frame and rocking wall, a relatively good uniformity of story drift distribution is obtained and the higher modes effect caused by the full releasing of the rocking wall is mitigated. The model, the derived interstory drift spectra and drift concentration factor spectra can serve as useful tools for preliminary resilience oriented design purpose.

Seismic performance and damage incurred by monolithic concrete self-centering rocking walls under the effect of axial stress ratio

Self-centering rocking walls offer the possibility of minimizing repair costs and downtimes, and also nullify the residual drift after seismic events, thanks to their self-centering properties. In this paper, the effect of axial stress ratio on the behavior of monolithic self-centering rocking walls is investigated by utilizing a developed finite element model. To verify the validity of the finite element model, results and observed damage in the model are compared with those of a full-scale wall test. The axial stress ratio is varied from 0.024 to 0.30 while keeping the other structural parameters constant. For qualitative damage evaluation, the observed damage in the model compared with expected damage states of desired performance levels. In order to evaluate the incurred damage quantitatively, the amount of crushing and damage in the wall is calculated by utilizing several ratios (crushing ratio and damage ratio). Furthermore, seismic response factors (i.e., μ, R and Cd) are calculated for different axial stress ratio values. The obtained results showed that, in order to satisfy the requirements of desired performance levels, the maximum axial stress ratio should be approximately within the range of 0.10–0.15. In addition, the maximum overall damage ratio and crushing ratio are suggested to be less than 5%. For axial stress ratio higher than 0.15, the flag-shaped pattern of hysteresis curves completely disappeared and the variation of displacement ductility is less sensitive to axial stress ratio. Considering the maximum axial stress ratio limited to 0.150, values of 4 and 3.5 are conservatively proposed as a period-independent response modification factor and displacement modification factor of the investigated structural wall, respectively.

Assessment of seismic design response factors of air traffic control towers

Air Traffic Control (ATC) towers are among the most vital structures in each airport. Due to inadequate information regarding the seismic design and assessment of these types of structures, practicing engineers may refer to building codes. However, taking into account the special dynamic behavior of ATC towers, instructions and recommendations provided in building codes often do not comply with the required seismic performance levels of ATC towers. In this study, seismic behaviors of three in-service ATC towers with a dual concrete core lateral load resisting system were studied through pushover and incremental dynamic collapse analysis. Seismic design response factors of the reference towers were calculated. It was found that seismic design response factors adopted by the design code did not provide a uniform safety margin for all reference ATC towers. It was also observed that shorter towers have significantly higher response modification factors compared to taller towers. For the studied towers, a structural over-strength factor of 2.4 and a displacement amplification factor of 4 were obtained.

Evaluation of Seismic Response Factors for Eccentrically Braced Frames Using FEMA P695 Methodology

This paper reports details of a numerical study undertaken to evaluate seismic response factors for steel eccentrically braced frames (EBFs) using the FEMA P695 methodology. Six archetypes were designed by making use of the current U.S. specifications, and their behavior was assessed by making use of nonsimulated collapse models. Results indicate that the current values of response factors result in designs with higher collapse probabilities than expected. Two modifications were developed to bring the collapse probability of these archetypes to acceptable levels. The first modification is on the deflection amplification factor while the second one is on the response modification coefficient. Six archetypes were redesigned using the proposed modifications and reevaluated using the FEMA P695 methodology. The results indicate that the proposed modifications are adequate to satisfy the target collapse probability. Maximum and cumulative link rotation angles were observed to be less than the predefined limits.

Seismic response factors of reinforced concrete pedestal in elevated water tanks

Reinforced concrete (RC) elevated water tanks are critical structures that are expected to remain functional after severe earthquakes in order to serve the water system networks. Despite this significant role, the number of research studies which investigated the nonlinear seismic response of RC pedestals in elevated water tanks is very limited. In the current codes and standards, the seismic response factors are mainly based on engineering judgement. In this paper, a systematic approach is employed to establish the seismic response factors for a wide range of elevate water tank sizes and RC pedestal dimensions commonly built in industry. In total, forty-eight model configurations (prototypes) are selected and designed based on current codes and standards. The finite element (FE) method is then used for nonlinear static (pushover) analysis of the prototypes. The pushover curve of each prototype is developed and the seismic response factors are determined accordingly. The effect of various parameters such as fundamental period, height to diameter ratio, seismic design category, and tank size on the seismic response factors of elevated water tanks is evaluated. Furthermore, the cracking propagation pattern in RC pedestal is studied. The result of the study shows that the tank size is a critical parameter affecting the seismic response of elevated water tanks. It is recommended not to use the same seismic response factors for all RC elevated water tanks regardless of the tank size. In addition, two different patterns of cracking depending on the height to diameter ratio of the pedestal are detected and discussed.

Seismic Behavior of Single Layer Schwedler Domes

Space structures can efficiently resist seismic loads due to their lightweight, geometry, high residual strength and high redundancy. Determination of seismic response factor of space structures is essential for based on equivalent static method. Seismic behavior of single layer Schwedler domes is studied in this paper. Six domes with different spans and same number of nodes and elements as well as loading conditions are modeled using finite element method. Nonlinear static and dynamic analyses are carried out to study the seismic behavior of these domes. The force-displacement diagrams are used to obtain a formula for predicting the fundamental natural period. Using the proposed equation, response modification factor, Rw, is determined from these analyses. Moreover, ductility curves are compared at different levels of the dome. Finally, a formula is proposed for calculation of natural period of vibration and response modification factor of Schwedler domes.

Seismic performance evaluation of staggered wall structures using Fema P695 procedure

In this study the seismic performance of six and 12-storey staggered wall structures with a middle corridor is evaluated based on the Fema P695 procedure. The validity of the seismic response factors used for seismic design of the model structures is also evaluated following the procedure. The analysis results of the prototype structures are compared with those of structures with increased coupling beam depth or increased rebar ratio of coupling beams. The adjusted collapse margin ratios of the model structures obtained from incremental dynamic analyses turn out to be larger than the limit states specified in the Fema P695, which implies that the analysis model structures have enough safety margin for collapse against design level earthquakes. It is also concluded that the response modification factor used in the design of the model structures is valid.

Seismic performance assessment of steel corrugated shear wall system using non-linear analysis

A new approach to develop seismic response factors for the design of structural systems has recently been developed by the Applied Technology Council and published in the FEMA P-695 document. The FEMA P-695 assessment methodology provides a comprehensive and objective approach to evaluate the performance factors based on non-linear structural analysis, while considering the uncertainties in design requirements, supporting test data, and the non-linear model. The goal of the methodology is to ensure that buildings designed with the selected performance factor have an acceptably low likelihood of structural collapse under extreme (rare) earthquake ground motions. The methodology is based on the design and assessment of representative archetypical building designs, whose collapse performance is evaluated through a series of non-linear static and dynamic analyses using numerical models that are calibrated to experimental test data. This methodology is applied to evaluate the seismic performance factors for a newly proposed light-framed steel shear wall seismic force resisting system, developed by Tipping Mar and Associates of Berkeley, California. The system consists of a steel corrugated sheet shear wall for use in mid-size residential and commercial structures. The calibration of the non-linear analysis model parameters to experimental data uses genetic algorithms. The system archetypes evaluated in this study are shown to meet the FEMA P-695 acceptance criteria for a seismic response modification factor of R equal to 4.

Assessment of seismic design response factors of concrete wall buildings

To verify the seismic design response factors of high-rise buildings, five reference structures, varying in height from 20- to 60-stories, were selected and designed according to modern design codes to represent a wide range of concrete wall structures. Verified fiber-based analytical models for inelastic simulation were developed, considering the geometric nonlinearity and material inelasticity of the structural members. The ground motion uncertainty was accounted for by employing 20 earthquake records representing two seismic scenarios, consistent with the latest understanding of the tectonic setting and seismicity of the selected reference region (UAE). A large number of Inelastic Pushover Analyses (IPAs) and Incremental Dynamic Collapse Analyses (IDCAs) were deployed for the reference structures to estimate the seismic design response factors. It is concluded that the factors adopted by the design code are adequately conservative. The results of this systematic assessment of seismic design response factors apply to a wide variety of contemporary concrete wall buildings with various characteristics.

Towards a new base shear format in future NBCC seismic provisions

Recent trends in the specifications of earthquake design forces are moving away from spectral amplification of ground motion towards direct evaluation of spectral values. Also, the 1988 Saguenay earthquake produced strong evidence for the need to modify the present provisions for low period structures in eastern North America. A new database consisting of 75 time histories was assembled and an extensive parametric study was undertaken to prepare new seismic response factors (S curves) for the National Building Code of Canada (NBCC). These time histories were divided into five categories (15 time histories each) on the basis of their frequency content as measured by their peak ground acceleration to peak ground velocity ratios, ranging from very high (≈3) to very low (≈0.5). Mean and mean + one standard deviation response spectra for one-degree-of-freedom and multi-degree-of-freedom systems were computed for the five categories using several normalizing (scaling) rules for the time histories. The results were compared and spectral amplification factors are presented. Spectra based on peak spectral velocity scaling were compared with spectra based on the present peak ground velocity scaling approach, and some differences are noted. Also, comparisons with the design spectra given in the 1991 edition of the National Earthquake Hazard Reduction Program provisions are presented. On the basis of this study, new S curves are proposed for consideration in the development of future editions of the NBCC. Key words: earthquake engineering, design spectra, building codes, amplification, ground motion, acceleration, velocity, ratio.

On the dynamic foundation factor for the National Building Code of Canada: low to medium rise buildings

Site-specific seismic response factors for low-period building structures are presented as an alternative to the recently proposed foundation factor F* for inclusion in the seismic provision of the National Building Code of Canada. These factors are not explicit functions of the site vibration period, and, therefore, are more suitable for the design of small to medium rise buildings for which only limited site investigations are routinely carried out. Key words: earthquake engineering, design spectra, site-specific, building codes.

Seismic isolation in New Zealand

Bridges, buildings, and industrial equipment can be given increased protection from earthquake damage by limiting the earthquake attack through seismic isolation. A broad summary of the seismic responses of base-isolated structures is of considerable assistance for their preliminary design. Seismic isolation as already used in New Zealand consists of a flexible base or support combined with some form of energy-dissipating device, usually involving the hysteretic working of steel or lead. This paper presents examples of the New Zealand experience, where seismic isolation has been used for 42 bridges, 3 buildings, a tall chimney, and high-voltage capacitor banks. Additional seismic response factors, which may be important for nuclear power plants, are also discussed briefly.

Reply: Evaluation of the seismic response factor introduced in the 1985 edition of the National Building Code of Canada

The seismic loading provisions included in the 1985 edition of the National Building Code of Canada simulate the dynamic response of structures using a seismic response factor, which has three branches depending upon the relationship between the velocity-related seismic zone Zv and the acceleration-related zone Za. This paper utilizes three ensembles of actual seismic strong motion records to evaluate the seismic response factor; each ensemble has acceleration/velocity ratios corresponding to one of the three branches of the seismic response factor. These strong motion time histories are used as input to relatively simple elastic models of frame and wall structures in order to obtain dynamic seismic response factors. The comparison of these dynamic factors with those specified in the NBCC 1985 indicates that the code factors are generally quite satisfactory, with the exception of the case of frame structures with low fundamental periods located such that Za is two zones higher than Zv. The paper reference...

Discussion: Evaluation of the seismic response factor introduced in the 1985 edition of the National Building Code of Canada

Discussion: Evaluation of the seismic response factor introduced in the 1985 edition of the National Building Code of Canada

Evaluation of base shear provisions in the 1985 edition of the National Building Code of Canada

A statistical analysis is performed to evaluate the base shear provisions in the 1985 edition of the National Building Code of Canada (NBCC 1985). Three sets of real earthquake records are selected to represent seismic ground motions with low, normal, and high peak acceleration to velocity (a/v) ratios. Single degree of freedom stiffness degrading systems are used as structural models; three damage indicators are employed to measure structural damage. The yield strength of the systems is specified in two different ways: (a) a single seismic response factor is used, irrespective of the a/v ratios of the input ground motions; (b) three different seismic response factors are used in the short-period range, depending upon the a/v ratios of the input ground motions, as suggested in NBCC 1985. A comparison of the statistical results of the three damage parameters for the systems designed with these two methods of strength specification indicates that the NBCC 1985 base shear provisions provide consistent control over structural damage when the structural systems are subjected to ground motions with different a/v ratios. Key words: earthquakes, ground motions, response spectra, stiffness degrading systems, seismic design, base shear, yield strength, inelastic response, damage parameters.