Seismic Force Reduction Factor Research Articles

Performance-based seismic design of self-centering steel moment frames with SMA-bolted connections

This paper proposes a performance-based seismic design (PBSD) method for self-centering moment-resisting frames with shape memory alloy (SMA)-bolted endplate connections. PBSD can be used to achieve different performance objectives, resulting in several benefits, such as cost-effectiveness and customization of the design. This study develops a PBSD framework by establishing a relationship between the fundamental period, ductility demand, and seismic force reduction factor and using an energy-balanced concept. The design method is facilitated using an artificial neural network (ANN)-based predictive tool and an efficient experimentally-validated phenomenological model for SMA-bolted endplate connections. Maximum drift and ductility ratios are adopted as performance objectives. Two 3- and 6-story prototype frames are designed and evaluated to illustrate the proposed PBSD method. The seismic response and collapse safety of the prototype frames at different shaking intensities are evaluated. The results show that the prototype frames designed using the proposed PBSD framework meet the prescribed design objectives and the collapse safety requirements in FEMA P695. The illustrative examples confirm that the designed moment frames possess the intended self-centering capability with negligible residual deformations as low as 0.05% at the maximum considered earthquake (MCE) hazard level. The results also confirm that the designed frames exhibit uniform drift distribution along their height.

Performance-based design of self-centering energy-absorbing dual rocking core system

The Self-centering Energy-absorbing Dual Rocking Core system (denoted as the SEDRC system) is a newly developed high-performance steel lateral force-resisting system that can achieve negligible residual inter-story drifts and avoid structural damage during rare earthquakes. Compared to many existing re-centering systems, the SEDRC system also has larger deformability and can obtain a more uniform inter-story drift responses when subjected to ground motions. This research focuses on developing a performance-based design procedure for the SEDRC systems. The seismic force reduction factor model and constant-ductility demand model have been derived via parametric nonlinear dynamic analyses of single-degree-of-freedom systems with the hysteretic behavior of the SEDRC system for developing the Displacement-Based Design (DBD) procedure. Following the developed DBD method, three six-story SEDRC systems with different parameters have been designed to achieve the desired performance objectives. Systematic numerical studies, including nonlinear static analyses, nonlinear dynamic analyses, and incremental dynamic analyses, have been conducted to validate whether the designed SEDRC system can obtain the prescribed performance target and investigate the effect of some design parameters on the seismic responses of the SEDRC systems. According to the results from the numerical studies, it can be observed that the three SEDRC systems designed through the proposed DBD method can successfully obtain the desired performance target. Moreover, higher inter-story drift at the bearing of the shear friction spring damper, as well as the higher enhanced yield-strength ratio of BRBs, can enhance the collapse-resistant capacity of the SEDRC system. Higher bearing inter-story drift can further reduce the residual inter-story drift leading to a lower collapse probability of the SEDRC system subjected to rare seismic events.

Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods

Seismic force reduction factor (SFRF) spectra of shear-type multi-degree-of-freedom (MDOF) structures are investigated. The modified Clough model, capable of considering the strength-degradation/hardening and stiffness-degradation, is adopted. The SFRF mean spectra using 102 earthquake records on a typical site soil type (type C) are constructed with the period abscissa being divided into three period ranges to maintain the peak features at the two site-specific characteristic periods. Based on a large number of results, it is found that the peak value of SFRF spectra may also exist for MDOF, induced by large high-mode contributions to elastic base shear, besides the mentioned two peak values. The variations of the stiffness ratio λk and the strength ratio λF of the top to bottom story are both considered. It is found that the SFRFs for λF ≤ λk are smaller than those for λF > λk. A SFRF modification factor for MDOF systems is proposed with respect to SDOF. It is found that this factor is significantly affected by the story number and ductility. With a specific λF (= λk0.75), SFRF mean spectra are constructed and simple solutions are presented for MDOF systems. For frames satisfying the strong column/weak beam requirement, an approximate treatment in the MDOF shear-beam model is to assign a post-limit stiffness 15%-35% of the initial stiffness to the hysteretic curve. SFRF spectra for MDOF systems with 0.2 and 0.3 times the post-limit stiffness are remarkably larger than those without post-limit stiffness. Thus, the findings that frames with beam hinges have smaller ductility demand are explained through the large post-limit stiffness.

Geometric Parameters and Behavior Factor of Knee-Braced Steel Frames Using Nonlinear Static Pushover (NSP) Analyses

During the recent years, the new knee-braced frame (KBF) system has been interested to achieve a proper seismic behavior. Briefly introducing KBF, the present study evaluates the geometric parameters and behavior factor of multi-story knee-braced steel frames. The studied models include three-, five- and eight-story steel CBFs, EBFs and KBFs. Using linear static analyses, the present study evaluates lateral stiffness of knee-braced frames and plots their co-stiffness curves. Using co-stiffness curves, then, the best range is determined for geometric parameters of KBFs to achieve the proper stiffness. In addition, ductility-related seismic force reduction factor (Rμ), incremental resistance coefficient (RS), and behavior factor (R) are calculated for the frames using incremental nonlinear static analyses, and compared with the corresponding concentric and eccentric frames.

Seismic performance evaluation of Egyptian code-designed steel moment resisting frames

Despite the fact that steel is a ductile material, the significant damage, during earthquake events, highlighted the need to thoroughly investigate the seismic performance of steel structures. Seismic design procedures have been developed to enable structures to achieve specific acceptable level of damage under dynamic loads in accordance with particular levels of ductility. The ductility of steel moment resisting frames is developed through flexural yielding of beams, shear yielding of column panel zones, and flexural yielding of columns. Meanwhile, the frame must develop the required ductility without failure in the beam-to-column connection. The observations on panel zone behavior revealed that it can afford high ductility; however, localized deformations at corners of panel zone may increase the likelihood of fracture in vicinity of beam flange welds. On the other hand, the observations on flexural yielding behavior of columns reported potential soft story collapse. Consequently, counting on ductility due to shear yielding of panel zone and flexural yielding of columns is not recommended. Hence, the focus of this study has been directed toward flexural yielding of frame beams. The effect of beam profile slenderness (according to the Egyptian code design limits) has been examined against ductility, over-strength and redundancy with numerical assessment for the anticipated seismic force reduction factor. The reduction factor has been evaluated using both the N2-method and the time history analysis method. Accordingly, a guideline has been established for the Egyptian code provisions to enable professionals to assign the steel moment resisting frame between adequate-ductility, intermediate-ductility and limited-ductility.

Design of steel frames equipped with BRBs in the framework of Eurocode 8

Buckling restrained braces (BRBs) have been investigated extensively by means of experimental tests and their large ductility has been pointed out by many studies. Nevertheless, Eurocode 8 (EC8) does not provide any rules for design of steel frames with BRBs. For this reason, a design procedure for steel frames equipped with BRBs is proposed in this paper. The proposed design procedure is obtained by modifying the rules stipulated in EC8 for steel chevron braced frames. As a consequence, the obtained design procedure is consistent with the framework of EC8. BRBs are designed in terms of ductility and strength based on two parameters: the design storey drift Δud, i.e. the maximum accepted storey drift demand for earthquakes with a given probability of occurrence, and the behaviour factor q, which is a seismic force reduction factor correlated with the expected ductility of the structure. Beams and columns are designed according to capacity design principles derived from those given in EC8 with reference to steel chevron braced frames.The design procedure is applied to a set of multi-storey frames with BRBs assuming different values of Δud and q. Their seismic response is evaluated by nonlinear dynamic analysis for two seismic excitation levels. The BRBs are modelled by a refined numerical model calibrated on the basis of a wide database of experimental data. For each value of Δud, the highest values of q leading to seismic response that does not exceed the Significant Damage and Near Collapse limit states are determined. Then, the suggested behaviour factor is given as a function of the design storey drift.

Seismic force reduction factor for steel moment resisting frames with supplemental viscous dampers

Damping is one of the parameters that control the performance of structures when they are subjected to seismic, wind, blast or other transient shock and vibration disturbances. By adding supplemental viscous dampers, the energy input from a transient deformation is absorbed, not only by the structure itself, but also by the supplemental dampers. The aim of this study is to evaluate the values of both damping and ductility reduction factors for steel moment resisting frames with supplemental linear viscous dampers. Two-dimensional finite element models have been established for a range of low to mid rise buildings with different parameters: number of floors; number of bays; and number of dampers with different supplemental damping ratios (from 5% to 30%). A parametric study has been performed using time history analyses and a well-documented research method (N2-method). In addition, an equation has been proposed for each reduction factor based on regression analysis for the obtained results. The results of the Time history analyses are compared with those of a modified N2-method. Moreover, a comparison with values specified in the European code EC8 and the Egyptian code ECP-201 has been performed.

Predicting collapse loads for buildings subjected to seismic shock

In this paper an analytical expression that estimates the collapse load of a generic class of multi-storey, uniform, moment-resisting steel frames is presented. This expression is validated and calibrated with nonlinear pushover analyses (NPA) and incremental dynamic analyses for a set of buildings, of differing heights, that are designed according to the Eurocodes. The efficacy of different seismically induced load profiles in NPA is discussed with a preferred profile suggested for this class of structural system. The relationship between the actual seismic force reduction factor and code specified behavior factors is underlined.

Dynamics of inelastic base‐isolated structures subjected to analytical pulse ground motions

SUMMARYStructural design code provisions worldwide prescribe relatively small seismic force reduction factors for seismically base‐isolated structures, making their response to design‐level earthquake excitation essentially elastic. This paper uses the method of dimensional analysis to prove that; in most cases, this is not a conservative design approach but a necessity that emerges from the dynamics of base‐isolated structures. It is shown that allowing typical base‐isolated structures to yield results in large displacement ductility demands for the structure. This phenomenon is caused by the change in the nature of the ground motion excitation as it is transmitted to the structure through the seismic base isolation system as well as by the change in the distribution of displacements between the structure and the isolation bearings caused by yielding of the isolated structure. Copyright © 2013 John Wiley & Sons, Ltd.

Seismic Performance Assessment of Partially Grouted, Nominally Reinforced Concrete-Masonry Structural Walls Using Shake Table Testing

An experimental program has been carried out to study the performance of partially grouted, nominally reinforced (PG-NR) concrete block structural walls under in-plane seismic loading on a shake table. Five reduced-scale structural walls were constructed and tested under scaled versions of the 1940 El Centro, California earthquake, using its N-S component record with a constant axial compression load that represented a single-story building. The test walls were grouped into three categories. Type I and III walls had reinforcement at the wall end cells only, with vertical reinforcement ratios of 0.07 and 0.12%, respectively, based on the gross cross-sectional area of the walls. Type II walls were similar to Type I walls, but with an additional reinforcement bar located midlength of the wall with a vertical reinforcement ratio of 0.10%, also based on the gross cross-sectional area of the wall. The experimental results were documented and discussed with respect to wall lateral load capacity, stiffness degradation, period shift, displacement ductility levels attained, and relevant seismic-force reduction factors. The test results showed that PG-NR masonry walls can comprise a ductile seismic force-resisting system. Subsequently, PG-NR masonry walls have the potential to bridge the gap between unreinforced and reinforced masonry systems. The use of PG-NR masonry also results in a reduced cost compared with traditional reinforced masonry systems used in seismic zones that are typically fully grouted within the plastic hinge zones and require higher reinforcement ratios.

Seismic Response Modification Factors for Reinforced Masonry Structural Walls

The current North American design standards provide seismic force modification factors for the rectangular masonry structural walls category only; no similar provisions for flanged and end-confined masonry structural walls exist. This study demonstrates that seismic force reduction factor (R) values calculated for rectangular walls was close to 5.0, which is consistent with the value stipulated by the ASCE 7, and was 36 and 90% higher for the corresponding flanged and end-confined walls. The deflection amplification factor (Cd) values calculated for rectangular walls were higher than specified in the ASCE 7 for the special reinforced masonry wall category. Values of the ductility-related force modification factor (Rd) for flanged and end-confined walls were, respectively, at least 30 and 100% higher than those of rectangular walls specified in the National Building Code of Canada (NBCC). Quantification of the seismic response parameters within this study is expected to facilitate adoption of the flanged a...

Displacement capacity of masonry buildings as a basis for the assessment of behavior factor: an experimental study

The results of shaking table tests of a series of 1:5 scale masonry building models have been used for the assessment of values of structural behavior factor q for masonry structures, seismic force reduction factors proposed for the calculation of design seismic loads by Eurocode 8, European standard for the design of structures for earthquake resistance. Six models have been tested, representing prototype buildings of two different structural configurations and built with two different types of masonry materials. The study indicated that the reduction of seismic forces for the design depends not only on the type of masonry construction system, but also on structural configuration and mechanical characteristics of masonry materials. It has been also shown that besides displacement and energy dissipation capacity, damage limitation requirement should be taken into account when evaluating the values of behavior factor. On the basis of analysis of experimental results a conclusion can be made, that the values at the upper limit of the proposed range of values of structural behavior factor q for unreinforced and confined masonry construction systems are adequate, if pushover methods are used and the calculated global ductility of the structure is compared with the displacement demand. In the case where elastic analysis methods are used and significant overstrength is expected, the proposed values are conservative. However, additional research and parametric studies are needed to propose the modifications.

Effect of gravity columns on mitigation of drift concentration for braced frames

In strong earthquake events, multi-story concentrically braced steel frames (CBFs) are prone to form a story-collapse mechanism after buckling and yielding of the braces in a story. With the addition of continuous gravity columns and the increased lateral stiffness and strength they provide, however, it becomes possible to reduce the concentration of story drift and prevent the story collapse. Nonlinear dynamic analysis is implemented for a three-story CBF, and it is demonstrated that a drift concentration is inevitable, particularly in the first story, when the CBF is subjected to a set of large ground motions with a probability of exceedance of 2% in 50 years. A simplified theoretical formulation is presented to characterize the effect of gravity columns. Two cases are considered: gravity columns perfectly fixed, and gravity columns pinned at the base. It is noted that significant mitigation of drift concentration can be achieved, particularly when gravity columns are fixed at the base. Nonlinear time-history analysis is further performed to validate the theoretical observations and quantify the stiffness/strength demands of gravity columns to avoid drift concentration. The analysis results support the trends and observations obtained from the theoretical formulation. Finally, numerical simulations are implemented with the seismic force reduction factor D s , slenderness ratio of braces λ , and number of stories, as major analysis variables. The results demonstrate that a few (e.g. four) fixed-base gravity columns can lead to collapse prevention for reasonably designed low-rise CFBs under the set of large ground motions.

Development of Seismic Force Reduction and Displacement Amplification Factors for Autoclaved Aerated Concrete Structures

This paper addresses the development and application of a rational procedure to select the seismic force reduction factor ( R) and the displacement amplification factor ( Cd) for the design of autoclaved aerated concrete (AAC) structures. The values of R and Cd are proposed based on a combination of laboratory test results and numerical simulation. The test results are obtained from 14 AAC shear-wall specimens tested under simulated gravity and quasi-static reversed cyclic lateral loads. Analytical responses are predicted using nonlinear analysis models whose hysteretic characteristics are based on the experimentally observed responses. Using an iterative procedure, typical AAC structures are designed using successively larger trial values of the factor, R, until the structure's response (either ductility or drift) exceeds the experimentally determined capacity. A lower fractile of those critical values, modified for probable structural overstrength, is taken as a reasonable value of 3 for R. Using an analogous procedure, a reasonable value of Cd is determined as 3. These values will undoubtedly be refined based on field experience, just as they have been for other structural systems.

Seismic performance of RC frames designed for three different ductility levels

The concept of “making structures ductile” has prevailed in modern earthquake-resistant building design. In this context, questions remain regarding the selection of adequate ductility levels and the corresponding seismic force reduction factor q for a specific class of structures, whereas the detailing requirements to ensure the desired ductility continue to be refined. In the current investigation, three simple frames were designed for different ductility levels according to EC8 [Eurocode 8: Design provisions for earthquake resistance of structures. CEN (European Commission for Standardisation)/TC250/SC8, 1994] and their actual performance when subjected to earthquake simulation tests are observed and compared. Results indicate that under the “ductility for seismic force reduction” trade-off scheme, the frame designed for high ductility (thus large q factor) tends to attract more extensive damage due to large yield excursion, resulting in certain performance reduction. Insufficient confinement could lead to degrade hysteretic behaviour in a rather sensitive manner. Satisfactory performance was observed in the frame designed for medium ductility where both the seismic force reduction factor and the overall ductility were in the order of 3–4. In general, the overall and local ductility demands and the q-factors were observed to correlate in a rather predictable manner.

In-plane floor flexibility effects on torsionally unbalanced systems

This paper presents the results of an analytical work addressed to understand the effects of in-plane floor flexibility on torsionally unbalanced (TU) systems subjected to bidirectional firm-soil earthquake records. The study uses a structural system consisting of a linear-elastic diaphragm supported by non-linear frames oriented along two orthogonal directions. The diaphragm is modelled with plane-stress finite elements and frames with stiffness-degrading flexural elements. Results indicate that an increase of in-plane diaphragm flexibility leads to a reduction of frame displacements for systems with initial lateral period of vibration T > 0.4 s. For systems with T ≤ 0.4 s, in-plane Boor flexibility can lead to significant frame displacement increments (50 per cent higher). Results show that these variations on displacements decrease for increasing values of both the seismic-force reduction factor and the system initial lateral period.

Effects of torsion factors on simple non-linear systems using fully-bidirectional analyses

An ensemble of earthquake records is used to carry out non-linear analyses of simple torsionally unbalanced systems considering both resisting elements and earthquake components along two perpendicular directions. These fully bidirectional analyses are focused to study the effect of the following factors: (i) seismic-force reduction factor; (ii) factors α and δ used to compute the design eccentricity; (iii) initial lateral period; and (iv) initial stiffness eccentricity. Results indicate that the amplification factor α can be specified as a function of the force reduction factor, the lateral uncoupled period, and the stiffness eccentricity. It is concluded that the coefficient δ depends on the lateral period, the stiffness eccentricity, and the geometrical eccentricity. It was observed that negative shears caused by torsion should be neglected in the design of the stiff element, particularly in the case of systems with large stiffness eccentricity. Results suggest that additional studies should be performed to verify the assumed (partial) equivalence between unidirectional (resisting elements and earthquake components along one direction only) and fully bidirectional analyses to study building torsion problems.

Effects of torsion factors on simple non‐linear systems using fully‐bidirectional analyses

An ensemble of earthquake records is used to carry out non-linear analyses of simple torsionally unbalanced systems considering both resisting elements and earthquake components along two perpendicular directions. These fully bidirectional analyses are focused to study the effect of the following factors: (i) seismic-force reduction factor; (ii) factors α and δ used to compute the design eccentricity; (iii) initial lateral period; and (iv) initial stiffness eccentricity. Results indicate that the amplification factor α can be specified as a function of the force reduction factor, the lateral uncoupled period, and the stiffness eccentricity. It is concluded that the coefficient δ depends on the lateral period, the stiffness eccentricity, and the geometrical eccentricity. It was observed that negative shears caused by torsion should be neglected in the design of the stiff element, particularly in the case of systems with large stiffness eccentricity. Results suggest that additional studies should be performed to verify the assumed (partial) equivalence between unidirectional (resisting elements and earthquake components along one direction only) and fully bidirectional analyses to study building torsion problems. Copyright © 1999 John Wiley & Sons, Ltd.

Establishing R w and C d Factors for Confined Masonry Buildings

Seismic design provisions, including the Chilean seismic code, prescribe seismic design forces by reducing a linear elastic response spectra using a response modification factor. The codes also estimate expected maximum inelastic displacement that may occur during a severe earthquake, by amplifying the elastic displacement computed from the design seismic forces by a displacement amplification factor. In this paper, the seismic force reduction factor R w and displacement amplification factor C d are computed for typical confined masonry buildings, comparing base shear and first-story drift that develop in the structure when linear or nonlinear behavior is adopted. The computations are performed after analyzing several three and four story buildings. These buildings were subjected to the action of a number of earthquakes records obtained in Chile on March 3, 1985 and in Mexico on Sept. 19, 1985. The R w factor, evaluated for this type of building, depends both on the structure's wall density and on the source mechanism of the earthquake; in contrast to most code recommendations, the ratio of R w/C d obtained is less than 1.

Estimating seismic drifts of multistory reinforced concrete frames

AbstractIn order to estimate maximum roof and story drifts occurring in major earthquakes, seismic design provisions usually specify a deflection amplification factor (DAF) to amplify elastic design drifts. A comparison of several seismic design provisions indicated that the deflection amplification factor in both the UBC and NEHRP Recommended Provisions, being equal to 3Rw/8 and Cd, respectively, is very low and could lead to unconservative drift estimations. Since a reliable estimate of actual seismic drifts is essential for developing a performance‐based seismic design provision to control both structural and non‐structural damage, an analytical study of the seismic response of three instrumented reinforced concrete building frames located in California was first conducted. In addition to analytical studies, reported test results from shaking table testing of reduced‐scale multistory reinforced concrete frames were used to evaluate the deflection amplification factor. It is confirmed from both the analytical and experimental evidence that drifts developed in major earthquakes are much higher than those predicted by the UBC or NEHRP approach. It is recommended that the deflection amplification factor be increased to at least the seismic force reduction factor (Rw in UBC and R in NEHRP) for estimating maximum drifts.