Seismic Force Modification Factors Research Articles

Numerical assessment of TMS 402/602-22 and CSA S304-14 seismic design provisions for partially grouted reinforced masonry shear walls failing in flexure

Despite the economic benefits of using partially grouted reinforced masonry shear walls (PG-RMSWs) as a seismic force resisting system (SFRS) in low-rise buildings, using such a system in mid- and high-rise buildings is still questionable. This is because the literature lacks comprehensive studies investigating different seismic design provisions adopted for rectangular and flanged PG-RMSWs of aspect ratios greater than 2.0 and failing in flexure. Therefore, this study aims to conduct a comprehensive numerical assessment of the seismic design provisions of the North American masonry standards (i.e., TMS 402/602–22 and CSA S304–14) for designing different categories of rectangular and flanged PG-RMSWs failing in flexure. In this regard, 108 PG-RMSWs were designed and modeled using the Extreme Loading for Structures (ELS) software. Afterward, some changes were proposed to the current seismic design provisions in CSA S304–14 and TMS 402/602–22 for rectangular and flanged PG-RMSWs. In addition, a comparison was made between the seismic design provisions for PG-RMSWs and FG-RMSWs, designed according to each RMSW category, to investigate the expected differences in the behavior based on the applied seismic design provisions. Accordingly, additional 36 FG-RMSWs were designed according to CSA S304–14 and TMS 402/602–22. These additional walls were then modeled on the ELS and compared with their PG counterparts. The results show that both standards can be safely used to design rectangular and flanged PG-RMSWs only when using the two proposed provisions for each standard. For CSA S304–14, the possibility of updating clause 16.8.5.2 is concluded, allowing the use of PG-RMSWs without limitations. New seismic force modification factors were also proposed for TMS 402/602–22 for the design of rectangular and flanged PG-RMSWs. Finally, the comparison between rectangular PG and FG-RMSWs failing in flexure and designed according to CSA S304–14 and TMS 402/602–22 shows that the behavior of PG-RMSWs failing in flexure is comparable to FG-RMSWs under certain circumstances. This study is considered a significant step to prove the potential for more economical and safe usage of PG-RMSWs in mid- and high-rise buildings.

Seismic collapse performance of high-rise mass timber building with buckling-restrained braced frames

The present paper proposes a hybrid building system with the buckling-restrained brace and Glulam frames (BRBGF). For a highly seismic location of Vancouver, Canada, an 18-story building is designed with BRBGF as the lateral load-resisting system for the seismic hazard of NBC 2020. A nonlinear analytical model is developed and validated with the experimental data. Further, 30 pairs of ground motion records are selected to represent the complex seismicity of Southern British Columbia consisting of Shallow Crustal, Subduction Interface, and In-slab faulting mechanisms. The BRBGF system is found to achieve the target of maximum inter-story drift of 2.5% for the 2,475-year return period event. The building also passes the FEMA P695 criteria for acceptable collapse margin for seismic force modification factors of Rd=4 and Ro=1.2. The results from the study indicate the feasibility of high-rise timber buildings in highly seismic regions.

Methodology for determination of seismic force modification factors in Canada: Performance-based unified procedure

The National Building Code of Canada (NBC) employs seismic force modification factors (i.e. ductility-related factor, Rd, and an overstrength-related factor, Ro) for different Seismic Force Resisting Systems (SFRSs), which, since 2005, are largely based on engineering judgment and qualitative comparisons of seismic response characteristics of different SFRSs. Currently, there is no unified procedure in Canada for systematically quantifying these values, which has potentially led to perceived inconsistent levels of performance between buildings built with different SFRSs. While some research has been carried out in Canada to quantitatively evaluate the seismic response of different SFRSs using the FEMA P695 methodology with some modifications, inconsistencies exist among different research works. Moreover, the number of archetypes developed in these studies was limited, due to the computationally laborious incremental dynamic analysis (IDA) step in FEMA P695. Therefore, there is a need for a consistent and efficient methodology for structural performance assessment of different SFRSs in Canada. The proposed performance-based unified (PBU) procedure is to systematically quantify Rd and Ro factors for different SFRSs in the NBC. The PBU procedure is designed to be a performance-based approach (vs the risk-based approach of FEMA P695). In addition, our procedure is devised to optimize the number of archetypes through a two-level screening procedure using a nonlinear pushover and time history analyses before running the IDA. To validate the PBU procedure, we developed 21 different concrete moment frame archetypes covering various key parameters. The results verify the efficiency of the screening feature of the PBU procedure by a significant reduction in the number of archetypes requiring IDA.

Development of ductility-related modification factor for CLT-coupled wall buildings with replaceable shear link coupling beams

The desire of using sustainable materials has reignited the interest in timber-based construction. Researchers and practitioners are developing novel timber-based structural solutions. Cross-laminated timber (CLT)-coupled wall is a recently proposed system for potential use in mid- and high-rise timber construction. The National Building Code of Canada, however, does not include this system and, consequently, the seismic force modification factors are not available. This study evaluated the ductility-related force modification factor ( Rd) using the FEMA P-695 procedure. Nine archetype buildings were designed considering different design parameters: building storey height, CLT wall configuration, and coupling ratios. Using 30 ground motion records (bi-directional), rigorously selected for seismicity of Vancouver, BC, Canada, incremental dynamic analyses were performed. Collapse margin ratios were calculated to assess the adequacy of the trial Rd factors. Using an over-strength factor of 1.5, Rd = 4 is found to be acceptable for this system.

Seismic performance assessment of conventional construction concrete moment-resisting frame buildings in Canada using the FEMA P695 methodology

National Building Code of Canada (NBC) specifies 45 Seismic Force Resisting Systems to ensure the safety of building structures. Conventional construction concrete moment-resisting frame (CC-CMF) is one of these systems whose seismic response has not been systematically studied in Canada. This paper is an attempt to study the seismic performance of this system using the FEMA P695 methodology. In this regard, different archetype configurations were developed and analyzed through nonlinear static and dynamic analyses. Performance assessment results show that the CSA and NBC requirements for CC-CMF system represent the lower bound of values for seismic force modification factors, and conservatively meet life safety objectives presented in the NBC. Furthermore, different scenarios were considered for identifying ductility-related seismic force modification factor from pushover curves. The effect of height and gravity load levels on seismic force modification factors and collapse margin ratios are also presented by comparing archetypes having different configurations.

Effective stiffness and period-dependent seismic response modification factors for flexure-dominated fully-grouted reinforced masonry rectangular shear walls

The wall effective elastic stiffness, displacement ductility, and seismic force modification factors are important force-based seismic design (FBD) parameters for reinforced masonry (RM) shear walls. The effective stiffness, ke of reinforced masonry shear walls (RMSW) is crucial in computing the natural period and thus the elastic forces, and essential also in computing the displacements corresponding to the design seismic forces. This study analyzes previously reported test results of forty-three flexure-dominated fully-grouted rectangular RMSWs subjected to quasi-static cyclic load to evaluate the FBD parameters adopted by Canadian and American standards. In this study, based on the experimental results of 43 tested walls, a new stiffness reduction factor is proposed considering the effect of axial stress, vertical reinforcement ratio, and horizontal reinforcement ratio. Moreover, the seismic force modification factors are compared to the Canadian and US codes. The results showed that ductility related reduction factors should be dependent on the wall natural frequency and there is a room to relax the current proposed code values. In addition, incremental dynamic analysis was performed using a simplified numerical model to study the effect of dynamic loading on response modification factors and stiffness characteristics of the walls.

Seismic performance parameters of fully grouted reinforced masonry squat shear walls

The displacement ductility, ductility-related seismic force modification factor, and the effective elastic stiffness are important force-based seismic design (FBD) parameters for reinforced masonry (RM) shear walls. In addition, stiffness degradation and equivalent viscous damping, are crucial displacement-based seismic design (DBD) parameters. This study analyzes previously reported test results of eight RM shear-dominated fully-grouted rectangular squat walls subjected to cyclic lateral excitations to evaluate the FBD and DBD parameters. The main variables of the tested walls are the level of axial compressive stress, vertical and horizontal reinforcement ratio, anchorage end detail, and the spacing of horizontal and vertical reinforcement. However, all tested walls had the same shear span to depth ratio equal to 1.25. The evaluated FBD parameters are compared to the Canadian, European and American standards. Moreover, based on the analysis, equations for the stiffness degradation of RM shear walls relative to their top drift limit or displacement ductility, are developed and presented for the examined walls. The ductility-related seismic force modification factor is computed on average 2.6, and 3.9, based on equal energy and equal displacement idealization, respectively. The US, and European standards ignore the axial stress effect on wall’s elastic effective stiffness and highly overestimate its value for the tested walls. This study presents, based on the tested walls, a guide design values for squat shear-dominated walls category that can be used in FBD and DBD.

Numerical study on seismic force modification factors of hybrid light wood frame structures connected to a stiff core

Seismic force modification factors of structures are specified in building codes or design standards based on structural materials and types of lateral load resisting systems (LLRSs). For a hybrid building system consisting of multiple structural materials and/or more than one type of lateral load resisting systems, the National Building Code of Canada requires that the lowest value of seismic force modification factors of these LLRSs be assigned for the seismic design of the whole building. This requirement is conservative and in need of a review. In this project, the seismic force modification factors of hybrid building systems were investigated through numerical modeling analysis. These hybrid buildings consist of a mid-rise light wood frame sub-system connected to a reinforced masonry core sub-system by a ductile connection. Incremental dynamic analysis was conducted on these hybrid buildings using commercial software, ABAQUS, together with a subroutine that describes the hysteretic performance of the sub-systems and their inter-connections with the Bouc-Wen-Baber-Noori model. Results show that a value larger than the lower value of the two sub-systems can be assigned for seismic design of these hybrid buildings. In this study it was demonstrated that meaningful relationships exist between the seismic modification factors of a hybrid structure and the mechanical characteristics, including the relative strength and ductility, of the sub-systems and their inter-connections.

Seismic force modification factors for partitions in low- rise reinforced concrete buildings

Present codes of practice do not consider the effect of arrangement of partitions in the plan of structure on the seismic demands of these non-structural components. In this paper, a modification factor has been proposed to modify provisions for those seismic demands. Seventy two regular low-rise reinforced concrete moment frames, supporting some partitions, exposed to seven appropriate ground motions. The nonlinear seismic response history analysis considering out-of-plane behavior of partitions has been conducted using the OpenSees platform. The average values of peak responses from those earthquakes were obtained. The forces generated using the analytical method, which some of them verified with existing study results, were compared with the values from the code and a factor denoted as seismic force modification factor, W, was proposed. A parametric study has been carried out to study the effect of dominent parameters such as the arrangement of partitions, partition to structure height ratio, and length to height ratio of partitions on the W values. For the majority of the models, the W values are larger for partitions located further with respect to the center of floor. Moreover the modification factor could be as large as 1.85 for the partitions located in the middle floors.

Numerical evaluation: AISI S400 steel-sheathed CFS framed shear wall seismic design method

Seismic design provisions for steel-sheathed cold-formed steel framed shear walls, specific to Canada, are not provided in the existing AISI S213 Standard “North American Standard for Cold-Formed Steel Framing – Lateral Design”. A multi-phase approach was adopted in order to develop appropriate seismic design provisions for inclusion in the new AISI S400 Standard “North American Standard for Seismic Design of Cold-Formed Steel Structural Systems”. The approach included the extensive displacement based testing and dynamic testing of shear walls, the analysis of the test data results, the development and calibration of dynamic numerical models in OpenSees, and lastly, the dynamic response history analyses of twelve archetype buildings designed for the seismic hazard in three cities; Halifax (low seismic), Montreal (medium seismic) and Vancouver (high seismic). It is this last phase of the study that is documented herein. Fragility curves were developed from the buildings' response to 44 scaled ground motion records following a method adapted from the FEMA P695 analysis methodology. The results showed that the design method is appropriate, including the seismic force modification factors of Rd=2 and Ro=1.3. Improvement to the predicted seismic response of CFS framed buildings could be forthcoming if one were to account for the contribution of the non-structural gypsum wall panels.

Design of steel sheathed cold-formed steel framed shear walls

A method for the design of steel sheathed cold-formed steel framed shear walls has been developed for inclusion in the American Iron and Steel Institute's North American standards for lateral design using a comprehensive database of single-storey shear wall tests carried out in Canada and in the United States. The wall configurations differed in terms of wall aspect ratio, framing and sheathing thickness, screw fastener schedule and framing reinforcement. The Equivalent Energy Elastic–Plastic (EEEP) analysis approach was used to derive key design information from the test data, including: nominal shear resistance, a resistance factor, an over-strength factor for capacity based seismic design and ‘test-based’ seismic force modification factors for ductility and over-strength.

Strength Reduction Factors: A Unified Analytic Expression for Narrowband and Broadband Ground Motion Records

Strength reduction factors are an important component of the force modification factors used in the calculation of seismic code forces, as they account for the effect of the nonlinear hysteretic behavior of the structure. They are expressed as the ratio between the elastic strength demand and the inelastic strength demand induced in a structure by the earthquake. The evaluation of strength reduction factors has applications in the substantiation of seismic force modification factors in building design codes and in the direct application of the capacity spectrum method. The paper presents a study performed on two sets of accelerograms having different spectral content types, i.e. narrow frequency band records and broad frequency band records. Based on constantductility spectra of strength reduction factors, computed with 50% and 10% probability of exceedance, a unified analytic formula is developed, to describe the variation with ductility and vibration period of these factors. By modifying the values of the coefficients of the variables, the formula can be adapted for each type of spectral content. The formula is further refined, by determining a new set of coefficients, to also account for the influence of the predominant period of the ground motion in the case of narrow frequency band records.

Analytical study on seismic force modification factors for cross-laminated timber buildings

With two producers in operation and over 20 buildings already constructed or in planning process, use of cross-laminated timber (CLT) is gaining popularity in Canada. Since CLT as a structural system is currently not included in the National Building Code of Canada (NBCC), one of the most important issues are the values for the force modification factors for seismic design of CLT structures when NBCC equivalent static force procedure is used. In this study, a test-calibrated numerical model for CLT shear walls was applied to develop the design resistances for typical CLT wall configurations. An estimation of a possible range of Rd-factors was obtained by developing design variations for three multi-storey CLT apartment buildings. By specifying the desired seismic performance in terms of inter-storey drift, it is concluded that an Rd-factor of 2.0 will likely provide desirable building performance during the design earthquake level event in Vancouver, B.C.

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...

Evaluation of the AISI S213 seismic design procedures through testing of strap braced cold-formed steel walls

The North American standard for the design of lateral systems constructed of cold-formed steel (CFS) (AISI S213), which is published by the American Iron and Steel Institute (AISI), was updated in 2007. Included in this update were changes to the provisions related to strap braced walls. The 2007 version of AISI S213 includes requirements for the brace material and the use of capacity design principles; as well, the engineer is directed towards using welded connections to avoid possible net section fracture of the braces. Screw-connected braces may be used if shown to perform in a ductile fashion. The research described herein was undertaken to evaluate typical weld and screw-connected single-storey strap braced wall configurations with respect to their ability to resist lateral in-plane loads in the inelastic range of behaviour; that is, the results were used to verify the new strap braced wall seismic design provisions in AISI S213. A total of 44 tension-only X-braced walls ranging in size from 610×2440 mm 2 to 2440×2440 mm 2 (aspect ratios from 4:1 to 1:1), designed and detailed following a capacity-based approach, were tested under lateral loading using monotonic and reversed cyclic protocols. The strap braces were expected to undergo gross cross-section yielding along their length, while the other elements in the seismic force resisting system (SFRS) were selected to be able to carry the probable brace capacity. A summary of the test program is provided, including design approach, failure modes and ductility measures. The scope of the research also included the determination of “test-based” seismic force modification factors based on the measured ductility and overstrength of the test walls for comparison with the R-values recommended in AISI S213.

Development of seismic force modification factors for cold-formed steel strap braced walls

Seismic force modification factors to be used in conjunction with the National building code of Canada are recommended for two cold-formed steel (CFS) concentrically braced frame categories; limited ductility (LD) (Rd = 2.0, Ro = 1.3, height limit 20 m) and conventional construction (CC) (Rd = 1.25, Ro = 1.3, height limit 15 m, not permitted in high seismic zones). Nonlinear time history dynamic analyses of multi-storey CFS framed structures were carried out following an approach adopted from the Federal Emergency Management Agency (FEMA) P695 on the quantification of building seismic performance factors. Input earthquake records (both synthetic and recorded) were scaled to the site specific uniform hazard spectra for Vancouver, Calgary, Québec City, and Halifax. The calculated inelastic storey drifts and the failure probabilities from the FEMA P695 incremental dynamic analysis procedure showed that the Canadian seismic design procedures for type LD and CC strap braced walls in the American Iron and Steel Institute (AISI) S213 North American CFS lateral design standard are acceptable for the multi-storey buildings that were analysed.

P-Δ Effects on Seismic Force Modification Factors for Modified-Clough and EPP Hysteretic Models

Based on the elastic-plastic time-history analysis of SDOF(single degree of freedom) systems for the Modified-Clough(MC) model and the elastic perfectly-plastic (EPP) model, this paper carried out a study of the seismic force modification factors Rμ (SFMF) both when the P-Δ effects are not allowed for ( Rμ) and when they are allowed for ( R'μ). 370 earthquake records from 4 site & soil conditions, 74 to 106 records for each site, were used to calculate the structural response. The structural periods varied from 0.1 to 6sec and the ductilities were taken to be 2,3,4,5 and 6. The stability index θ were varied from 0.025 to 0.1. The ratio spectra S of Rμ to R'μ were constructed to analyze the influence of P-Δ effects on the SFMF. It is found that the spectral values of S depend on the ductility, the stability index and the normalized period T / TgR. The results indicate that the influence of P-Δ effect is different for the two hysteretic models. The increase in strength demand to maintain constant ductility in the presence of P-Δ effects using the EPP model is greater than that given by the modified- Clough model.

Seismic Performance Parameters for Reinforced Concrete-Block Shear Wall Construction

The focus of the current study is to analyze previously reported test results to evaluate equivalent plastic hinge lengths for concrete-block shear walls and to extract related seismic performance parameters. Inelastic curvatures at the base of the walls are the main source of plastic deformation for flexurally dominated walls. With adequate estimation of the plastic hinge length and more realistic values for inelastic curvatures at the base of the wall, top wall displacement can be predicted more accurately. For the walls analyzed, measured compressive strains close to the base of the wall at maximum load were significantly higher than the strains specified by North American codes. The strains, although may not alter the wall strength, significantly affect the displacement ductility at maximum load. The analysis showed that the equivalent plastic hinge length varied between approximately 30 and 60% of the wall length at a drift of 1%. The product of the seismic force modification factors (for ductility a...

Inelastic yielding strength demand coefficient spectra

Currently, earthquake action is obtained by dividing the elastic acceleration spectra by a seismic modification factor, and the latter is also a spectrum actually. The dynamic inelastic response of single-degree-of-freedom (SDOF) systems for modified-Clough hysteretic model with stiffness degradation when subjected to reverse loading were analyzed. Total 370 earthquake records belonging to four site and soil conditions with each containing 74–106 records were used as excitations. The formulae for elastic strength demand coefficient η e and the seismic force modification factor R μ were proposed. It is found that the both types of spectra have different characteristic periods, respectively. Two sets of inelastic yielding strength demand coefficients were calculated and compared. The results show that if the elastic η e and the R μ spectra were both normalized by the characteristic period T gR, the inelastic η y μ spectra are not in good agreement with those derived directly from statistical analysis. Therefore, the inelastic η y μ spectra normalized by the characteristic period T ga were constructed directly, and the obtained curves were quite similar for the four site types. The inelastic η y μ spectra increase with the period when T< T ga and then descend exponentially with the period. Simple formulae for both the averaged spectra and the spectra with 90% probability guaranty are proposed, and they are in excellent agreement with the statistically obtained curves.

Seismic force modification factors for modified-Clough hysteretic model

Based on the elastic–plastic time-history earthquake analysis of SDOF (single degree of freedom) systems, this paper describes an investigation of the seismic force modification factor R for the modified-Clough hysteretic model. In total 370 earthquake records belonging to 4 site conditions, with each containing 74 to 106 records, are used to calculate the structural response and finally the factor R . The structure periods vary from 0.1 to 6 s and the displacement ductility is taken to be 2, 3, 4, 5 and 6 respectively. Damping ratios of 0.0, 0.035 and 0.05 and post-yield stiffness ratios of 0.0, 0.05, 0.1 and 0.2 are used in the analysis. It is found that the most important factor determining the R is the ductility. The damping and post-yield stiffness only have a secondary effect in the short period range. The R spectra values increase with system periods, from 1 to the maximum value when the system has the same period as the site, and then decrease rapidly, close to the ductility in the long period range. The R spectra are correlated with the normalized system period T / T g to maintain the peak characteristics of the R spectra near the characteristic periods T g for different earthquake records. The dramatic increase of R values at the site period T g is explained through constructing similar R spectra for the EPP (elastic–perfectly plastic) SDOF model under sinusoidal excitation. Simple formulae are proposed for the R spectra which are expressed as multiplication of functions of the ductility, damping and post-yield stiffness. The peak characteristics of the R spectra at T / T g = 1 are maintained. Both the averaged spectra and the spectra with 90% probability are presented. Three other hysteretic models: elastic–perfectly plastic (EPP), shear–slipped (SSP) and bilinear elastic (BILE), are analyzed to separate the effects of ductility, energy-dissipating capacity and stiffness degradation in the modified-Clough model on R spectra. Their results are compared with each other. It is found that structures with the modified-Clough model will experience lateral strength demands typically (5%–25%) smaller than those of the EPP models with periods 0.6 < T / T g < 3 . Comparisons between R factors for EPP and BILE or SSP models show that the effect of energy-dissipating capacity on R spectra is statistically evident only in the short period range, and the maximum decrease in R values for the latter two models is by 50% at most. With increasing period, the effect of energy-dissipating capacity is negligible. This suggests that the effect of the energy-dissipating capacity is not so great as we expected even in the low period range, and it has nearly no effect on the R spectra in the middle and long period range.