Performance-based Plastic Design Research Articles

Determination of response modification coefficient of SPSW in RC frame using plastic design method

ABSTRACT In the last few decades, the idea of using thin steel plate shear walls (SPSW) as a resistant system against lateral loads in designing and reinforcing buildings has been of concern to researchers and designers. In this research, we studied the response modification coefficient (R), the overstrength factor (Ω0), and the deflection amplification factor (C d ) in a reinforced concrete special moment frame (RC-SMF) with thin SPSW. We used the performance-based plastic design (PBPD) method. For this purpose, we consider frames with SPSW systems with different story numbers. Static pushover analysis is performed on these frames using the strip model in OpenSees software. OpenSees software is the Open System for Earthquake Engineering Simulation located at http://opensees.berkeley.edu. Simulation results were compared with experimental results, and acceptable matching was observed between the two. Finally, the values of response modification coefficient (R), overstrength factor (Ω0), and deflection amplification factor (C d ) for RC-SMF with thin SPSW were calculated based on the Uang method. The ultimate limit design method proposed them as 9.37, 2.21, and 11.06.

A two-level performance-based plastic design method for multi-story steel frames with double-yielding systems

The performance-based seismic design (PBSD) is usually conducted under design basis earthquakes (DBE), and then, the performance of the designed structures is examined under maximum considered earthquakes (MCE). As a result, it is challenging to simultaneously satisfy the performance targets associated with the DBE and MCE levels. To this end, this study proposes a two-level performance-based plastic design (PBPD) method. The fused steel frames exhibiting trilinear capacity curves are selected as the example structures. The peak interstory drift ratios under the DBE and MCE levels are defined as the performance targets and they are explicitly utilized at the beginning of the design procedure. The expressions of two energy modification factors are first obtained by establishing energy balance equations for single-degree-of-freedom (SDOF) systems under the DBE and MCE levels, respectively. Nonlinear time history analyses (NLTHA) for SDOF systems with various trilinear capacity curves are conducted to derive necessary design parameters. The versatility and flexibility of this design method are achieved by enabling both the primary and secondary yielding systems to yield under the DBE level. To demonstrate and validate the proposed design method, a six-story benchmark steel frame equipped with idealized metallic yielding damping braces is selected and designed with two sets of performance targets. The nonlinear static and NLTHA results proved that the designed structures can simultaneously meet the prescribed performance targets under both DBE and MCE levels.

Performance-based seismic design method for disc spring-based self-centering viscous dissipative braced steel frame

Disc spring-based self-centering viscous damper (SCVD) has emerged as a novel technology, offering velocity-dependent energy dissipation and exceptional self-centering capabilities. Integrating this damper in structural bracing systems can effectively enhance passive control over critical structural demands such as peak deformation, residual displacement, and floor acceleration. Nevertheless, a seismic design method specifically tailored for self-centering viscous dissipative braced steel frames (SCVDFs) needs further refinement. This study proposes a performance-based seismic design (PBSD) method for SCVDFs, which is grounded in the performance-based plastic design (PBPD) approach. The proposed procedure primarily considers the effects of two critical hysteresis parameters: the post-activation stiffness ratio and the viscous damping ratio. To verify the effectiveness of the design method, a set of SCVDFs was designed, each utilizing different combinations of design parameters. Nonlinear static and dynamic analyses were performed on these archetypes to evaluate their seismic performance. The evaluation findings demonstrated that the properly designed SCVDFs can achieve the expected design performance and effectively suppress the peak inter-story drift, residual inter-story drift, and peak absolute floor acceleration of the structure, thereby achieving a favorable trade-off in the design outcome and maximizing the advantages of the SCVDF in seismic resilience.

Performance-based plastic design and seismic fragility assessment for chevron braced steel frames considering aftershock effects

Observations from past earthquakes demonstrated that buildings in high seismic regions might be exposed to several aftershocks following the mainshock which can significantly increase the damage level. Since aftershocks have the potential to increase the vulnerability of buildings damaged under mainshocks, it is crucial to consider aftershock effects in the structural design phase. Performance-based Plastic Design (PBPD) method is an innovative seismic design method in which the building designed by this method shows a desirable performance under severe ground motions. PBPD allows the designer to avoid time-consuming trial and error process of analyses that are usually done in Performance-based Design method to reach a desirable performance. However, this efficient method is only valid for mainshocks only and does not consider aftershock effects in the structural design process. In this study, initially, the seismic performance (interstory drift and plastic hinges distribution) of the three 3-, 6-, and 9- story PBPD designed Chevron-braced Steel frames (CBSF) are compared under mainshocks (MS) and mainshock-aftershock (MS-AS) sequences. Subsequently, a PBPD method is developed for CBSFs considering the aftershock effects in the structural design process. Incremental dynamic analysis (IDA) has been performed using a suite of mainshocks and aftershock ground motions to develop a design base shear modification factor. Using the developed method, the performance of CBSFs under MS and MS-AS sequences is evaluated and compared with the existing PBPD method. Fragility curves are developed to compare the seismic vulnerability of the frames designed based on PBPD and proposed PBPD methods under MS-AS sequences. The outcomes of this study provide a practical design approach for CBSFs under MS-AS sequences and shows that the structures designed using developed PBPD method show more desirable behavior under MS-AS sequences compared with the structures designed using the conventional PBPD method.

Modified performance-based plastic design for self-centering structures

The Performance-Based Plastic Design method (PBPD), developed on the energy concept, has been frequently used in technical literature as a performance-based design method for various structures. However, implementing the method for self-centering (SC) structures, which can concentrate damage in replaceable members and reduce residual deformation, encounters difficulties due to selecting an overall energy modification factor regardless of structural geometry, ductility, and energy absorption capacity. In this study, considering the behavior of self-centering structures, the PBPD method is modified to implement any SC structure with a specific energy modification factor. The proposed method was then implemented to design two braced SC structures with different height, cable, and damper configurations. For comparison, the designed structures and similar structures designed by force method under identical conditions were subjected to nonlinear dynamic and pushover analysis employing eleven far-field earthquake records. The results show that the structures designed by the energy method with different heights and configurations exhibit average seismic response close to the target performance response while maintaining cable linearity. While in the force method, the cables did not remain linear in some cases, and the structures were designed with about 20 % deviation of mean response to the target performance. Furthermore, assessing the proposed approach with analytical results in terms of absorbed energy reveals that the accuracy of the proposed method in forecasting the structures' input energy was more than 87 %. The results indicated that the modified energy method is simple, accurate, straightforward, and efficient for the PBPD of SC structures.

Performance-based plastic design of high-strength steel framed-tube structures fused with replaceable shear links

This study proposes high-strength steel framed-tube structures fused with replaceable shear links (HSS-FTSLs) to improve the seismic performance and post-earthquake reparability of traditional steel framed-tube structures. The conventional seismic design commonly uses the capacity design method, which primarily focuses on the ductility of the structures, resulting in localized damage concentrated on individual floors. An improved performance-based plastic design (I-PBPD) method is proposed for HSS-FTSLs based on the energy balance concept, target drifts, and preselected failure mechanisms. The proposed I-PBPD method considers the influence of post-yield stiffness of the structures. The seismic performance objectives for HSS-FTSLs are categorized into four levels, accompanied by the interstory drifts and residual interstory drifts corresponding to these objectives. The capacity curve for HSS-FTSLs is assumed as a tri-linear form to correspond with the failure modes. Three HSS-FTSL prototype structures with various heights are designed through the I-PBPD method. Nonlinear pushover and dynamic analyses were carried out to investigate their seismic performance. The results indicate that the HSS-FTSL structures designed using the I-PBPD method can achieve the expected failure modes and performance objectives under earthquakes of varying intensities, exhibiting exceptional seismic performance.

Studi Kinerja Struktur Beton Bertulang Beraturan Yang Didisain Dengan Performance Based Plastic Design

Indonesia is a country that has a very high level of seismicity. It is necessary to plan a building structure that can withstand the earthquake load. Indonesia has adopted guidelines on earthquake resistance planning procedures for buildings and non-buildings. This guideline uses the Performance-Based Seismic Design (PBSD) concept. Performance-Based Plastic Design (PBPD) is a structural analysis with the concept of energy methods which was initially used on steel structures. For reinforced concrete structures this method can also be used using the C2 coefficient. To determine the performance level of structures designed using the Performance-Based Plastic Design method, an analysis of the five-story reinforced concrete structure was carried out. Next, the structure will be analyzed using pushover loads. From the structural performance analysis, the structural ductility value based on Performance-Based Plastic Design (PBPD) was 3.014. The performance level is based on the capacity spectrum at the immediate occupancy level.

The Modified Energy-based Method for Seismic Evaluation of Structural Systems with Different Hardening Ratios and Deterioration Hysteresis Models

Prediction of target displacement in structural systems plays a significant role in performance-based design and rehabilitation of structures. In this study, the γ factor for different hardening ratios, including 1, 2, 3, 5, 7.5, 10, and 15 percentages, stiffness-strength-deterioration models, and soil type classes is determined to modify the energy balance equation in performance-based plastic design (PBPD). Statistical results indicate that the effect of the hardening ratio, deterioration, and soil type class on the capacity curve is considerable. Therefore, a simple equation based on the period of the vibration and ductility is suggested to estimate the γ factor in different structural systems. Moreover, four 1-, 3-, 7-, and 12-story moment steel structures with various hardening ratios in the material are designed to validate the proposed method. The suggested values for the γ factor show exact results compared to collected displacements from time history analysis, while the error in the previous work was considerable. Statistical results showed that the mean error in the previous method in estimating target displacement for 1-, 3-. 7-, and 12-story structures is about 15%, 20%, 20%, and 32%, respectively. Conversely, the mean error in this study for estimating target displacement of 1-, 3-. 7-, and 12-story structures is about 10%, 7%, 6%, and 15%, respectively. Finally, the proposed method is examined on the empirical reinforced concrete (RC) bridge pier simulated numerically with fiber-based modeling. Similarly, the suggested equation estimates the target displacement appropriately for the concrete model compared to achieved displacements from nonlinear dynamic analysis.

Seismic performance evaluation and design of resilient knee braced frames equipped with shape memory alloy knee braces and replaceable energy-dissipating connections

This paper proposes a novel seismic resilient knee braced frame (KBF) and focuses on seismic performance evaluation and design. In this novel system, the shape memory alloy (SMA) knee braces (KBs) and replaceable energy-dissipating (RED) connections are the key components. The SMA KBs mainly provide self-centering capacity, and the RED connections mainly offer energy-dissipating capacity. To reveal the seismic performance characteristics, the 3- and 6- story KBFs are selected as the example structures. The proposed systems are designed by a modified performance-based plastic design method, which distributes the seismic energy to the SMA KBs and the RED connections by defining an energy distribution factor p. In what followed, nonlinear static and nonlinear time history analysis are conducted. It indicates that these systems could well meet the prescribed performance targets, although they are designed using different p values. In current work, the potentially optimal p value is found to be 0.1, which represents the case where 10% of seismic energy is allocated to the SMA KBs. The advantages of the novel KBF are twofold: 1) the consumption of SMA material is significantly reduced, because the RED connections are the major damping source; 2) the damaged RED connections can be conveniently repaired or replaced, because the frames could nearly return to original position, owing to the SMA KBs.

Seismic design of hybrid braced frames with self-centering braces and fluid viscous damping braces

Combining self-centering braces (SCBs) and fluid viscous damping braces (FVDBs) in parallel emerges as a promising seismic-resistant strategy, because it has the potential of simultaneously controlling peak deformation, peak acceleration, peak base shear and nearly eliminating residual deformation. However, the corresponding seismic design method is still under development. To this end, this paper extended the performance-based plastic design (PBPD) method to hybrid braced frames (HBFs) equipped with SCBs and FVDBs. The PBPD method selected target drift and yield mechanism at the very beginning of the design procedure, and then it derived the design base shear using energy equivalent concept. The key step was to obtain the constant-ductility spectra of the equivalent single-degree-of-freedom systems through nonlinear time history analysis (NLTHA). The regression functions of the spectra were then incorporated with the PBPD procedure. A six-story steel frame was selected for demonstrating the design method. A total of 4 HBFs were designed by defining 4 levels of viscous damping ratio (ξv) supplemented by FVDBs. The seismic responses of the designed HBFs were examined by subjecting them to 20 earthquake ground motions. The NLTHA results indicated that the designed HBFs can well satisfy the performance targets. The design method was robust, although the ξv values were varied in a wide range. The design method may also shed light to the other types of hybrid systems with displacement- and velocity- dependent damping braces.

Performance-based plastic design of multi-story hybrid braced frames with buckling-restrained braces and shape memory alloy braces

By employing two or more types of braces, hybrid braced frames (HBFs) combine the merits of the adopted braces and offsets their drawbacks. However, the corresponding seismic design method is still under development. To this end, this paper develops a performance-based seismic design (PBSD) method, based on the performance-based plastic design (PBPD) method. In current work, the buckling-restrained braces (BRBs) and shape memory alloy braces (SMABs) are introduced, because they are known for high energy-dissipating capacity and excellent self-centering capability, respectively. The participation extent of BRBs and SMABs is controlled by the stiffness contribution factor. The equations governing the design results are derived and the step-by-step procedure is detailed. A six-story benchmark frame is selected to demonstrate the design method. The designed HBF is subjected to a suite of earthquake ground motions, and the mean demands of seismic responses are compared against performance targets. It indicates that the HBF designed by the design method can well meet the design targets. A parametric analysis is conducted to reveal the effect of changing the stiffness contribution factor on the seismic demands of the HBF. This study validates the proposed design method for HBF, and it may also shed light to the PBSD method of the structures equipped with the other types of displacement-dependent damping braces.

Seismic performance of knee-braced frames equipped with NiTi BRBs

Knee braces (KBs) are often installed at locations near to the beam-to-column connections in frames. In comparison to concentrical and eccentrical braces, KBs have advantages of occupying less space, less affecting the architectural view, and ease of installing and replacing if necessary. As a comparative analysis, this paper evaluates the seismic performance of knee braced frames (KBFs) equipped with steel or NiTi buckling-restrained braces (BRB). Through machining raw bars into bamboo shape, this paper fabricated two types of KBs and conducted cyclic loading tests on reduced-scale specimens. The testing results show that both KBs have stable cyclic properties under loading reversals. The steel BRB has typical elasto-plastic hysteresis, whereas the NiTi BRB has a flag-shape hysteresis. At the system level, the 3- and 6- story KBFs were first designed by performance-based plastic design (PBPD) method and then subjected to a suite of earthquake records. It indicated that the KBFs equipped with either steel or NiTi BRBs can well meet the prescribed drift target. The major advantage of NiTi BRBs over steel BRBs is that they successfully eliminated residual drift ratios for the protected frames, which means the KBFs with NiTi BRBs have higher seismic resilience.

Performance‐based plastic design and seismic performance evaluation of twisted diagrids with shear links

Performance‐based plastic design and seismic performance evaluation of twisted diagrids with shear links

Comparative study and performance evaluation of steel moment resisting frames design with: Force-based design and performance-based plastic design

Incremental Dynamic Analysis (IDA), Nonlinear Response History Analysis (NLRHA) and Nonlinear Static Pushover Analysis (NSPA) has been carried out to evaluate seismic performance of Steel Moment Resisting Frames (SMRF). SMRF’s are used as the lateral resisting systems which consist of columns and beams joined by welding or using high strength bolts or combination of both. The resistance offered to the lateral forces is due to rigid frame action which develops bending moment and shear force in the frame members and joints. The 9-storey SMRF is been evaluated for two frames designed by Force Based Design (FBD) method and Performance Based Plastic Design (PBPD) method. The FBD frame is designed by using codal provision of ASCE 7 (American Based Seismic Code) and AISC (American Institute of Steel Construction) whereas PBPD frame is designed as per proposed work of Lee and Goel (2001) in which energy balance equation and pre-selected yield mechanism is considered. The evaluation study showed that the PBPD method for steel moment resisting frame is significantly more efficient in achieving a certain inelastic displacement/ductility for given seismic hazards compared to the existing design standards/specification for this system. By Nonlinear Static Pushover Analysis (NSPA) the PBPD method has achieved the target yield drift of 1.11% and FBD method has achieved 1.22% where the assumed yield drift was 1%. From NLRHA the percentage difference in achieved ductility factor for frame design by FBD method is 46.28% whereas for PBPD method it is 16.81%. From IDA inter storey drift is observed maximum in AISC design frame compared to PBPD design frame. Therefore, PBPD method frames responded as intended in design with much improved performances over those of the corresponding FBD method.

Seismic fragility analysis of buckling-restrained brace-strengthened reinforced concrete frames using a performance-based plastic design method

An easily-operated performance-based plastic design (PBPD) method for buckling-restrained braced (BRB) reinforced concrete (RC) moment frames is adopted in this research to strengthen existing moment frames by BRBs. The appropriate range of the story base shear ratio p (i.e., the ratio of the base shear resisted by the BRBs to that of the total system) is suggested through a seismic fragility analysis. With an earthquake ground motion set of thirty far-field records, the seismic fragility analysis and risk assessment of an 8-story RC moment frame structure and its strengthened structures with BRBs are reported in this article, in which the fragility curves for different limit states and the corresponding annual exceedance probability are calculated. The applicability of 16 ground motion intensity measures (IMs) in the fragility analysis of the structure before and after strengthening under three damage limit states is further reviewed. As indicated by the fragility analyses, a higher seismic resistance capacity can be obtained for the strengthened structure when the ratio p varies between 0.5 and 0.8. The seismic performance of the structures strengthened using the PBPD method can increase steadily till the advent of the preset target ultimate drift limit, after which the improvement efficiency decreases. The IM Sa,gm(Ti) that considers both effects of softened period and higher mode has a better performance in each limit state of the structure both before and after strengthening.

Development, seismic performance and collapse evaluation of steel moment-resisting knee braced frame

This paper introduces and assesses the seismic and collapse behavior of a new lateral load-resisting system referred to as steel Moment-Resisting Knee Braced Frame (MKF). A design method following the Performance Based Plastic Design (PBPD) procedure is proposed to analyze the structure and size the structural members. A prototype frame part of an office building located in Vancouver, British Columbia, Canada is then selected to demonstrate the design method and evaluate the performance of the proposed system. The prototype MKF is also designed using the conventional elastic approach in accordance with the National Building Code (NBC) of Canada. The seismic performance and collapse response of the proposed system are examined using the nonlinear static analysis, nonlinear response history analysis (NLRHA) and incremental dynamic analysis (IDA) performed on the prototype five-story MKF under potential sources of seismicity in the west coast of Canada including shallow crustal, subduction interface and subduction intraslab events. Fragility curves are finally developed using results of the IDA to obtain the collapse probability of the system. The results of the analyses are compared to those obtained from a steel Moment-Resisting Frame (MRF) counterpart designed in accordance with the PBPD and elastic approaches. Findings of the study show that the proposed steel MKF can efficiently satisfy the code-specified story drift limit and manifest the yielding mechanism assumed in design. The MKF designed according to the PBPD approach offers the lightest structure among all frames studied and yields a collapse probability lower than that of the MKF designed as per the elastic design method. The proposed system can be used in seismic design of steel multi-story buildings as an alternative to conventional steel MRFs.

Seismic fragility analysis of CFT frames with buckling-restrained braces and steel braces under long- and short-duration ground motions

This study presents the seismic behaviour and the effect of ground motion duration on the probabilistic seismic fragility for the concrete-filled steel tube (CFT) frames with buckling-restrained braces (BRB-CFTF) and conventional steel braces (SB-CFTF). The nine-storey BRB-CFTF and SB-CFTF prototype structures were designed based on the performance-based plastic design method. One scaled single-storey single-bay BRB-CFTF and one buckling-restrained brace (BRB) extracted from the prototype structure were cyclically tested and analyzed. Finite element (FE) models of the two braced frame structures were developed and validated by available test results. The results obtained from nonlinear dynamic analyses showed that the designed two structures achieved expected performance objectives in terms of the inter-storey drift and member energy-dissipating demand. The selection of engineering demand parameter (EDP) quantifying structural response and intensity measure (IM) representing ground motion hazard level was performed to determine optimal indicators for identifying duration effect prior to establishment of fragility curves. The results indicated that the overall damage index (ODI) as the EDP can clearly distinguish the influence of duration effect on structural cumulative damage. The optimal IM relative to ODI was believed to be the combined duration- and spectrum-related INP-D, because of desirable balance among the efficiency, sufficiency and scaling robustness. The BRB-CFTF and SB-CFTF structures were more vulnerable to all limit states under long-duration ground motions than those under short-duration ones at the same seismic hazard level, and the probability of exceedance for a given INP-D of the SB-CFTF was generally larger than that of the BRB-CFTF. The influence of ground motion duration on the cumulative damage for the BRB-CFTF and SB-CFTF structures is suggested to be considered in structural seismic design and analysis.

Improved performance-based plastic design method for post-tensioned connection systems

Performance-based plastic design (PBPD) was initially proposed as a method for retrofitting existing structures. The PBPD method gradually became a general approach for designing new structures. This method is a direct method to obtain design base shear and leads to design structures being more economical compared to traditional methods. PT connections were developed after the Northridge earthquake. The self-centering could restore the connection to its original position without damage to the beams and columns. High-strength post-tensioned cables are used to restore the structure to its initial position in PT connections. Also, energy dissipaters (for example, top and bottom angles) are used to increase ductility. In this study, a proposed relationship between the ductility (µ), period (T), and response reduction factor (R) is presented for structures with pinching or flag-shaped behavior, and the effect of the parameters on R has been investigated. Also, a new design approach for structures with PT-steel connections with top-and-bottom angles is presented. The results show that R primarily depends on the post-yield stiffness ratio (α), the yield stress ratio (or energy dissipation) (β), ductility (µ), soil type, etc. Nonlinear time-history analysis indicates that designed models based on the proposed approach satisfy drift limits. The results show that the proposed relationship can be quite suitable for designing PT connections using the PBPD approach.

Development of Performance Based Plastic Design of EBF Steel Structures Subjected to Forward Directivity Effect

Performance-based plastic design (PBPD) is a method which considers the inelastic behavior of a structure for the seismic design that follows a pattern in which a pre-selected yield mechanism is defined for each type of structural system. Despite the general adequacy of this method compared to the code-based method, the need to further improve this method against Forward-Directivity, the well-known characteristic of near-fault ground motions, is of high importance. On the other hand, Eccentrically Braced Frame (EBF) is considered to be an efficient conventional steel-framed system that combines the advantages of moment-resisting frame and concentrically braced frame. In this study, attempts have been made to improve the conventional PBPD method in order to consider the effect of forward-directivity. To this end, the energy modification factor (γ) was modified by recalculating ductility demand µ and ductility reduction factor Rµ of three 6-, 12-, and 18-story EBF structures. Using incremental dynamic analysis, these structures were subjected to 12 well-known near-fault ground motions, and accordingly, the modified energy factor (γ′) was obtained for each set. Then, an equation was proposed to calculate the γ′ based on the fundamental period of the structure. As expected, the code-based designed structures exceeded the allowable drift limits. Although the structures which were designed based on conventional PBPD followed the pre-selected yield mechanism and performed better, they exceeded the drift limits as well. Consequently, the structures which were re-designed using modified energy factor γ′ could well satisfy the acceptance criteria as well as achieving the desirable yield mechanism.

Probabilistic seismic performance evaluation of composite frames with concrete-filled steel tube columns and buckling-restrained braces

The concrete-filled steel tube (CFT) composite frames using blind bolts and buckling-restrained braces (BRBs) have been studied with the development of building industrialization and energy dissipation technology. However, there has been no research so far on the probabilistic seismic fragility analysis for the blind-bolted end-plate CFT composite frames with BRBs (BRB-BECFT). Therefore, a total of 6-, 9-, 12- and 20-story BRB-BECFT prototype structures were designed based on the performance-based plastic design method. The results obtained from nonlinear static and dynamic analyses indicated that the four structures achieved predefined performance objectives in terms of story drift, joint rotation, and BRB ductility demand. Subsequently, fragility curves including non-collapse and collapse states were established to evaluate the behavior of the structure for a given intensity measure using the incremental dynamic analysis approach. Meanwhile, the geometric mean of spectral acceleration over a period range (Sa,avg) was selected as the intensity measure to assess the structural collapse capacity. Results showed that the adoption of Sa,avg can result in 32–42% lower data dispersion for the determination of collapse point, and simplification of the process of calculation of the collapse margin ratio of a structure. Furthermore, based on the combination of Sa,avg, residual story drift and BRB core plate strain, a framework of probabilistic seismic damage analysis of structures for combined damage evaluation at three levels of the system, subsystem, and component was summarized and conducted by the 6- and 12-story case study. This is practically useful to assess structural damage state after an earthquake because it could present more information on the probability distribution of various damage scenarios.