Performance-based Plastic Design Method Research Articles

Improved PBPD method for dual steel system considering the global effect of space frames

Performance-based plastic design (PBPD) method has been proposed to design single bay planar frames for twenty years. For a dual steel system, such as an eccentrically braced frame (EBF) structure, there will be both EBF bays and moment resisting frame (MRF) bays. So, the global effect between different frame bays cannot be considered when designing the global structure using the traditional PBPD method. In this paper, a ten-story high-strength steel composite K-shaped eccentrically braced frame (HSS-K-EBF) structure was firstly used for performance design and analysis based on a single bay EBF. The results show that the global structural model obtained by direct performance design of the single bay model cannot achieve the desired performance objectives. To this end, an improved PBPD method for the dual steel system was proposed considering the global effects of space frames. The elastic and elastic–plastic shear distribution relations were calculated for different bays of the frames including EBFs and MRFs. The performance objectives of the global structure were designed and evaluated more accurately by considering the over-strength contribution of shear links and the plastic development rate index ξ of energy dissipation members. The improved PBPD method was used to design the ten-story global HSS-K-EBF structure. The results of nonlinear dynamic time history analysis show that the improved PBPD method can ensure that the plastic damage distribution of energy dissipation members of different bays is more uniform and the plastic damage degree is more consistent with expectations.

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 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.

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.

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.

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.

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.

Seismic Response of Performance Base Designed Building : A Review

A review on Performance Based Plastic Design method (PBPD) for RCC building has been presented in this paper with detailed manner. The first is the study of Performance Based Plastic Design method relating with IS code method. And then secondly review includes the research gap that is to apply this method on Irregular Buildings and to observe the efficiency of Design and Cost analysis comparing to IS code recommendations. When a Structure is designed by IS Code (IS 456: 2000) recommendations, it satisfies the strength as well as serviceability standards. But when an earthquake hits the structure, it leads to collapse which leads to loss of life as well as property. A Recently developed PBPD method can be a promising & efficient seismic design approach as it counteract total collapse of structure. This method is becoming popular due to its total collapse prevention. The paper addressed the relevant examination of provisions as specified in the appropriate design standard and software-based finite element analysis conducted by various authors, as well as a review of the problem, in order to reach a meaningful conclusion for the study. Also, a suggestion for the scope of future development is to study the Design as well as Cost efficiency of Performance Based Plastic Design of Various Irregular RCC buildings which will be a new or important aspect of the study. Despite the fact that fewer papers have been published in this area than in others, this report covers a broad range of research efforts and progress into the New Performance based Plastic Design method & seismic behavior of irregular buildings, demonstrating the field’s growing interest.

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.

New performance-based plastic design and evaluation of blind bolted end-plate CFT composite frames with BRBs

The blind bolted end-plate connection to concrete-filled steel tube column (BECFT) composite frame with buckling-restrained braces (BRBs, BRB-BECFT) is a novel dual structure system that combines advantages of fast assembly ability for BECFT connections, great energy dissipation capacity for BRBs coupled with BECFT connections and superior gravity load-carrying capacity for concrete-filled steel tube (CFT) columns. Given authors’ prior experimental and theoretical studies on the BRB-BECFT structure system, and as no design method is as far introduced for this system with adequate accuracy, a new plastic design procedure based on the modified energy balance and global yield mechanism in the framework of performance-based plastic design method was proposed. The post-yielding stiffness and overall yield inter-story drift of the BRB-BECFT structure system was considered to improve the accuracy of the design base shear. Meanwhile, the BRB-BECFT structure system was decomposed into the BRB system and BECFT frame system to simplify the design process. Moreover, some formulae to avoid structural adverse yield mechanism were derived. The semi-rigid characteristic of BECFT connections was introduced into the structural global yield mechanism by work-energy principle to ensure the deformation consistency between inter-story drift and BECFT connection rotation. Finally, four prototype structures with 6, 9, 12 and, 20 stories were designed as examples to illustrate the effectiveness and robustness of the proposed design method. The results of nonlinear time-history analyses showed that the designed structures successfully achieved the pre-selected performance objectives in terms of the inter-story drift, residual drift, BECFT connection rotation, and BRB ductility demands.

Strength, Deformation and Fragility assessment of Reinforced Concrete Moment Resisting frame designed by Force Based Design and the Performance Based Plastic Design method for Seismic loads

A 20 storied Reinforced Concrete (RC) Moment Resisting Frame (MRF) has been analysed and designed by Force Based Design (FBD) method and the Performance Based Plastic Design (PBPD) method. The PBPD frames were designed for all the three performance levels namely Immediate Occupancy, Life safety and Collapse Prevention of the basic safety objective. The guidelines of the Indian Standard codes along with established principles of design have been incorporated in the study. Nonlinear static pushover analysis was the tool used to evaluate the seismic performance of the frames in terms of strength and deformation. The fragility assessment has been carried out in terms of Spectral displacement obtained from the pushover analysis results for different specified damage states. Results indicate that PBPD method excels the FBD method, both in terms of seismic performance and fragility.

Displacement Analysis of RC Frames and its Seismic Performance Appraisal

In India when structure engineer’s analysis and design a structure like buildings, they are checking it for displacement because of safety and control of damages; so in this paper a set of frames with different height of reinforced moment resisting frames were analyzed by two popular methods of performance-based plastic design method and direct displacement-based design method. For calculation of base shear, the IS code has been used in both methods and ETABS software used for seismic performance evaluation by nonlinear static pushover analysis. The results of analysis with different methods compared by suitable parameters and graphs, such as: (a) story lateral force, (b) beam seismic moment, (c) displacement profile and (d) capacity curve. Results show acceptable performance in 2 methods in terms of capacity and deformation.

Plastic design of knee-element connection frames (KCFs) using mechanism control

In the past two decades, extensive research has been conducted to evaluate the seismic performance of Knee-element Connection Frames (KCFs) and to determine the most efficient configurations. KCFs are of particular advantage over other load-resisting systems in terms of their ample access for maintenance and enhanced structural performance. This paper presents an enhanced energy-based plastic design for KCFs using mechanism control. The design methodology developed in this study constitutes the design criteria employed in Performance-based Plastic Design (PBPD) and Theory of Plastic Mechanism Control (TPMC) at the same time. In this design approach, the external forces are derived from the energy balance equation directly considering second-order effects, and design is carried out according to the PBPD method. Then, undesired collapse mechanisms are identified and prevented by the use of a Design-Capacity Ratio-based (DCR-based) approach as the controlling criteria. To evaluate the design performance, nonlinear static and dynamic analyses were performed. The results indicate an acceptable correlation between the expected general yield mechanism and structural response and an acceptable economy in terms of material usage compared to comparable moment resisting frames.

Seismic performance quantification of buckling-restrained braced RC frame structures under near-fault ground motions

The near-fault ground motion records with forward directivity (FS) and fling-step (FS) effects are characterized by the obvious velocity-pulses which will impose high seismic energy input to the building structures. The buckling-restrained braces (BRB) are one of the most commonly adopted lateral-force resisting and energy-dissipating components and BRBs are increasing configured in reinforced concrete (RC) frame structures to form a dual structural system (BRB-RCF). This paper presents the seismic performance quantification of BRB-RCFs subjected to near-fault ground motions with FD and FS effects. Suits of BRB-RCFs corresponding to different story numbers, BRB-resisted story shear ratios and BRB configuration types (single diagonal, inverted-V and V-type), were designed using the performance-based plastic design method. Three sets of 36 near-fault ground motions with FS, FD and non-pulse effects were selected. The seismic response including the maximum interstory drift ratio, floor acceleration, BRB ductility, BRB-resisted actual story shear ratio, etc., were investigated. Furthermore, the actual BRB-resisted story shear ratio was quantified and the design BRB-resisted story shear ratio was suggested. The analytical results can provide significant insights to the behavior quantification of BRB-RCFs when subjected to near-fault ground motions.

Development of the Performance-Based Plastic Design Method by Considering the Effects of Aftershocks

ABSTRACT One of the efficient methods for seismic design of structures is Performance-based Plastic Design (PBPD) in which by choosing the desired yield mechanism and the target drift at the beginning of the design, unlike that in conventional design methods, there is no need for a time-consuming process of trial and error to achieve the desired performance. On the other hand, recent earthquakes have shown that aftershocks can increase the damage to a building after the main earthquake and thereby threaten the safety of the inhabitants. However, the seismic hazard of aftershocks is still not explicitly included in the current design codes. In this study, attempts have been made to develop the PBPD method for considering the effects of aftershocks. For this purpose, by performing an incremental dynamic analysis (IDA), the ductility factor μ and the ductility reduction factor Rμ of six PBPD frames (2-, 4-, 6-, 8-, 10-, and 12-story) were calculated under mainshock and mainshock-aftershock sequences. Then, the energy modification factor γ, which is related to the two parameters μ and Rμ, was calculated for both the mainshock and the mainshock-aftershock sequences. An equation is presented in order to calculate the ratio of the energy modification factor of the mainshock-aftershock sequence to the mainshock energy modification factor () according to the design period, and the factor obtained is multiplied by the energy modification factor γ so that the effect of aftershock can be considered for the frame design, and by using this modification, the performance of the frame under the mainshock-aftershock sequence can be improved. The results of the time-history analysis performed on the modified PBPD frames show better performance by the frames designed on the basis of modified PBPD than the frames designed on the basis of the original PBPD method under MS-AS sequences in terms of inter-story drift and rotation of plastic hinges.