Performance-based Plastic Design Method Research Articles

Performance-based plastic design of composite partially-restrained steel frame-reinforced concrete infill walls with concealed vertical slits

In order to reasonably predict the seismic demand of composite partially-restrained steel frame-reinforced concrete (RC) infill walls with concealed vertical slits (PSRCW-CVS) subjected to the near-fault earthquake records with strong velocity-pulse effect, an innovative performance-based plastic design (PBPD) approach is developed in current study. The maximum effective cyclic energy (MECE), which can reflect this phenomenon that the structural dissipated input energy from near-fault pulse earthquake record commonly focuses on the largest yield excursion, is introduced and adopted as a new design indicator (ΔEh,max). The design base shear is determined according to the instantaneous energy balance concept and pre-selected desirable yield mechanism, which considers that the MECE demand obtained from MECE spectrum at target ductility ratio is equivalent to the instant energy supply from structural components. Additionally, the MECE calculating formula of each component of PSRCW-CVS structure is also provided. Four PSRCW-CVS illustrations (5-storey and 10-storey) with different target ductility ratio were designed according to the proposed PBPD methodology, and their seismic behaviors corresponding to the rare earthquake level were assessed through nonlinear time-history analysis method using the selected near-fault earthquake records with velocity-pulse effect. The analytical results show that four PSRCW-CVS structures can achieve the intended seismic behavior in terms of MECE, inter-story drift ratio, and residual inter-story drift ratio. The PSRCW-CVS structure exhibits the ideal progressively developed plastic mechanism. The reliability and reasonability of this PBPD method combined with MECE spectrum are verified, and it can be easily extended to other dual lateral load resisting systems.

Seismic Performance and Cost Comparison of Concentrically Braced Frames Designed By Performance-Based Plastic Design and Force-Based Design Method

Comparative study of 5, 10 and 15 storied steel Concentrically Braced Frames (CBF) designed by Performance Based Plastic Design (PBPD) method and Force Based Design (FBD) method is presented here. The parameters selected for comparison of the frames are (a) Lateral load distribution (b) Design sections of members (c) Seismic performance and (d) Cost. It is observed that the lateral load's distribution in case of PBPD frames is found more factual. The column sections of PBPD frames are heavier, and brace sections are lighter compared to FBD frames given the fact that PBPD is designed for higher ductility factor. The PBPD method gives a better seismic performance by achieving the predetermined failure mechanism and avoiding total collapse. Taller structures offer cost-effectiveness for PBPD method.

An improved performance-based plastic design method for seismic resilient fused high-rise buildings

The performance-based plastic design (PBPD) method generally relies on the nonlinear response of equivalent elastic-perfectly-plastic single degree of freedom system. It usually cannot achieve the design of three performance objectives simultaneously and may not consider the high mode effect of structure, which is significant for high-rise building. In this paper, a trilinear force-displacement model indicating three prescribed performance objectives at three seismic hazard levels is adopted to improve the PBPD method. The proposed improved PBPD method is derived based on multiple degrees of freedom system, while the high-mode effect and post-yield stiffness of the structure is considered. It can be used for designing seismic resilient fused high-rise buildings. A novel dual system composed of steel energy-dissipative column (EDC) and moment resisting frame (MF) is employed for application of the proposed method. This dual system has its fuse members decoupled from the gravity-resisting system, and the performance-based design of this system is discussed as well as its application for high-rise buildings. To demonstrate the effectiveness of the proposed method, a 20-story EDC-MF structure system is designed using the improved PBPD method. A detailed numerical model of the designed EDC-MF system is then built, and nonlinear dynamic response analyses at different seismic intensities are performed to verify the actual structure performance. Results show that the designed structure can achieve the prescribed yielding mechanism and performance objectives at three seismic hazard levels, and the EDC-MF system can be effectively applied to high-rise building as a seismic resilient fused structure.

Application of Performance-Based Plastic Design (PBPD) method for 3D steel structures

The Performance-Based Plastic Design (PBPD) method, introduced last decade, is an energy-based procedure. This method which is proposed for 2D frames has several stages. At the first stage, a pre-selected global yield mechanism and a target drift are selected. Then, the energy equilibrium equation is developed for a frame to calculate the base shear. At the end stage, designing the beams and columns is done for just one-bay of the planar frame. Since in PBPD-2D procedure the components of energy equilibrium equation are based on the planar frames, it does not consider the adjacent frames effect in 3D design problems so it is necessary to do research about developing PBPD method in 3D frames. The main scope of this paper is to apply the 3D effect on PBPD method. In the current research, the nonlinear distribution of base shear in plan has been found by nonlinear time-history analysis and processed by artificial neural networks. To fortify the results and analyses, 3D and nonlinear modeling is chosen. In the current research, the effect of earthquake power in the nonlinear base shear distribution in plan is considered by looking at the earthquake magnitude and the PGA. Since the earthquake energy is the best structural damage index, in this way, one can design 3D structures by PBPD method adjusted to the desired damage level. In this regards, three special moment frames are designed according to PBPD-2D procedure and proposed PBPD-3D procedure. The results of nonlinear time-history analysis show that the PBPD-2D method could not satisfy the weak beam- strong column criterion and the global yield mechanism in 3D designing, whereas the proposed method in this research, PBPD-3D, satisfies the mentioned criterion successfully.

Displacement-Based Design of RC Frames Using Design Spectra of Indian Code and Its Seismic Performance Evaluation

A set of 4-, 8-, 12-, and 15-storied reinforced concrete moment resisting frames were analysed and designed by direct displacement-based design method and performance-based plastic design method. The design spectra of Indian Standard IS 1893:2016 have been used for the calculation of base shear after its proper synchronization with respect to both the methods. The seismic performance evaluation was done by nonlinear static pushover analysis, and the parameters of comparison were (a) pushover curves, (b) storey drifts and (c) response reduction factor. Results show satisfactory performance of both the methods in terms of capacity and deformation. The response reduction factor values obtained for both approaches are greater than the IS 1893:2016-specified value which indicate the enhanced ductility for both methods.

Robustness of Performance-Based Plastic Design Method for SMABFs

Shape memory alloys (SMAs) are gaining increasing attentions from earthquake engineering community, due to the superleastic property, which is capable of offering energy dissipation capacity and recentering ability to various structural systems. SMA braced frames (SMABFs) are emerging as promising frames with advanced seismic resilience. Recently, the performance-based plastic design (PBPD) method was developed for such structural system. However, the robustness of this design approach still needs rigorous examinations by addressing the effects of defining different performance targets or using different seismic design spectra in the design procedure. In doing so, examinations were carried out from two perspectives. The first one set various performance targets combining different interstory drift ratio and brace ductility demand in the design procedure based on the design basis earthquake spectrum, and then the resulting SMABFs were subjected to earthquake ground motions corresponding to design basis hazard level. The second one conducted the design procedure at three seismic hazard levels representative of frequently occurred earthquake, design basis earthquake, and maximum considered earthquake, respectively, and then assessed the seismic performance upon earthquakes associated with three seismic intensities. The analytical results show that the designed frames as per the PBPD method always coincide with the performance targets very well, regardless of the prescribed targets and adopted design spectrum. Therefore, this paper provided sound results which successfully demonstrated the high robustness of the previously developed PBPD method for SMABFs.

Seismic Behavior and Dissipated Plastic Energy of Performance-Based-Designed High-Rise Concrete Structures with Considering Soil–Structure Interaction Effect

Since the structure and foundation are built on soil, the soil is the major platform by which seismic vibrations are transmitted to the structure, and has noticeable effects on the response and behavior of structure during earthquakes. In this research, the recently introduced Performance-based plastic design (PBPD) and its modified Performance-based plastic design (MPBPD) method in which soil and structure interaction effect has been considered underwent the seismic evaluation. In order to do evaluation, a twenty-floor concrete structure with MPBPD method and conventional PBPD was designed and analyzed in accordance with the time history of the 22 far-field quake records. In this study, cone model is employed for modeling the soil and foundation. With a detailed three-dimensional finite element model of a twenty-story high-rise structure constructed and exploited in the OpenSees software, it is attempted to consider a more realistic behavior of the structure. The results of six related parameters with the maximum response of the structure demonstrate the efficiency and performance of the MPBPD method for the purpose of considering the SSI effect, compared with the conventional method of PBPD. The Results show that, in the MPBPD design method, maximum displacement, acceleration, inter-story drift and shear force dropped leading to a better distribution of energy in the structure compared to the PBPD method.

Experimental and Analytical Study of Eccentrically Braced Frames Combined with High-Strength Steel

In the structure of high-strength steel composite eccentrically braced steel frames (HSS–EBFs), the links and braces are made of Q345 steel, while the non-energy-dissipation segments (columns and beams) are made of high-strength steel (HSS). HSS reduces the cross-section of the members and increases the economic efficiency. Here, four groups of K-HSS–EBFs are designed by performance-based plastic design method in this paper, which includes 5-storey, 10-storey, 15-storey and 20-storey, and each group contain four different link length (900, 1000, 1100 and 1200 mm). The cyclic test loading was applied to 1:2 scale three-storey K-type HSS–EBFs (K-HSS–EBFs) with shear links to investigate their seismic performance. The results indicate that the as-prepared K-HSS–EBF structure exhibits excellent bearing capacity, ductility, and energy dissipation. We also find that the fracture of the link web in the second storey led to the degradation of the load-carrying capacity. The non-designated yield members remained in the elastic stage, whereas the links ultimately experience inelastic rotations, and thus dissipate the energy in the K-HSS–EBFs. Moreover, nonlinear pushover analyses and nonlinear dynamic analyses are conducted, and the loading capacity, link rotations, ductility, interstory drifts and failure mode under rare earthquake of all models are compared. The results indicate that K-HSS–EBFs with different link length have similar deformation characteristic and failure mode under pushover analysis or rare earthquakes, and the interstory drifts, link rotations and ductility of HSS–EBFs are increased with rising the link length.

Improved Performance-Based Plastic Design for RC Moment Resisting Frames: Development and a Comparative Case Study

The performance-based plastic design (PBPD) method employs the global yield mechanism and target drift to design reinforced concrete moment resisting frames (RC-MRFs), which satisfies both the drift and strength limits without iterations. However, different structural systems have different hysteretic behaviors and the influence on the energy balance equation has not been dealt with in a quantitative manner. Moreover, the gravity loads are not considered in the plastic design procedure, which makes the beam design not within the safe margin for low and moderate seismic regions. In this paper, an improved PBPD method for RC-MRF is developed. Furthermore, a case study of seven-story RC-MRF is designed using both the improved PBPD and conventional equivalent static force design (ESFD) approaches. Comprehensive comparative analyses are performed in terms of nonlinear static pushover analysis, nonlinear dynamic analysis and seismic loss estimation. The results illustrate that the PBPD procedure can reduce the seismic losses. Hence, it is proved that PBPD is a viable and more robust design procedure as compared to the conventional ESFD procedure.

Performance-Based Seismic Design and Parametric Assessment of Linked Column Frame System

Linked column frame system, as a new seismic load-resisting system, has a proper seismic behavior in various performance objectives due to ductile behavior of replaceable link beams. Thus, returning to occupancy after moderate earthquake is rapid and low-cost. Performance-based seismic design methods should be used for this system in order to have proper seismic behavior. In this study, by using performance-based plastic design method, a highly accurate and simple design procedure is proposed for this system. 9 prototype structures with 3, 6 or 9 stories and with 3, 4 or 5 bays are selected for parametric design and assessment. For assessment of the designed structures, nonlinear static and dynamic analyses with models according to experimental test results of the members and recommended ground motion records of FEMA P695 are used. According to analyses results, the designed structures in three hazard levels meet the performance objectives.

A lateral load pattern based on energy evaluation for eccentrically braced frames

Performance-Based Plastic Design (PBPD) method has been recently developed to evaluate the behavior of structures in different performance levels. The PBPD method utilizes a base shear force and a lateral load pattern that are estimated based on energy and yielding mechanism concepts. Using of current lateral force pattern results in weak structural members in upper stories of a structure so that the values of the story drift in these stories are larger than the target drift, particularly in high-rise buildings. Therefore, such distribution requires modifications to overcome this drawback. This paper proposes a modified lateral load pattern for steel Eccentrically Braced Frames (EBFs) based on parametric study. In order toachieve the modified load pattern, a group of 26 EBFs has been analyzed under a set of 20 earthquake ground motions. Additionally, results of nonlinear dynamic analyses of EBFs have been post-processed by nonlinear regression analysis in order to derive the new load pattern. To prove the efficiency of present study, three EBFs as examples were designed by modified pattern and current PBPD distribution. Inelastic dynamic analyses results showed that the story drifts using modified lateral load pattern were well within the target values in comparison with current pattern in PBPD, particularly where the effect of the height is significant. The modified load pattern reduces the possibility of underdesigning in upper levels and overdesigning in lower levels of the frames.

Considering the Soil Effects on Design Process of Performance-Based Plastic Design for Reinforced Concrete Structures

In this research, Performance-Based Plastic Design (PBPD) method has been modified according to the proposed method for considering Soil–Structure Interaction (SSI) effects. In the proposed modified method, based on the existing relationships and in order to maintain the simplicity of the PBPD design method, two important parameters have been modified in the PBPD design method. These two parameters include the modification of the vibration period of the structure due to the effect of SSI and the lateral target displacement modification, which is a key parameter in the evaluation of the structural performance. Efforts have been made to refine the modifications to maintain the simplicity and robustness of the PBPD equations. Finally, design base shear force of the PBPD method has been corrected due to the SSI effect regarding the modified relationships. By making the modifications, in order to better understand this method, structures with a number of different floors, including the 4, 8, 12, and 20 spatial space moment frames, are designed and compared with the results of designing the method without the effect of SSI and design method based on the capacity.

Performance-Based Plastic Design of Moment Frame-Steel Plate Shear Wall as a Dual System

Steel Plate Shear Wall (SPSW) is an emerging seismic load-resistant system that, compared to other systems, enjoys the advantages of stable ductile behavior, fewer detailing requirements, rapid constructability, and economy. American seismic provisions decree that a SPSW should be designed as a moment frame with a web infill plate. Specifically, in case of buildings taller than 160 ft, it decrees that a dual system must be used. This paper presents a method of Performance-Based Plastic Design (PBPD) to design steel moment frame-SPSW as a dual lateral load-resisting system. PBPD method uses pre-selected target drift and yield mechanism as its main criteria. For a specified hazard level, the design base shear is calculated based on energy work balance method, employing pre-selected target drift. Plastic design of dual frame system has been performed to meet the pre-selected yield mechanism. As presented in the paper, design procedure involves solving a system of five equations with five variables to determine the proportion of SPSW and moment frame shear, shear wall thickness, and beam/ column sections. It has been considered that a four-story structure is designed with the proposed method. Seismic performance of this dual frame system, designed with the proposed method, is evaluated by nonlinear static and dynamic analysis for both Design Basis Earthquake (DBE) and Maximum Credible Earthquake (MCE). Result analysis is in accord with the assumptions, satisfying all the performance objectives. PBPD is a direct design method in which no iteration is needed to achieve the performance objectives. Determining the proportion of SPSW and moment frame shear is an exclusive capability of this procedure.

Performance-based plastic design method of high-rise steel frames

Under major earthquakes, high-rise steel moment frames designed according to the current codes will experience an inelastic deformation, which is difficult to predict and control. According to the principle of work-energy balance, a performance-based plastic design (PBPD) methodology is put forward for the design of high-rise steel frames in this study. In this method, the target drift and yield mechanisms are pre-selected as key performance criteria. The design base shear in a given earthquake level is calculated based on the work-energy balance principle that the work required to push the structure monotonically to the target drift is equal to the energy needed by an equivalent single degree of freedom to reach the same state. The plastic design is utilized to design the frame components and connections so as to attain the desired yield mechanism and behavior. The method has been adopted to design a ten-story steel moment resisting frame, and has been validated by nonlinear dynamic time history analyses and pushover analysis. The results indicate that the frames develop targeted strong column sway mechanisms, and the story drifts are less than the target values, thus satisfying the anticipated performance objectives. The addressed method herein can form a basis for the performance-based plastic design of high-rise steel moment resisting frames.

New performance-based seismic design method for structures with structural fuse system

In structural systems combined with structural fuse system, the replaceable fuse elements, with their ductile behavior, are an adequate solution for protecting main structural members and reducing the destructive effects of earthquakes, during and after the event. Relatively low cost and easy repair process in these systems leads to rapid return to occupancy after an earthquake. Performance-based design of these systems is a complicated process because of the interactions between two systems, and so far, no simplified method is introduced for this purpose with adequate accuracy. In this study, by using the performance-based plastic design method (PBPD), an iterative, simple and highly accurate procedure is introduced for designing these dual systems. This method is based on separating the two structural systems considering their interactions. There are three performance objectives in this method: first, elastic behavior in low earthquake hazard level for immediate occupancy, second, inelastic behavior of fuse in moderate earthquake hazard level for rapid repair, and third, inelastic behavior of the whole structure in very high earthquake hazard level for collapse prevention. As design examples, structures with linked column frames (LCF) were chosen. Three structures with 3, 6 and 9 stories, were designed with this method. To evaluate the proposed method, nonlinear static and dynamic analysis was applied, and structures were modeled according to experimental results of the members and ground motions representing various seismic hazard levels. Analyses results showed that the designed structures achieved the performance objectives. Moreover, in moderate earthquake hazard level, only fuse members yielded and other structural members remained elastic.

Evaluation of collapse-resistance of special truss moment frames as per FEMAp695 approach

Special Truss Moment Resisting Frame (STMF) is one of the lateral force-resisting systems in which the input seismic energy is allowed to dissipate at the predefined special regions of the steel truss members. Past studies have shown that STMFs designed based on the prescriptive force-based design method recommended by the current codes as well as the performance-based plastic design (PBPD) method have shown to achieve the desired performance levels in terms of the target drift and yield mechanisms under Design-basis earthquake (DBE) hazard level. However, there is a need to evaluate their collapse-resistance potential of such systems under the extreme earthquake loading conditions. In this study, the collapse performance of a mid-rise nine-story STMFs designed based on the current code (ASCE) procedure as well as PBPD method has been investigated in accordance with the FEMAp695 recommendations. The collapse margin ratio computed for both ASCE and PBPD STMFs using the nonlinear incremental dynamic analyses under the amplified levels of seismic hazards has been compared with the recommended values. Finally, a progressive collapse analysis has been conducted for the PBPD STMF to investigate its load redistribution potential under a column-removal scenario.

Performance-Based Plastic Design Method for Steel Concentrically Braced Frames Using Target Drift and Yield Mechanism

Under severe earthquakes, steel concentrically braced frames (SCBFs) will experience large inelastic deformations in an uncontrolled manner. According to the energy-work balance concept, a performance-based plastic design (PBPD) methodology for steel concentrically braced frames was presented here. This method uses pre-selected target drift and yield mechanism as key performance limit states. The designed base shear for selected hazard levels was derived based on work-energy balance equations. Plastic design was performed to design bracing members and connection nodes in order to achieve the expected yield mechanism and behavior. The method has been successively applied to design a six-storey steel concentrically braced frame. Results of inelastic dynamic analyses showed that the story drifts were well within the target values, thus to meet the desired performance requirements. The proposed method provided a basis for performance-based plastic design of steel concentrically braced frames.

Earthquake-resistant design of buckling-restrained braced RC moment frames using performance-based plastic design method

In this study, a performance-based plastic design (PBPD) method for dual system of buckling-restrained braced reinforced concrete moment-resisting frames (RC-BRBFs) is developed. Trilinear force–deformation relationship of the dual RC-BRBF system was approximated as the bilinear capacity curve to derive the yield displacement. The design base shear was determined based on the energy balance equation which accounted for the energy dissipation capacity quantified by Large Takeda model. Plastic design procedure were presented to derive the section internal forces. The proposed methodology was verified through a 5- and 10-story RC frame structures with chevron-configured BRBs. Numerical model was established and validated to assess the seismic performance through nonlinear static pushover analysis and time history analyses using FEMA P695 recommended ground motions. The analytical results show both RC-BRBFs can achieve the intended performance levels in terms of capacity curves, yield mechanism, story drift ratio distribution, residual drift, maximum ductility and cumulative ductility demands. Furthermore, the developed design procedure can be easily extended to other BRB configurated dual structural systems to achieve the desired seismic performance.

Development of the Performance Based Plastic Design for Steel Concentric Braced Frames and Evaluation by Energy Methodology

This paper presents the development of performance based plastic design (PBPD) method to design steel concentric braced frames (SCBFs). The design base shear is obtained based on energy-work balance equation using preselected target drift and yield mechanism. Also, the energy-work balance can be applied to estimate seismic demands, herein called the energy spectrum method. PBPD method was originally developed to design SCBFs. The results were too conservative. For further improvement, this paper presents some modifications such as C2-Factor method and P-delta effect in energy-work balance equation to give a better estimate of design base shear. For validity, three baselines frames (3, 6, 9-story) are designed according to AISC 2005 seismic provisions (Baseline frames). Then, the frames are designed based on the Original PBPD method (Original PBPD method). Finally, they are designed based on modifications applied on PBPD method (Modified PBPD frames). These frames are subjected to extensive inelastic pushover and time-history analyses. The Results show that the Modified PBPD frames meet all the intended performance objectives in terms of yield mechanisms and target drifts whereas the Baseline frames show very poor response due to premature brace fractures leading to unacceptably large drifts and instability. Also, Modified PBPD frames show that the structures having 20%–25% weight less than the Original PBPD can meet the performance objectives. Moreover, the drift demands obtained from energy spectrum method significantly correspond with the results of time history analyses.

Performance-based plastic design method for steel concentric braced frames

This paper presents a performance-based plastic design (PBPD) methodology for the design of steel concentric braced frames. The design base shear is obtained based on energy–work balance equation using pre-selected target drift and yield mechanism. To achieve the intended yield mechanism and behavior, plastic design is applied to detail the frame members. For validity, three baseline frames (3, 6, 9-story) are designed according to AISC (Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Chicago, 2005) seismic provisions (baseline frames). Then, the frames are redesigned based on the PBPD method. These frames are subjected to extensive nonlinear dynamic time-history analyses. The results show that the PBPD frames meet all the intended performance objectives in terms of yield mechanisms and target drifts, whereas the baseline frames show very poor response due to premature brace fractures leading to unacceptably large drifts and instability.