Microsoft Word - ETASR_V12_N2_pp8278-8283 Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8278-8283 8278 www.etasr.com Abdelhamid et al.: Lateral Reliability Assessment of Eccentrically Braced Frames Including Horizontal … Lateral Reliability Assessment of Eccentrically Braced Frames Including Horizontal and Vertical Links Under Seismic Loading Fayçal Abdelhamid LGC-ROI, Civil Engineering Laboratory - Risks and Structures Interactions, Faculty of Technology University of Batna 2 Batna, Algeria f.abdelhamid@univ-batna2.dz Mohamed Saadi LGC-ROI, Civil Engineering Laboratory - Risks and Structures Interactions, Faculty of Technology University of Batna 2 Batna, Algeria m.saadi@univ-batna2.dz Djarir Yahiaoui LGC-ROI, Civil Engineering Laboratory - Risks and Structures Interactions, Faculty of Technology University of Batna 2 Batna, Algeria djarir.yahiaoui@univ-batna2.dz Noureddine Lahbari LGC-ROI, Civil Engineering Laboratory - Risks and Structures Interactions, Faculty of Technology University of Batna 2 Batna, Algeria n.lahbari@univ-batna2.dz Received: 20 January 2022 | Accepted: 1 February 2022 Abstract-Eccentrically Braced Frames (EBFs) have been widely used in the last decades and proved their efficiency to resist strong earthquake intensities by providing suitable ductility and lateral stiffness. Using the PBPD method for the design, EBFs can fulfill the target performance objectives under major earthquakes. The most commonly used configurations are the K- shaped and the recent Y-shaped EBFs, which have the advantage that the links are independent of the beam and can be easily replaced after an earthquake without serious damage to the beam and slab. This study focused on the lateral reliability of both systems under seismic loading. Nonlinear static pushover and Incremental Dynamic Analysis (IDA) were performed on 5-story and 10-story K- and Y-shaped EBFs. A series of 14 near- and 7 far-field seismic records were considered to analyze and compare the inter-story drifts of both systems using the Seismostruct software. Moreover, Peak Ground Accelerations (PGA) and the different performance levels were also examined. Keywords-eccentric braces; short links; incremental dynamic analysis; performance based design; interstory drift I. INTRODUCTION During the last 50 years, many studies have been carried out through experimental and numerical research with the aim of better understanding the behavior of Eccentrically Braced Frame (EBF) systems and developing adequate design methods to improve their performance against seismic and wind loads. This lateral load-resisting system, originated from Japan, combines the advantages of both Moment Resisting Frame (MRF) and Concentrically Braced Frame (CBF) by ensuring high elastic stiffness and energy dissipation during severe earthquakes. One of the most important key parameters that controls the behavior of EBF systems is the segment e between braces or brace to the column. This segment, called the link, acts as a structural fuse to dissipate the energy induced by earthquakes in a building. The remaining parts of the structure are designed to remain essentially elastic when links yield. The link length ratio ρ is a function of e, plastic shear Vp, and plastic moment Mp capacities of the link [ρ=e/(Mp/Vp)]. Depending on the length ratio (ρ), shear yielding controls the behavior of short links while flexural yielding is predominant in long links. The experimental research conducted in [1-4] showed that short links exhibit better performance under cyclic loadings in terms of ductility and strength. A link is classified as short if ρ<1.6, while links with ρ>2.6 are considered long. These practical limitations were proposed through experimental studies of various link specimens [3, 5-7] and were adopted by many design specifications, including AISC 341-10 [8]. The effect of adding stiffeners to improve the strength and energy dissipation capacity of links] to achieve a better performance of shear links and avoid web local buckling and strength degradation has been highlighted in [3, 9-10. Unlike shear links, stiffeners in long links may not prevent flange buckling but could limit strength degradation [11]. Intermediate stiffeners may be useful in flexural links if a significant axial force is acting on the link [12]. Various numerical modeling techniques of links were developed in [10, 13-14] to demonstrate their accuracy with experimental results. More recently, a simplified approach was presented in [15] by modeling elements with concentrated hinges at the ends. This approach has been used in numerical studies [16, 17] Corresponding author: Fayçal Abdelhamid Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8278-8283 8279 www.etasr.com Abdelhamid et al.: Lateral Reliability Assessment of Eccentrically Braced Frames Including Horizontal … highlighting some deficiencies in the cyclic response of links. In [18], the previous element model was improved using the uniaxial material model of Zona and Dall'Asta to define the responses of the flexural and shear hinges. The efficiency of this approach was highlighted by comparing numerical and test results. More element models have been developed to model steel links and members in the EBFs. The model developed in [19, 20] was improved in [21] by combining axial, shear, and flexural hinges in the elements to demonstrate the accuracy of the proposed approach. Alternative EBF systems were presented in [22] to improve the performance of structures by integrating a damping system to resist lateral loading. In [23], a linkage system was proposed that combined Pall friction and rotational friction damper to improve energy dissipation capacity. In practical applications, systems with horizontal links (K- type) are the most commonly used because of their excellent performance during earthquakes. Systems with vertical links (Y-type) have also shown great cyclic performance in the experiments conducted in [24-26]. However, some deficiencies were observed at the conjunction of the vertical link and the braces due to significant out-of-plane deformations. The main goal of this study is to compare the lateral reliability of the EBF, including horizontal and vertical links, through nonlinear pushover and incremental dynamic analysis. For this purpose, 14 near-field and 7 far-field seismic records were selected to study the behavior of 5-story and 10-story EBF models. The parameter considered for the comparison of the two systems was the inter-story drift. II. NUMERICAL MODELING VERIFICATION STUDY As a first step, model validation was carried out to ensure that numerical results could represent the behavior of EBFs under real conditions. To achieve this purpose, the experimental test conducted in [27] was used to build a numerical model using the Seismostruct 2021 software [28]. The specimen tested in [27] and compared with the numerical model was a single-story single-bay 1/2 scale Y-EBF made with high-strength steel. The height and width of the specimen were 1.8m and 3.6m respectively, while a short link with a length of 0.5m was used. Table I highlights the welded H- shaped sections and the materials of the specimen elements. A vertical load of 400kN was applied to the top of the column to simulate the axial force transferred to it by the superstructure. Monotonic loading and pseudostatic tests were performed at a loading speed of 0.05mm/s until structural failure [27]. TABLE I. SECTIONS AND MATERIALS OF THE SPECIMEN ELEMENTS Members Sections Material Column H150××150×6×10 Q460 Beam H225×125×6×10 Q460 Link H225×125×6×10 Q345 Brace H125×120×6×10 Q460 Based on the experimental data, a numerical model was developed using Seismostruct 2021 [28]. The element type defined in the numerical model for beam and column was the inelastic plastic-hinge force-based frame element "InfrmFBPH", where hinges were located at both ends of beam and column. An inelastic truss element was used for the braces, and an inelastic plastic hinge displacement-based frame element InfrmDBPH was assumed for the link, as shown in Figure 1. The software automatically assigns the fibers of the section at the element’s end with a sufficient number to ensure an adequate reproduction of the stress-strain distribution across the cross-section of the member. Fig. 1. The numerical model of the studied specimen. The modeling parameters used for the link were selected according to tables 9-7 of the ASCE 41-17 standard [29]. A bilinear stress-strain steel model with kinematic strain hardening was also defined for elements with their corresponding property values. Pushover analysis was performed by imposing an incremental force at the top of the column until the model failed. The resulting capacity curve was compared with the experimental test results obtained in [27]. The comparison of the experimental and the numerical results is shown in Figure 2. The ultimate base shear of the experimental test was approximately 680kN, while a value of 618kN was recorded in the simulation model. The results appear to agree with the experimental evaluation with a maximum relative error of 9%. Therefore, it can be concluded that numerical modeling is capable of simulating the response of the specimen with sufficient accuracy and can be used to predict the dynamic behavior of EBFs. Fig. 2. Numerical model vs experimental test results. Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8278-8283 8280 www.etasr.com Abdelhamid et al.: Lateral Reliability Assessment of Eccentrically Braced Frames Including Horizontal … III. PUSHOVER AND INCREMENTAL DYNAMIC ANALYSIS In [27], four groups of Y-type EBFs of 5, 10, 15, and 20 storeys were designed, using a performance-based seismic design method, according to the Chinese seismic code for buildings [30]. Ordinary and high-strength steel was used for each group to be compared in terms of bearing capacity, lateral stiffness, story drift, link rotation, and failure modes. The prototypes were characterized by a peak ground acceleration of 0.3g with a 10% probability of exceedance over 50 years. All frames had a typical story height of 3.6m, 3 bay spans of 7.2m, and a vertical link length of 0.8m. Welded H-sections were used for all frame members except for the column where box sections were assigned. Among the 8 designed Y-type EBFs, frames with 5 and 10 storeys made with ordinary steel (Q345) were investigated. Additional EBF models were also studied in parallel, including horizontal (K-type) instead of vertical links, using the same cross-sections and geometrical dimensions as the selected models to ensure a fair comparison. Pushover analysis was performed for all prototypes using the same member modeling parameters as for the verification model. Connections were considered rigid for all models. The material yield strength used for all the element members was the nominal value of ordinary steel Q345 (fy=345MPa), and the elastic modulus was equal to 2.06×105MPa. The dead and live loads applied on the floor were 5.0kN/m² and 2.0kN/m 2 , respectively. For the roof, the dead and live loads were 6.0kN/m² and 2.0kN/m². A snow load was also assigned to the roof with a value of 0.35kN/m² [27]. The fundamental periods obtained from the modal analysis of the investigated prototypes are shown in Table II, while the adopted sections for all members are presented in Tables III and IV. Incremental Dynamic Analysis (IDA) was also applied using a set of selected ground motion records from the PEER NGA database (14 near-field earthquakes and 7 far-field earthquakes), as recommended in FEMA695 [31]. Each earthquake represents a particular seismic intensity and is used multiple times at different scales so that the structure is subjected to a wide range of elastic and inelastic behavior. Tables V and VI highlight the ground motion records used in this analysis. The Newmark integration method was used with β=0.25 and γ=0.5. The IDA offers various advantages compared to the pushover analysis and has proved its accuracy by considering the effect of higher modes in the analysis [32-33]. Fig. 3. 5-story Y-type and K-type prototypes. Fig. 4. 10-story Y-type and K-type prototypes. TABLE II. FUNDAMENTAL PERIODS Models T1 (s) T2 (s) T3 (s) 5-story Y-type 0.722 0.273 0.164 5-story K-type 0.610 0.225 0.137 10-story Y-type 1.296 0.465 0.270 10-story K-type 1.191 0.415 0.231 TABLE III. 5-STORY EBF MEMBER SECTIONS Story Beam Link Column with brace Column with no brace Brace 5 H410×150×6×10 H330×150×4×10 400×400×16 300×300×12 H200×200×8×12 4 H440×150×10×16 H420×180×6×10 450×450×18 350×350×16 H200×200×10×16 3 H490×180×10×16 H410×180×8×12 500×500×18 350×350×16 H200×200×10×16 2 H520×200×10×16 H470×180×8×12 550×550×20 400×400×18 H220×220×10×16 1 H550×200×10×16 H500×180×8×12 550×550×20 450×450×18 H220×220×10×16 TABLE IV. 10-STORY EBF MEMBER SECTIONS Story Beam Link Column with brace Column with no brace Brace 10 H440×160×6×10 H320×140×5×10 350×350×16 350×350×12 H200×200×10×16 9 H480×200×8×12 H310×150×8×14 400×400×16 350×350×12 H200×200×10×16 8 H490×200×10×16 H430×180×8×14 450×450×18 400×400×16 H220×220×10×16 7 H530×220×10×16 H420×200×10×16 450×450×20 400×400×16 H220×220×10×16 6 H560×240×10×16 H470×200×10×16 500×500×20 450×450×18 H220×220×10×16 5 H540×240×12×18 H510×200×10×16 500×500×20 450×450×18 H250×250×10×16 4 H570×240×12×18 H470×200×12×18 550×550×22 500×500×20 H250×250×10×16 3 H590×240×12×18 H490×200×12×18 550×550×22 500×500×20 H250×250×10×16 2 H610×240×12×18 H510×200×12×18 600×600×25 550×550×20 H250×250×10×16 1 H620×240×12×18 H520×200×12×18 600×600×25 550×550×20 H250×250×10×16 Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8278-8283 8281 www.etasr.com Abdelhamid et al.: Lateral Reliability Assessment of Eccentrically Braced Frames Including Horizontal … TABLE V. NEAR-FIELD GROUND MOTION RECORDS Earthquake Name Year Station Name Magnitude Rjb (km) Cape Mendocino 1992 Petrolia 7.0 9.5 Darfield_ New Zealand 2010 TPLC 7.0 6.11 Duzce_ Turkey 1999 Lamont 1062 7.1 9.14 Erzincan_ Turkey 1992 Erzincan 6.7 2.0 Gazli_ USSR 1976 Karakyr 6.8 3.92 Imperial Valley-06 1979 Chihuahua 6.5 7.29 Irpinia_ Italy-01 1980 Sturno (STN) 6.9 6.78 Kobe_ Japan 1995 Port Island 6.9 3.31 Kocaeli_ Turkey 1999 Yarimca 7.5 1.38 Loma Prieta 1989 Saratoga - Aloha Ave 6.9 7.58 Nahanni_ Canada 1985 Site 1 6.9 2.48 Niigata_ Japan 2004 NIG017 6.8 4.22 Northridge-01 1994 N Hollywood - Coldwater Can 6.7 7.89 Superstition Hills-02 1987 Superstition Mtn Camera 6.5 5.61 TABLE VI. FAR-FIELD GROUND MOTION RECORDS. Earthquake Name Year Station Name Magnitude Rjb (km) Imperial Valley-06 1979 Delta 6.5 22.03 Irpinia_ Italy-01 1980 Calitri 6.9 13.34 Loma Prieta 1989 Gilroy Array #4 7.0 13.81 San Fernando 1971 LA-Hollywood Stor FF 6.6 22.77 Spitak_ Armenia 1988 Gukasian 6.7 23.99 Superstition Hills-02 1987 Westmorland Fire Sta 6.5 13.03 Tabas_ Iran 1978 Boshrooyeh 7.4 24.07 TABLE VII. LIMIT STATES OF EBF ACCORDING TO FEMA 356 Limit states Recommended drifts (%) Immediate occupancy (IO) 0.5 Life safety (LS) 1.5 Collapse prevention (CP) 2.0 The demand parameter considered was the inter-story drift ratio (maximum inter-story drift of all storeys). The performance levels and their corresponding drift values for EBF are presented in Table VII according to FEMA356 [34]. IV. RESULTS AND DISCUSSION The seismic reliability of EBFs having K-type and Y-type links was investigated using non-linear static pushover and incremental dynamic analysis on 5 and 10-story frames. A. Pushover Analysis The EBFs with vertical links exhibited higher inter-story drifts, especially in the intermediate storeys. The difference was about 20% between the drift of the K and Y types for the 5-story model (maximum inter-story drift at the 3rd floor) and 53% for the 10-story model (maximum inter-story drift at the 5th floor). The inter-story drift is more significant as the height of the structure increases. The K-type system exhibited more important lateral stiffness than the Y-type system in all cases. According to [30], the link deformation reaches the plastic limit state when the drift value of the story exceeds 2%. The results, shown in Figure 5, indicate that the yielding of the links in the Y-type models has already occurred for the intermediate stories, while in the K-type models the links reach the plastic limit state. B. Incremental Dynamic Analysis (IDA) A series of IDAs were performed on the selected EBF models to examine the performance of the K and Y types at different earthquake intensities and to evaluate the peak ground accelerations corresponding to each specific limit state of the structures. The maximum inter-story drift recorded for the 5 and 10-story studied prototypes under the 21 selected earthquakes are shown in Figures 6 and 7, where the Peak Ground Acceleration (PGA) was selected as the intensity measure, and the maximum inter-story drift ratio was selected as the response measure. The limit states IO, LS, and CP at 0.5, 1.5, and 2% respectively, are shown in Figures 6 and 7. The results in Figure 7 show that the corresponding PGA for the different damage levels is higher for models with horizontal links (K-type). In the 5-story EBFs, a PGA of 0.73g was recorded for the K-type model against 0.4g for Y-type at the collapse prevention level. For the 10-story EBFs, the K- type model reached the limit of 2% drift ratio at a PGA of 0.5g while the Y-type model reached the same limit at 0.31g. To attain the collapse prevention performance level, the K-type systems required 1.7 times higher average intensity than the Y- type systems. It should be noted that as the height of the frame increases, the intensity that leads to the yielding of links decreases. This implies that shorter frames in general exhibit higher levels of reliability. The results in Figure 7 also show that the links in both systems produced intensities above the intensity corresponding to the design hazard level, that is 0.3g. Therefore, the performance-based seismic design method once again proved its efficiency in providing structures with good lateral stiffness to sustain subsequent earthquake intensities. (a) (b) Fig. 5. Inter-story drift ratio at 2% target (a) 5-story (b) 10-story models. Engineering, Technology & Applied Science Research Vol. 12, No. 2, 2022, 8278-8283 8282 www.etasr.com Abdelhamid et al.: Lateral Reliability Assessment of Eccentrically Braced Frames Including Horizontal … (a) (b) Fig. 6. IDA curves of 5-story models (a) K-type (b) Y-type. (a) (b) Fig. 7. IDA curves for 10-story models (a) K-type (b) Y-type. A clear comparison between the median IDA curves of 5 and 10-story prototypes is shown in Figure 8. (a) (b) Fig. 8. Median IDA curves (a) 5-story models (b) 10-story models. V. CONCLUSIONS This study investigated the lateral performance of EBFs including horizontal and vertical links. Modeling accuracy was examined using the Seismostruct software by comparing the modeling results with the experimental test conducted in [27]. The selected 5- and 10-story EBF models were analyzed using nonlinear pushover and incremental dynamic analysis over a series of 21 seismic records. The inter-story drifts obtained from the K- and Y-type EBF prototypes were compared under the same loading conditions. The following conclusions can be drawn: • The results indicate that both K-type and Y-type systems can sustain major earthquake intensities and the links can meet the target performance objectives. However, the K- type system may absorb excessive seismic energy and provide better lateral stiffness by conferring smaller inter- story drifts to the structure compared to the Y-type system. The links in both systems start to yield in the intermediate floors but at different intensities (higher for the K-type models). Low-rise EBFs exhibit higher levels of reliability in general, where links reach the plastic limit state at higher intensities than the intensity corresponding to the design hazard level. • With the same cross-sections, the K-type system exhibited better performance under the same loading conditions compared to the Y-type system. 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