Microsoft Word - numero_66_art_17_4294.docx A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 273 Behavior of a Multi-Story Steel Structure with Eccentric X-Brace Abdulkhalik J. Abdulridha Department of Civil Engineering, College of Engineering, Al-Nahrain University, Jadriya, Baghdad, Iraq Abdulkhalik.J.AbdulRidha@nahrainuniv.edu.iq, https://orcid.org/0000-0001-6403-2325 ABSTRACT. Eccentrically Braced Frames (EBFs) outperform moment- resisting frames in seismically active regions because of their strength, stiffness, energy dissipation, and ductility. Conventional bracing systems, such as X, Y, V, or K types, are utilized to enhance structural integrity. This study employs computational modelling to analyze multi-story steel buildings featuring an eccentric X-brace system. In this investigation, 120 multi-story steel frame buildings were selected. These multi-story structures comprise six- , nine-, and twelve-story geometries. ETABS built a full-scale FE model of multi-story structures. The study's parametric variables are the X-brace eccentricity, steel X-brace section size, and X-braced placement. Steel X- braces may have an eccentricity of 500, 1000, or 1500 millimeters. The ETABS model was validated when its findings matched experimental data. According to the data, the eccentric X-brace increases top-story displacement more for 6-story multi-story structures than for 9- and 12-story ones. Eccentric X- braces reduced lateral stiffness, allowing more significant floor movement. Eccentric and diagonal braces offer less lateral rigidity than concentrically braced frames due to their flexibility. Eccentricity reduces stiffness, even if the X-braced component has a larger cross-section. EBFs may migrate horizontally. Since the EBF absorbs more energy, changing the X-brace section size and eccentricity affects its ductility. KEYWORDS. Eccentrically braced frames, EBFs, Numerical analysis, Seismic load, Eccentric X-braces, ETABS. Citation: Abdulridha, A. J., Behavior of a Multi-Story Steel Structure with Eccentric X- Brace, Frattura ed Integrità Strutturale, 66 (2023) 273-296. Received: 14.05.2023 Accepted: 29.08.2023 Online first: 01.09.2023 Published: 01.10.2023 Copyright: © 2023 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION teel Braced Frames (BFs) are commonly employed to provide rigidity and strength when subjected to lateral loading. During a seismic event, the steel-braced frames added to the structure dissipate energy. These frameworks deform plastically under tension and collapse under compression, whereas beams and columns are intended to remain in the elastic zone [1–4]. Eccentrically braced frames are a modern lateral force-resisting system designed to effectively and predictably sustain seismic events. As shown in Fig. 1, eccentric bracing employs braces that are not perpendicular to the columns or do not meet the floor beams. Buildings equipped with comprehensive and well-designed EBFs that are earthquake-resistant exhibit ductile behavior. The shear or flexural yielding of a connecting element provides evidence of S https://youtu.be/d_oelsRs1fI A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 274 this. The brace's eccentricity relative to the beam's midpoint or columns' centerlines may link them. Comprehensive and balanced hysteresis loops result from ductile yielding, which indicates exceptional energy dissipation. This quality is essential for resisting intense seismic activity. During seismic activity, horizontal forces are induced at the level of a structure's foundation, which can contribute to vibration issues. If the frequency of this excitation is comparable to the structure's inherent frequency, the vibrations can become quite powerful and result in resonance. So, this can result in significant displacement of the structure and even its collapse. [5–7] Figure 1: Alternative bracing configurations for EBFs [5]. Stratan et al. [8] conducted a cycle test on an eccentric brace using four different link lengths (e = 400, 500, 600, and 700 mm). Their findings show that the stiffeners' distance from one another in the joint significantly impacts their effectiveness. Short-range connections' speeds were controlled via web shear. As a result of the bolt coming loose at the shank, the lengthy links would have been more fragile. Popov and Engelhardt [5] concluded that the beam would fail if the link length to beam length ratio exceeded 0.5. Under the current conditions, the benefits of bracing are minimal. However, when the link length is shortened, the elasticity rises. Complexity increases in eccentric bracing connections compared to their simpler concentric counterparts, as seen in Fig. 2. Figure 2: Typical eccentric construction bracing connections [5]. The initial stage of finite element modeling involves creating a geometric representation of the structure. Each element's material behavior and boundary conditions are divided into smaller forms. These smaller forms are connected to specific nodes, forming a mesh that is then analyzed [9–13]. It is essential to include computational modeling of the structure. The FE model can help with several tasks, such as finding the best place to put sensors, updating the model based on sensor measurements or a condensed model, measuring and locating structural changes (like damage), figuring out how reliable something is, and predicting how it will react under different simulated loading conditions. [14-21] Concentric X-braced steel frames are popular due to their ability to withstand earthquakes and wind loads. The diagonals disperse seismic energy that would otherwise be lost by plasticizing under strain and bowing under compression. For instance, beams and columns are frequently designed to have flexibility [22, 24]. According to the American AISC 341-16 [23], we must consider the compressed diagonal. Failure to do so would result in a violation of the regulation. An elastic analysis has been requested [23, 25]. This study assumes that all bracing has the anticipated strength in tension or compression to withstand seismic activity before buckling. Considering the anticipated strength of the in-tension diagonal and the expected strength of the compressed diagonal post-buckling is necessary for the plastic analysis requested [23, 25]. The two phases of conduct are linked differently. Canadian [26] and Japanese [27] standards require two tests. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 275 The previous studies primarily concentrated on eccentrically braced steel frames [28, 29]. Popov [30, 31] reviewed the current literature on EBFs and suggested various design modifications using the capacity design technique. Sullivan [32] proposed a design strategy based on direct displacement for eccentrically braced steel structures. This method considers the axial deformation of columns and supports and provides formulas for determining a structure's tale drift ratio and yield strength. Several studies [33–37] have examined the cyclic inelastic behavior of steel braces. These studies demonstrate that steel braces exhibit non-symmetrical hysteretic behavior, which includes strength loss under compressive stress and persistent deformations. Multiple experimental studies have demonstrated that steel reinforcements are prone to failure after repeated loading cycles. In addition, the effective buckling length and the elastoplastic properties of the material play a significant role in determining their reactivity [38–41]. Nip et al. [42] examined steel bracing with square and rectangular-shaped hollow cross-sections. The test results confirmed that the diagonal rods exhibit non-symmetrical hysteretic behavior and that their compressive strength decreases after a few compression cycles. Other investigations [43–45] have also found similar results. MYTHOLOGY everal EBF-related research has been undertaken, but they have yet to focus on the inquiry of eccentric X-braced steel frames, which is necessary here. El Centro seismic movements [46] are considered, along with 120 steel structural models. In this paper, eccentric X-braces in steel frames are the primary focus of the modeling efforts. The geometries of these high-rises range from 6 to 9 to 12 stories. The complex FE model of multi-story buildings was developed with the help of ETABS [47]. The parameters under study are the X-brace eccentricity, X-brace steel section size, and X-braced location. For steel X-braces, the eccentricity may range from 500 to 1500 mm. Each story's frame with eccentric X-braces is set at the building's corner (SC) and side (SS) to provide seismic force resistance in both orthogonal directions. Structure and architectural design information for multi-story structures are detailed on this page. It also discusses the static and dynamic properties of multi-story buildings in the context of a computer model. SCHEMATIC OF EARTHQUAKE GROUND MOTIONS AND STRUCTURES DESIGN OF ECCENTRIC X-BRACED FRAMES his paper contains the study of G+6, G+9, and G+12 multi-story steel buildings beam column system with eccentric steel X-braces containing no shear walls subjected to the El-Centro earthquake [46] and modeled using ETABS V20, which is finite-element-based software [47] Modal frames built to ASCE 7 [48] standards for needed design strength and AISC 341 [23] standards for seismic design was analyzed in this work. All framing members are made of A992 steel with a yield strength of 345 MPa. In this study, the size of the building in the plan was 27.5 m x 27.5 m, each panel was a 5.5 m x 5.5 m square frame with a height of 3 m for each story and was constructed using H-shaped steel, and the X- braces were installed on the diagonals. In this study, there are a total of 120 buildings, with 40 being 6-story structures (18 m in height), 40 being 9-story structures (27 m in height), and the remaining 40 being 12-story structures (36 m in height). The parametric study examines the eccentricity of steel X-braces, the size of the steel X-brace section, and the location of the X-brace. Three types of eccentricity of steel X-braces adopted are 500, 1000, and 1500 mm, respectively. The sections of the diagonal X-brace were H-shaped. Five steel section sizes (W-6x12, W-6x15, W-6x16, W-6x20, and W-6x25 ) were selected for the X-brace, and an adopted multi-story steel building with an X-brace section of W-6x16 was used as a control building to compare. The X-brace section's properties are shown in Tab. 1. There are two configurations of the location of the X-braces adopted in this study: EBFs in all stories are arranged at the corner on the perimeter of the buildings, and eccentric X-braces in all stories are arranged at the side on the perimeter of the buildings. As seismic force-resisting systems in both orthogonal directions, the plan and 3D elevation of the studied 6-story, 9-story and 12-story with corner position of steel X-brace (SC) and side (SS) on the perimeter of the buildings, as depicted in Figs. 3 and 4, respectively. The alternative eccentricity of bracing arrangement of EBF’s of steel buildings are shown in Fig. 5. Tabs. 2–3 illustrate the specifications of numbered steel structures with six-story, nine-story, and twelve-story heights and distinct X-brace sections. In order to transfer lateral stresses to the Concentric Braced Frames (CBFs) and EBFs, the floor system is made up of 100 mm thick concrete on a metal deck with steel shear bolts welded to floor beams and cast-in-place concrete decking with a "non-flexible" diaphragm. The x-type bracing system ensures the lateral stability of the building frame. The columns and girders of a ''gravity-only frame'' are joined utilizing shear beam-to-column connections (fully rigid), which can only support the weight of gravity. Dead and live loads for homes are expected to operate on the structure in S T A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 276 addition to lateral stresses brought on by earthquake base excitation. Using the ETABS software, we determined the active gravity load to be (self-weight), and we set the superimposed dead load on each level to 2.5 kN/m2. The total live load, including the terrace, was calculated to be 4.79 kN/m2 using ASCE 7 [48]. Figure 3: Plan and 3D elevation of the studied 6-story, 9-story and 12-story with corner position of steel X-brace (SC). A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 277 Figure 4: Plan and 3D elevation of the studied 6-story, 9-story and 12-story with side position of steel X-brace (SS). Figure 5: Alternative eccentricity of bracing arrangement of EBF’s of steel buildings. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 278 X- brace section Area (mm2) Depth (mm) Web thickness (mm) Flange width (mm) Flange thickness (mm) Ix (mm⁴) Iy (mm⁴) Sx (mm³) Sy (mm³) Zx (mm³) Zy (mm³) Weight (kg/m) KL/r W6x12 2290 153 5.84 102 7.11 9.2×10⁶ 1.24×10⁶ 120×10³ 24.6×10³ 136×10³ 38×10³ 18 6.24 W6x15 2860 152 5.84 152 6.6 12.1×10⁶ 3.88×10⁶ 159×10³ 51×10³ 177×10³ 77.8×10³ 22.5 3.47 W6x16 3060 160 6.6 102 10.3 13.4×10⁶ 1.84×10⁶ 167×10³ 36.1×10³ 192×10³ 55.6×10³ 24 6.59 W6x20 3790 157 6.6 153 9.27 17.2×10⁶ 5.54×10⁶ 220×10³ 72.3×10³ 246×10³ 110×10³ 29.8 3.63 W6x25 4740 162 8.13 154 11.6 22.2×10⁶ 7.12×10⁶ 274×10³ 91.9×10³ 310×10³ 140×10³ 37.1 3.97 Table 1: Details of the sections properties of steel X-brace (W-6x12, W-6x15, W-6x16, W-6x20 and W-6x25). No. of story Story No. Eccentricity (mm) X-brace position (Corner) X-brace position (Side) Building code Beam section Column section Brace section Building code Beam section Column section Brace section 6 1 0 SC6-B16-1 W10x30 W8x24 W6x16 SS6-B16-1 W10x30 W8x24 W6x16 2 W10x30 W8x24 W6x16 W10x30 W8x24 W6x16 3 W10x30 W8x20 W6x16 W10x30 W8x20 W6x16 4 W10x26 W8x20 W6x16 W10x26 W8x20 W6x16 5 W10x26 W6x20 W6x16 W10x26 W6x20 W6x16 6 W10x26 W6x20 W6x16 W10x26 W6x20 W6x16 9 1 0 SC9-B16-1 W10x33 W10x39 W6x16 SS9-B16-1 W10x33 W10x39 W6x16 2 W10x33 W10x39 W6x16 W10x33 W10x39 W6x16 3 W10x33 W10x39 W6x16 W10x33 W10x39 W6x16 4 W10x30 W10x31 W6x16 W10x30 W10x31 W6x16 5 W10x30 W10x31 W6x16 W10x30 W10x31 W6x16 6 W10x30 W10x31 W6x16 W10x30 W10x31 W6x16 7 W10x26 W8x31 W6x16 W10x26 W8x31 W6x16 8 W10x26 W8x31 W6x16 W10x26 W8x31 W6x16 9 W10x26 W8x31 W6x16 W10x26 W8x31 W6x16 12 1 0 SC12-B16-1 W10x39 W12x45 W6x16 SS12-B16-1 W10x39 W12x45 W6x16 2 W10x39 W12x45 W6x16 W10x39 W12x45 W6x16 3 W10x39 W12x45 W6x16 W10x39 W12x45 W6x16 4 W10x33 W12x45 W6x16 W10x33 W12x45 W6x16 5 W10x33 W10x39 W6x16 W10x33 W10x39 W6x16 6 W10x33 W10x39 W6x16 W10x33 W10x39 W6x16 7 W10x30 W10x39 W6x16 W10x30 W10x39 W6x16 8 W10x30 W10x39 W6x16 W10x30 W10x39 W6x16 9 W10x30 W8x35 W6x16 W10x30 W8x35 W6x16 10 W10x26 W8x35 W6x16 W10x26 W8x35 W6x16 11 W10x26 W8x35 W6x16 W10x26 W8x35 W6x16 12 W10x26 W8x35 W6x16 W10x26 W8x35 W6x16 Table 2: Details of the members design of steel buildings with 6, 9 and 12-story with concentric X-brace. No. of story X-brace position Eccentricity (mm) e/L Building code Brace section Building code Brace section Building code Brace section Building code Brace section Building code Brace section 6 Corner 0 0 SC6-B12-1 W6x12 SC6-B15-1 W6x15 SC6-B16-1 W6x16 SC6-B20-1 W6x20 SC6-B25-1 W6x25 500 0.094 SC6-B12-2 W6x12 SC6-B15-2 W6x15 SC6-B16-2 W6x16 SC6-B20-2 W6x20 SC6-B25-2 W6x25 1000 0.188 SC6-B12-3 W6x12 SC6-B15-3 W6x15 SC6-B16-3 W6x16 SC6-B20-3 W6x20 SC6-B25-3 W6x25 1500 0.282 SC6-B12-4 W6x12 SC6-B15-4 W6x15 SC6-B16-4 W6x16 SC6-B20-4 W6x20 SC6-B25-4 W6x25 Side 0 0 SS6-B12-1 W6x12 SS6-B15-1 W6x15 SS6-B16-1 W6x16 SS6-B20-1 W6x20 SS6-B25-1 W6x25 500 0.094 SS6-B12-2 W6x12 SS6-B15-2 W6x15 SS6-B16-2 W6x16 SS6-B20-2 W6x20 SS6-B25-2 W6x25 1000 0.188 SS6-B12-3 W6x12 SS6-B15-3 W6x15 SS6-B16-3 W6x16 SS6-B20-3 W6x20 SS6-B25-3 W6x25 1500 0.282 SS6-B12-4 W6x12 SS6-B15-4 W6x15 SS6-B16-4 W6x16 SS6-B20-4 W6x20 SS6-B25-4 W6x25 9 Corner 0 0 SC9-B12-1 W6x12 SC9-B15-1 W6x15 SC9-B16-1 W6x16 SC9-B20-1 W6x20 SC9-B25-1 W6x25 500 0.094 SC9-B12-2 W6x12 SC9-B15-2 W6x15 SC9-B16-2 W6x16 SC9-B20-2 W6x20 SC9-B25-2 W6x25 1000 0.188 SC9-B12-3 W6x12 SC9-B15-3 W6x15 SC9-B16-3 W6x16 SC9-B20-3 W6x20 SC9-B25-3 W6x25 1500 0.282 SC9-B12-4 W6x12 SC9-B15-4 W6x15 SC9-B16-4 W6x16 SC9-B20-4 W6x20 SC9-B25-4 W6x25 Side 0 0 SS9-B12-1 W6x12 SS9-B15-1 W6x15 SS9-B16-1 W6x16 SS9-B20-1 W6x20 SS9-B25-1 W6x25 500 0.094 SS9-B12-2 W6x12 SS9-B15-2 W6x15 SS9-B16-2 W6x16 SS9-B20-2 W6x20 SS9-B25-2 W6x25 1000 0.188 SS9-B12-3 W6x12 SS9-B15-3 W6x15 SS9-B16-3 W6x16 SS9-B20-3 W6x20 SS9-B25-3 W6x25 1500 0.282 SS9-B12-4 W6x12 SS9-B15-4 W6x15 SS9-B16-4 W6x16 SS9-B20-4 W6x20 SS9-B25-4 W6x25 12 Corner 0 0 SC12-B12-1 W6x12 SC12-B15-1 W6x15 SC9-B16-1 W6x16 SC9-B20-1 W6x20 SC9-B25-1 W6x25 500 0.094 SC12-B12-2 W6x12 SC12-B15-2 W6x15 SC9-B16-2 W6x16 SC9-B20-2 W6x20 SC9-B25-2 W6x25 1000 0.188 SC12-B12-3 W6x12 SC12-B15-3 W6x15 SC9-B16-3 W6x16 SC9-B20-3 W6x20 SC9-B25-3 W6x25 1500 0.282 SC12-B12-4 W6x12 SC12-B15-4 W6x15 SC9-B16-4 W6x16 SC9-B20-4 W6x20 SC9-B25-4 W6x25 Side 0 0 SS12-B12-1 W6x12 SS12-B15-1 W6x15 SS9-B16-1 W6x16 SS9-B20-1 W6x20 SS9-B25-1 W6x25 500 0.094 SS12-B12-2 W6x12 SS9-B15-2 W6x15 SS9-B16-2 W6x16 SS9-B20-2 W6x20 SS9-B25-2 W6x25 1000 0.188 SS12-B12-3 W6x12 SS9-B15-3 W6x15 SS9-B16-3 W6x16 SS9-B20-3 W6x20 SS9-B25-3 W6x25 1500 0.282 SS12-B12-4 W6x12 SS9-B15-4 W6x15 SS9-B16-4 W6x16 SS9-B20-4 W6x20 SS9-B25-4 W6x25 Table 3: Details of numerical steel buildings with 6, 9 and 12-story with various X-brace section. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 279 THE FINITE ELEMENT MODEL USING ETABS he finite element analysis program ETABS [47] is used extensively throughout this study to examine the structural behavior of the simulated steel building prototypes. The finite element model includes representations of the composite deck slab, central girders, steel bracings, secondary beams, and steel columns. The suggested structural models are three-dimensional finite element models. The composite slab is cut into shell elements for each panel in the "xy" plane, and the framing beams are cut into the same number of slab elements. The concrete on a metal deck slab with four- node shell components represents six degrees of freedom. Frame components are used to replicate the core girders, braces, secondary beams, and steel columns. The benefits of beam and truss components are combined in the frame element. In contrast to the beam element, which may deform in both shear and rotation at each edge, the truss element can only deform in one direction (axially). The time-history analysis is a method for investigating how a structure responds dynamically to varying loading over time. Time history dynamic analysis was performed to reproduce seismic base excitation by analyzing building models for ground acceleration time history of the EL-Centro earthquake ground motion [46]. In order to account for material nonlinearity and P-∆ effects in the study, a damping ratio of 5% was chosen. The inelastic behavior of the structural portion or system caused material nonlinearity. When a structural system is warped, P-∆ effects examine how well it can sustain a load in equilibrium. GROUND ACCELERATION-TIME HISTORY DATA he historic El-Centro (Imperial Valley) earthquake, estimated to have measured a magnitude of 7.1 on the Richter scale [46], posed an essential risk to these structures because of its relatively low peak ground acceleration (PGA) of 0.3 g. The letter g represents the acceleration due to gravity, which is 9.81 meters per second squared. The El-Centro earthquake was one of the earliest to collect extensive data on large-scale motion, making it a benchmark. Seismically safe construction codes, such as ASCE 7, were formed due to these studies. El-Centro's extensive motion data gave engineers crucial insights that helped them create buildings more resistant to earthquakes. For the following ASCE 7 [48] load combinations (the first equation was used for this study), Eqns. (1) through (4) may be used to depict the time dependence of the ground acceleration due to an earthquake: 1.2                0.15D Ev Eh L S    (1) 1.0    0.7    0.7D Ev Eh  (2) 1.0    0.525    0.525    0.75    0.1D Ev Eh L S    (3) 0.6    0.7    0.7D Ev Eh  (4) Where D represents the dead load, L represents the live load, S represents the superimposed load, Ev represents the vertical seismic load effect, and Eh represents the horizontal seismic load effect. Figure 6: The El-Centro -1940 record acceleration time series (a) in the x direction, and (b) in the y direction [46]. T T A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 280 OUTLINE OF EXPERIMENTAL PROGRAM his work used the experimental study published by Alptug and Mevlut [49] to calibrate numerical findings and confirm their applicability; a short overview is given below. In Fig. 7, Alptug and Mevlut [49] show the features of a steel frame specimen indicative of their experimental test. Concentration was measured in single-bay, two-story, steel-braced buildings. The static lateral loading (pushover analysis) method was applied to an X-braced steel frame and specimens with a 100x100x3 mm cross-section. High-strength shafts were placed into the holes in the solid laboratory slab and then hammered into the ground to anchor the specimen firmly. Tab. 4 displays the profiles in a cross-section. Figure 7: Details of steel frame specimen (a) experimental [49] and (b) ETABS. Square section (mm) Ax (mm2) Ix (mm4) Iy (mm4) ix (mm) iy (mm) Welx (mm3) Wely (mm3) Wplx (mm3) Wply (mm3) 100×100×3 1140 1.77*106 1.77*106 39.4 39.4 35400 35400 41200 41200 Table 4: Profile properties [49] CONCLUSIONS AND RESULTS - CERTIFICATION RESULTS comparison of numerical and experimental data [49] is shown in Fig. 8. This graph shows how well the ETABS model fits with the experimental data. The ETABS to experimental axial compressive strength ratio (PNum. / PExp) and the maximum longitudinal displacement (Δ Num / Δ Exp) fall between 1.03 and 1.04. Specimens exposed to stress testing are shown with experimental and numerical damage in Fig.9. The numerical technique correctly predicts the test frame's load-bearing capabilities, maximum displacement, and failure mechanism. Given that the samples differ by less than 10%. This finding is consistent with Harba and Abdulridha [50] and Risan et al. [51]. Figure 8: The experimental [49] and ETABS lateral load –displacement curves. T A A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 281 Figure 9: Damage under lateral load as measured experimentally [49] and predicted by ETABS. FINDINGS ON CONTROLLED-STEEL BUILDINGS ince this research aims to assess the earthquake resistance of a steel multi-story structure equipped with an eccentric X-brace, the findings must be as consistent as possible. The X-brace section of the control steel structures is W6 x 16 inches, and the buildings range in height from 6 to 12 stories. Tabs. 5 show the numerical outcomes of the W6x16 X-brace sectioned multi-story buildings (6, 9, and 12). The behavior of lateral displacements and lateral drift due to seismic stress is shown in Figs. 10 through 12 as a function of the eccentricity of the X-brace. X-brace position Building code Eccentricity (mm) e/L Displacement X-direction (mm) Increasing % Displacement Y-direction (mm) Increasing % Max. Drift X- direction Increasing % Max. Drift Y- direction Increasing % Corner SC6-B16-1 0 0 171.5 - 88.2 - 0.016 - 0.006 - SC6-B16-2 500 0.094 197.2 14.9 99.6 12.9 0.017 6.3 0.007 16.7 SC6-B16-3 1000 0.188 316.9 84.7 158.2 58.8 0.023 43.8 0.010 66.7 SC6-B16-4 1500 0.282 375.8 119.1 159.4 0.8 0.028 75.0 0.011 83.3 Side SS6-B16-1 0 0 158.9 - 78.8 - 0.015 - 0.006 - SS6-B16-2 500 0.094 196.7 23.8 110.5 40.2 0.017 13.3 0.008 33.3 SS6-B16-3 1000 0.188 309.0 94.4 158.6 43.5 0.022 46.7 0.010 66.7 SS6-B16-4 1500 0.282 367.4 131.2 159.4 0.5 0.027 80.0 0.011 83.3 Corner SC9-B16-1 0 0 397.5 - 227.8 - 0.021 - 0.013 - SC9-B16-2 500 0.094 406.3 2.2 269.7 12.9 0.021 0 0.014 7.7 SC9-B16-3 1000 0.188 482.0 21.3 354.4 79.4 0.023 9.5 0.018 38.5 SC9-B16-4 1500 0.282 432.9 8.9 384.8 80.7 0.025 19.1 0.019 46.2 Side SS9-B16-1 0 0 391.0 - 224.3 - 0.021 - 0.012 - SS9-B16-2 500 0.094 401.6 2.7 256.2 40.2 0.021 0 0.014 16.7 SS9-B16-3 1000 0.188 491.6 25.7 331.6 101.3 0.023 9.5 0.018 50.0 SS9-B16-4 1500 0.282 435.4 11.4 377.9 102.3 0.026 23.8 0.018 50.0 Corner SC12-B16-1 0 0 484.7 - 380.4 - 0.020 - 0.015 - SC12-B16-2 500 0.094 467.1 -3.6 382.9 0.7 0.021 5.0 0.017 13.3 SC12-B16-3 1000 0.188 406.9 -16.1 379.6 -0.2 0.019 -5.0 0.016 6.7 SC12-B16-4 1500 0.282 388.0 -19.9 376.2 -1.1 0.021 5.0 0.015 0 Side SS12-B16-1 0 0 474.0 - 400.0 - 0.020 - 0.014 - SS12-B16-2 500 0.094 464.4 -2.0 372.4 -6.9 0.020 0 0.015 7.2 SS12-B16-3 1000 0.188 409.0 -13.7 360.5 -9.9 0.019 -5.0 0.016 14.3 SS12-B16-4 1500 0.282 389.2 -17.9 369.6 -7.6 0.020 0 0.015 7.2 Table 5: Numerical results of the 6, 9 and 12-story buildings with X-brace with section of W6x16. S A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 282 Figure 10: The 6-story buildings behavior (a) Story - lateral displacement curves and (b) Story -lateral drift curves. Figure 11: The 9-story buildings behavior (a) Story - lateral displacement curves and (b) Story -lateral drift curves. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 283 Figure 12: The 12-story buildings behavior (a) Story - lateral displacement curves and (b) Story -lateral drift curves. EFFECT OF ECCENTRIC X-BRACING ON THE STORY LATERAL DISPLACEMENT he impact of bracings may be studied using story lateral displacement tables and graphs. It is found that the lateral displacements at each story level may be significantly increased at the top story level by adding different eccentric bracing patterns to the basic frame structure. The chart shows that for multi-story buildings with six stories and an X-brace section of W6x16 at the corner position, the lateral displacement rises by 14.9%, 84.7%, and 119.1% as eccentricity increases. Moreover, for multi-story buildings with a W6x16 eccentric X-brace section at the side position, an increased eccentrically braced frame increased lateral displacement by 23.8%, 94.4%, and 131.2%. For 9-story multi-story buildings with an X-brace section of W6x16 in the corner position, increasing the eccentricity of the bracing from 0 to 1500mm increased the lateral displacement of by 12.9 percent, 79.4 percent and 80.7 percent, respectively. Furthermore, for multi-story buildings with an X-brace section of W6x16 at the side position, increases in eccentrically braced frames from 0 to 1500mm resulted in increasing the lateral displacement of by 40.2, 101.3 and 102.3 percent, respectively. For 12-story multi-story buildings with an X-brace section of W6x16 at the corner site, the lateral displacement decreased by 3.6%, 16.1%, and 19.9% as the eccentricity of the bracing increased. Furthermore, for multi-story buildings with a W6x16 eccentric X-brace section at the side position, the lateral displacement decreased by 2.0%, 13.7%, and 17.9% as stories increased. Compared to 9- and 12-story multi-story structures, the findings show that eccentric X-braces are superior at minimizing upper-story displacement in 6-story multi-story buildings. Lateral displacement at each floor rose as the eccentricity of the eccentric X-brace did since the structure became less stiff laterally. T A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 284 EFFECT OF ECCENTRIC X-BRACING ON THE STORY DRIFT ables and figures in story lateral drift format may be used to study the impact of bracings. Different eccentric bracing patterns are added to the basic frame structure, improving lateral displacements at each story level and significantly increasing the displacement at the top story level. The chart shows that the lateral drift of 6-story multi-story buildings with an X-brace section of W6x16 at the corner increased by 16.7%, 66.7%, and 83.3% when eccentric bracing was added to the frame. Furthermore, for 6-story multi-story buildings with an X-brace section of W6x16 in the side position, an increased eccentrically braced frame increased lateral drift by 33.3%, 66.7%, and 83.3%. For 9-story multi-story buildings with an X-brace section of W6x16 at the corner position, the maximum lateral drift was increased by 7.7%, 38.5% and 46.2%, respectively, when the eccentricity of the frame was raised from 0 to 1500mm. For 9- story multi-story buildings with an X-brace section of W6x16 at the side position, the maximum lateral drift was increased by 16.7, 50 and 50 %, respectively, for increases in eccentrically braced frames from 0 to 1500mm. The maximum lateral drift for 12-story multi-story buildings with a W6x16 X-brace section at the corner increased by 13.3%, 6.7%, and 5% when the eccentric bracing of the frame was increased. Also, for multi-story buildings with 12 stories and an X-brace section of W6x16 in the side position, the lateral drift increased by 7.2%, 14.3%, and 7.2% as the eccentricity of the bracing increased. Based on the data, eccentric X-braces are better suited for six-story buildings than nine- or twelve-story buildings to avoid story drift. When designing a building with six stories, increasing the eccentricity of the X-brace reduces the lateral stiffness of the structure, causing a more significant lateral displacement on each floor. Buildings with nine and twelve stories have improved the basic frame structure's lateral stiffness, reducing story displacements and, consequently, deviations at each level. The previous figures show that eccentric X-braces are stiffer than concentrically supported edges. So, displacement, drift, relatively increased, and base shear will all be magnified in a system with eccentric bracing. Lateral height drift is more pronounced between eccentric X-brace and other lower-level supports. As a result of their low horizontal rigidity, eccentric X-braces can provide more structural variation than concentrically supported edges. Due to a reduction in the earthquake's effect with altitude, inter-story drift is reduced. Compared to eccentric X-braces, the lateral stiffness of edges braced using concentric X-braces is the greatest. EFFECT OF ECCENTRICITY OF X-BRACE ON THE SEISMIC BEHAVIOR ne can examine its maximal base shear to demonstrate how much force an earthquake may exert on a structure's foundation. Tab. 6 displays the maximum allowable lateral displacement, drift, and base shear for the X-braced control steel structure models. Figs. 13 through 15 depict the compression of the maximal base shear generated at the foundation of each steel building model subjected to applied seismic pressures. Figs. 16–18 show how the base shear changes over time for 6-story, 9-story, and 12-story buildings with W6x16 X-brace sections in the corners. Figs. 19–21 show how the time hysteresis of base shear changes for buildings with six, nine, or twelve stories and a W6x16 eccentric X-brace in the side position. No. of Story X-brace position (Corner) X-brace position (Side) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Base shear Vmax (kN) Maximum Brace force (kN) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Base shear Vmax (kN) Maximum Brace force (kN) 6 0 SC6-B16-1 171.5 0.0157 11354.5 1657.8 0 SS6-B16-1 158.9 0.0151 9918.9 1401.8 500 SC6-B16-2 197.2 0.0168 11197.2 2137.9 500 SS6-B16-2 196.7 0.0166 11146.2 2043.9 1000 SC6-B16-3 316.9 0.0231 8451.4 2411.9 1000 SS6-B16-3 309.1 0.0216 8321.9 2286.7 1500 SC6-B16-4 375.8 0.0276 7042.7 2783.1 1500 SS6-B16-4 367.4 0.0269 6962.9 2674.1 9 0 SC9-B16-1 397.5 0.0211 10805.8 1596.2 0 SS9-B16-1 391.0 0.0210 10705.3 1530.9 500 SC9-B16-2 406.3 0.0203 9601.1 1887.6 500 SS9-B16-2 401.6 0.0207 9799.0 1825.0 1000 SC9-B16-3 482.1 0.0227 6910.3 2276.6 1000 SS9-B16-3 491.6 0.0233 6738.1 1916.7 1500 SC9-B16-4 432.9 0.0249 4751.2 2388.4 1500 SS9-B16-4 435.4 0.0255 4832.8 1916.8 12 0 SC12-B16-1 484.7 0.0201 7586.2 1467.4 0 SS12-B16-1 474.0 0.0197 7185.0 1052.8 500 SC12-B16-2 467.1 0.0204 7571.1 1828.7 500 SS12-B16-2 464.4 0.0196 7311.1 1460.8 1000 SC12-B16-3 406.9 0.0188 5346.9 1731.3 1000 SS12-B16-3 409.1 0.0187 5264.5 1642.3 1500 SC12-B16-4 388.0 0.0206 4152.9 1736.4 1500 SS12-B16-4 389.2 0.0203 4260.3 1716.3 Table 6: Numerical results of the 6, 9 and 12-story buildings with X-brace with section of W6x16. T O A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 285 Figure 13: Base shear-lateral displacement curve of the 6-story buildings Figure 14: Base shear-lateral displacement curve of the 9-story buildings. Figure 15: Base shear-lateral displacement curve of the 12-story buildings. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 286 Figure 16: Comparison of time hysteresis of base shear for different cases of the 6-story buildings with X-brace section of W6x16 at corner position. Figure 17: Comparison of time hysteresis of base shear for different cases of the 9-story buildings with X-brace section of W6x16 at corner position. Figure 18: Comparison of time hysteresis of base shear for different cases of the 12-story buildings with X-brace section of W6x16 at corner position. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 287 Figure 19: Comparison of time hysteresis of base shear for different cases of the 6-story buildings with X-brace section of W6x16 at side position. Figure 20: Comparison of time hysteresis of base shear for different cases of the 9-story buildings with X-brace section of W6x16 at side position. Figure 21: Comparison of time hysteresis of base shear for different cases of the 12-story buildings with X-brace section of W6x16 at side position. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 288 The influence of eccentricity on X-bracings may be studied with base shear (Vmax) and maximum brace force tables and figures. For 6-story structures with an X-brace section of W6x16 at the corner position had a 1.38%, 25.57% and 37.97%, respectively reduced in base shear as the eccentricity of the bracing frame increased from 0 to 1500mm. Also, for multi- story buildings with a 6-story height and an X-brace section of W6x16 in the side position, an increase in eccentrically braced frames resulted in a decrease in base shear of 1.83 percent, 26.71 percent, and 38.67 percent, respectively. Multi-story buildings with 9 stories with an X-brace section of W6x16 at the corner position saw an increase in eccentrically braced frames decrease base shear by 11.14%, 36.05%, and 56.03%. Also, for 9-story multi-story buildings with X-brace section W6x16 at side position, an increase in eccentrically braced frames from 0 to 1500mm resulted in decrease base shear by 9.31%, 37.64%, and 55.27%. For multi-story buildings with 12 stories and an X-brace section of W6x16 at the corner, the eccentrically braced frame resulted in a 0.19 percent, 29.52 percent, and 45.26 percent decrease in base shear. In addition, for 12-story multi-story buildings with an X-brace section of W6x16 in the side position, an increase in eccentrically braced frames decreased base shear by 3.63%, 30.61%, and 43.84%. For 6-story structures with an X-brace section of W6x16 at the corner position had a 28.96%, 45.49% and 67.88%, respectively increased in brace force as the eccentricity of the bracing frame increased from 0 to 1500mm. Also, for multi- story buildings with a 6-story height and an X-brace section of W6x16 in the side position, an increase in eccentrically braced frames resulted in an increased in brace force of 23.28 percent, 37.94 percent, and 61.30 percent, respectively. Multi-story buildings with 9 stories with an X-brace section of W6x16 at the corner position saw an increase in eccentrically braced frames increased brace force by 18.26%, 42.63%, and 49.63%. Also, for 9-story multi-story buildings with X-brace section W6x16 at side position, an increase in eccentrically braced frames from 0 to 1500mm resulted in increased brace force by 14.33%, 20.07%, and 20.09%. For multi-story buildings with 12 stories and an X-brace section of W6x16 at the corner, the eccentrically braced frame resulted in a 24.62 percent, 17.98 percent, and 18.33 percent increase in brace force. In addition, for 12-story multi-story buildings with an X-brace section of W6x16 in the side position, an increase in eccentrically braced frames changed in brace force by – 0.45%, 11.92%, and 16.96%. Eccentric X-braces decrease brace force in six-story multi-story buildings more than nine- or twelve-story ones. The X- brace force increased as eccentricity lowered lateral stiffness. The eccentricity of the X-brace decreases the structure's lateral stiffness, boosting steel frame ductility and minimizing base shear hysteresis. Figs. 13–15 show that the eccentric X-brace bends faster along a wall than at a corner. Low-rise frames dissipate more energy, proving the eccentric X-brace works better. Eccentricity influenced the braced frame's strength, stability, and ductility since the horizontal links' length indicated the system's energy dissipation capacity. Short links (little eccentricity) rapidly affect shear in the connections, whereas longer links (large eccentricity) may bend. Shorter linkages (small eccentricities) improve shear-yielding efficiency. Otherwise, more eccentricity increases flexural yielding, whereas shorter connections with less eccentricity increase shear yielding. Eccentric braces are more flexible. Thus, their lateral rigidity is lower than that of concentrically braced frames, particularly diagonally braced ones. Eccentric braces delay the building's reaction to an earthquake, giving residents more time to leave, while structural bracing reduces ground vibrations. Eccentrically braced frames last longer and are the most versatile. Eccentric X-braces are flexible but less rigid than concentrically braced frames. Eccentric X-braces have excellent ductility but low lateral stiffness, making seismic design difficult. The numerical method correctly estimates lateral displacement, maximum drift, and base shear. It matches Abolfazl and Imanpour [52], Tian et al. [53] and Wang et al. [54]. EFFECT OF THE CHANGING IN X-BRACE SECTION ON THE BEHAVIOR OF BUILDINGS his part will examine how modifying the X-brace section influences the building assembly. The X-brace included H-shaped diagonals. Five steel sections were chosen for the X-brace (W-6x12, W-6x15, W-6x16, W-6x20, and W- 6x25), and a multi-story steel structure using the W6x16 X-brace section was used as a control. Maximum lateral displacement, drift, and base shear for the X-brace steel section (W-6x12, W-6x15, W-6x16, W-6x20, and W-6x25) at corner and side positions are shown in Tabs. 7–9. The story-lateral drift of the 6-story buildings with varying X-brace sections at the corner and side locations is also shown in Fig. 22. The 9-story buildings with corner and side X-brace sections of various kinds demonstrate lateral drift in Fig. 23. The twelve-story structures with various eccentric X-brace sections in the corners and sides are seen drifting laterally in Fig. 24. The effects of altering the eccentric X-brace section may be analyzed using horizontal movement charts and tables. There is a 17.76% rise in lateral story displacement for buildings with six stories with corner X-braces when the X-brace section is reduced from W-6x16 to W-6x12 and an 18.02% decrease when the X-brace section is reduced from W-6x16 to W-6x25. When the eccentricity was 500 mm, the results were an increase of 16.27 percent and a drop of 16.02 percent with a smaller X-brace section. When the eccentricity was 1000 mm, the results were an increase of 6.5 percent and a decrease of 13.0 T A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 289 percent, respectively. Reduced by 5.85% but increased by 3.0%, the X-brace portion was used when the eccentricity was 1500 mm. The lateral drift of the story rise by 14.01%, 17.85%, and 5.62% when the eccentricity was modified from 0 to 1000 mm and dropped by 15.92%, 5.35%, and 2.16% when the X-brace section was changed. The X-brace cross-section decreased by 0.72% but increased by 1.08% with an eccentricity of 1500 mm. Story lateral displacement increased by 10.69%, 14.18%, and 5.43% and decreased by 18.75%, 15.81%, and 11.9% for 6- story buildings with eccentric X-braces at side positions. To achieve an eccentricity of 1500 mm, a reduction of 4.24% and an increase of 5.4% were applied to the X-brace section. The lateral drift of the story increased by 5.96%, 18.67%, and 0% when the eccentricity varied from 0 to 1000 mm and decreased by 26.49%, 0%, and 10.18% when the eccentricity varied from 0 to 1000 mm due to changes in the X-braces section. For an eccentricity of 1500 mm, we saw a decrease in the X- brace area of 1.86% and 3.72%. For the buildings with nine stories with corner X-braces, the story lateral displacement was found to shift by 4.5 percentage points, 2.65 percentage points, 6.67 percentage points, and -3.8 percentage points when the X-brace section was decreased, and by -3.8 percentage points, -4.4 percentage points, -11.4 percentage points, and 12.05% when the X-brace section was raised, all with increasing eccentricity. When the X-brace section was lowered, the story lateral drift changed by -4.73%, 1.48%, 3.94%, and -4%; when it was elevated, the numbers were 4.73%, 2.96%, -10.57%, and 1.61%. A reduction in the X- brace section reduces the lateral displacement of the story by 4.65%, 3.18%, 4.39%, and -3.3% as eccentricity rises. In contrast, an increase in the X-brace section reduces the lateral displacement by 1.99%, -1.72%, -9.9%, and 9.07%. Additional variations in the story lateral drift of -5.23%, 0.48%, 1.72%, and -6.3% were caused by reducing the size of the X-brace, whereas increases of 4.3%, 2.89%, -8.58%, and -0.4% were caused by increasing the section of the eccentric X-brace. For the buildings with twelve stories with corner X-braces, the story lateral displacement was found to decrease by 2.99%, 0.41%, 0.88%, and 0.15% when the X-brace section was reduced, 6.5%, 4.75%, 6.43%, and 1.67% when the X-brace section was raised, and by 2.48%, - 0.49%, 0%, and 0.97% when the eccentricity was increased. Additionally, changes in the story lateral drift of 3.98%, 0%, -4.25%, and -6.79% were caused by reducing the size of the X-brace, whereas changes of -1.11%, 0.25%, -2.51% and -0.61% were caused by increasing the section of the X-brace, respectively. For decreasing and increasing X-brace sections with increasing eccentricity, lateral story displacement decreased by 7.81%, 1.11%, 6.5%, and 1.69%, respectively. Alterations in the story lateral drift of 1.52%, 0.51%, -1.07%, and 1.48% were also seen for X-brace sizes decreasing from large to small and of 3.56%, 1.02%, -4.27%, and -4.93% for eccentric X-brace sizes rising. X-brace position (Corner) X-brace position (Side) No. of Story Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Vmax (kN) Maximum Brace force (kN) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Vmax (kN) Maximum Brace force (kN) 6 0 SC6-B12-1 201.8 0.0179 11354.6 1640.3 0 SS6-B12-1 175.9 0.0160 11257.4 1590.2 SC6-B15-1 181.9 0.0157 11504.9 1676.4 SS6-B15-1 162.9 0.0150 10166.4 1442.3 SC6-B16-1 171.5 0.0157 11354.5 1657.8 SS6-B16-1 158.9 0.0151 9918.9 1401.8 SC6-B20-1 160.9 0.0150 10453.9 1552.1 SS6-B20-1 142.8 0.0130 10698.8 1515.0 SC6-B25-1 140.6 0.0132 10728.8 1567.9 SS6-B25-1 129.1 0.0111 10658.6 1512.3 500 SC6-B12-2 229.3 0.0198 10628.6 1931.4 500 SS6-B12-2 224.6 0.0197 10774.4 1900.7 SC6-B15-2 199.2 0.0177 11138.7 2102.2 SS6-B15-2 199.4 0.0175 11153.6 2028.5 SC6-B16-2 197.2 0.0168 11197.2 2137.9 SS6-B16-2 196.7 0.0166 11146.2 2043.9 SC6-B20-2 180.7 0.0161 11043.8 2190.2 SS6-B20-2 181.1 0.0169 10876.3 2048.9 SC6-B25-2 165.6 0.0159 10562.6 2182.9 SS6-B25-2 165.6 0.0166 10067.1 1954.4 1000 SC6-B12-3 337.5 0.0244 7925.4 2120.2 1000 SS6-B12-3 325.9 0.0242 8199.2 2104.0 SC6-B15-3 322.3 0.0238 8400.3 2358.7 SS6-B15-3 315.6 0.0231 8408.9 2255.6 SC6-B16-3 316.9 0.0231 8451.4 2411.9 SS6-B16-3 309.1 0.0216 8321.9 2286.7 SC6-B20-3 293.3 0.0230 8556.2 2493.2 SS6-B20-3 286.1 0.0235 8430.5 2409.2 SC6-B25-3 275.7 0.0236 8889.2 2637.8 SS6-B25-3 272.2 0.0238 8921.7 2594.2 1500 SC6-B12-4 387.1 0.0273 6354.9 2381.1 1500 SS6-B12-4 387.3 0.0274 6364.7 2306.7 SC6-B15-4 381.0 0.0279 6852.0 2685.2 SS6-B15-4 373.3 0.0273 7042.8 2653.3 SC6-B16-4 375.8 0.0276 7042.7 2783.1 SS6-B16-4 367.4 0.0269 6962.9 2674.1 SC6-B20-4 362.7 0.0268 7669.2 3135.9 SS6-B20-4 359.6 0.0273 7824.8 3076.8 SC6-B25-4 353.8 0.0278 8144.8 3229.0 SS6-B25-4 351.8 0.0279 8049.4 3290.2 Table 7: Numerical results for various X-brace sections of the 6-story buildings. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 290 No. of Story X-brace position (Corner) X-brace position (Side) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Vmax (kN) Maximum Brace force (kN) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/ mm) Vmax (kN) Maximum Brace force (kN) 9 0 SC9-B12-1 415.4 0.0201 8761.0 1299.7 0 SS9-B12-1 409.2 0.0199 9430.7 1347.3 SC9-B15-1 402.4 0.0209 10288.4 1520.8 SS9-B15-1 393.3 0.0211 10501.4 1500.1 SC9-B16-1 397.5 0.0211 10805.8 1596.2 SS9-B16-1 391.0 0.0210 10705.3 1530.9 SC9-B20-1 382.1 0.0210 11813.2 1745.4 SS9-B20-1 396.2 0.0212 11468.4 1643.4 SC9-B25-1 382.3 0.0221 12598.2 1879.8 SS9-B25-1 398.8 0.0219 13110.6 1880.1 500 SC9-B12-2 417.1 0.0206 8042.1 1530.2 500 SS9-B12-2 414.4 0.0208 8628.8 1536.3 SC9-B15-2 410.5 0.0202 9105.2 1783.7 SS9-B15-2 404.3 0.0203 9577.5 1766.7 SC9-B16-2 406.3 0.0203 9601.1 1887.6 SS9-B16-2 401.6 0.0207 9799.0 1825.0 SC9-B20-2 397.9 0.0211 10100.0 2043.5 SS9-B20-2 394.7 0.0212 10110.2 1938.9 SC9-B25-2 388.3 0.0209 10535.0 2182.2 SS9-B25-2 394.7 0.0213 10457.4 2081.7 1000 SC9-B12-3 514.3 0.0236 6031.6 1813.0 1000 SS9-B12-3 513.2 0.0237 5877.1 1577.0 SC9-B15-3 493.3 0.0231 6781.9 2190.1 SS9-B15-3 499.3 0.0235 6664.6 1867.1 SC9-B16-3 482.1 0.0227 6910.3 2276.6 SS9-B16-3 491.6 0.0233 6738.1 1916.7 SC9-B20-3 456.3 0.0209 7004.6 2564.7 SS9-B20-3 471.5 0.0221 6784.6 2005.7 SC9-B25-3 426.3 0.0203 7035.8 2754.7 SS9-B25-3 442.8 0.0213 7022.7 2201.1 1500 SC9-B12-4 416.3 0.0239 4800.8 2157.7 1500 SS9-B12-4 420.9 0.0239 4822.3 1738.6 SC9-B15-4 427.4 0.0241 4723.4 2365.3 SS9-B15-4 429.7 0.0249 4665.2 1835.5 SC9-B16-4 432.9 0.0249 4751.2 2388.4 SS9-B16-4 435.4 0.0255 4832.8 1916.8 SC9-B20-4 461.5 0.0253 4966.0 2464.3 SS9-B20-4 458.0 0.0252 4917.1 2136.8 SC9-B25-4 485.1 0.0253 5696.5 2682.4 SS9-B25-4 474.9 0.0254 5848.2 2549.4 Table 8: Numerical results for various X-brace sections of the 9-story buildings. No. of Story X-brace position (Corner) X-brace position (Side) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Vmax (kN) Maximum Brace force (kN) Eccentricity (mm) Building ID Δu max (mm) Drift max (mm/mm) Vmax (kN) Maximum Brace force (kN) 12 0 SC12-B12-1 470.2 0.0206 7132.8 1339.7 0 SS12-B12-1 468.7 0.0200 7453.2 1160.9 SC12-B15-1 473.9 0.0201 7836.3 1467.7 SS12-B15-1 465.4 0.0194 7515.9 1098.4 SC12-B16-1 484.7 0.0201 7586.2 1467.4 SS12-B16-1 474.0 0.0197 7185.0 1052.8 SC12-B20-1 505.8 0.0209 7813.0 1517.7 SS12-B20-1 490.7 0.0206 8235.4 1205.1 SC12-B25-1 516.2 0.0209 8103.7 1694.1 SS12-B25-1 511.0 0.0204 8225.9 1208.2 500 SC12-B12-2 465.2 0.0203 6377.1 1624.3 500 SS12-B12-2 465.6 0.0197 5958.8 1340.2 SC12-B15-2 469.9 0.0206 7317.4 1730.9 SS12-B15-2 467.2 0.0199 7159.9 1450.7 SC12-B16-2 467.1 0.0204 7571.1 1828.7 SS12-B16-2 464.4 0.0196 7311.1 1460.8 SC12-B20-2 468.7 0.0201 7647.2 2039.1 SS12-B20-2 468.6 0.0194 7381.0 1446.5 SC12-B25-2 489.3 0.0204 7351.8 2147.5 SS12-B25-2 469.6 0.0198 6900.9 1391.7 1000 SC12-B12-3 403.3 0.0186 5228.3 1496.4 1000 SS12-B12-3 398.8 0.0185 5294.0 1411.7 SC12-B15-3 405.1 0.0188 5280.1 1620.0 SS12-B15-3 404.5 0.0187 5283.1 1567.7 SC12-B16-3 406.9 0.0188 5346.9 1731.3 SS12-B16-3 409.1 0.0187 5264.5 1642.3 SC12-B20-3 419.3 0.0186 5207.4 2106.2 SS12-B20-3 424.9 0.0185 5316.8 1882.1 SC12-B25-3 433.1 0.0180 5861.3 2519.6 SS12-B25-3 435.7 0.0179 5796.0 2020.0 1500 SC12-B12-4 388.6 0.0208 3290.2 1349.8 1500 SS12-B12-4 386.8 0.0206 3305.1 1342.8 SC12-B15-4 386.2 0.0207 3890.1 1638.2 SS12-B15-4 387.4 0.0205 4079.4 1645.8 SC12-B16-4 388.0 0.0206 4152.9 1736.4 SS12-B16-4 389.2 0.0203 4260.3 1716.3 SC12-B20-4 392.3 0.0198 4559.2 2046.9 SS12-B20-4 393.4 0.0195 4770.2 2017.8 SC12-B25-4 394.5 0.0192 4880.2 2316.6 SS12-B25-4 395.8 0.0193 5165.2 2234.8 Table 9: Numerical results for various X-brace sections of the 12-story buildings. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 291 Figure 22: The story-lateral drift at x-directions of the 6-story buildings with the various types of X-brace sections at the corner and side positions. Figure 23: The story-lateral drift at y-directions of the 9-story buildings with the various types of X-brace sections at the corner and side positions. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 292 Figure 24: The story-lateral drift at y-directions of the 12-story buildings with the various types of X-brace sections at the corner and side positions. When the eccentric X-brace is at a corner position, modifying its section is most successful in reducing the brace force for 6-story multi-story structures, as opposed to 9- and 12-story multi-story buildings. Large sections are required for eccentric X-braces to resist earthquake stresses, which drives up the cost of the materials used compared to bracing structures, reducing section size. The study results may show the X-bracing system's ability to strengthen the building's stiffness and minimize displacement. To compensate for eccentricity's effect on rigidity loss, expanding the X-braced member's cross- section may help. Moreover, the horizontal movement of eccentric X-braces is more significant. The ductility of the eccentric brace frame varies greatly depending on the X-brace section and eccentricity since an eccentric X-brace can absorb tremendous energy. Height, eccentricity, section size, and the position of the X-brace in steel all influence the frequency with which an architectural design arises in nature. Natural frequency and period of all buildings is shown in Tabs. 10 and 11. A structure's natural frequency is more significant at lower heights and decreases with increasing eccentricity and increases the section size. Because the side position is more flexible, the natural frequency of a structure with an X-brace in the side position is upper than that of a structure with 6-story with an X-brace in the corner and the natural frequency of a structure with an X-brace in the side position is lower than that of a structure with 9 and 12-story with an X-brace in the corner. Eccentricity (mm) Building ID Frequency cyc/sec Building ID Frequency cyc/sec Building ID Frequency cyc/sec Building ID Frequency cyc/sec Building ID Frequency cyc/sec Building ID Frequency cyc/sec 0 SC6-B12-1 0.821 SC9-B12-1 0.506 SC12-B12-1 0.349 SS6-B12-1 0.864 SS9-B12-1 0.500 SS12-B12-1 0.346 SC6-B15-1 0.862 SC9-B15-1 0.526 SC12-B15-1 0.359 SS6-B15-1 0.894 SS9-B15-1 0.516 SS12-B15-1 0.354 SC6-B16-1 0.873 SC9-B16-1 0.531 SC12-B16-1 0.362 SS6-B16-1 0.901 SS9-B16-1 0.521 SS12-B16-1 0.356 SC6-B20-1 0.903 SC9-B20-1 0.548 SC12-B20-1 0.371 SS6-B20-1 0.925 SS9-B20-1 0.534 SS12-B20-1 0.363 SC6-B25-1 0.931 SC9-B25-1 0.564 SC12-B25-1 0.379 SS6-B25-1 0.946 SS9-B25-1 0.546 SS12-B25-1 0.369 500 SC6-B12-2 0.789 SC9-B12-2 0.490 SC12-B12-2 0.340 SS6-B12-2 0.793 SS9-B12-2 0.484 SS12-B12-2 0.337 SC6-B15-2 0.820 SC9-B15-2 0.504 SC12-B15-2 0.348 SS6-B15-2 0.819 SS9-B15-2 0.496 SS12-B15-2 0.343 SC6-B16-2 0.829 SC9-B16-2 0.509 SC12-B16-2 0.350 SS6-B16-2 0.826 SS9-B16-2 0.500 SS12-B16-2 0.345 SC6-B20-2 0.857 SC9-B20-2 0.521 SC12-B20-2 0.357 SS6-B20-2 0.846 SS9-B20-2 0.509 SS12-B20-2 0.350 SC6-B25-2 0.884 SC9-B25-2 0.534 SC12-B25-2 0.363 SS6-B25-2 0.863 SS9-B25-2 0.518 SS12-B25-2 0.354 1000 SC6-B12-3 0.639 SC9-B12-3 0.409 SC12-B12-3 0.292 SS6-B12-3 0.648 SS9-B12-3 0.409 SS12-B12-3 0.292 SC6-B15-3 0.661 SC9-B15-3 0.421 SC12-B15-3 0.299 SS6-B15-3 0.669 SS9-B15-3 0.419 SS12-B15-3 0.298 SC6-B16-3 0.668 SC9-B16-3 0.424 SC12-B16-3 0.301 SS6-B16-3 0.676 SS9-B16-3 0.422 SS12-B16-3 0.300 SC6-B20-3 0.690 SC9-B20-3 0.435 SC12-B20-3 0.307 SS6-B20-3 0.694 SS9-B20-3 0.431 SS12-B20-3 0.305 SC6-B25-3 0.711 SC9-B25-3 0.446 SC12-B25-3 0.313 SS6-B25-3 0.711 SS9-B25-3 0.439 SS12-B25-3 0.309 1500 SC6-B12-4 0.518 SC9-B12-4 0.336 SC12-B12-4 0.244 SS6-B12-4 0.529 SS9-B12-4 0.338 SS12-B12-4 0.245 SC6-B15-4 0.536 SC9-B15-4 0.345 SC12-B15-4 0.250 SS6-B15-4 0.545 SS9-B15-4 0.346 SS12-B15-4 0.250 SC6-B16-4 0.542 SC9-B16-4 0.349 SC12-B16-4 0.252 SS6-B16-4 0.551 SS9-B16-4 0.349 SS12-B16-4 0.252 SC6-B20-4 0.571 SC9-B20-4 0.357 SC12-B20-4 0.257 SS6-B20-4 0.566 SS9-B20-4 0.357 SS12-B20-4 0.257 SC6-B25-4 0.576 SC9-B25-4 0.366 SC12-B25-4 0.262 SS6-B25-4 0.581 SS9-B25-4 0.364 SS12-B25-4 0.261 Table 10: Natural frequency of all buildings. A. J. Abdulridha, Frattura ed Integrità Strutturale, 66 (2023) 273-296; DOI: 10.3221/IGF-ESIS.66.17 293 Eccentricity (mm) Building ID Period sec Building ID Period sec Building ID Period sec Building ID Period sec Building ID Period sec Building ID Period sec 0 SC6-B12-1 1.218 SC9-B12-1 1.974 SC12-B12-1 2.863 SS6-B12-1 1.157 SS9-B12-1 1.997 SS12-B12-1 2.890 SC6-B15-1 1.160 SC9-B15-1 1.900 SC12-B15-1 2.780 SS6-B15-1 1.118 SS9-B15-1 1.935 SS12-B15-1 2.820 SC6-B16-1 1.145 SC9-B16-1 1.880 SC12-B16-1 2.758 SS6-B16-1 1.109 SS9-B16-1 1.918 SS12-B16-1 2.802 SC6-B20-1 1.107 SC9-B20-1 1.822 SC12-B20-1 2.694 SS6-B20-1 1.081 SS9-B20-1 1.871 SS12-B20-1 2.750 SC6-B25-1 1.073 SC9-B25-1 1.771 SC12-B25-1 2.637 SS6-B25-1 1.057 SS9-B25-1 1.831 SS12-B25-1 2.706 500 SC6-B12-2 1.266 SC9-B12-2 2.039 SC12-B12-2 2.935 SS6-B12-2 1.261 SS9-B12-2 2.062 SS12-B12-2 2.965 SC6-B15-2 1.219 SC9-B15-2 1.981 SC12-B15-2 2.869 SS6-B15-2 1.221 SS9-B15-2 2.014 SS12-B15-2 2.910 SC6-B16-2 1.205 SC9-B16-2 1.964 SC12-B16-2 2.850 SS6-B16-2 1.210 SS9-B16-2 2.000 SS12-B16-2 2.895 SC6-B20-2 1.166 SC9-B20-2 1.916 SC12-B20-2 2.797 SS6-B20-2 1.182 SS9-B20-2 1.963 SS12-B20-2 2.854 SC6-B25-2 1.131 SC9-B25-2 1.872 SC12-B25-2 2.748 SS6-B25-2 1.158 SS9-B25-2 1.930 SS12-B25-2 2.818 1000 SC6-B12-3 1.564 SC9-B12-3 2.443 SC12-B12-3 3.417 SS6-B12-3 1.541 SS9-B12-3 2.443 SS12-B12-3 3.421 SC6-B15-3 1.511 SC9-B15-3 2.375 SC12-B15-3 3.339 SS6-B15-3 1.494 SS9-B15-3 2.384 SS12-B15-3 3.353 SC6-B16-3 1.495 SC9-B16-3 2.354 SC12-B16-3 3.314 SS6-B16-3 1.479 SS9-B16-3 2.366 SS12-B16-3 3.332 SC6-B20-3 1.449 SC9-B20-3 2.296 SC12-B20-3 3.249 SS6-B20-3 1.440 SS9-B20-3 2.318 SS12-B20-3 3.277 SC6-B25-3 1.405 SC9-B25-3 2.242 SC12-B25-3 3.187 SS6-B25-3 1.405 SS9-B25-3 2.274 SS12-B25-3 3.228 1500 SC6-B12-4 1.927 SC9-B12-4 2.971 SC12-B12-4 4.090 SS6-B12-4 1.889 SS9-B12-4 2.955 SS12-B12-4 4.071 SC6-B15-4 1.864 SC9-B15-4 2.891 SC12-B15-4 3.997 SS6-B15-4 1.832 SS9-B15-4 2.882 SS12-B15-4 3.986 SC6-B16-4 1.844 SC9-B16-4 2.865 SC12-B16-4 3.966 SS6-B16-4 1.814 SS9-B16-4 2.859 SS12-B16-4 3.959 SC6-B20-4 1.749 SC9-B20-4 2.795 SC12-B20-4 3.886 SS6-B20-4 1.766 SS9-B20-4 2.797 SS12-B20-4 3.888 SC6-B25-4 1.735 SC9-B25-4 2.728 SC12-B25-4 3.808 SS6-B25-4 1.721 SS9-B25-4 2.740 SS12-B25-4 3.828 Table 11: Period of all buildings. Regarding structural performance, modifying the bracing section increases ultimate loads while slightly decreasing displacement. Changing the bracing section area in an eccentric frame influences the stresses at failure, the displacement at failure, and the ductility value. Greater bracing area results in higher ultimate pressures but lower ultimate displacement and less ductility. Almost all buildings need to be designed to disperse energy when earthquakes occur. They need to disperse the energy without compromising the structure's integrity so that the stresses from earthquakes and gravity may be transferred to the foundation. Modern performance-based seismic engineering in steel structures has several design goals. Eccentric X-braces are a beneficial structural component of an appropriate structural typology for accomplishing these goals. In order to resist severe earthquakes, buildings need a frame structure with high lateral strength and stiffness and good energy dissipation capabilities. Regarding strength and flexibility, eccentric X-braces are hard to beat. They feature the best of both moment-resisting and concentrically braced frames. The first computational studies of typical eccentrically braced structures subjected to lateral static stresses found that eccentric X-braces were better at handling earthquakes. CONCLUSIONS ur findings on how eccentricity and cross-section of X-braces influence the performance of steel frame multi- story structures were analyzed using the latest version of the ETABS program. Possible conclusion:  In multi-story buildings with six stories, the eccentric X-brace is more effective in preventing top-story displacement than in buildings with 9 or 12 stories.  The stability and ductility of the eccentrically braced frame were affected by the length of the horizontal links (eccentricity), which reflected the system's energy dissipation capability.  The efficiency of shear-yielding is influenced by the shear in the links, which is affected by the shear in the story. Shorter horizontal link lengths with small eccentricities are more effective in achieving shear-yielding efficiency. However, longer links with large eccentricities may experience bending.  The lateral rigidity of eccentric X-brace frames is lower than that of concentrically braced frames, particularly when diagonal bracing is used. However, the eccentricity-induced stiffness loss may be recovered by increasing the cross- section area of the X-braced component.  The ductility of an eccentric brace frame (EBF) changes noticeably as the X-brace section and eccentricity change because EBFs absorb more energy and move more horizontally.  The ultimate load, ultimate displacement, and ductility values of all eccentric frame types are sensitive to the bracing section's area. While increasing the ultimate loads, increasing the ultimate bracing section size reduces the ultimate displacement and ductility values. Under seismic stresses, most buildings should be built to disperse energy.  This investigation showed that the finite element model could provide reliable predictions of EBF behavior. ETABS analysis and experimental findings were in excellent accord. The ETABS model successfully captured all of the critical features of the chosen structures. O A. J. 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