Effect of pre-tensioning force on behavior of Buckling Restrained Brace (BRB) supported by double pre-tensioning system

The study explores the feasibility of a new all-steel buckling restrained brace (BRB) with the double pre-tensioning system as an alternative to conventional concentrically braced frames by using finite element method (ABAQUS program), And to verify modeling, use U-V1 specimen results and compare them with test results. The restraining element in an all-steel BRB is built from a rectangular plate with a double cross arm and cables, making it easy to fabricate, inspect, and replace after a severe earthquake. Numerical analyses were conducted on four groups: first group of specimens using dynamic loading to achieve the minimum thickness for stable hysteretic behavior and high efficiency for BRB, and three groups of specimens using monotonic loading to achieve the best pre-tensioning forces value in steel 37, 44 and 52 for greater efficient use of all steel BRB. The results showed a 66% improvement in bearing capacity, with the external restraining case thickness reduced to 20 mm, making it lightweight, economical, and easy to maintain. The specimens with a pre-tensioning force of 70 kN, 50 kN and 40 kN providing a 31%, 51% and 73.2 % for steel 37, 44 and 52 respectively over than the design specimen without pre-tensioning system.


INTRODUCTION
oncentrically braced frames are commonly used as lateral resisting systems in steel structures.They provide high stiffness but have low ductility because of out-of-plane buckling [1,2].Energy-absorbing dampers can serve as effective damping systems [3][4][5][6].By forming plastic hinges, these dampers prevent structural members from entering the nonlinear phase and buckling bracing members at intermediate seismic levels.This reduces the dynamic response of the structure to seismic loading [7][8][9][10].

C
The Buckling Restrained Brace (BRB) is a structural system designed to overcome limitations in moment-resisting frames (MRFs) and concentrically braced frames (CBFs) by providing sufficient stiffness and ductility.It consists of a central steel core enclosed in a buckling-restraint mechanism, which generates and dissipates energy through stable tension-compression hysteretic cycles, preventing brace buckling [11][12][13].BRB development consists of three phases: The initial external restraining system comprises a concrete-infilled steel section combined with a steel core, which can take the form of a plate, I section, or other steel cross-section [14][15][16][17].The complexities of pouring and curing concrete pose challenges in achieving precise configuration of the steel core and the gap between the concrete and steel core.All-steel BRB offers advantages such as easy on-site assembly, reduced weight, convenient replacement of inner core members, and inspection and reuse of external restraining systems [18,19].Researchers have further advanced the concept in earthquake engineering, developing various BRBs to maximize their potential in the field [19,20].Studies are ongoing to investigate the behavioral characteristics of BRBs, and there are advancements in the development of new devices [21][22][23][24][25][26].In Japan, BRBs have been successfully tested for seismic protection of steel buildings, although their usage is currently limited.In this context, BRBs are considered as hysteretic dampers and are incorporated into momentresisting frame MRFs that possess high stiffness and strength.Additionally, a dual system can be achieved by utilizing concentrically braced frames CBF with BRBs placed parallel to the MRF [27][28][29].External restraining systems employ hollow cross-sections with either rectangular or circular shapes.To enhance the capacity of BRBs, it is necessary to increase the thickness of the element in relation to the inner core plate [30][31][32][33].External restraining systems enable the inner core members to yield completely, leading to enhanced lateral stiffness and stable dissipation of hysteretic energy [34].Buckling-restrained braces (BRBs) offer lateral stiffness and energy absorption during seismic events.They are commonly used in framed structures, long-span structures, and bridge structures to enhance the lateral resistance, energy dissipation capacity, and ductility [35,36].A new type of all-steel BRB, called pre-tensioned cable-stayed BRB (PCS-BRB), is proposed.This design adds a supplementary structural system of pre-tensioned cables and cross-arms on the exterior of a typical BRB.The external restraining system comprises of cable-stayed and outer restraining tubes, which enhance its external flexural stiffness.This design is suited for stadiums, high building, and other buildings where PCS-BRBs are exposed to high loads Guo et al [32,37,38].Externally, pre-tensioned cable systems have been found to effectively increase the load-carrying capacity of slender compression members.This can be achieved by incorporating lateral cross-arms into the external casing discovered that a pre-tensioned system with a single cross-arm significantly enhances the member's overall capacity and improves the hysteretic response of BRB members.This method has demonstrated an improvement in the overall performance of BRBs [38].This research aims to enhance rectangular BRBs with pre-tensioning systems.Finite Element Analysis (FEA) was used to investigate the impact of different configurations and initial pre-tensioning force values on traditional all-steel BRB members, in this study was performed through the following steps: -Verification study on rectangular BRB using 3D finite Element Analysis.
-Using double pre-tensioning system on rectangular BRB to minimize thickness of external case.
-Parametric study on different parameters (pre-tensioning force value -steel grade).

NUMERICAL SIMULATION AND VERIFICATION
he main components of the studied BRB specimen are core plate, which represents the main item of the specimen, external case laterally supported by pre-tensioning steel cables to prevent the out-of-plane buckling.Two cross arms perpendicular to the external case were provided to connect the cables to the case.The steel core plate consists of a yielding segment, steel core projections, and transition segments.The axial friction between the core and the external case was avoided through a 2.5 mm gap between them.The FEA commercial code Abaqus 2020 [39] was used to simulate the behavior of the BRB.The eight-node solid element with linear reduced integration (C3D8R) was used to simulate the 3D model elements, including core, external case, and pre-tensioning cables, as shown in Fig. 1.The core plate lateral deformations put the core plate into contact with the external case, the surface-to-surface contact was utilized to simulate that contact.The contact properties used in normal and tangential directions were hard contact property and Coulomb-Mohr friction, respectively.The friction coefficient was 0.1.The Abaqus/Explicit analysis tool offers two approaches to constraint enforcement: "Hard" Contact, which uses the Lagrange multiplier technique, and "Penalty contact enforcement," T which prevents surface separation after contact.A coupling constraint was used to prevent axial slipping of the external case.The specimens were fixed from one end, allowing free axial movement at the other end at which the load was applied.The boundary conditions were applied to both ends through two reference points.The load was applied through two steps; the first steps included the application of the pre-tensioning force in cables, while a cyclic loading was utilized in the second step.A verification study on previous research was performed followed by a parametric study.A 50 mm mesh size was considered in the current study.The steel core plate and other model components were simulated using a bi-linear elasticplastic stress-strain relationship, considering strain hardening effects as per AISC 358-16.

Verification
In this step, the model was verified against the experimental results of a BRB specimen tested by Wang et al [40].where the tested specimen dimension (U-V1) is 1650 mm in total length, with a core plate yielding segment length (Ly) of 900 mm and width (w) of 10 mm as shown in Fig. 2 Figure 2: U-V1 specimen dimension.
The specimen underwent a cyclic load protocol.The initial axial stiffness in the elastic stage was measured using a strain amplitude of 0.75 y  .for the first four cycles.The subsequent loading phases consisted of variable strain amplitude (VSA) loading with increasing amplitudes, followed by constant strain amplitude (CSA) loading with a 2.0% amplitude.The

PARAMETRIC STUDY
his section inspected a five-story RC building with 6 m column spacing in both directions, X and Y, as shown in Fig. 5.The analysis and design were performed using the CSI ETABS program[41], according to ASCE [42] and ACI-318.The control BRB specimen was designed as a traditional all-steel member.A double-pre-tensioning system was provided to the external case, as shown in Fig. 1, in order to reduce the out-of-plane instability.The external case, provided with the pre-tensioning system, was redesigned to maintain the same load capacity, with a minimized thickness (Tc).The studied specimen's dimensions are presented in Fig. 6.
The study investigated the effect of different parameters on the behavior of 42 all-steel BRB models.The studied models were divided into four groups, as shown in Tab. 1.The initial pre-tensioning force was 40 kN, and different thicknesses were studied to achieve the same response as the traditional BRB control specimen in group G1. was applied to the double T pre-tensioning system.Groups G2, G3, and G4 were designed to study the effect of different material properties and a wide range of pre-tensioning forces (T0), as shown in Tab. 2.

Numerical simulation and loading
To consider the core plate imperfection and manufacturing defects, the first buckling mode was obtained through a nonlinear analysis.The specimens were subjected to cyclic loading with an incremental axial displacement at five levels.The applied displacements were ±5.70 mm (∆by) for the first two cycles, ±14.25 (0.5 ∆bm) mm for the second two cycles, ±28.50 (1.0 ∆bm) mm for the third two cycles, ±42.75 mm (1.5 ∆bm) for the fourth two cycles, and ±57.00 mm (2.0 ∆bm) for the fifth two cycles as shown in Fig. 7 [43].Where ∆by and ∆bm represent the core plate yield displacement and brace axial deformation corresponding to the design story drift, respectively.

The minimum thickness for the double pre-tensioning system
A parametric study was conducted to find the minimum thickness for the external case of the double pre-tensioning stem.
T study compared the compression stage of the backbone curve, as shown in Fig. 8, the deformed shape along the core plate length, and overall hysteretic load-displacement curves.The results showed that providing the double pre-tensioning system to specimens of P40-T50-St37 mm and P40-T40-St37 mm thickness achieved higher capacities and balanced hysteretic behavior.However, decreasing the external case thickness from P40-T30-St37 mm to P40-T15-St37 mm led to degradation in axial stiffness and a deformed core plate shape, as shown in Fig. 9.The P40-T20-St37 mm thickness was considered as the minimum thickness for the external case of the double-pre tensioned model, saving about 66% of the outer case thickness compared to the control BRB.

EFFECT OF INITIAL PRE-TENSIONING FORCE
his section studied the effect of the initial pre-tensioning force value, where the pre-tensioning force is first applied uniformly to all cables using stress es.ABAQUS then iteratively adjusts the stress difference among the cables until the desired pre-tensioning force is attained.A wide range from 10 to 120 kN was assigned to the initial pre-tensioning force.The BRBs capacity (P) were obtained and compared to that of the control BRB (P0).Fig. 10 shows that increasing the initial pre-tensioning force increased the member load capacity with an ascending rate up to 70 kN, 50 kN, and 40 kN for steel St37, St44, and St52, respectively.As shown in Fig. 10

EFFECT OF STEEL TYPE
n this section, the impact of steel type on the performance of all steel BRB with a double pre-tensioning system is examined.The variation in pre-tensioning force (∆T) concerning the axial deformation of the core is illustrated in Figs.11 to 13, considering different initial pre-tensioning forces.The variation in pre-tensioning force was determined as the difference between the actual pre-tensioning force value (T) and the initial pre-tensioning force value (T0) where the pre-tensioning force value (T) was extracted from the middle point of the cable.

Steel 37
In Range I (from 10 kN to 30 kN), insignificant additional pre-tensioning forces appeared in cables for 20 kN and 30 kN.T I On the other hand, after reaching a displacement of 90 mm, an additional pre-tensioning force was registered except for the case of 10 kN, as illustrated in Figs.11(a).Moreover, increasing the initial pre-tensioning force had no effect on the overall behavior of the BRB specimen as a result of necking phenomena that was noticed in the inner core accompanied with local buckling at low loading range.

Steel 44
For steel 44, an additional pre-tensioning force occurred in case of both range I and II.The force started to appear when the core axial deformation reached 50-60 mm and 75-85 mm for range I and II, respectively as shown in Fig. 12 (a) and (b).
For both ranges III and IV, no additional pre-tensioning force was observed in cables up to failure.Moreover, the necking phenomena occurred at loading range higher than that of steel 37.

Steel 52
Using steel 52 enhanced the contribution of the pre-tensioning cables as an additional pre-tensioning force appeared in the first three ranges (I, II, and III) as shown in Fig. 13

CONCLUSIONS
his paper presented a study of the effect of the pre-tensioning forces system on the behavior of an all-steel buckling restrained brace (BRB) using a numerical analysis program (ABAQUS).This study aimed to investigate the effectiveness of adding a double pre-tensioning system to traditional BRB members to reduce thickness.The main parameters studied were the initial pre-tensioning force value in the cables and its impact on member capacity, as well as the effect of steel used, where used three types of steel with different grades as the strength of the element increases as the steel grade.During this study, these outcomes were achieved.
• The axial compressive load-carrying capacity of traditional buckling restrained brace can be effectively enhanced by applying the proposed pre-tensioning system.
• The specimens with additional double pre-tensioning system with force in cable 70 kN, 50 kN, and 40 kN provided the capacity of BRB member by 31%, 51%, and 73.2 % for steel 37, 44, and 52, respectively, over than the capacity of design specimen without a pre-tensioning system.
• With the addition of the double pre-tensioning system on BRB member, it reduces the thickness of the external member by 66% (from 60 mm to 20 mm).
• The application of the pre-tensioning system increased the axial capacity of all studied BRB specimens.
• Increasing the pre-tensioning force value increased the BRB capacity up to 10 kN, 60 kN, and 80 kN for steel 37, 44, and 52, respectively.

Figure 10 :
Figure 10: Effect of initial pre-tensioning force range.

Figure 11 :Figure 12 :
Figure 11: Difference in cable pretension force for all ranges for steel 37.

Figure 13 :
Figure 13: Difference in cable pretension force for all ranges for steel 52.