Numerical modelling and analysis of buckling-restraint braces in frame buildings due to seismic loads

Buckling-Restraint Braces (BRB) is a new type of bracing system with energy dissipation mechanisms developed to improve the behaviour of conventional braces. In this system, the bracing member is placed in a metal or concrete casting that prevents this member from experiencing failure due to the lateral buckling. By implementing these changes, the brace's behaviour in compression is identical to its behaviour in tension, which is accompanied by yielding of material and therefore buckling does not occur. In this paper, the effect of the BRB system on the seismic performance of a typical frame is evaluated using the finite element method. Numerical studies using ABAQUS software are conducted to develop a 3D model of a BRB system, considering the nonlinearity effects of material and geometrical deformation. The BRB component is analysed under the cyclic loading protocol recommended by FEMA 450 and the resultant hysteretic behaviour of BRB is compared with the experimental work. The results show that the application of this system in structures may improve the stability of the structural system and enhance the energy dissipation mechanisms in the buildings. As a result, the structural design will be safer and more economical.


Introduction
Buckling-Restrained Braces (BRB) has been introduced to overcome the strength degradation of standard braces in steel structures. BRB systems are a new type of bracing system with energy dissipation mechanisms developed to improve the behaviour of ordinary braces. The system was invented in Japan in the early 80s and was tested in the middle of the 80s. The implementation of the BRB system started in Japan during the 90s, and its response towards various earthquake events made United States transfer this technology in 1998 and followed by its testing and simulation on the BRB model took place in 1999. Further, it was implemented successfully on various US projects [1]. BRB systems usually comprise a thin plate, a steel box which is filled with concrete material. In this system, the bracing member is placed in a metal or concrete casting that prevents this member to experience lateral bucking. By implantation of these changes, the behaviour of brace in compression is identical to its behaviour in tension which accompanied by yielding of material and therefore bucking does not occur. As a result, it shows better ductility and energy dissipation mechanism than the conventional braces. The application of this system in frame structures may not only improve the safety of the structural systems, but it may also reduce the size of the other components and sections. As a result, the structural design will be more economical. Fig. 1 shows a steel frame that is braced using Chevron BRB systems. These bracing systems can resist the lateral loads incorporating the identical behaviour in both tension and compression by providing enough stiffness and strength [2]. The conventional bracing systems have the inherent problem of behavioural differences in tension and compression. In these bracing systems, the load-bearing capacity mechanism under the strong earthquake motions is mainly provided by reciprocating axial tension loads and withstand compression loads in the post buckling regime. The buckling of the braces leads to a profound reduction in compression resistance, stiffness and dissipation energy mechanisms. Experimental research on special concentrically bracing frames (SCBF) carried out by Uriz et al. [3] at Berkeley University demonstrated the poor seismic ductility and weak nonlinear seismic performance in compression due to the characteristic buckling behaviour of the braces under seismic loads. Fig. 2 shows the components and behaviour of a type of unbonded BRB system in one cyclic loading regime in comparison to a conventional bracing system [4,5].

Fig. 2.
Components of a type of unbonded BRB system and sustained cyclic behaviour of the BRB (solid line) vs conventional braced system with buckling mode (dashed line) [5]. In the previous research, simple modelling techniques have been used without considering the effects of nonlinearity of steel and concrete material and geometry. In addition, the contact between different parts of the BRB system specially the contact between the main steel core and concrete in the simulation has not been properly addressed. The concrete is a brittle material and cracking will occur when principal tensile stress exceeds the tensile strength of concrete. In the previous research, this mechanism of concrete cracking due to tensile loading and its effects on the BRB hysteretic behaviour has not been addressed.
In this research, the effect of the BRB system on seismic performance of a frame building is evaluated using Finite Element Method FEM. Numerical studies using ABAQUS 3D Finite Element software [6] is conducted to develop a model for this type of bracing system considering the effects of nonlinearity of material and geometry and contact between steel and concrete material. The results of the numerical studies are further verified using the available experimental tests that have been conducted on a typical frame structure by other researchers.

Finite element modelling of BRB
To verify the FEM model developed in the current research, the experimental study carried out by Mirtaheri et. al [7] is selected. In this experiment, four different sizes of the BRB system were tested, and the results were compared with the OPENSEES numerical model. In this research, Abaqus software is used to model the 3D behaviour of 1 m sample as shown in Fig. 3. The material properties and the loading protocol based on the FEMA 450 [8] are shown in Table 1 and Fig. 4. This load protocol is used to apply the hysteretic loading on the BRB systems and is identical to the loading protocol that was used in the experiment done by Mirtaheri et al [7].    5 shows the finite element model and mesh size of the different components of the BRB model. In this research to simulate the BRB component accurately 3D solid element with 8-node linear brick, reduced integration C3D8R are used. Interaction between the outer steel box and the concrete are defined using the surface to surface interaction considering the 0.5 friction coefficient between steel and concrete. Since a rubber material is used to fill the gap between the concrete and the core plate no friction is assumed between the core plate and the concrete and therefore friction coefficient ignored. In this case only normal contact is defined to model the lateral constraint applied by the concrete to the core plate when loading returns to the compression mode.   6 illustrates the pinned boundary condition that is applied at the left end of the BRB system. The displacement loading protocol shown in Fig. 4 is applied at the right end of the core surface to analyse the system due to hysteretic loading. The local coordinate system is located at the left end of the BRB system.

Results and discussion
This section presents the results of the FEM modelling of the BRB system. The von Mises criterion for the yielding of material is selected for this purpose. The load-displacement of the BRB system predicted in this study is illustrated in Fig. 7 (a) and compared with the measured curve by Mirtaheri et al. [7] as shown in Fig. 7 (b). The results show a good agreement between numerical modelling and experimental investigations and the difference is less than 5 %. Figures 8 show the von Mises contour plot at different cycles of loading. The time in this analysis is not the physical time, but it represents the number of cycles of the loading. To get more insights about the behaviour of the BRB system, one should see the displacement of the loading protocol at the critical cycles as shown in Fig 4. At each cycles the BRB either takes the tension or compression loading. It can be observed that, the BRB core exhibits large plastic strain without any failure due to buckling while the loading cycle returns to the compression mode. This behaviour approves the efficiency of the current design and modelling.

Conclusion
The BRB systems are novel energy dissipations components used in building design to resist seismic loads. The FEM model developed in this study is verified by comparing the 3D model constructed using full nonlinear behaviour in material and geometry with the experimental work done by Mirtaheri et. al [7]. The results indicate a good agreement between the FEM model developed in this research and the load-displacement curve was measured by the experiment. Further, the application of this system in frame structures may improve the stability of the structural system, enhance the dissipation mechanisms of the bracing and reduce the size of the other components and sections. Therefore, the structural design will be safer and more economical. In this study a single BRB component is assessed due to hysteretic loading considering the 3D finite element modelling. It is suggested that in the future works, the effects of this bracing system in enhancing the load bearing capacity of the multistorey buildings can be studied considering the actual seismic forces using nonlinear dynamic analysis.
We acknowledge the fund provided for this research from Cape Peninsula University of Technology.