Theoretical and Numerical Studies of Elastic Buckling and Load Resistance of a Shuttle-Shaped Double-Restrained Buckling-Restrained Brace
Abstract
:1. Introduction
2. Shuttle-Shaped Double-Restrained Buckling-Restrained Brace
3. Elastic Buckling Behavior of an SDR-BRB
3.1. Simplified Model and Equilibrium Equation
3.2. Theoretical Solution for Elastic Buckling Load
3.3. Establishment and Verification of the Finite Element Model
4. Numerical Analysis of the Load-Carrying Capacity of an SDR-BRB
4.1. Effect of the Restraining Ratio
4.2. Effect of the Initial Imperfection
4.3. Effect of the Gap of the Core and the External Restraining Member
4.4. Effect of the Core Diameter–Thickness Ratio
4.5. Determination of the Critical Restraining Ratio
5. Conclusions
- (1)
- Based on the equilibrium method, the formula for the elastic buckling load of the SDR-BRB is derived and verified by the eigenvalue buckling analysis method. The results show that the theoretical solution is in good agreement with the numerical solution, with discrepancies of less than 5%. As the geometric parameters of the external restraining member increase, the elastic buckling load of the SDR-BRB also increases, among which the tapering ratio γ has the greatest effect. To achieve the high load-carrying efficiency of the SDR-BRB in engineering applications, a larger tapering ratio γ should be preferred.
- (2)
- The restraining ratio is an important affecting factor on the overall stability and failure mode of the SDR-BRB. When the restraining ratio is relatively small and the external restraint stiffness is insufficient, the SDR-BRB suffers from a single-wave symmetrical failure mode of midspan buckling instability. When the restraining ratio is relatively large, the SDR-BRB can not only meet the full-section yield of the core, but also have a certain plastic deformation and strengthening ability, allowing it to be considered as a load-carrying type of the BRB that meets the ductility requirements.
- (3)
- Parametric analysis shows that the initial imperfection and gap have significant effects on the ultimate load-carrying capacity and stability of the SDR-BRB. The larger the initial imperfection and gap, the faster the ultimate load-carrying capacity of SDR-BRB decreases, and the earlier the overall instability failure occurs. In addition, the excessive diameter–thickness ratio is also not conducive to the stable behavior of the SDR-BRB. To ensure that the SDR-BRB has a stable load-carrying capacity, it is recommended that the core diameter–thickness ratio should not exceed 25.
- (4)
- The fitting formula for the critical restraining ratio of SDR-BRB considering the influences of initial imperfection and gap is proposed. Compared with the finite element results, the calculation errors are less than 10%, which shows that the formula has good reliability and high accuracy and can provide a design reference for the practical application of this new type of BRB.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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0 | 0.2 | 0.4 | 0.6 | 0.8 | 1.0 | ||
0.1 | 1.1544 | 5.01 | 6.32 | 7.84 | 9.14 | 9.77 | π2 |
0.2 | 0.7100 | 6.14 | 7.31 | 8.49 | 9.39 | 9.81 | π2 |
0.4 | 0.3572 | 7.52 | 8.38 | 9.12 | 9.62 | 9.84 | π2 |
0.6 | 0.1856 | 8.50 | 9.02 | 9.46 | 9.74 | 9.85 | π2 |
0.8 | 0.0772 | 9.23 | 9.50 | 9.69 | 9.81 | 9.86 | π2 |
1.0 | 0 | π2 | π2 | π2 | π2 | π2 | π2 |
No. | l | d1 × t1 | d2 × t2 | de1 | de2 | γ | l1 | λ | te | β |
---|---|---|---|---|---|---|---|---|---|---|
1-1 | 10,000 | 120 × 20 | 140 × 8 | 200 | 200~600 | 0~2 | 5000 | 0.5 | 12 | 0.06 |
1-2 | 10,000 | 120 × 20 | 140 × 8 | 200 | 400 | 1 | 0~10,000 | 0~1 | 12 | 0.06 |
1-3 | 10,000 | 120 × 20 | 140 × 8 | 200 | 400 | 1 | 5000 | 0.5 | 4~24 | 0.02~0.12 |
2-1 | 20,000 | 200 × 30 | 240 × 18 | 350 | 350~1050 | 0~2 | 10,000 | 0.5 | 21 | 0.06 |
2-2 | 20,000 | 200 × 30 | 240 × 18 | 350 | 700 | 1 | 0~20,000 | 0~1 | 21 | 0.06 |
2-3 | 20,000 | 200 × 30 | 240 × 18 | 350 | 700 | 1 | 10,000 | 0.5 | 7~42 | 0.02~0.12 |
3-1 | 30,000 | 300 × 40 | 350 × 23 | 500 | 500~1500 | 0~2 | 15,000 | 0.5 | 30 | 0.06 |
3-2 | 30,000 | 300 × 40 | 350 × 23 | 500 | 1000 | 1 | 0~30,000 | 0~1 | 30 | 0.06 |
3-3 | 30,000 | 300 × 40 | 350 × 23 | 500 | 1000 | 1 | 15,000 | 0.5 | 10~60 | 0.02~0.12 |
l | d1 × t1 | d2 × t2 | de1 | de2 | γ | l1 | λ | te | β | ζ |
---|---|---|---|---|---|---|---|---|---|---|
20,000 | 200 × 30 | 240 × 18 | 350 | 525~625 | 0.50~0.78 | 10,000 | 0.5 | 21 | 0.06 | 1.39~2.22 |
30,000 | 300 × 40 | 350 × 23 | 500 | 760~900 | 0.52~0.80 | 15,000 | 0.5 | 30 | 0.06 | 1.31~2.10 |
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Shi, J.; Jin, S.; Xu, L.; Liu, Y.; Zhang, R. Theoretical and Numerical Studies of Elastic Buckling and Load Resistance of a Shuttle-Shaped Double-Restrained Buckling-Restrained Brace. Buildings 2023, 13, 1967. https://doi.org/10.3390/buildings13081967
Shi J, Jin S, Xu L, Liu Y, Zhang R. Theoretical and Numerical Studies of Elastic Buckling and Load Resistance of a Shuttle-Shaped Double-Restrained Buckling-Restrained Brace. Buildings. 2023; 13(8):1967. https://doi.org/10.3390/buildings13081967
Chicago/Turabian StyleShi, Jun, Shuangshuang Jin, Lueqin Xu, Yangqing Liu, and Ruijie Zhang. 2023. "Theoretical and Numerical Studies of Elastic Buckling and Load Resistance of a Shuttle-Shaped Double-Restrained Buckling-Restrained Brace" Buildings 13, no. 8: 1967. https://doi.org/10.3390/buildings13081967