台灣位於環太平洋地震帶上，為了提升建築物的耐震能力，斜撐構架是一種常見的減震技術。而為了改善傳統斜撐在挫屈後之強度迅速下降且韌性不足的特性，近年來研究人員開發了一種名為抗彎消能斜撐（Naturally Buckling Brace, NBB）的新型鋼斜撐構件設計。於前期的單軸試驗和子構架試驗已經證實了抗彎消能斜撐具有提早降伏、提供能量消散的特點，且可延遲挫屈時機。此外，抗彎消能斜撐的強度和勁度可透過三線性迴歸公式模型計算，已經可以有效反應抗彎消能斜撐從降伏到挫屈後之強度發展，而抗彎消能斜撐於單軸試驗中發現，在細長比越大時，拉壓強度不對稱性會越大，因此必須避免使用細長比較大之抗彎消能斜撐，這較難配置在跨距較大之斜撐構架中。本研究以K字型的型式配置抗彎消能斜撐，發現可有效降低其拉壓強度不對稱的發生，並將此想法結合間柱應用於抗彎構架中，命名為K形斜撐耐震間柱（K-shape Braced Stud Columns, KBSC），以此方式也可以使用細長比較小之斜撐應用在跨距較長之抗彎構架中，並且也能充分發揮抗彎消能斜撐的性能。首先以此概念先進行KBSC力學行為的討論，包含NBB、斜撐柱和其交會區，透過有限元素分析證實其可有效改善拉壓強度之不對稱性，並藉由參數分析針對斜撐柱撓度提出一建議值供設計使用。本研究進而完整建立K形斜撐耐震間柱本身，以及含K形斜撐耐震間柱抗彎矩構架系統之設計方法與步驟流程。最後，將配置了KBSC之抗彎構架進行耐震性能之研究，先利用OpenSees分析軟體建立構架分析模型，並透過靜態側推分析評估其可有效提升構架強度和勁度，並藉由側推曲線評估各桿件塑鉸發生之時機，而非線性動態歷時分析量化之結果顯示，配置了KBSC後，構架的變形反應明顯下降，斜撐皆會提早降伏提供構架之消能行為，在易損曲線上也顯示在反應較大的地震下，建築物仍保有良好的耐震性能。

Taiwan is located in the seismic zone of the Circum-Pacific seismic belt. In order to enhance the seismic resilience of buildings, diagonal bracing is a common technique for seismic reduction. To address the rapid strength degradation and inadequate toughness of traditional diagonal bracing after buckling, researchers have developed a new type of steel bracing component known as Naturally Buckling Brace (NBB) in recent years. Preliminary uniaxial tests and substructure tests have confirmed that NBB exhibits early yielding, energy dissipation, and delayed buckling characteristics. Furthermore, the strength and stiffness of NBB can be calculated using a trilinear regression formula, effectively reflecting the strength development of NBB from yielding to buckling.
In addition, it has been observed in uniaxial tests that the greater the slenderness ratio, the larger the tensile-compressive strength asymmetry. Therefore, it is necessary to avoid using NBB with a larger slenderness ratio, as it is more challenging to incorporate into bracing structures with larger spans. This study employs a K-shaped configuration for NBB, which effectively reduces the occurrence of tensile-compressive strength asymmetry. This concept is further combined with an intermediate column for application in braced frames, named K-shape Braced Stud Columns (KBSC). This allows the use of NBB with a smaller slenderness ratio in braced frames with longer spans while fully utilizing the performance of NBB.
The study initiates a discussion on the mechanical behavior of KBSC, including NBB, bracing columns, and their intersection, confirming through finite element analysis that it effectively improves tensile-compressive strength asymmetry. Parameter analysis is conducted to propose a recommended value for the deflection of bracing columns in design. The research then establishes the design method and step-by-step process for the seismic braced Stud Column system with K-shaped bracing.
Finally, seismic performance studies are conducted on the braced frames configured with KBSC. Using OpenSees analysis software, a structural analysis model is established, and static pushover analysis is employed to evaluate the effective enhancement of structural strength and stiffness. Pushover curves are used to assess the timing of plastic hinge occurrences in members. Nonlinear dynamic time-history analysis quantifies the results, indicating that with the inclusion of KBSC, the deformation response of the structure significantly decreases. The bracing elements yield early, providing energy dissipation behavior, and vulnerability curves demonstrate that the building maintains good seismic performance even under larger seismic responses.

[1] Hsiao, P.C. et al. (2019). “Slenderness Effect in Naturally Buckling Braces Under Seismic Loads.” Journal of Structural Engineering, ASCE
https://ascelibrary.org/doi/10.1061/%28ASCE%29ST.1943-541X.0002612
[2] Hsiao, P.C. et al. (2020). “Effect of Far-Field and Near-Fault Cyclic Loadings on Seismic Performance of Naturally Buckling Braces in Pairs.”
https://www.sciencedirect.com/science/article/abs/pii/S0141029620303941?via%3Dihub
[3] 錢泊崧 (2022)." 改良式隅撐型抗彎消能斜撐參數分析與實尺寸構件試驗研究”，國立臺灣科技大學營建系研究所碩士論文
[4] Hsiao, P.C. et al. (2016). “Development and Testing of Naturally Buckling Steel Braces.” Journal of Structural Engineering, ASCE, 142(1).
[5] Hsiao, P. C., Lehman, D. E., and Roeder, C. W. (2013). “A model to simulate special concentrically braced frames beyond brace fracture.” Earthquake Eng. Struct. Dyn., 42(2), 183–200.
[6] Hsiao PC, Lehman DE, Roeder CW. “Evaluation of the Response Modification Coefficient and Collapse Potential of SCBFs.” Earthquake Eng. Struct. Dyn., 2013;42(10):1547-1564.
[7] Hsiao PC, Liao WC. Effects of Hysteretic Properties of Stud-type Dampers on Seismic Performance of Steel Moment Resisting Frame Buildings. J. of Structural Engineering, ASCE 2019;145(7).
[8] Watanabe, A., Hitomi, Y., Saeki, E., Wada, A., and Fujimoto, M. (1988). “Properties of brace encased in buckling-restraining concrete and steel tube.” Proc., 9th World Conf. on Earthquake Engineering, Japan As sociation for Earthquake Disaster Prevention, Tokyo, 719–724.
[9] Black, C., Makris, N., and Aiken, I. (2002). “Component testing, stability analysis and characterization of buckling-restrained unbonded braces (TM).” Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
[10] Tsai, K. C., et al. (2008). “Pseudo-dynamic tests of a full-scale CFT/BRBF frame. Part 1: Specimen design, experiment and analysis.” Earthquake Eng. Struct. Dyn., 37(7), 1081–1098.
[11] Christopoulos, C., and Montgomery, M. (2013). “Viscoelastic coupling dampers (VCDs) for enhanced wind and seismic performance of highrise buildings.” Earthquake Eng. Struct. Dyn., 42(15), 2217–2233.
[12] Lehman, D. E., and Roeder, C. W. (2008). “Improved seismic design of concentrically braced frames and gusset plate connections.” Proc., Structures Congress 2008, ASCE, Reston, VA, 1–10.
[13] 廖偉潔 (2018)." 複合式抗彎間柱於結構耐震性能提升之分析研究”，國立中興大學土木工程系研究所碩士論文
[14] 張友郕 (2021)." 含鋼耐震間柱抗彎構架系統耐震性能評估與核心剪力降伏型間柱構件之耐震行為研究”，國立臺灣科技大學營建系研究所碩士論文
[15] 李承益 (2021)." 抗彎消能斜撐構架耐震性能評估與隅撐型抗彎消能斜撐試
驗研究”，國立臺灣科技大學營建系研究所碩士論文
[16] FEMA P695 Quantification of building seismic performance factors FEMA P695 ATC-63 project report. Federal Emergency Management Agency, Washington, D.C., 2008.
[17] SEAOC blue book, (1999). “ Recommended Lateral Force Requirement and Commentary”, Structural Engineering Association of California (SEAOC), 7th Edition, Sacramento, CA.
[18] FEMA, Recommended seismic design criteria for new steel moment-frame buildings, Report No. FEMA-350, SAC Joint Venture, Federal Emergency Management Agency, Washington, DC, 2000.
[19] FEMA, Recommended seismic evaluaton and upgrade criteria for existing welded steel moment-frame buildings, Report No. FEMA-351, SAC Joint Venture, Federal Emergency Management Agency, Washington, DC, 2000.
[20] OpenSeesCommand_Manual
https://opensees.berkeley.edu/wiki/index.php/Command_Manual