本研究旨在探討不同外邊長之鍍鋅鋼方形管，在承受不同控制曲率之循環彎曲負載下，其外邊長變化量隨循環圈數之演變行為，並建立描述其臨界變化特性的力學行為模型。研究方法以外邊長分別為 20、30、40 與 50 mm 之鍍鋅鋼方形管為研究對象，施加控制曲率為 ±0.5、±0.6、±0.7 與 ±0.8 m⁻¹ 的循環彎曲負載，並量測其外邊長變化量。
實驗結果顯示，外邊長變化量與循環圈數之關係呈現明顯的棘齒狀累積成長行為，並可區分為初始階段、穩定成長階段與破壞前階段三個階段。研究發現，外邊長與控制曲率皆對循環圈數具有顯著影響。隨著外邊長增加，方形管抵抗挫曲之能力降低，變形累積的速度加快，導致循環圈數明顯減少，且此現象在外邊長大於 30 mm 時尤為顯著。此外，隨控制曲率增加，變形累積趨於顯著，循環圈數亦隨之縮短。
最後，本研究依據實驗結果建立外邊長變化量與循環圈數關係之理論公式，理論預測結果與實驗數據可達合理吻合；同時亦提出可描述臨界外邊長變化量與控制曲率關係之經驗公式。

This study aims to investigate the evolution of outer side length variations in galvanized steel square tubes with different side lengths subjected to cyclic bending loads under various controlled curvatures. Furthermore, it seeks to establish a mechanical model describing their critical variation characteristics. In this study, galvanized steel square tubes with outer side lengths of 20, 30, 40, and 50 mm were subjected to cyclic bending loads at controlled curvatures of ±0.5, ±0.6, ±0.7, and ±0.8 m⁻¹, and the variations in their outer side lengths were measured. Experimental results indicate that the relationship between the variation in outer side length and the number of cycles exhibits distinct ratcheting accumulation behavior, which can be categorized into three stages: the initial stage, the stable growth stage, and the pre-failure stage. The study found that both the outer side length and the controlled curvature significantly influence the number of cycles. As the outer side length increases, the tube's buckling resistance decreases and the rate of deformation accumulation accelerates, leading to a significant reduction in the number of cycles. This phenomenon is particularly pronounced when the outer side length exceeds 30 mm. Additionally, as the controlled curvature increases, deformation accumulation becomes more significant, and the number of cycles shortens accordingly. Finally, based on the experimental results, a theoretical formula relating the variation in outer side length to the number of cycles was established. The theoretical predictions show reasonable agreement with the experimental data. An empirical formula describing the relationship between the critical variation of the outer side length and the controlled curvature is also proposed.

1. Kyriakides S. and Shaw P. K., “Response and Stability of Elastoplastic Circular Pipes Under Combined Bending and External Pressure”, International Journal of Solids and Structures, Vol. 18, pp. 957-973 (1982).
2. P. K. Shaw and S. Kyriakides, “Inelastic analysis of thin-walled tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 21, No. 11, pp. 1073-1100 (1985).
3. S. Kyriakides and P. K. Shaw, “Inelastic buckling of tubes under cyclic loads”, Journal of Pressure Vessel Technology, Vol. 109, No. 2, pp. 169-178 (1987).
4. E. Corona and S. Kyriakides, “On the collapse of inelastic tubes under combined bending and pressure”, International Journal of Solids and Structures, Vol. 24, No. 5, pp. 505-535 (1988).
5. E. Corona and S. Kyriakides, “An experimental investigation of the degradation and buckling of circular tubes under cyclic bending and external pressure”, Thin-Walled Structures, Vol. 12, No. 3, pp. 229-263 (1991).
6. E. Corona and S. Vaze, “Buckling of elastic-plastic square tubes under bending”, International Journal of Mechanical Science, Vol. 38, No. 7, pp. 753-775 (1996).
7. W. F. Pan, T. R. Wang and C. M. Hsu, “A curvature-ovalization measurement apparatus for circular tubes under cyclic bending”, Experimental Mechanics, Vol. 38, No. 2, pp. 99-102 (1998).
8. W. F. Pan and Y. S. Her, “Viscoplastic collapse of thin-walled tubes under cyclic bending”, ASME Journal of Engineering Materials and Technology, Vol. 120, No. 4, pp. 287-290 (1998).
9. K. L. Lee, W. F. Pan and J. N. Kuo, “The influence of the diameter-to-thickness ratio on the stability of circular tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 38, No. 14, pp. 2401-2413 (2001).
10. K. H. Chang, W. F. Pan and K. L. Lee, “Mean moment effect on circular thin-walled tubes under cyclic bending”, Structural Engineering and Mechanics, Vol. 28, No. 5, pp. 495-514 (2008).
11. K. H. Chang and W. F. Pan, “Buckling life estimation of circular tubes under cyclic bending”, International Journal of Solids and Structures, Vol. 46, No. 2, pp. 254-270 (2009).
12. K. L. Lee, C. Y. Hung and W. F. Pan, Variation of ovalization for sharp-notched circular tubes under cyclic bending, Journal of Mechanics, Vol. 26, No. 3, pp. 403- 411 (2010).
13. K. L. Lee, C. Y. Hung and W. F. Pan, Variation of ovalization for sharp-notched circular tubes under cyclic bending, Journal of Mechanics, Vol. 26, No. 3, pp. 403- 411 (2010).
14. K. L. Lee, C. M. Hsu and W. F. Pan, The influence of mean curvatures on the collapse of sharp-notched circular tubes under cyclic bending, Journal of Chinese Society of Mechanical Engineering, Vol. 34, NO. 5, pp. 461-468 (2013).
15. K. L. Lee, C. C. Chung and W. F. Pan, “Growing and critical ovalization for sharp-notched 6061-T6 aluminum alloy tubes under cyclic bending”, Journal of Chinese Institute of Engineers, Vol. 39, No. 8, pp. 926-935 (2016).
16. K. L. Lee, K. H. Chang and W. F. Pan, “Effect of notch depth and direction on stability of local sharp-notched circular tubes subjected to cyclic bending”, International Journal of Structural Stability and Dynamics, Vol. 18, No. 7, 1850090 [23 pages] (2018).
17. K. L. Lee, M. L. Weng and W. F. Pan, “On the failure of round-hole tubes under cyclic bending”, Journal of Chinese Society of Mechanical Engineering, Vol. 40, No. 6, pp. 663-673 (2019).
18. K. L. Lee, Q. Y. Wen and W. F. Pan, “Response of round-hole tubes with different hole sizes and positions under pure bending relaxation”, Informatica Journal, Vol. 32, No. 8, pp. 48-65 (2021).
19. K. L. Lee, Y. C. Tsai and W. F. Pan, “Mean curvature effect on the response and failure of round-hole tubes submitted to cyclic bending”, Advances in Mechanical Engineering, Vol. 13, No. 11, pp. 1-14 (2021).
20. 溫慶源, “不同外徑/壁厚比與不同圓孔直徑圓孔管在循環彎曲負載下橢圓化成長與臨界橢圓化之研究”,國立成功大學工程科學研究所碩士論文(2022).
21. M. C. Yu and W. F. Pan, “Failure of elliptical tubes with different long-short axis ratios under cyclic bending in different directions”, Metals, Vol. 13, No. 11, 1891(2023).
22. W. F. Pan and Y. A. Chen, “Response and fracture of EMT carbon steel round-hole tubes with different hole orientations and different hole diameters under cyclic bending”, Applied Sciences, Vol. 14, No. 13, 5475. (2024).
23. C. J. Su and W. F. Pan, “Minor axis variation and critical minor axis variation of elliptical tubes under cyclic bending”, Informatica Journal, Vol. 36, No. 2, pp. 1-20 (2025).