13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- time span to which iRΔ takes the smallest values. By application of principle of least variance, identification of the most reliable time range to detect micro/macro- fatigue crack growth in the wires of cable has been made possible. The results coincided with the empirical practice in engineering. Over the past decades, the scale of range research interest has been extended to micro, nano and even pico effects. Scale interactive effects for the most part have not been made transparent until the space-time scale rages were extended to the extremes. These problems have been tentatively explored in the framework of principle of least variance. With the advent of defect-detecting techniques of 21st century, structural health monitoring system (SHMS) [14] is increasingly installed in the bridges that are newly put on. Collected data are astronomical and interpretation of the field data can be more challenging, since the modern sensors are so accurate that both micro- and macro-effects are often mingled. Theory of least variance together with dual scale modern provides a potential solution for defect detection in SHM. Further applications of theory of least variance to multiscale system and structures are expected. This will be left for future studies. Acknowledgements Project supported by SPSFC (the Shanghai Postdoctoral Sustentation Fund, China, Grant No. G200-2R-1238) is appreciated. The author is indebted to Professor George C. Sih for his guidance. References [1] P. C. Paris, The growth of cracks due to variations in load. Ph. D. Dissertation, Department of Mechanics, Lehigh University, 1962. [2] G. C. Sih, Simultaneous occurrence of double micro/macro stress singularities for multiscale crack model. J. Theoret. Appl. Fract. Mech. 46 (2006) 87-104. [3] G. C. Sih, X. S. Tang, Z. X. Li, A. Q. Li, K. K. Tang, Fatigue crack growth behavior of cables and steel wires for the cable-stayed portion of Runyang bridge: Disproportionate loosening and/or tightening of cables. J. Theoret. Appl. Fract. Mech. 49(1) (2008) 1-25. [4] G. C. Sih, Principle of least variance for dual scale reliability of structural systems. J. Theoret. Appl. Fract. Mech. 54 (2010) 137-140. [5] G. C. Sih, K. K. Tang, Assurance of reliable time limits in fatigue depending on choice of failure simulation: Energy density versus stress intensity. J. Theoret. Appl. Fract. Mech. 64(2) (2010) 117-126. [6] G. C. Sih, K. K. Tang, On-off switching of theta-delta brain waves related to falling asleep and awakening. J. Theoret. Appl. Fract. Mech. (2013) http://dx.doi.org/10.1016/j.tafmec.2013.03.001 [7] G. C. Sih, K. K. Tang, Sustainable time and stability of hippocampal and cortical EEG theta waves. J. Theoret. Appl. Fract. Mech. (2013), dx.doi.org/10.1016/j.tafmec.2013.01.001 [8] G. C. Sih, K. K. Tang, Sustainable reliability of brain rhythms modeled as sinusoidal waves with frequency-amplitude trade-off. J. Theoret. Appl. Fract. Mech. 61 (2012) 21-32. [9] Q. B. Ou, Construction of Runyang Bridge: Cable-stayed Portion. China Communications Press, Beijing, 2005. [10] S. Y. Wang, Z. J. Dang. Research on heavy-load high fatigue stress amplitude cable and anchorage of cable-stayed bridge. J. of Bridge Construction, 3(2002) 14-16.(in Chinese) [11] Editorial Board, Practical Handbook of Engineering Materials. Chinese Standard Press, Beijing, 2002. [12] G. C. Sih, Crack tip mechanics based on progressive damage of arrow: hierarchy of singularities and multiscale segments. J. Theoret. Appl. Fract. Mech. 51(1) (2009) 11-32. [13] G. C. Sih, Ideomechancis of transitory and dissipative systems associated with length, velocity, mass and energy. J. Theoret. Appl. Fract. Mech. 51(3) (2009) 149-160. [14] J. P. Ou, H, Li, Structural health monitoring in mainland China: review and future trends. Struct. Health Monit. 9(3)(2010) 219-231.
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