Suspension Link

 Suspension Bridge Essay

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Dirt Dynamics and Earthquake Executive 30 (2010) 769–781

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Soil Dynamics and Earthquake Architectural

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Geradlinig vertical vibration of suspension bridges: An assessment continuum models and some new results Вґ J. Enrique Luco a, Jose Turmo b, n

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Department of Structural Architectural, University of California, Hillcrest, La Jolla, California, UNITED STATES Civil Architectural Department, School of Castilla-La Mancha, Villa Real, Italy

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Content history: Received 10 July 2009 Approved 30 March 2009 Keywords: Suspension link Suspension cable Vibrations Entier model Thready response

summary

The classical continuum version for the linear up and down vibrations of any suspension connection (Bleich ou al., 1950 [1]) is definitely re-examined. The principal objective with the study should be to extend the definitive deductive and numerical results of Irvine and Caughey (1974) [2], Irvine and Griffin (1976) [3] and Irvine (1980, 1981) [4, 5] for the normal frequencies, setting shapes, and modal contribution factors intended for an extensible suspension cable connection, which be based upon one dimensionless parameter associated with the suppleness of the cable connection, to the circumstance of a stiffened suspension connect in which the response depends as well on a second dimensionless parameter related to the stiffness in the girder. The continuum suspension bridge unit is also used to understand the pattern of variant of mode designs as a function of wire elasticity and girder stiffness, which has been proven by West et al. (1984) [6] to be considerably more complex than that to get a suspension cable. Finally, the threshold disposee of free vibrations that would make incipient slackening of the hangers are identified. & 2009 Elsevier Limited. All privileges reserved.

1 ) Introduction With all the advent of effective computational ways to analyze the dynamic response of postponement, interruption bridges (e. g. [7–12]), the emphasis has changed via simple continuum models that could be used to analyze a class of bridges to extremely detailed discretized models used to analyze particular links. The objective of this paper is usually to return to some of the earlier entier models [1] that have not been totally analyzed. Although not as general, the less difficult continuum versions are useful to distinguish the key dimensionless parameters that control the dynamic response of the connection and to conduct extensive parametric analyses. These kinds of models likewise lead to estimated formulae suitable for preliminary models, and to standard results which you can use to test the accuracy of numerical versions. The study of the dynamics of suspended cabling, pertinent to suspension connections but with no inclusion with the stiffening girder, was initiated by Poisson in 1820 with his equations of motion for a cable connection element put through general pushes. Solutions for the totally free vertical heurt of inextensible cables had been presented by Rohrs [13], Routh [14], Rannie and von Karman [15], Pugsley [16], Saxon and Cahn [17] and Goodey [18]. The consequence of the elasticity of the cable television were released in 1945 by Vincent [19], and later by Bleich et al. [1]. The definitive analytical focus on the geradlinig theory of a suspended flexible cable, including an explanation pertaining to the

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Corresponding author. E-mail addresses: jose. [email protected] es (J. Turmo).

change from a taut thread to an inextensible suspended wire of little sag, was presented by simply Irvine and Caughey [2] and Irvine [5]. These writers introduced a dimensionless unbekannte that reflects the effect of the elasticity from the cable around the natural eq of sto?. This variable also affects the method shapes, and, in particular, the amount of internal nodes in a provided mode. Western et ing. [20] analyzed the free of charge vertical heurt of a revoked cable by simply representing the cable like a discrete set of axially deformable linkages and confirmed the mode form transitions described by...

Recommendations: [1] Bleich F, McCullough CB, Rosecrans R, Vincent GS. The mathematical theory of oscillation in suspension bridges. 1950. Washington: US Government Printing Office; 1950. [2] Irvine HM, Caughey TK. The linear theory of free heurt of a revoked cable. Process of the Royal Society of London, Series A 1974; 341(1626): 299–315.

[3] Irvine HM, Griffin JH. On the dynamic response of a revoked cable. Foreign Journal of Earthquake Engineering and Strength Dynamics 1976; 4: 389–402. [4] Irvine HM. The estimation of earthquake-generated extra tension in a suspension connect cable. Foreign Journal of Earthquake Engineering and Strength Dynamics 80; 8: 267–73. [5] Irvine HM. Cable structures. Cambridge, Mass: UBER Press; 1981. [6] West HH, Suhoski JE, Geschwindner LF. Normal frequencies and modes of suspension connections. Journal of Structural Engineering, ASCE 1984; 110(10): 2471–86. [7] Abdel-Ghaffar AM. Cost-free lateral heurt of postponement, interruption bridges. Journal of the Structural Division—ASCE 78; 104(3): 503–25. [8] Abdel-Ghaffar AM. Free of charge torsional vibrations of suspension bridges. Record of the Structural Division—ASCE 1979; 105(4): 767–88. [9] Abdel-Ghaffar AM. Vertical vibration analysis of suspension system bridges. Diary of the Strength Division—ASCE 80; 106(10): 2053–75. [10] Ganev T, Yamazaki F, Ishizaki H, Kitazawa M. Response analysis of the Higashi-Kobe Connection and adjacent soil in the 1995 Hyogoken-Nanbu earthquake. Earthquake Engineering and Structural Characteristics 1998; 27(6): 557–76. [11] Hua XG, Chen ZQ, Ni YQ, Ko JM. Flutter evaluation of long- span connections using ANSYS. Wind and Structures 3 years ago; 10(1): 61–82. [12] Li ZX, Zhou TQ, Chan THT, Yu Y. Multi-scale numerical examination on active response and damage in long-span connections. Engineering Buildings 2007; 29(7): 1507–24. [13] Rohrs JUGENDHERBERGE. On the oscillations of a suspension chain. Transactuions of the Cambridge Philosophical World 1851; 9(Part III): 379–398. [14] Routh EJ. In: Advanced mechanics of stiff bodies, 6th ed., 1955. Dover Publications; 1868. [15] Rannie WD, von Karman T. The failure of the Tacoma narrows bridge. Government Works Agency; 1941. [16] Pugsley A. On the natural frequencies of suspension organizations. Quarterly Record of Technicians and Used Mathematics 1949; 2(Part 4): 412–418. [17] Saxon DS, Cahn AS. Modes of vibration of a suspended sequence. Quarterly Diary of Technicians and Used Mathematics 1953; 6(Part 3): 273–85. [18] Goodey WJ. On the all-natural modes and frequencies of any suspended chain. Quarterly Record of Mechanics and Applied Mathematics 1961; 14: 118–27. [19] Vincent GS. Actions of the convention on wind flow effects upon buildings and structures, volume. 2 . Teddington, England: H. M. S i9000. O.; p. 488–515. [20] West YOU DO NOT NEED :, Geschwindner LF, Suhoski JOU. Natural vibrations of suspension system cables. Log of the Structural Division, ASCE 1975; 101(ST11): 2277–91. [21] Veletsos SINCE, Darbre GR. Free vibration of parabolic cables. Log of Structural Engineering, ASCE 1983; 109(2): 503–19. [22] Triantafillou MS. Linear aspect of cords and stores. Shock and Vibration Process 1984; of sixteen: 9–17. [23] Hagedorn S, Schafer W. On nonlinear free-vibrations of the elastic cable. International Log of Non-Linear Mechanics 1980; 15(4-5): 333–40. [24] Luongo A, Rega G, Vestroni F. Planar nonlinear totally free vibrations associated with an elastic cable. International Log of Non-Linear Mechanics 1984; 19: 39–52. [25] Triantafillou MS. Mechanics of cords and stores. Shock and Vibration Break down 1987; 19: 3–5. [26] Triantafillou MS. Dynamics of cables, towing cables and mooring devices. Shock and Vibration Process 1991; 23: 3–8. [27] Nayfeh AH, Pai PF. In: Geradlinig and nonlinear structural mechanics. New York: Wiley Interscience; 2005. [28] Buonopane SG, Billington DP. Theory and good suspension connection design via 1823 to 1940s. Record of Structural Engineering 1993; 119(3): 954–77. [29] Reissner H. Oscillations of postponement, interruption bridges. Record of Applied Mechanics 1943; 10(1): 23–32. [30] Steinman DB. In: A practical treatise on suspension system bridges. Ny: Wiley; 1953. [31] Pugsley A. In: The theory of suspension connections. London: Edward Arnold; late 1960s. [32] Hayashikawa T, Watanabe N. Up and down vibration of Timoshenko light suspension bridges. Journal of Engineering Mechanics Division, ASCE 1984; 128: 341–56. [33] Kim MY, Kwon SD, Kim NATIONAL INSURANCE. Analytical and numerical study on cost-free vertical sto? of shear-flexible suspension links. Journal of Sound and Geruttel 2000; 238(1): 65–84. [34] Abdel-Ghaffar ARE. Suspension bridge vibration: Entier formulation. Record of the Architectural Mechanics Division—ASCE 1982; 108(6): 1215–32. [35] Cobo M, Aparicio AC. Preliminary static analysis of suspension connections. Engineering Set ups 2001; 23(9): 1096–103. [36] McKenna PJ, Walter T. Nonlinear amplitude in a suspension system bridge. Organize for Rational Mechanics and Analysis 1987; 98: 167–77. [37] Glover J, Lazer AC, McKenna PJ. Presence and balance of large-scale nonlinear oscillations in postponement, interruption bridges. Unces. Angew. Math. Phys. 1989; 40: 172–200. [38] Choi YS, Jen KC, McKenna PJ. The structure in the solution set for periodic oscillations within a suspension connect model. IMA Journal of Applied Mathematics 1991; 47(3): 283–306. [39] Chen Y, McKenna PJ. Traveling dunes in a nonlinearly suspended light: Theoretical benefits and statistical observations. Record of Differential box Equations 97; 136: 325–55. [40] Humphreys LD, McKenna PJ. Multiple periodic alternatives for a non-linear suspension connection equation. IMA Journal of Applied Mathematics 1999; 63(1): 37–49.

CONTENT IN PRESS

J. Enrique Luco, L. Turmo / Soil Mechanics and Earthquake Engineering 31 (2010) 769–781 781

[41] Lazer AIR CONDITIONER, McKenna PJ. Large-amplitude routine oscillations in suspension connections - new connections with nonlinear-analysis. SIAM Review 1990; 32(4): 537–78. [42] McKenna PJ, Moore KS. The global structure of periodic solutions to a suspension system bridge physical model. IMA Journal of Applied Math concepts 2002; 67: 459–78. [43] Humphreys LD, McKenna PJ. When a mechanical system should go nonlinear: unforeseen responses to low-periodic shaking. The Math. Assoc. of Was. 2005; 112: 861–75.

[44] Holubova-Tajcova G. Mathematical modeling of postponement, interruption bridges. Mathematics and Computer systems in Ruse 1999; 50(1-4): 183–97. [45] Turmo, J, Luco, JE. Effect of hanger flexibility upon dynamic response of suspension bridges, published for syndication. [46] Timoshenko, SP. Theory of suspension system bridges, Journal of the Franklin Institute 43; 235(3, 4): 213, 327. [47] Timoshenko SP, Young DH. Theory of constructions. New York: Mc-Graw-Hill; 1965. [48] Thomson WT. Vibration intervals at Tacoma Narrows. Anatomist News Record 1941; P477(March): 61–2.


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