• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.611-620
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• 2017

A new theory of weightless sagging planer elasto-flexible cables under point loads is developed earlier by the authors and used for predicting the nonlinear dynamic response of cable-suspended linear elastic beams. However, this theory is not valid for nonlinear elastic cracked concrete beams possessing different positive and negative flexural rigidity. In the present paper, the flexural response of simply supported cracked concrete beams suspended from cables by two hangers is presented. Following a procedure established earlier, rate-type constitutive equations and third order nonlinear differential equations of motion for the structures undergoing small elastic displacements are derived. Upon general quasi-static loading, negative nodal forces, moments and support reactions may be introduced in the cable-suspended concrete beams and linear modal frequencies may abruptly change. Subharmonic resonances are predicted under harmonic loading. Uncoupling of the nodal response is proposed as a more general criterion of crossover phenomenon. Significance of the bilinearity ratio of the concrete beam and elasto-configurational displacements of the cable for the structural response is brought out. The relevance of the proposed theory for the analysis and the design of the cable-suspended bridges is critically evaluated.

• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.465-498
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• 2011

Concrete structures are generally cracked in flexural tension at working loads. Concrete beams with asymmetric section details and crack patterns exhibit different flexural rigidity depending upon the sense of the applied flexural moment. In this paper, three different models, having the same natural period, of such SDOF bilinear dynamical systems have been proposed. The Model-I and Model-II have constant damping coefficient, but the latter is characterized by two stiffness coefficients depending upon the sense of vibration amplitude. The Model-III, additionally, has two damping coefficients as well. In this paper, the dynamical response of Model-III to sinusoidal loading has been investigated and compared with that of Model-II studied earlier. It has been found that Model-III exhibits regular and irregular sub-harmonics, jump phenomena and strong sensitivity to initial conditions, forcing frequency, system period as well as the sense of peak sinusoidal force. The constant sustained load has been found to affect the natural period of the dynamical system. The predictions of Model-I have been compared with those of the approximate linear model adopted in present practice. The behaviour exhibited by different models of the SDOF cracked elastic concrete structures under working loads and the theoretical and practical implications of the approach followed have been critically evaluated.