Aerodynamic stability of cable-supported bridges using CFRP cables

To gain understanding of the applicability of carbon fiber reinforced polymer (CFRP) cable in cable-supported bridges, based on the Runyang Bridge and Jinsha Bridge, a suspension bridge using CFRP cables and a cable-stayed bridge using CFRP stay cables are designed, in which the cable’s cross-sectional area is determined by the principle of equivalent axial stiffness. Numerical investigations on the aerodynamic stability of the two bridges are conducted by 3D nonlinear aerodynamic stability analysis. The results showed that as CFRP cables are used in cable-supported bridges, for suspension bridge, its aerodynamic stability is superior to that of the case using steel cables due to the great increase of the torsional frequency; for cable-stayed bridge, its aerodynamic stability is basically the same as that of the case using steel stay cables. Therefore as far as the wind stability is considered, the use of CFRP cables in cable-supported bridges is feasible, and the cable’s cross-sectional area should be deter-mined by the principle of equivalent axial stiffness.

Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances

A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments.The steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.

Parameters of static response of carbon fiber reinforced polymer(CFRP) suspension cables

The feasibility of longer spans relies on the successful implementation of new high-strength light weight materials such as carbon fiber reinforced polymer(CFRP). First, a dimensionless equilibrium equation and the corresponding compatibility equation are established to develop the cable force equation and cable displacement governing equation for suspension cables, respectively. Subsequently, the inextensible cable case is introduced. The formula of the Irvine parameter is considered and its physical interpretation as well as its relationship with the chord gravity stiffness is presented. The influences on the increment of cable force and displacement by λ2 and load ratio p′ are analyzed, respectively. Based on these assumptions and the analytical formulations, a 2000 m span suspension cable is utilized as an example to verify the proposed formulation and the responses of the relative increment of cable force and cable displacement under symmetrical and asymmetrical loads are studied and presented. In each case, the deflections resulting from elastic elongation or solely due to geometrical displacement are analyzed for the lower elastic modulus CFRP. Finally, in comparison with steel cables, the influences on the cable force equation and the governing displacement equation by span and rise span ratio are analyzed. Moreover, the influences on the static performance of suspension bridge by span and sag ratios are also analyzed. The substantive characteristics of the static performance of super span CFRP suspension bridges are clarified and the superiority and the characteristics of CFRP cable structure are demonstrated analytically.