Cable Sag Effect Research Articles

Elastic-Plastic Seismic Behavior of Long Span Cable-Stayed Bridges

This paper investigates the elastic-plastic seismic behavior of long span cable-stayed steel bridges through the plane finite-element model. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the stay cable sag effect, axial force-bending moment interaction, and large displacements. Material nonlinearity arises when the stiffening steel girder yields. The example bridge is a cable-stayed bridge with a central span length of 605 m. The seismic response analyses have been conducted from the deformed equilibrium configuration due to dead loads. Three strong earthquake records of the Great Hanshin earthquake of 1995 in Japan are used in the analysis. These earthquake records are input in the bridge longitudinal direction, vertical direction, and combined longitudinal and vertical directions. To evaluate the residual elastic-plastic seismic response, a new kind of seismic damage index called the maximum equivalent plastic strain ratio is proposed. The results show that the elastic-plastic effect tends to reduce the seismic response of long span cable-stayed steel bridges. The elastic and elastic-plastic seismic response behavior depends highly on the characteristics of input earthquake records. The earthquake record with the largest peak ground acceleration value does not necessarily induce the greatest elastic-plastic seismic damage.

Ultimate Behavior of Long-Span Cable-Stayed Bridges

The study described here investigates the nonlinear static and ultimate behavior of a long-span cable-stayed bridge up to failure and evaluates the overall safety of the bridge. Both geometric and material nonlinearities are involved in the analysis. The geometric nonlinearities come from the cable sag effect, axial force-bending interaction effect, and large displacement effect. Material nonlinearities arise when one or more bridge elements exceed their individual elastic limits. The example bridge is a long-span cable-stayed bridge of a 605 m central span length with steel box girder and reinforced concrete towers under construction in China. Based on the limit point instability concept, the ultimate load-carrying capacity analysis is done starting from the deformed equilibrium configuration due to bridge dead loads. The effects of the steel girder hardening and the girder support conditions on the ultimate load-carrying capacity of the bridge have been studied. The results show that the geometric nonlinearity has a much smaller effect on the bridge behavior than material nonlinearity. The overall safety of a long-span cable-stayed bridge depends primarily on the material nonlinear behavior of individual bridge elements. The critical load analysis based on the bifurcation point instability concept greatly overestimated the safety factor of the bridge. The ultimate load-carrying capacity analysis and overall safety evaluation of a long-span cable-stayed bridge should be based on the limit point instability concept and must trace the load-deformation path of the bridge from applied loads to failure.

Vibration of Inclined Sag Cables with Oil Dampers in Cable-Stayed Bridges

This paper presents both free and forced vibration analyses of inclined cables, including the effects of cable sag, equipped with oil dampers in cable-stayed bridges by using a hybrid method recent...

Parametric studies on cable-stayed bridges

Parametric studies on cable-stayed bridges are performed in the paper for investigating the individual influence of different sources of nonlinearity in such bridges. The sources of nonlinearity in the cable-stayed bridge mainly include the large deflection, beam-column and cable sag effects. The influence of such kind of effects on the analysis and the structural behavior of cable-stayed bridges has been detailedly examined in the study. A finite element procedure for the nonlinear analysis of cable-stayed bridges is first set up, and then detailed parametric studies for the initial shape analysis and static deflection analysis of such bridges are carried out. The numerical results show that in the initial shape analysis the cable sag effect is most important and the other two effects are insignificant. However, in the static deflection analysis of cable-stayed bridges the large deflection effect plays the key role, the beam-column effect is also significant but minor than the large deflection effect and the cable sag effect becomes the least important one.

Initial shape of cable-stayed bridges

A finite element computation procedure for determining the initial shape of cable-stayed bridges under the action of dead load of girders and pretension in inclined cables is presented. The system equation of cable-stayed bridges including the nonlinearities due to large displacement, beam-column, and cable sag effects is first set up and then solved using the Newton-Raphson method on increment-iterationwise. Based on a reference configuration and an assumed cable pretension force, the equilibrium configuration under dead load is found. Further, by adjusting cable forces, a ‘shape iteration’ is carried out and a new equilibrium configuration, i.e., a more reasonable initial shape, can be determined. The shape iteration is repeated until the desired tolerance is achieved. Numerical results show that a more accurate initial shape having reasonable prestress distribution and less deflection of girders can easily be determined by the proposed procedure.

Initial shape of cable-stayed bridges

A finite element computation procedure for determining the initial shape of cable-stayed bridges under the action of the dead load of girders and pretension in inclined cables is presented. The system equation of cable-stayed bridges including the nonlinearities due to large displacement, beam-column, and cable sag effects is first set up and then solved using the Newton-Raphson method in an increment-iterationwise approach. Based on a reference configuration and an assumed cable pretension force, the equilibrium configuration under dead load is found. Further, by adjusting cable forces, a ‘shape iteration’ is carried out and a new equilibrium configuration, i.e., a more reasonable initial shape, can be determined. The shape iteration is repeated until the desired tolerance is achieved. Numerical results show that a more accurate initial shape having reasonable prestress distribution and less deflection of girders can easily be determined by the proposed procedure.

Internal resonance and non-linear response of a cable under periodic excitation

The coupled non-linear equations of motion of a sagged cable in its first symmetric mode of in-plane and out-of-plane oscillations are solved by the method of multiple scales for its forced vibration response. The cases of both internal and external resonances are considered. A uniform lateral load is assumed to act along with an in-plane harmonic component, similar to a situation under vortex-induced oscillation. The quadratic non-linearity terms in the equations of motion are shown to affect the cable behaviour significantly when the in-plane frequency is about twice the out-of-plane frequency of oscillation. A stability analysis is performed on the steady state solutions. The effect of cable sag on these solutions and their stability is studied indirectly through the internal resonance parameter. The influence of the lateral load component, with and without internal resonance, on the stability regions is discussed.