AERODYNAMICS OF CABLE STAYED BRIDGES

Abstract

The present day long span cable supported bridges are amongst the more flexible of the CIVILENGINEERING structures, and, are prone to aerodynamic oscillations. Vibrations of some existing bridges like Golden Gate, Deer Isle and some others have influenced the need for continued research into the phenomena of aerodynamic effects on long span bridges. Cable stayed bridges with composite I-Girder decks have come into greater use recently, because of advantages that they offer in terms of speedy construction and economy besides meeting the stiffness criteria. However, there has not been any comprehensive study on their aerodynamic behaviour. It was therefore decided to study the behaviour of composite I-Girder cable stayed bridges in this thesis. Under the influence of wind, a long span bridge may undergo any of the following types of motions: (i) Flutter : in which the bridge deck displays exponentially growing motions that are limited only by structural non-linearities or failure, (ii) Buffeting : in which the bridge moves in random manner that reflects the random characteristic of wind, but is stable, and (iii) Vortex induced vibrations: characterised by the wake of the bridge deck forming a street of alternating vortices where the frequency of shedding approximately coincides with the natural frequency of vibration of the bridge in one of its natural mode of vibration, causing the bridge to oscillate with amplitudes which may far exceed the permissible values. Scanlan et al.(1969,1986,1988) have developed a system identification technique in which 'section model' of the deck is used for evaluating the flutter derivatives in an attempt to establish the flutter criterion for the bridge decks. They however applied the concept to truss and box girder deck bridges. Okauchi et al.(1979) carried out experiments in the field, and tested a large section model of the bridge deck (1:10 scale) to confirm the reliability of wind tunnel studies. Davenport(1972) developed a simplified approach and proposed a 'taut-strip' model to study the behaviour of cable bridges. Miyata et al.(1992) carried out studies in Japan on full size models of suspended bridges using especially designed and built large boundary layer wind tunnel. The present study was undertaken with a view to find the influence of the following parameters on the aerodynamic behaviour of the cable stayed bridges with this type of deck: 1. Relative span of the bridge 2. Type of flow : smooth and turbulent 3. Simulated eddy sizes as given by appropriate integral scales (v) 4. fairings : over part and lull length of the deck 5. Wind incidence angle The method of 'section model test' to obtain flutter derivative coefficients has been used. It is partly experimental and partly theoretical and offers the advantage of the use of a much larger geometrical scale for the model (enhancing the accuracy of scaling effects). The theory involves the modal analysis of the system for which inverse iteration with Sturm sequence technique (Bathe and Wilson, 1987) has been used. Necessary softwares and graphics packages have also been developed for analysis and presentation. Following the success of pilot test runs on a rectangular section, the section model of a composite I-girder deck (Bridge #1) was made to a scale of 1:60 and tested under two flow conditions- smooth flow and three grid generated turbulent flows. The spectral densities of the turbulence were measured and non-dimensionlized spectrum was found to corroborate with that of the atmospheric spectra (Simiu and Scanlan,1986). Computer programmes were developed to acquire data through Keithely DAC system. The raw data was smoothened by filtering the noise for which Asystant+ software was used. Finally, FORTRAN programmes were developed to determine the various flutter derivatives. Vertical flutter of the section model was not observed during the tests. This is also * confirmed from the trend for the coefficient H,(K) for all wind incidence angles under smooth flow conditions, where it is found to increase with the reduced velocity and follows a monotonic trend. In case of grid generated flows the trend of H,(K) is not regular but it shows substantial increase in magnitude. Torsional flutter is observed in all cases, the critical onset velocity varying with the test condition. This is confirmed from the trend for A2(K), the derivative representing the effect of aerodynamic damping. At the point of critical velocity the total damping becomes zero indicated by derivative A2(K) changing sign from -ve to -l-ve. Also steady-state torsional amplitudes are observed only under smooth flow. Further, based on the derivative A2(K), results for the critical velocity are found to be as follows: (i) For the unmodified bridge section critical velocity varies from 36 m/sec to 54 m/sec as the wind incidence angle change from -5 to +5 degrees. (ii) In case of the fully faired bridge section, critical velocity varies from 49 m/sec to 70 m/sec as the wind incidence angle changes from -5 to +5 degrees. (iii) The threshold velocity varies, increasing with increase in the structural damping. (vi) Making use of the flutter derivatives, the aerodynamic stability criterion for the prototype bridge could be analysed. In case of Bridge #1 it was found that the first unsymmetrical torsional mode is having a tendency to get into the critical flutter zone at a wind speed of 81.2 m/sec. This tendency was significantly delayed (92.4 m/sec) in case of the faired deck section. In case of Bridge #2, the tendency to get into the critical flutter zone was at a velocity of 46.5 m/sec. Interestingly, for this bridge, with a main span of 457.2 m, which is much larger than that of Bridge #1, no significant change was observed with the fairing attached to the deck section. This could be due to its modal characteristics being significantly different from those of Bridge #1. The buffeting response of the two bridges was analysed using the Simiu spectra (1986) for wind loading, which yields results as following: (i) Bridge #1 has a maximum excursing edge deflection at the quarter span points of the order of 0.8 m and 0.3 m in the vertical and torsional modes respectively at a wind speed of 50 m/s. (ii) Bridge #2 shows a maximum excursing edge deflection at the mid span point of the order of 3.4 m and 3.6 m in the vertical and torsional modes respectively at a wind speed of 50 m/sec. The main findings of this work are as follows: (i) From the flutter derivatives determined from section model tests it is observed that the upstream turbulence has considerable effect on the values of the flutter derivatives, the turbulence improving the bridge deck stability. (ii) The wind angle of attack also influences the derivatives considerably. With an increase in the wind incidence angle beyond +3 degrees, the stability of section model was found to increase in the torsional modes of vibration. (iii) The fairings improve the stability of the section model. (iv) Buffeting response of the cable stayed bridges of the form studied is maximum near the quarter-span point for short spans (around 200 m main span) and near the mid-span point for longer spans (around 450 m main span). (