ANALYSIS OF CABLE STAYED BRIDGES

Abstract

The available work on cable stayed bridges gives very little information about the non-linear and the threedimensional behaviour of these bridges. There are also no suitable guidelines for the designer to select the dimen sions and the sectional properties of the elements of the bridge. The work contained in this thesis is a step towards providing some of the above information. The investigations embodied in this thesis include linear as well as large deflection analyses of certain chosen cable bridge systems. The analytical results are validated by verification with the results of load tests on a bridge model. The work also includes a study of bridge behaviour under certain idealised loading cases and the influence of variation in the stiffness and geometrical parameters of the system. The thesis proceeds to present charts based on the above study, which should be helpful to the designer in choosing design parameters. Another important study contained herein is concerned with the erection stresses of a radiat ing type cable stayed bridge when constructed by the double cantilever method. Acomparison of the results as obtained " by three dimensional and two-dimensional linear analyses is made which shows that the values of forces and deflect ions given by the space, frame analysis are smaller for IV unsymmetrical loads and are almost equal for symmetrical loads. The effect of large deflections on the behaviour of the bridge is investigated. A non-linear plane frame analysis of the radiating, harp and star arrangements is Y carried out, in which the effect of variation in the girder flexibility and the support conditions at the tower base is also investigated. Nonlinear space frame analysis is carried out for the harp and radiating arrangements. It is found that the nonlinearity due to large deflections is generally very small. The nonlinear values of the forces and deflections are smaller than the linear values. As may be expected, the nonlinearity increases with the flexibility of the structure. Investigations into the behaviour of cable stayed bridges during erection are carried out in two parts. In the first part, the study is concerned with the effect of varia tion in panel lengths on the girder moments. Two bridges each with 36 cables are analysed, the panel lengths being equal in one case but unequal in the other. This study indicates that in the initial stages of erection, the girder moments, cable tensions and the vertical deflections are smaller in the bridge with unequal panel lengths but in the later stages, these forces and deflections become larger than those in the bridge with equal panel lengths. In the second part of the study a sequence is established to reduce V the girder moments by prestressing the cables as the erection proceeds. The analysis of bridges with 12, 20, 28 and 36 cables shows that the girder moments during erection are reduced considerably. The final girder moments in all the above cases become very close to those in a continuous beam with non-deflecting supports. In the chapter on parametric study, the effects of various parameters viz. stiffness of cables, girders and towersj number of cables? length of the central panel; tower height to total span ratio, and side to main span ratio, on the cable tensions and tower and girder moments are investigated by varying one or more parameters at a time. The main results of this study are the followingj (a; The flexural rigidity of the towers does not affect appreciably the behaviour of the bridge, (b) An increase in the flexural rigidity of the girders leads to increase in girder moments but decrease in girder deflections and cable tensions- (c) With an increase in cable rigidity the cable tensions increase while the girder moments and deflee tions decrease. (d) The effect of change in the length of the central panel on the cable tensions and the hogging vi girder moments is small. The positive girder moments are much smaller in bridges with smaller central panel length as compared to those with larger length of the central panel. (e) The sagging girder moments and the cable ten sions decrease with an increase in the tower height. The effect of the tower height on the hogging girder moments is small. A comparison of the behaviour of the harp and radiat ing arrangements shows that the cable tensions, girder moments and deflections are larger in the case of harp arrangement as compared to radiating arrangement. Consequently the cost of cables and girders as well as their combined cost is higher in the harp arrangement as compared to the radiating arrangement. Load tests are carried out on a perspex model of the proposed second Hooghly bridge. These show that the load deflection relationship is, in general, linear. The difference in the theoretical and experimental values of the deflection is less than 5per cent, the theoretical values being smaller. The cable tensions show wider variation. Finally design curves incorporating the variation of the various parameters are plotted for the maximum tension in the cables, and the positive and negative girder moments. VI1 The radiating arrangements with 12, 20, 28 and 36 cables are considered. The side to main span ratios are taken as O.35, 0.40, 0.45 and O.5O and the tower height to the total span ratios as 0.075, 0.100 and O.I25. A stiffness parameterrelating the extensional stiffness of cables to the flexural stiffness of girders is introduced and two values of this parameter, viz. 83OOO and 62000 are used in drawing the design charts.