Cable initial tension
Initial tensions T of the cables are very sensitive against the convergence of the nonlinear analysis. The tension forces T can be estimated on the basis of a two cables will carry a section of the deck by the its vertical component Fz. The cables force horizontal component Fx will accumulate to the maximum compression in the deck plates at the pylon. Figure and equation for Fz are shown in the Excel file from which the cable initial tension T are calculated. Table 1 shows the initial tensions T calculated on the angle v between the cable and the deck. The lower angle v, the bigger tension T is needed. E.g. the cable no. 10 needed an initial force of 2.15 times bigger than no. 1. The total vertical reaction FZ of the bridge is calculated from the cantilever bridge model where the pylon density is set to 0, and the deck girder are support at the centre two points. This model is also used to control the linear behaviour of the bridge before it is set to nonlinear analysis. Table 2 shows the ratio of the converged cable axial force Fx to the tension T. SFx and MFx are the cable force Fx in the side span and the main span, respectively. The required factors SFac and MFac on the input tension T will be discussed in the next section. Table 3 shows the selected stay cables from e.g. DYWIDAG. There are three types of cables selected after the initial T with 43, 55 and 73 strands. E.g. a DG-P43 will have a strength of 43x279kN=11997kN where 279kN is the ultimate strength of each strand. The ratio of T to DG-P43 at cable no. 1 is 5033/11997=0.42
Figure: Initial tension T, converged axial Fx and DYWIDAG cable ultimate load
The following notices are registered for the cable initial tension forces § The T force can enter directly as input for the cable initial tension in Lusas "Stress and Strain" if the (Thickness, Density factor)=(175mm, 0.191) is used for the top and bottom plate of deck. However, this equivalent density required a coarse mesh for the cable elements to obtain convergence. As the results the natural mode shapes and frequencies must be used with cautions and it is not applied here.
§ Using (Thickness, Density)=(175mm, 7.85tons/m3), different factors SFac and MFac on the cables tension T are tuned manually to obtain the convergence in this case study.
Because the tension T calculated from a linear relation between the deck weight (kN) and the cable Fz, the nonlinear axial force Fx converged from Lusas is expecting to vary from the assumed T, and the DZ displacement at the deck point will not be 0. | 
