123456789_123456789_1 123456789 Case Study and Research123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_1234567 Page 1  2  3  4  5  6  7  8  9  10

 123456789_123456789_1 123456789 Cable-stayed bridge during construction

 Cable-stayed BridgeModel ExamplesModel descriptionInputBIM modelAnalysis modelLandscape modelICDAS Basis of DesignWorkflow of SoftwareAdditional features 123456789_123456789_1 123456789 Cable initial tensionInitial 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 itsvertical component Fz. The cables force horizontal component Fx will accumulate to the maximum compressionin the deck plates at the pylon. Figure and equation for Fz are shown in the Excel file from which the cable initialtension 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. Thetotal vertical reaction FZ of the bridge is calculated from the cantilever bridge model where the pylon density is setto 0, and the deck girder are support at the centre two points. This model is also used to control the linear behaviourof 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 inthe side span and the main span, respectively. The required factors SFac and MFac on the input tension T will bediscussed in the next section.  Table 3 shows the selected stay cables from e.g. DYWIDAG. There are three types of cables selected after the initialT with 43, 55 and 73 strands. E.g. a DG-P43 will have a strength of 43x279kN=11997kN where 279kN is the ultimatestrength 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 loadThe 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 nonlinearaxial force Fx converged from Lusas is expecting to vary from the assumed T, and the DZ displacement at the deckpoint will not be 0.

 123456789_123456789_1 123456789 The cable equivalent elastic modulus Eequi is given by Ernst formula [65,1] whereE = cable material effective elastic modulus, assumed 210E6 kN/m2A = cable  cross sectional area (m2)LH = horizontal projected length of the cable (m)q = weight per unit length of the cable (kN/m)T = cable tension force (kN) The table below shows the factor FacE should be multiplied on E-modulus for the cables All cables are assumed (E-modulus, Diameter) = (1.0x210E6kN/m2, 0.100m)

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 123456789_123456789_1 123456789 ICDAS   •    Hans Erik Nielsens Vej 3   •    DK-3650 Ølstykke   •    E-mail: th@icdas.dk    •   Tel.: +45 20 20 33 78   •   CVR no.: 34436169 123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_123456789_12345