Nodes 155

The drawings of the bridge outline the final geometry of the bridge. In geometric modelling, the nodal location, or rather the way of applying the section properties to the generated elements must be considered. If no other eccentric connection is defined, the nodes lay in the centreline of the sections. In this model, the nodal coordinates of the girder define the upper part of the deck.

In MiDAS, an eccentric connection is considered using the Offset function for the cross section properties.

In the girder, a linear gradient of 5% can be found in the side span up to Segment 7, which is the first segment in the main span. With the girder elevation given as 20.00 metres at the abutment and 23.50 metres at the pylon, the girder elevation is defined by the function

20

The girder shape in the main span can be expressed as a following type:

EL

where g2 and g1 describe the girder gradient at the start and end point of the function and G.EL the girder elevation at the point x = 0, located at the start point of the function. With Equation 5-1, the last value becomes to y₁(86.30)=0.05*86.30+20=24.315. The remaining girder length L between the first segments in the main span is 311.4 meter. In order to achieve a girder elevation of 28.35 metres in the centre of the bridge, as this value is given in the plans, the girder gradient is increased to 5.183%. With the calculated values, Equation 5-2 can be given as:

24.315

For the final modelling, the x-coordinates are located in the centre of the main span. Figure 5-2 illustrates the determined girder shape. The detailed node coordinates are given in the appendix.

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20 22 24 26 28 30

-250 -200 -150 -100 -50 0 50 100 150 200 250

side span main span

Figure 5-2: Girder elevation in the side and main span [m]

The pylon nodes are generated in the centreline of the pylon. Figure 5-3 illustrates the location of the cable-pylon connection as constructed on the site and the distance to the centreline as modelled for the analysis. Because of the dependence of the forces in the cables on the angle between the pylon and the cable, attention should be paid for modelling these details accurately.

There are two possible ways of taking this situation into consideration: One is to use an eccentric connection between elements representing the cables and the pylon nodes, or to define extra nodes located in the working point (W.P.C) and to use ridged links to fix them with the pylon. The other option is to extend the cable elements and model the working point B (W.P.B.) to properly generate the angle of the cables. This second option is used for modelling the bridge in MiDAS. The calculation sheet for the working point B, as well as a list of the coordinates of nodal location, is presented in the appendix.

The same situation is found in the girder–cable connections, but in this case, additional nodes are generated. For Cable 1 to 4, the extra nodes are located –1.71 metres in dz and -1.84 metres in dx direction; for Cable 5 to 15, the nodes are generated -0.54 metres in dz direction relative to the girder nodes. Figure 5-5 shows the nodes and ridged links used to connect the nodes with the girder nodes.

By this method, the angle between the pylon-cable and the girder-cable can be modelled properly, so that the determined cable forces will consider the real existing angle.

Figure 5-3: Working points at the pylon Figure 5-4: Working points at the girder

Figure 5-5: Cable-girder connection and tied down condition using elastic links

5.4.2 Elements

Beam elements are used to model the girder and the pylon. Generally, the element has 6 degrees of freedom per node, reflecting axial, shear, bending and torsional stiffness. Since a two-dimensional analysis is performed, in the Structural Type option the model is defined to be in the x-z plane, so that the degrees of freedom in dy-direction are ignored. The beam element is formulated on the basis of the Timoshenko Beam Theory reflecting shear deformations.

Concentrated loads, distributed loads, temperature gradient loads and prestress loads can be applied to beam elements.

The cables are modelled with a truss element, which means that sagging effects are neglected.

Firstly, it is assumed that these are negligible, but they are included in the final construction stage analysis.

The set back is a common procedure in the construction of cable-stayed bridges. This is usually done before the closure and the addition of the key segment. This is a highly non-linear process, and using truss elements in a finite element analysis may cause significant errors. The set back

Chapter 5: Model of the Second Jindo Bridge 158

is not modelled in this analysis but it should be mentioned to consider this problem in case of any other analyses in which it is included.

In a final analysis, the sagging effects of the cables are considered and the truss elements are changed to Tension-Truss Cable elements, which consider the effective stiffness in a linear analysis by applying the Ernst-formula.

Figure 5-6 shows the element location and its numbering. An element table is also given in the appendix.

Figure 5-6 Element numbers