Modelling stepped arch spans in LimitState:RING
|Figure 1: Stepped multi-span arch bridge modelled in LimitState:RING
While the majority of multi-span bridges comprise arches that spring from the same level at either side of the intermediate pier, many have staggered springing levels. On first glance it would appear that this type of bridge cannot easily be represented in LimitState:RING, but this is not the case. With a little careful modification to the span geometry, stepped arch spans can readily be incorporated into the LimitState:RING model.
This quick tip explains how to do this. You can download the LimitState:RING source file here.
1. Select a ‘user defined shape’ for the span profile
|Figure 2: User-defined shape (multi-segment) dialog
You can use either multi-segment or interpolated shape and switch between the two at any time to see which gives the most accurate representation of the modelled bridge. However, the best results tend to be achieved using multi-segment arches.
2.Introduce the step into the geometry
To step down
At the right end of the span, in the profile data, add an extra point. Make the x dimension marginally higher than the span of the arch (by, say 0.1mm) and reduce the y position to the level at which you wish the next arch to spring from. Depending on the height of the step, you may need to introduce additional blocks into the arch to ensure that there are a sufficient number in the barrel section.
To step up
At the left end of the span, in the profile data, add an extra point. Make the x dimension marginally higher than zero (by, say 0.1mm) and increase the y position to the level at which you wish the arch to spring from. Continue to enter the span points but with the additional height added. Depending on the height of the step, you may need to introduce additional blocks into the arch to ensure that there are a sufficient number in the barrel section.
3. Check the geometry of the structure is credible
|Figure 3: Fixing the contact surfaces of the vertical section.
It is the aim to have the geometry match the real life situation as closely as possible. If the vertical sections of the step are misaligned or significantly curved then you might need to add additional points or adjust the existing ones in order to ensure that the profile becomes vertical as quickly as possible after the springing. This might take a little trial and error.
4. Check the response of the structure
Once the model has been generated and loading applied, it is prudent to solve and check the response of the structure to determine whether further modification is required. For instance, should the vertical side walls be found to hinge when this would not be expected, or if the springing contacts are rotated beyond the horizontal, you may wish to fix the contact surfaces in these areas against hinging and sliding. To do this:
- Select the ‘rectangle select’ tool (either from the toolbar or the Tools menu).
- Draw a rectangle that encompasses all the intra-block contact surfaces in the vertical step section.
- In the Property Editor, select Contacts from the drop-down menu.
- Set ‘Permit hinges’ to false.
- Repeat and set ‘Permit sliding’ to false.