## Question

When trying to enter a user-defined, multi-segment arch profile, LimitState:RING warns me that:The span could not be constructed using the points entered. Tip: User-defined spans are constructed using multiple segments of circles

What can I do?

## Solution

There are various methods that you may wish to try to obtain a valid arch profile for your model.

Defining an arch profile using segments of circles requires the ends of adjacent curves to be tangential to each other in order to generate an overall shape that is convex. An irregular profile may cause the LimitState:RING curve-fitting procedure to generate a profile containing concave regions, which are not permissible and would result in the warning message above. Listed below are some methods that can be used to avoid concave regions.

Note that, after trying any of the methods suggested, you should always check that the profile generated is sensible (i.e. that the profile is a reasonable approximation of the arch shape and measurements are within an acceptable tolerance of those measured).

### Use an interpolated profile

The profile may work better if entered as a **User-defined (interpolated) **shape rather than as segments of circles. Try switching the type and see if this has an effect.

### Nudge some of the data points

It is possible that the profile can be made valid by 'nudging' some of the points up or down by a few millimetres. The easiest way to tell which points may be the best candidates for this is to enter the profile into Excel and generate a graph from them - any irregular readings are then easily spotted (especially if you make the graph curve 'smooth'). Moving any of the points by a disproportionate amount (e.g several centimetres) should be avoided unless you are confident that the survey measurement is a misreading.

### Use fewer data points

Using a high number of data points increases the chances of a concave region being encountered (which is the cause of the warning message). Reducing the number of points used can therefore reduce the chances of an invalid profile. However, you should avoid lowering the number of points to such a level that the profile is no longer representative of the real-life bridge.

### Use a CAD package to determine valid data points

If the above measures do not work, you can also generate a new set of data points using a CAD package:

- Using a CAD program, draw the original profile using all of the available data points.
- Starting at the highest point (usually the crown), work down each side using
**3-point**or**point-point-tangent**curves to draw an alternative profile in close approximation to the original; always remembering that there should be a continuous tangent between adjacent curves (i.e the tangent at the end of one curve should be the same as the tangent at the beginning of the next). - Delete the original profile so that only the new one is visible.
- Get the
*x*and*y*co-ordinates for the two profile endpoints (*i.e.*the springings) and the points where the curves intersect. - Enter these points, in order, into LimitState:RING.

With a little trial and error, you should be able to quickly generate a profile that closely matches the original but contains fewer data points and does not generate concave regions.