Authored by Peter Debney

I am often asked about form finding tension structures but the other day I was asked how to do one that I have not done before: an asymmetric bridge.

Form-finding is a method that determines the geometrically optimal structure to resist a set of tension forces. This may be a fabric surface or a net of cables, but the end result is a structure that has the minimum inherent energy yet has all the forces in balance.

Compression structures are different though. The minimum energy form for an arch, for example, is a pile of rubble. While tension forces stiffen, compression buckles. This means that to form-find an arch you need to cheat. Thankfully engineers of the past realised that ideal arches are mirror images of ideal catenaries: to form find an arch you simply need to turn it upside down. This means that to form find a compression structure you need to reverse the loads and put it all into tension.

So, to the bridge. I wasn’t initially given a form to work to, so I decided to make a tied arch bridge with a deck that snakes like an S in plan. Constructing the deck’s form was a simple matter of using the flex command from within GSA; likewise I flexed the arch (coincident bar and spacer elements) into a parabolic arch of a suitable rise.   Manually added ties completed the basic geometry.

As discussed above, to form find the arch I need to put it into tension, but I could not reverse the load on the ties as that would put them into compression, and neither could I simply apply point loads for the hangers as the force direction must change as the arch moves. I decided I needed to make mirror image copies of the ties above the arch to pull it into shape.

While GSA can mirror elements and nodes through a plane, I needed to mirror about a parabola. The easiest way I could think of was to copy the node coordinates into Excel and use the functions there to create the new locations, having first reordered the node numbers along a vector using the Manage Data command. I then copied the new nodes back into GSA and added the extra ties.

The last step before form finding was to ensure that the deck and real hangers would not interfere, so I created a Stage containing just the arch and upper hangers. I also created a similar one for the “real” geometry for the subsequent static analyses.

Having set the form finding soap film target prestresses, I could then form find the analysis stage to determine the arch geometry and prestress.

That completed, I just needed to reverse the arch prestress loads in the loads table using the function command, copy the tie prestress into the “real” hangers, and change the arch Bars into Beams to produce the result you can download below.

Is this the final form? Well, no. For one thing such a form find tends to be an iterative process and so some elements of the above exercise will need repeating; for another I didn’t include all the necessary forces.

What have I left out and how should you deal with it? I look forward to hearing your suggestions.

Here is the GSA arch model. Note that it is in 8.7 format, so you will need that version or higher to open it.