When we think about caterpillar tunnels we think of temporary or movable structures that can be used for multiple things on a farm. While they are an inexpensive way to cover crops and animals or store equipment they do have their limitations. Most caterpillar tunnels have one center purlin for strength at the apex of the tunnel. While this is the usual setup, some have added additional purlins for stability and strength. This sounds like an obvious solution, but this is actually the opposite of the truth. When additional purlins are added to the left and right of a center purlin it often creates pockets where snow and water can accumulate instead of falling off of the side of the tunnel as with just one center purlin. The result is additional weight on the top of the tunnel and, in the worse case scenario, caterpillar bow failure. Look at this link to see a trial of this very question: Caterpillar Structural Trial
The center purlin design is the best way to shed weight and water off of the caterpillar tunnel and onto the ground. If additional support is needed in a caterpillar tunnel it is suggested to brace every other bow from the inside with 2 X 4's at the joint(s) you are concerned about.