Challenge Level

A bridge, which balances on two supports and bears a central weight, is to be made in a triangular pattern, as in the diagram. Each segment of the bridge will be either a rope, which must be under tension to be stable, or a spring, which must be under compression to be stable.The pin joints are light and move freely, but will break if subjected to any net force.

In this problem we investigate which parts of the bridge must be ropes and which parts must be springs

Part 1: Imagine that the strut X feels a tension of some unknown magnitude. By considering the vector directions of the forces at the left hand support prove that Y must be in compression if there is to be no net force at the support. Extend this idea to determine which struts in the bridge must be in tension and which struts in the bridge must be in compression if there is to be no net force at
any of the pin joints.

Part 2: Is it possible to use ropes and springs to build a stable bridge of this shape with no net force at any of the pin joints if X is a spring?

For an extension of this problem, why not try the problem More Bridge Building ?