Poly Bridge

A simple bridge of three triangular elements spans a river and is carried by the foundation at AA and CC in the diagram. The connecting lines between the points correspond to steel girders, each of which can bear a maximum tensile and compressive load of 10 tons.

What is the minimum angle α\alpha needed so that a truck with a weight of 10 tons can safely cross the bridge?


  • Assume that the weight load of the truck is concentrated at point BB , so here a force of FB=(10tons)g\vec F_B = (10 \,\text{tons})\,\cdot \vec g acts on the bridge.
  • The bridge is held by the opposing forces FA=FC=12FB\vec F_A = \vec F_C = - \frac{1}{2} \vec F_B on points AA and CC . Calculate the forces acting along the steel girders.

Note: for every point of the polygon, the sum of all forces must be zero.


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