Arched structures are continuously curved support elements, which transfer loads primarily via compressive forces. When the shape of the arch is the inverse shape of a catenary, the arch only experiences compressive forces. The thrust line in the arch is the mirror of the string line.

Step 1

Fix the string with the two nails on the Styrofoam plate and let it hang freely (see Figure 1). The free hanging string takes the shape of a parabola, which also is the shape of the thrust line (see Figure 2).

Step 2

Arched structures require a large enough cross section to be stable. The more the axis of the arch approaches the shape of the thrust line, the smaller the needed cross-sectional height h of the arc. Draw an arch whose axis corresponds to the thrust line. Divide this arch into similar segments and number them (See Figure 2).

Step 3

Cut the individual segments of the arch out of the Styrofoam plate and build the arch with this segments (see Figure 3 and 4).

Since the arch shape follows the thrust line, only compression forces occur. As a result, the arch is stable. The minimum and maximum possible thrust lines are shown in the interactive drawing.

Interactive drawing: Minimum and maximum thrust lines in a masonry arch (http://www.block.arch.ethz.ch/eq/drawing/view/16)

Step 4

Draw a circular arch on the remaining piece of the Styrofoam. Number the sections, cut them out and construct the arch (Figure 5 and 6). This arch cannot be brought to be stable, because the thrust line is located outside its shape.