Three-hinged arches

An arch carries load mainly by compression along its curve instead of by bending. Masonry bridges have used this for two thousand years because stone is strong in compression and weak in tension. A three-hinged arch has pins at both springings and one at the crown. The crown hinge provides an extra condition, zero moment there, so the arch is statically determinate even though its supports give four reactions.

To analyse it, find the vertical reactions from moments of the whole arch about each springing, then take moments about the crown for one half to get the horizontal thrust H. The bending moment at any section is then the beam moment minus H times the arch rise at that section, M = M_beam − H y. If the arch's shape follows the funicular (thrust) line for the load, the moment is zero everywhere and the arch is in pure compression. For a uniform load over the span, that shape is a parabola, which is why parabolic arches suit bridge decks carrying evenly spread loads.

Because it is determinate, a three-hinged arch is not stressed by temperature change or support settlement, an advantage on poor ground. Two-hinged and fixed arches are stiffer and more common in modern concrete and steel bridges but need indeterminate analysis and must cope with thermal and rib-shortening effects. Horizontal thrust must always be resisted: by abutments, by rock, or by a tie as in a bowstring arch.