Mathematical Bridge

The Mathematical Bridge is the popular name of a wooden footbridge in the southwest of central Cambridge, United Kingdom. It bridges the River Cam about one hundred feet northwest of Silver Street Bridge and connects two parts of Queens' College. Its official name is simply the Wooden Bridge. It is a Grade II listed building.The bridge was designed by William Etheridge, and built by James Essex in 1749. It has been rebuilt on two occasions, in 1866 and in 1905, but has kept the same overall design. Although it appears to be an arch, it is composed entirely of straight timbers built to an unusually sophisticated engineering design, hence the name.A replica of the bridge was built in 1923 near the Iffley Lock in Oxford.The original "mathematical bridge" was another bridge of the same design, also commissioned by James Essex, crossing the Cam between Trinity and Trinity Hall colleges, where Garret Hostel Bridge now stands.Mathematical explanationThe arrangement of timbers is a series of tangents that describe the arc of the bridge, with radial members to tie the tangents together and triangulate the structure, making it rigid and self-supporting. This type of structure, technically tangent and radial trussing, is an efficient structural use of timber, and was also used for the timber supporting arches (centring) used for building stone bridges. Analysis of the design shows that the tangent members are almost entirely under compression, while the radial timbers are almost entirely subject to tension with very little bending stress, or to put it another way, the tangent and radial elements elegantly express the forces involved in arched construction.