Castigliano's Non-linear Analyses

The arch is assumed to be a statically indeterminate problem with equilibrium equations insufficient to sole the redundancy and therefore fine the actual line of thrust. Elastic theory is used due to the masonry being unable to resist tensile forces. Therefore non-linear methods such as Castigllano’s method are required. This method has been used in many computer packages to analyse masonry arch bridges. The models consist of various configurations of beam elements with the restraining elements of the backfill being simulated. This is defined as a function of the arch movement and tension is incorporated by the thinning of the arch section.