Heyman's assumption for reinforced concrete arches re-examined

In a previous paper 1] the well-known Heyman assumption (H.A.) for the limit design of a masonry arch was shown to be valid also for the limit design of a box-section reinforced-concrete arch. In 2] the more general case of failure under variable loads (incremental collapse or alternating plasticity) was discussed. Use of the H.A. avoids the construction of the elastic domain, that is the set, for each section, of all possible states MN in the elastic range. This is one of the great difficulties of classical analysis, if moving live loads must be considered, for example for bridge structures. The H.A. allows the stresses to be calculated at the outer fibres in the generic section, referring to only the intradosal and extradosal moments, so that it is possible to obtain the maxima of such stresses by using influence lines.Temperature changes have also been considered, as have wind and earthquake loading.Paper 2] deals with these cases, and the results agree well with the exact results. The present note is a complement to the previous work. In it, a plastic hinge is allowed to occur taking into account cracking of the concrete. The H.A. is shown to be also valid if the live load line of thrust is close to the centre-line of the arch, or the plastic safety factor of all the loads is required, dead load included.