Theory
ring2.0 idealises a masonry arch structure as an assemblage of rigid blocks and uses computational limit analysis methods to analyse the collapse state only. Although limit analysis, or ‘plastic’/ ‘mechanism’ analysis techniques were originally developed for steel components and structures, it has since been shown that these can be applied to masonry gravity structures, such as piers and arches. To help understand why limit analysis theory is applicable, compare and contrast the response of a steel column with uniform plastic cross-section and a weakly mortared masonry pier, both subject to a horizontal load F, as shown below It can be deduced that: 1. whilst the tensile and compressive strength of the steel column endow it with a finite plastic moment of resistance, Mp, the absence of tensile strength means that the masonry pier does not possess a comparable (i.e. strength derived) moment capacity; 2. however, the thickness and self weight of the pier mean that there is some resistance against overturning and the masonry pier could conceptually be considered as possessing a moment capacity, albeit one that varies with height (equal in magnitude to the normal force at a given cross-section multiplied by half the pier thickness); 3. furthermore, provided pier displacements do not become large, the resistance of the masonry pier against overturning at a given cross-section will remain broadly constant; 4. hence the response of the pier can be considered ‘ductile’, an important requirement in order for limit analysis theory to be applicable. This is clearly a very simple example. In arch bridges of rather more complex geometry ring2.0 uses rigorous mathematical programming techniques to identify the most critical of numerous possible failure modes (e.g. see this small selection of masonry arch failure modes). Further details of the underlying theory are provided in the Theory and Modelling Guide distributed with ring2.0.
