RING 1.5 Technical Details

RING 1.5 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:

Tower Pier

Figure 1  Laterally loaded (a) steel column, (b) masonry pier, and (c) idealised response curves

 It can be deduced that:  

  • 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; 

  • 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); 

  • 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; 

  • 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 RING uses rigorous mathematical programming techniques to identify the most critical of numerous possible failure modes (e.g. a very small selection of possible failure modes is shown here). Further details of the underlying theory are provided in the Theory and Modelling Guide now distributed with RING 1.5.


In Bolton, UK, in the early 1990's a number of 3m and 5m span bridges were tested in the laboratory. A key advantage of these tests over field tests was that the internal constructional details and material properties were known. RING was originally developed to assist with the interpretation of the results from these laboratory tests.

In the Table below sample RING 1.5 analysis results are presented alongside experimental test results (only bridges with detached spandrel walls are included since these behave in a two dimensional manner). The RING 1.5 data files for these runs are distributed with the software.   



Expt. collapse load (kN)

RING 1.5 analysis

Theor. / expt. collapse load

Limiting load dispersion angle 


Effective classical passive earth pressure coefficient

Theoretical collapse load


3m single span







3m single span; debonded arch rings







5m single span







5m single span; debonded arch rings







3m triple span






*approx. of the full classical passive pressure coefficient indicated by measured angle of friction of fill (60°)

+the experimental collapse load of this bridge was reduced by the sudden onset of partial ring separation

Table 1  Sample comparison between Bolton laboratory and RING 1.5 collapse loads  

 Also, in the late 1980’s and early 1990’s, the Transport and Road Research Laboratory (TRRL, now TRL) carried out a series of load tests to collapse on redundant arch bridges. Most bridges failed in four hinge mechanisms, although some of the bridges were reported as failing by ‘three hinge snap through’ or in ‘compression’ (material failure). It was likely that many of the bridges tested were restrained considerably by their attached spandrel walls and/or masonry backing.

In 2001 TRL were commissioned to independently validate RING 1.1 and other available masonry arch bridge analysis software. As part of the validation process it was decided that the programs would be used to predict the carrying capacities of 5 of the field bridges load tested more than a decade previously. Details taken from the TRL report relating to RING for 4 of the bridges are provided in Table 2 below (Strathmashie bridge was also modelled but was in poor condition and, because ‘none of [the] defects were modelled during the analysis, all the programs returned non-conservative results’).  


Theoretical /experimental collapse load









Table 2  Correlation between TRL field bridge test
and RING collapse loads
 (independently produced by TRL)  

It is evident that agreement between the RING predictions and the full-scale test results was found to be reasonably good. Thus the TRL report concluded that RING ‘gives good results’ and that ‘RING, with some investment in an improved solver, would be a very effective tool for most assessment engineers….’. The concern about the slow speed of the solver was largely addressed following the release of RING 1.5 which is up to 200 times faster than RING 1.1 which was used in the 2001 TRL study (N.B. the collapse load factors computed by RING 1.1 and RING 1.5 are essentially identical).

Based on this evidence Network Rail have confirmed that RING is a suitable program for use to assess masonry arch bridges on the UK rail network.

Copyright © 2007, CLADU, The University of Sheffield.

RING homepage

Information about theoretical background & validation

View sample RING screen images

Download RING!

Support information and list of Frequently Asked Questions (FAQ)