The Pennsylvania State University

The upper and lower bound theorems of plasticity have been shown to apply to the limit states analysis of the masonry arch. To apply the lower bound theorem, it suffices to find a distribution of internal forces satisfying equilibrium and limiting material conditions to show that the structure is stable. The upper bound theorem demonstrates that the structure is unstable under a set of loads in equilibrium in a kinematically admissible mechanism. This method is shown to be generally applicable to a masonry arch structure. The effect of sliding, abutment failure, and combined hinging and sliding can be considered in the determination of the capacity of arched masonry structures. Existing masonry arch bridges in the USA are reviewed, and are found to be susceptible to collapse modes involving sliding between voussoirs and at the abutments, in addition to the hinging mechanisms usually considered. Visual evidence of damage to existing masonry arch bridges tends to confirm the importance of these collapse modes.