Using Thrust Lines to Calculate the Kinematic Collapse Multiplier for Retrofitting Masonry Arch Bridges

Abstract

In the Kinematic Method applied to arch-type structures, Heyman computed the virtual work of the external applied forces using “any system of bending moments” balancing the forces themselves [1]. Similarly, the Consecutive Plastic Hinges theorem [2] considers “any thrust line”, balancing the forces themselves, in order to obtain the virtual work through the moments of the forces applied to an arch with respect to the plastic hinges, without computing the virtual displacements. If the thrust line runs through three of the four hinges of the arch, the virtual work of all the vertical and horizontal forces applied to the arch can be written as a simple single product. In many load cases, such an approach makes easier and much more user-friendly the estimate of the load multiplier, that is needed when analyzing an existing bridge and designing its retrofitting. The paper shows how the automatic construction of thrust lines allows to calculate not only the static multiplier (as is usually done) but also the kinematic multiplier of multi-span bridges, thus detecting the range that includes the collapse multiplier for the given model. This approach is applied to a real case in order to show how this computational tool may be of great help for retrofitting a masonry arch bridge.