Contemporary engineering analysis of masonry arches provides a model which is not adequate for analysis of the masonry system I’ve been describing on this blog (dual inverse mirror plane, or ‘dimp’). A new model is required to analyze this triangular interlocking system, which I shall attempt to describe.
The currently accepted engineering model makes three assumptions about masonry arches. (1) Masonry units have no tensile strength (2) Masonry units are infinitely strong in compression (3) Blocks (or voussoirs) never slide against each other. An arch modeled on these 3 assumptions is then viewed in cross section, and a catenary thrust force line is imposed on the wall thickness of the arch. If the thrust force line touches or exits the wall thickness, then a hinge is formed at that point (between two adjacent blocks or voussoirs) and the arch will buckle and collapse. If a large force is applied to the arch, the thrust force line will eventually touch or exit the inside (intrados) or outside (extrados) of the masonry arch, and failure will result in a hinging mechanism which causes the arch to buckle and collapse.
The dimp design can employ a tensile element, like a wire or cable within the wall thickness of the block. This feature gives the arch some tensile strength. When a large force is applied to this arch, the tensile action of the cable or wire counters this force and keeps the imaginary thrust force line more toward the center of the arch thickness. In addition to this tensile containment, another feature of the dimp comes in to play.
A large force applied to a dimp arch will first be contained by some of the tensile web, woven as great circle arcs. Instead of hinges forming when the thrust force line touches the intrados or the extrados, conjugate shearing occurs (as described here). Control joints allow block faces to slide against each other; they are actually designed to. This deformation is a strain (movement) resulting from excessive stress (applied force). The strain relieves the stress, and when the applied force is removed, the structure returns to its original state. The forces which restore a deformed arch are from gravity and the tensile elements. There is of course a limit to an applied force, beyond which a dimp arch will collapse, but it is greater than that of a conventional arch constructed from voussoirs of the same thickness.
Thus the currently accepted method of engineering analysis for masonry arches does not appear to work for the dimp design. First, an arch made of dimp blocks has tensile strength. Second, the blocks move (slide) against each other. Finally, instead of a hinging mechanism there is a conjugate shearing mechanism between blocks. It is a whole different model.
I am currently working toward a computer model to reflect this different engineering analysis. I hope to have it available to post here eventually.