A note on the catenary arch bending-moment-free paradox

Abstract

Based on the analogy between a hanging chain and a masonry arch, catenary has been for centuries considered to be an ideal arch shape, since it involves pure axial thrust. In recent studies, the equilibrium analysis of the catenary arch of finite uniform thickness under self-weight is revisited under Thrust line theory. Accordingly, it is the only shape in which a shear-free state is possible, but a bending-moment-free state cannot be attained since the thrust line coincident with the arch midline (geometrical axis) is not admissible. In the present research, the true location of centres of gravity of infinitesimal voussoirs—which are not coincident with the arch midline, is introduced into the consideration regarding bending-moments. It is shown that for a catenary arch, with rectangular cross-section, constant mass density and normal stereotomy, there is an admissible shear-free thrust line coincident with the arch centroidal axis. Since it is at a finite distance from the geometrical axis, such a shear-free state is not bending moment-free. However, since the deviation between the centroidal axis and the geometrical axis is small, the catenary shape can be rather viewed as a quasi-ideal shape.