Thrust Line Analysis of a Masonry Arch

Limit analysis by graphic statics. The arch is cut into radial joints, each voussoir and its spandrel reduced to a vertical load at its centroid, and the admissible lines of thrust found from the safe theorem. Zero tensile strength, rigid blocks and no sliding are assumed, after Heyman. Compressive stress at the joints is not checked. The force polygon stacks the voussoir weights to scale on the load line with the pole set at the horizontal thrust, so each ray is parallel to the corresponding segment of the thrust line and the pole distance is the thrust itself. A point load is applied vertically at the entered distance from the crown, positive to the right, and carried straight down onto the arch. The line load is drawn across the whole wall, but only the part of it over the arch’s own span is carried by the arch; the rest bears directly on the abutments.