Analysis of Arch Frames

The analysis of arch frames is presented by means of an extension of the moment-distribution method which automatically accounts for sidesway. In the fixed-end stage, the frame undergoes translation without rotation of the joints in such a manner that the fixed-end moments and the corresponding axial and shear forces are in equilibrium with the applied loads. In the distribution stage, the unbalanced moments at the joints are relaxed by a distribution procedure in which the joints are rotated, one at a time, while all other joints are restrained against rotation. Simultaneously, the frame is again allowed to translate; thus, the equilibrium established in the fixed-end stage is preserved. Because of the translation, moments are carried over not only to the far ends of the members under consideration, but also to the ends of other members. Final end moments result directly after completion of the distribution. This procedure has an advantage over the conventional moment-distribution method, in that no restraining forces are required during the distribution stage, and the final end moments are obtained directly in a single distribution operation.