Abstract

The article discusses the theoretical basis for the design of arch and vault structures. In the design of arches and vaults, it is essential to realize that the optimal shape of the arch is determined by the loading. This article clarifies the use of parabolic shapes in snow structures. If parabolic shape is used, it is required that, the vertical load is constant along the arch. This means that the snow thickness in the arch changes so that the thickness is smallest at the base.

Catenary, the shape of a hanging chain, is another well-known shape. We show analytical and numerical calculations yielding the optimal parameters for the catenary arch. It is demonstrated that the compression stress in a catenary arch is minimized when the span-to-height ratio of the catenary arch is 2,96.

Snow vaults should be compressed structures. This means that the arch thrust line should lie within the middle third of the arch cross section. The compression line is a familiar concept historically as a stone and concrete vault design principle. In snow and ice structures, the compression line should be designed to travel along the axis of the arch, resulting in a uniformly distributed compression stress in the cross section. The general design principle is to retrieve the moment-less shape of the structure, that is, to design the shape so that the thrust line is centric.

The extreme theoretical spans can be achieved when the moment-less arch is designed such that its compressive stress is uniform across the arch. The article illustrates the dimensions of a constant stress arch, a catenary arch, and a parabolic arch when the design is based on the same compressive stress level. The theoretic ultimate span and the shape of the constant stress snow arch is found when the span-to-height ratio is close to unity.

Guidelines for designing snow arches and vaults have been published. It should be noted that theoretically the correct form is the shape of the centreline of gravity of the arch. Because the snow structures have rather thick cross-sections, the shape of the inner surface of the vault may be different from the optimal shape of the centreline. The article presents calculations that illustrate this.