Form finding of arches and shell structures subjected to seismic loading

Abstract

The overall geometry of arches and shell structures plays an essential role in their capacity to withstand earthquakes, and shells in particular resist seismic loading extremely well because of their lightweight nature and high geometric stiffness. Seismic loading, however, is rarely considered when initially determining the form of arches and shells, although this could significantly improve their design’s material-efficiency and seismic performance. Therefore, in this dissertation the first computational methodologies are presented that generate shapes for arch and shell structures designed to sustain self-weight and seismic loading in a material-efficient way.

The research focuses on arches and shells that withstand the applied loads through compressive internal loading, making the developed forms suitable for construction in materials with substantial compressive strength such as unreinforced concrete, stone, earth, ice or masonry. Additionally, the resulting geometries are scalable as long as the compressive strength of the material is not exceeded.

A form finding algorithm for arches with varying thickness is presented that relies on a methodological application of a series of geometric manipulations of a thrust line, generated under combined gravity and horizontal loading. This algorithm is subsequently extended to find material-efficient forms for thin shells that can similarly withstand these loads. This is accomplished by corrugating the supporting edges of the shell so that a compressive load path can form within the depth of the supports. It is demonstrated that the obtained shapes are superior to non-form-found geometries in their material use and their horizontal pushover capacity through a kinematic limit state analysis for arches and by using a non-linear pushover analysis for corrugated shells.

Additionally, a second method for shells is developed that expands the 2D thrust line concepts to a 3D hanging net model approach obtained in a dynamic relaxation solver. This method accounts for self-weight combined with seismic loads acting in any horizontal direction. The approach yields single-layer shells with varying thickness or lighter double-layer interconnected thin shells.

As the first of their kind, the conceptual form finding approaches presented in this dissertation will facilitate the design of material-efficient and safe arches and shell structures in seismic zones.