Shell structures
On the relationship between moment hills, stress functions and thrust surfaces in the design of shell structures
P.J. Buskermolen (TU Delft - Architecture and the Built Environment)
A. Borgart – Mentor (TU Delft - Structural Design & Mechanics)
M. Turrin – Graduation committee member (TU Delft - Design Informatics)
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Abstract
This thesis aims to provide a better understanding on the relationship between the mechanical and geometrical properties of shell structures. In search hereof, an attempt is made to describe the thrust surface; a geometrical representation of the in-plane force trajectories through a structure. There exists a well-known relation between the parabolic shape of a (two-dimensional) catenary and the moment line of a simply-supported beam subjected to a distributed load, a relation which is similar to the three-dimensional case of shell structures. In this thesis, this relation is further exploited in the creation of various shell structures, using the moment hill of various simple plate cases. The moment hills of twistless plates as shell structures pose promising results with respect to shell-like behaviour. In the process of generating shell structures from moment hills of twistless plates, establishing the correct boundary conditions has proven to be essential in obtaining shell geometry with maximum shell-like behaviour. The Airy stress function is utilised to get further insight into the mechanical behaviour of shells. Exploiting the reciprocal relation between this Airy stress function and the diagram of forces allowed for both the design and analysis of shells. Taking the reciprocal figure of a discretised version of the Airy stress function results in a force polyhedron which by nature is in equilibrium. It was proven that the rules of graphic statics apply here, the angular defect between two planes then act as force vectors. By means of the force polyhedron a distinction can be made between tensile and compressive forces through any structure. Calculating the angular defect in an edge of the Airy stress polyhedron results in the force through its corresponding edge in its reciprocal figure. This thesis proposes multiple parametric tools with which the reciprocal figure of any Airy stress function can be created. These tools provide insight in the structural behaviour of a shell structure, and aid in the design of shells in the preliminary design stage.