A design and parametric study into large scale hyperbolic paraboloid shell and lattice structures

Hyperbolic paraboloids have moved from being just an interesting mathematical form to being an extremely useful structural form. Early structural forms came into prominence in Europe in the middle 1930's when early versions were constructed out of concrete with little structural theory. After the Second World War, interest began to grow as a simple structural basis for the design of the hyperbolic structural form was documented. All early models were constructed in concrete using a simple shell theory. At the same time, academic research developed better understandings using small scale models. Following the initial excitement with the new form coupled with a growing understanding of the properties of reinforced concrete that fortuitously occurred at about the same time, interest then began to fade as other structural forms took over. Currently the last decade has seen a renewed interest in the form, but with a construction based on lattice members and not continuous shells. This interest has been driven by the desirability of a form to cover large areas without intermediate columns and the hyperbolic paraboloid fills this requirement. Formal research however has never progressed beyond small scale continuous shell or lattice models. This thesis aims to investigate the hyperbolic paraboloid using large scale shell and lattice structures. Models are created and examined in a range of three sizes up to 100 metres in plan dimensions. Of course, a model of such size cannot be constructed in the laboratory due to cost and size constraints and therefore this research is conducted using the finite element method and a computer program. This research covers bifurcation buckling and elastic geometric non-linear buckling of hyperbolic paraboloid continuous shells and lattices under changing rise to span ratio and changing edge beam flexural stiffness. Results from the shell models are compared with the results from the similar sized lattice models where possible. Steel lattice structures are also examined for their elastoplastic response. Firstly, geometrically perfect shell and lattice structures are examined for perfect load distribution and then asymmetric load distribution. It was found that in the case of the load variations, no significant effects eventuated. Secondly, shells and lattice structures are then examined to determine the influence that increasing levels of imposed imperfections have on their buckling behaviour and elastoplastic force distribution. These imperfections are introduced to simulate the fabrication and construction errors that occur in real structures. It was found that the introduction of these imperfections was generally not detrimental and sometimes even in severe levels actually increased buckling performance. The suggestion is made that this may be a way to create new structures based on a known structural model pedigree. Finally, the mathematical determination of hyperbolic paraboloid shell buckling pressure and buckling wavelength proposed in 1955 by Reissner was checked against the finite element results in these large scale shell models. It was found that the buckling pressure did not agree with the original Reissner formula and a modification to that formula is proposed by the author. Furthermore, it was found that the Reissner buckling wavelength did agree with finite element buckling results.