Vector-product-based Graphic Statics and Graphic Kinematics for moment-resisting structures

cam.supervisorMcRobie, Allan
dc.contributor.authorAthanasopoulos, Georgios-Spyridon
dc.description.abstractThis research further expands Graphic Statics and Graphic Kinematics methods that focus on moment-resisting structures such as frames and beams. With the use of Vector Algebra, the main method presented here, the Gamma Superimposition Assembly method, establishes a certain design-and-analysis framework for moment-resisting structures with the definition of load paths by the designer. The procedure presumes a particular architectural hypothesis. A brief historiographical narrative of the main contributions in the field of Graphic Statics is given together with a closer review of the contributions made since the re-emergence of the field more recently. Additions made by the author and others present the three main research axes to be followed: kinematics, frames, and topology investigation. Graph Theory and design parameters are introduced to decompose structural frames and lines of action of imposed forces in to sets of overlapping loops. The establishment of a strategy based on load path selection for representing a structure and its loads with a set of loops is argued. These loops will allow for an intuitive understanding of moments. The key method of this research is then introduced, the Gamma Superimposition Assembly method and its key feature, the Gamma loop is presented for the visualization of moments. These moments then take the form of bending and torsion with projections following Vector Algebra principles. An original method for drawing torsion is shown. The summation of loops generates a final diagram that informs the design in terms of structural members properties, such as suggested thicknesses and/or boundary conditions. This research suggests that support types can be the result of the method, rather than initially defined. Force distribution among different loops is then discussed in order to optimize maximum bending moments and make the structure more efficient. An example of a grillage structure where all implications are taken into account is developed. A simple example of applying the method to a more avant-garde architecture geometry is given. In kinematics, the Gamma Superimposition Assembly method is integrated within the conjugated beam method and with the visual explanation of the principle of Virtual Work with examples of applying non-parallel forces on parallel planes. Volumetric shapes constructed with the use of vector products represent the virtual and the real internal and external work and deflections and bending moment diagrams are used to show deformation angles. Extensions of Maxwell’s Load Path Theorem are presented in the context of 3D frames and examples are given on how to choose different load paths. Topology optimization and geometry design based on load paths are elaborated and conclude with the introduction of the Steiner Tree as a potential topology for structural morphologies with efficient load paths. The research finishes with a synopsis, conclusions, and a projection of the developed methods onto the realm of architectural and structural engineering applications and education today.
dc.publisher.collegeGonville and Caius
dc.publisher.institutionUniversity of Cambridge
dc.rightsAll Rights Reserved
dc.subjectGraphic Statics
dc.subjectGraphic Kinematics
dc.titleVector-product-based Graphic Statics and Graphic Kinematics for moment-resisting structures
dc.type.qualificationnameDoctor of Philosophy (PhD)
pubs.licence-display-nameApollo Repository Deposit Licence Agreement
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