Saving appearances: treatment of anomalies in the projective geometry- graphic statics analogy скачать в хорошем качестве

Saving appearances: treatment of anomalies in the projective geometry- graphic statics analogy

Parallel Session 6, Graphic Statics Thomas Boothby & Nathan Brown from Penn State University, US & Annalisa Crannell from Franklin & Marshall College, US, present their work on projective geometry and graphic statics. The relationship between projective geometry and graphic statics can be developed and extended by considering the construction of the funicular polygon from the force polygon as a projective correlation (an incidence-preserving transformation from points to lines and lines to points). Similarly, transformations between two admissible funicular polygons in a concurrent force system is a projective collineation (an incidence-preserving transformation from points to points and lines to lines). For concurrent force systems, the understanding that the collineation between funicular polygons is a homology facilitates the construction of alternative funicular polygons, the composition of components of a force and the resolution of forces into components. For non-concurrent systems, the relation between funicular polygons is a product of more general projective transformations. The application of these transformations can facilitate finding an equivalent system of concurrent forces. Projective transformations can reduce some significant graphic statics problems to simple exercises in geometry. Examples include analysis of masonry arches and analysis of hybrid axial force/bending systems. Watch their presentation on "Saving appearances: treatment of anomalies in the projective geometry-graphic statics analogy" from the Spatial Structures 2020/21 Conference. #IASS #IASS2020_21 #SpatialStructures #Architecture #Structures #Engineering #LightweightStructures #CivilEngineering #StructuralEngineering #Conference #Construction #computationaldesign #nextgeneration #parallelsessions #US #Pennsylvania #funicularpolygons