| Abstract | Prostorna grafostatika bavi se rješavanjem statičkih problema u trodimenzionalnom prostoru. Ovaj rad analizira ključne aspekte prostorne grafostatike, definirajući osnovne pojmove kao što su točke, pravci, ravnine i sile. Naglasak je, vidljivo u primjerima, stavljen na zamjenu složenih sustava statički ekvivalentnim sustavima.
Teorijsko-metodološko polazište je analiza dostupne literature. Izrazi u teorijskom dijelu, pomoću Grassmannove algebre, prevedeni su u programski kod, pisan u Sage-u, koji znatno olakšava vizualizaciju.
Osim već navedenih pojmova točke, pravca, ravnine i sile, u radu su opisani i pojmovi Grassmannove algebre koja proučava svojstva višedimenzionalnih prostora, homogenih i Plückerovih koordinata kao i trodimenzionalnog projektivnog prostora te dualnosti koju vežemo s projektivnom geometrijom. Svi navedeni pojmovi čine neizostavne dijelove koji povezani u cjelinu čine da prostorna grafostatika u građevinarstvu, ali i u drugim srodnim strukama, omogućava bolje razumijevanje struktura pod različitim opterećenjima. |
| Abstract (english) | 3D graphic statics deals with solving static problems in three-dimensional space. This paper analyzes key aspects of 3D graphic statics, defining basic terms such as points, lines, planes and forces. The emphasis, as seen in the examples, is placed on replacing complex systems with statically equivalent systems.
The theoretical-methodological starting point is the analysis of the available literature. Expressions in the theoretical part, using Grassmann algebra, have been translated into program code, written in Sage, which significantly facilitates visualization.
In addition to the previously mentioned concepts of points, directions, planes and forces, the paper also describes the concepts of Grassmann algebra, which studies the properties of multidimensional spaces, homogeneous and Plücker coordinates, as well as three-dimensional projective space and duality associated with projective geometry. All these concepts form indispensable parts that, when connected into a whole, allow 3D graphic statics in construction, but also in other related professions, to provide a better understanding of structures under various loads. |
