Most of the algorithms are based on the research done by Block Research Group () and Polyhedral Structures Laboratory (). With this digital tool architects, engineers, students and researchers can create a parametrically driven system that is able to generate optimal structures of a particular aesthetics. For the expanded equation, each coefficient of the i, j, and k unit vectors must equal zero for static equilibrium.
The plug-in provides components for subdividing polyhedral cells, form-finding processes, computing forces, generating cross sections, etc. The main goal of developing this tool was to automate the process of generating force diagrams, to rapidly examine different design solutions as well as to explore the possibilities of connecting 3D Graphic Statics with other Grasshopper tools. This engineering statics tutorial introduces the concept of static equilibrium. The intensity of the force in the rod is proportional to the area of the brep face, while the orientation is generated iteratively until its direction coincides with the normal vector of the face. In a 3D world, a system will be in static equilibrium if it’s sum of forces i. Two polyhedral cells sharing the same brep face are equal to two adjacent nodes, interconnected by the rod. In short, the force diagram is represented as a set of closed convex polyhedral cells, and each polyhedron represents one node (within the form diagram). This force does not cause any change in the state, position, or shape of the car or the bridge. A car resting on a bridge exerts a considerable amount of force and pressure on the contact surface between the bridge and the car. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing. A paperweight on a desk is an example of static equilibrium. Therefore, designers have direct control over the form and the forces at the same time. Hence, the weight of a body is a prominent example of a static force. A stationary object (or set of objects) is in 'static equilibrium,' which is a special case of mechanical equilibrium. The change in one diagram will affect the geometry in other. In 3D graphic statics, the static equilibrium of structures is described by using two reciprocal diagrams and their geometric relationship – form and force.
3D Graphic Statics is a structural form-finding method for generating compression-only funicular structures.
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