Vector-Based 3D Graphic Statics: Transformations of Force Diagrams

The reciprocity between form and force diagrams in 2D graphic statics makes it possible to manipulate the form diagram while directly evaluating the redistribution of the forces within the force diagram. Conversely, after modifying the force diagram, the consequent transformation of the form diagram can be assessed at once. In the case of vector-based 3D graphic statics, the reciprocity between the diagrams is generally not achieved. This paper describes a series of transformations that can be applied to a vector-based 3D force diagram while allowing the corresponding 3D form diagram to adjust accordingly. Two categories of manipulations of the force diagram are described: global transformations that affect simultaneously all the elements of the diagram and local transformations, which permit the manipulation of individual elements of the diagram. Thanks to these transformations, the adjustment of the magnitude and the direction of the forces in vector-based 3D force diagrams can be used as an active operation in the structural design process

A novel progressive grid generation method for free-form grid structure design and case studies

Due to its high structural efficiency and aesthetics, free-form grid structures have been widely used in various public structures. However, it is neither a convenient nor an obvious task for engineers to create a discrete grid on a free-form surface that manifests the architect's intent. This paper presents an efficient design approach based on Coulomb's law to generate well-shaped and fluent grids for free-form grid structural design. In the method, nodes of the grid structure are considered to be interacting particles in an electric field and are added to the surface in a progressive way. The nodal position is determined by Monte Carlo simulation and the grid is generated by connecting the particles that are already in equilibrium. According to the different ways of adding particles, two variations of the method are introduced in this paper: point-based progressive method (PBPM), and curve-based progressive method (CBPM). Case studies are provided to demonstrate the effective execution of the proposed method. The results show that the proposed method can effectively avoid mapping distortion and generate grids with regular shape and fluent lines to meet the aesthetic requirements. Furthermore, the proposed method provides flexible control over the direction and size of the grid, which gives architects a more flexible choice

Cross-Reactivity in the Histoplasma Antigen Enzyme Immunoassay Caused by Sporotrichosis ▿

Several endemic mycoses cause cross-reactions in the Histoplasma antigen enzyme immunoassay. Herein, a positive Histoplasma antigen result has been recognized in a patient with sporotrichosis

A geometrical approach to assess levels of structural robustness in statically indeterminate concrete elements

Graphic statics represents a powerful tool in the field of structural design, because the reciprocity between form and force diagrams allows for a constant and simultaneous control of both the geometry and the magnitude of internal forces. Used by Robert Maillart in the early 20th century for bridge design, the method has been improved in the last decades thanks to its implementation within interactive parametrical software. This allows overcoming the relative obsolescence of graphic statics in terms of speed with respect to analytical and numerical methods. Graphic statics has recently been extended by Corentin Fivet [1], who has developed solution spaces for the points of the force diagram. These solution spaces show the set of structural forms in which equilibrium, boundary and yield conditions are fulfilled. When employed within the context of robustness assessment, these solution spaces can also be used as admissible geometrical domains, indicating the range of alternative force distributions that can be activated in the structure in case of damage [2]. Pursuing the ongoing research [3], this paper tackles using statically indeterminate strut-and-tie networks to model forces inside continuous reinforced concrete structure. These strut-and-tie networks take the shape of an orthogonal square mesh with 45° diagonals, representing potential rebar positions in concrete. Several damage scenarios are obtained by deleting one or more bars from the initial mesh; the associated admissible geometrical domains indicating potential force redistributions are drawn in each case. Ratios are then extracted from the comparison of admissible geometrical domains obtained for both intact and damaged cases, showing the structure’s level of ability to survive unexpected damage. The influence of several structural design concerns (such as geometry, material properties and reinforcement layout) on the possibility of force redistributions is finally outlined and depicted graphicall