A Practical Guide to Graphical Statics (original) (raw)
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International Journal of Solids and Structures, 2019
This article develops a vector-based 3D graphic statics framework that uses synthetic and intuitive graphical means for the analysis and design of spatial structures such as networks of bar elements in static equilibrium. It is intended to support the collaborative work of structural engineers and architects from the conceptual phase of the design process. Several procedures for the construction of a vector-based 3D force diagram for any given 3D form diagram with an underlying planar or non-planar graph are identified and described. In the non-planar case, the proposed procedures rely on the preliminary topological planarization of the graph by cutting the crossing edges and reconnecting them to one or more newly inserted auxiliary vertices. The resulting planar graph can be then used as a base for the assembly of the 3D force diagram, without altering the static equilibrium of the structure. An implementation of the proposed framework to real design scenarios is presented through two case studies. These examples show how to take advantage of the bi-directional manipulation of the diagrams in the structural design process.
Proceedings of the 34th Annual Conference of the Association for Computer Aided Design in Architecture (ACADIA)
This paper discusses the interactive design exploration of static equilibria using constraint-based graphic statics. Constraint-based graphic statics is a computerized framework improving the construction, the control and the capabilities of classical graphic statics substantially. It allows the designer to shape any flow of forces interactively by means of successive purely graphical operations applied either on a diagram representing its form or on another diagram representing its vectorial equilibrium. The first chapter contextualizes the essential role of this tool by expressing a critique about contemporary structural CAD tools and the narrow design chronology they impose. The paper then briefly browses the various key concepts and operations of constraint-based graphic statics. The last chapter highlights the various capabilities and benefits of this tool through a case study. As a conclusion, the paper illustrates how this fully graphical approach breaks new ground in terms of design chronology (for example, the parametric hierarchy can be freely reorganized), visual feedback and dynamic control over mechanical considerations.
Drawing and using free body diagrams: Why it may be better not to decompose forces
Physical Review Special Topics - Physics Education Research, 2015
In this study we investigated how two different approaches to drawing free body diagrams influence the development of students' understanding of Newton's laws, including their ability to identify real forces. For this purpose we developed a 12-item two-tier multiple choice survey and conducted a quasiexperiment. This experiment included two groups of first-year physics students from Rijeka (RG) (n e ¼ 27) and Split (SG) (n c ¼ 25) Universities. Students from both groups solved mechanics problems for a period of two class hours. The only difference was that RG students used the superposition of forces approach to solving mechanics problems and in SG the decomposition of forces approach has been used. The ANCOVA (n c ¼ 17, n e ¼ 17) showed a statistically significant difference in favor of RG, whereby the effect sizes were moderate to large, and the largest differences have been observed in the ability of identifying real forces. Students from the control group (SG) more often exhibited the misconception that forces and their components act on a body independently and simultaneously. Our results support the idea that the practice of resolving forces into the components may not be the most effective way to develop understanding of Newton's laws and the concept of force.
Physical Review Special Topics - Physics Education Research, 2013
Earlier research has shown that after physics instruction, many students have difficulties with the force concept, and with constructing free-body diagrams (FBDs). It has been suggested that treating forces as interactions could help students to identify forces as well as to construct the correct FBDs. While there is evidence that identifying interactions helps students in quantitative problem solving, there is no previous research investigating the effect of a visual-representation tool-an interaction diagram (ID)-on students' ability to identify forces, and to construct the correct FBDs. We present an empirical study conducted in 11 Finnish high schools on students (n ¼ 335, aged 16) taking their first, mandatory, introductory physics course. The study design involved groups of students having heavy, light, or no use of IDs. The heavy and light ID groups answered eight pairs of ID and FBD questions in various physical contexts and the no ID group answered two of the eight FBD questions. The results indicate that the heavy ID group outperformed both the light and the no ID groups in identifying forces and constructing the correct FBDs. The analysis of these data indicates that the use of IDs is especially beneficial in identifying forces when constructing FBDs.
Learning Statics by Visualizing Forces on the Example of a Physical Model of a Truss
Buildings, 2021
The article presents a new didactic tool helping in teaching the structures of students of the Faculty of Architecture. It is an attempt to solve the problem related to the difficulties in teaching structural systems among students of architecture. In the beginning, examples of Graphic-Statics tools supporting an intuitive understanding of the construction work are presented. Then a physical model of the truss was implemented, which responsively presents the values of internal forces using the colors of the luminous bars. The main part of the article describes the design elements of the truss model and presents how it works. Then, the influence of the model on the education of architecture students was checked by means of a questionnaire study. The results showed the great educational usefulness of the proposed solution.
Teaching and Assessing Polygons Using Technolgy
International Journal For Technology in Mathematics Education, 2011
Using dynamic geometry software to teach geometry can transform the way we approach teaching and learning. Meaningful technology based tasks allow students to discover mathematics on their own and construct their own understanding. Furthermore, they require active engagement of students and encourage higher level thinking. They challenge students to think about mathematical ideas in a new light. In the following article we will show how technology helped us create an engaging learning environment for a unit on Polygons as well as share strategies that have helped us implement technology effectively. Through various age appropriate activities students explore polygons and their properties, make conjectures, test them, reason about geometric ideas as well as demonstrate understanding and ability to apply their knowledge of polygons. For every lesson we prepare a "Sketchpad notebook". This "notebook" contains basic theory, a few solved examples (step by step), as well as problems for individual exploration/learning. Class usually begins with a discussion and a presentation of examples followed by individual work by students. At that time, we introduce new terminology and concepts students are not able to discover on their own. Then students work independently or in pairs on the assigned tasks (see figure 1 and figure 2).
2018
Through observations, pupils found it difficult to understand the fundamental concepts of equilibrium of force and its resolution. Disadvantages are increasing when they are exposed to the resolution of force on the x-axis and y-axis that are completely unfamiliar to themselves. If they fail to determine the direction of the forces involved, then they will have difficulty resolving the question of force-resolution. Overall, the problems faced by students are as follows: a. The students cannot determine the direction of force acting on the stationary object on a horizontal plane and inclined. b. The pupils cannot determine the direction of force acting on the stationary object on a horizontal plane and inclined. c. Students can not resolve the forces acting into its components d. Students face difficulties to solve questions about forces in equilibrium well The concepts introduced through the teaching tools I FORCE and I FORCE TABLE are based on Hands On Activity, Problem Based Learning (PBL), 21st Century Learning and learning strategies involving Visual, Audiotary and Kinestatic students (VAK) students as well as apply the concept of color. The instructional, I FORCE and I FORCE TABLE instructional tools are a new method that has never been developed by any individual or educational institution.