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--- | ||
description: Intteractive Graphic Statics in 2D based on compas_ags | ||
--- | ||
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# Interactive 2D Graphic Statics (IGS2) | ||
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![](.gitbook/assets/plugin\_title\_slides\_compas\_ags.jpg) | ||
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## About | ||
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Graphic statics is a well-known method for analysis and design of two-dimensional structures based on Cremona’s extensions of Maxwell’s theory of reciprocal figures. In graphic statics, the relation between form and forces of a structural system is contained in the reciprocal relation between two diagrams. A form diagram describes the geometrical configuration of the (axial) internal and external forces of a two-dimensional structural system, and a force diagram represents their equilibrium. The combination of these two diagrams allows for an intuitive evaluation of structural behaviour, performance and efficiency at a glance. The graphical nature of the method furthermore allows for a visual verification of both the evaluation process and results \[3,4], making it more transparent than arithmetic or numerical methods. |
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# Table of contents | ||
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* [Interactive 2D Graphic Statics (IGS2)](README.md) | ||
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## quick start | ||
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* [Quick install](quick-start/quick-install.md) | ||
* [Dev install](quick-start/installation.md) | ||
* [Workflow + UI](quick-start/workflow-+-ui.md) | ||
* [Tutorial](quick-start/tutorial.md) | ||
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## theoretical background | ||
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* [Introduction](theoretical-background/0.-motivation.md) | ||
* [Algebraic graph statics (AGS)](theoretical-background/algebraic-graph-statics.md) | ||
* [Interactive AGS](theoretical-background/interactive-ags.md) | ||
* [Constraints in IGS](theoretical-background/constraints-in-igs.md) | ||
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## documentation | ||
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* [Known Issues](documentation/known-issues.md) | ||
* [Command API](documentation/command-api.md) | ||
* [User Manual](documentation/user-manual/README.md) | ||
* [0. Initialisation](documentation/user-manual/0.-initialisation.md) | ||
* [1. form graph](documentation/user-manual/1.-form-graph.md) | ||
* [2. force graph](documentation/user-manual/2.-force-graph.md) | ||
* [3. assigning forces](documentation/user-manual/3.-assigning-forces.md) | ||
* [4. solve equilibrium matrix](documentation/user-manual/4.-solve-equilibrium-matrix.md) | ||
* [5. update force graph](documentation/user-manual/5.-update-force-graph.md) | ||
* [6. reciprocal diagrams](documentation/user-manual/6..md) | ||
* [Settings](documentation/user-manual/settings.md) | ||
* [Extensions](documentation/user-manual/extensions.md) | ||
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## Examples | ||
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* [Triangulated Truss](examples/4.-triangulated-truss.md) | ||
* [Funicular arch](examples/2..md) | ||
* [Constant-force truss](examples/wip-gable-truss.md) | ||
* [Maillart truss form-finding](examples/2.-maillart-truss.md) | ||
* [Manual Force Control](examples/manual-force-control.md) | ||
* [Arch pointed load](examples/arch-pointed-load.md) | ||
* [Staircase](examples/staircase.md) | ||
* [Suspended Bridge](examples/suspended-bridge.md) | ||
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## Additional Information | ||
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* [Background](additional-information/background.md) | ||
* [Releases](additional-information/releases.md) | ||
* [Workshops](additional-information/workshops.md) | ||
* [Legal terms](additional-information/legal-terms.md) | ||
* [FAQ](additional-information/faq.md) | ||
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## links | ||
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* [compas\_ags code](links/compas\_ags-code.md) | ||
* [compas\_ags releases](links/compas\_ags-releases.md) | ||
* [compas\_ags issues](links/compas\_ags-issues.md) |
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# Background | ||
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IGS is an implementation of Algebraic Graphic Statics (AGS) developed by the Block Reseach Group. More background is available in the research page: | ||
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{% embed url="https://block.arch.ethz.ch/brg/research/algebraic-graph-statics" %} |
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# FAQ | ||
|
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# Legal terms | ||
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### 1. Definition of the Software | ||
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Interactive Graphic Statics (IGS) is a software package for performing 2D graphic statics using the Algebraic Graphic Statics (AGS). IGS was developed by the [Block Research Group](https://block.arch.ethz.ch/). | ||
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The “Software” shall be considered the compiled IGS plugin to the [Rhinoceros®](https://www.rhino3d.com/) software of Robert McNeel and Associates, Seattle, and the corresponding documentation to IGS. For the avoidance of doubt, Rhinoceros® shall not be considered part of IGS and/or the Software and it is the LICENSEE’s responsibility to obtain the necessary Rhinoceros® license. Source code shall not be considered part of the Software. | ||
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### 2. License of ETH Zurich | ||
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ETH Zurich hereby grants a single, non-exclusive, world-wide, royalty-free license to use Software subject to all the terms and conditions of this Agreement to the LICENSEE. | ||
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### 3. The Scope of the License | ||
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#### a. Use | ||
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The Software may be used for commercial and/or non-commercial purposes. The LICENSEE retains all rights to results from such use. The LICENSEE and/or its employees may use the Software by himself/themselves, only. | ||
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#### b. Reproduction | ||
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Reproduction is prohibited except for the provisions of the applicable law (article 21 URG \[Bundesgesetz über das Urheberrecht, SR 231.1]). | ||
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#### c. Modification | ||
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Neither modification, combination with other commercial applications or other preparation of derivative works of the Software, nor reverse engineering, decompilation, disassembly or other reduction of any portion of the Software is permitted except for the provisions of the applicable law (article 21 URG \[Bundesgesetz über das Urheberrecht, SR 231.1]). | ||
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#### d. Distribution | ||
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Assignment to a third party is prohibited. | ||
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### 4. Obligations of LICENSEE | ||
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### a. Use | ||
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Any report or publication of results obtained by the Software has to be acknowledged by citing the publication listed under article 1. | ||
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### 5. Intellectual property and other rights | ||
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Ownership and intellectual property rights in and to the Software shall remain in ETH Zurich. | ||
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ETH Zurich reserves the right to withdraw distribution privileges from any group, individual, or organization for any reason. | ||
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### 6. Maintenance, support, upgrades or new releases | ||
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ETH Zurich has no obligation of maintenance, support, upgrades or new releases and disclaims all costs associated with serving, repair or correction. | ||
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### 7. Warranty | ||
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The Software is provided “as is”. ETH Zurich does not make any warranty of any kind. The LICENSEE assumes the entire risk as to the results and performance of the SOFTWARE. Disclaimed warranties include for example: | ||
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* warranty of merchantability, satisfactory quality and fitness for a particular purpose | ||
* warranty of accuracy of results, of the quality and performance of the Software | ||
* warranty of noninfringement of the intellectual property rights of third parties. | ||
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The tool was developed to support the user in the form finding process of vaulted compression structures in the early design phase. It is obvious that prior to any realization of structures based on designs obtained with RV2, a detailed structural analysis is necessary. | ||
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### 8. Liability | ||
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ETH Zurich disclaims all liabilities. ETH Zurich shall not have any liability for any direct or indirect damage except for the provisions of the applicable law (article 100 OR \[Schweizerisches Obligationenrecht]). | ||
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### 9. Termination | ||
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In the case of fundamental breach through the LICENSEE, this Agreement may be terminated by ETH Zurich at any time. On termination all copies of the Software have to be destroyed. | ||
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### 10. Severability | ||
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If any provisions of this Agreement will become invalid or unenforceable, such invalidity or enforceability shall not affect the other provisions of Agreement which shall remain in full force and effect provided that the basic intent of the parties is preserved. The parties will in good faith negotiate substitute provisions to replace invalid or unenforceable provisions which reflect the original intentions of the parties as closely as possible and maintain the economic balance between the parties. | ||
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### 11. Applicable law | ||
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This Agreement as well as any and all matters arising out of it shall exclusively be governed by and interpreted in accordance with the laws of Switzerland, excluding its principles of conflict of laws. | ||
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### 12. Jurisdiction | ||
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If any dispute, controversy or difference arises between the Parties hereto in connection with or out of this Agreement, the parties hereto shall first attempt to settle it amicably. Should settlement not be achieved, the Courts of Zurich-City shall have exclusive jurisdiction. | ||
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**By using IGS, you indicate your acceptance of these legal terms.** |
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# Releases | ||
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The latest releases of IGS can be found in the GitHub repository release page: | ||
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{% embed url="https://github.com/BlockResearchGroup/compas-IGS/releases" %} |
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# Workshops | ||
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IGS is one of the tools used for the "Computational Structural Design I - 2021" course at ETH Zürich. The link for the course notes is provided below: | ||
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{% embed url="https://blockresearchgroup.gitbook.io/csd1-2021" %} | ||
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More workshops coming soon! |
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# Command API | ||
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The list with all commands possible in IGS is presented below: | ||
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![](<../.gitbook/assets/image (193).png>) |
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# Known Issues | ||
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## I can not initiate IGS | ||
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If you face problems to initiate IGS and receives the following message: | ||
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`Unknown command: 'IGS__init'` | ||
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Please try running the command `EditPythonScript` as this command activates the Python environment in Rhino. | ||
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Then close the pop-up window and try to initialise the plug-in again. | ||
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## My form/force diagram disappear | ||
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This is usually related to the fact that you initiated IGS in a different window or even that you initiated IGS before opening the file with the lines to work on. | ||
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Please close Rhino and start it again by initialising the plug-in. |
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# 0. Initialisation | ||
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For working with IGS in a Rhino session the plug-in must be initialised. The button Initialise IGS should always be pressed first to activate the commands.  | ||
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![](<../../.gitbook/assets/image (65).png>) | ||
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After pressing this button the following welcome window displays where the users are asked to accept our [Terms & Conditions](../../additional-information/legal-terms.md). |
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# 1. form graph | ||
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The input form diagram representing the structure should be a **planar graph** with leaf edges representing the boundary conditions (loads and supports). | ||
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This user manual gives a more detailed explanation of the [tutorial](../../quick-start/tutorial.md) developed to the single panel truss example represented in the image below: | ||
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![](<../../.gitbook/assets/image (39).png>) | ||
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## The input sketch | ||
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The structural problem above should be translated to **straight segments** in Rhino. The following shows the "sketch" that is necessary to create the form diagram. | ||
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![](../../.gitbook/assets/ags\_sequence-01.jpg) | ||
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As mentioned above, edges should be added to represent loads and boundary conditions. | ||
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## Form graph | ||
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![](<../../.gitbook/assets/image (3).png>) | ||
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Once this set of lines is inserted in IGS the leaf edges are lighlighted in green and internal edges are black. | ||
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A few rules should be observed to create this form graph. The graph should not contain overlaps, and it should not containt 2-valent nodes, as in the figure below: | ||
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![Highlight on invalid inputs for the form graph](<../../.gitbook/assets/image (100).png>) | ||
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## Directed form graph | ||
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![](../../.gitbook/assets/ags\_sequence-03.jpg) | ||
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Inside IGS, this graph is interpreted as a directed graph described by the matrix **C** defined below: | ||
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![](<../../.gitbook/assets/image (19).png>) | ||
|
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# 2. force graph | ||
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The form graph has a dual graph associated to it. This dual graph is defined below, and after the equilibrium is computed this dual graph transforms in the force diagram of the problem. | ||
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## Dual graph | ||
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The dual graph of the single panel truss is depicted below. It is created by following the spaces of the form diagram.  | ||
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![](../../.gitbook/assets/ags\_sequence-04.jpg) | ||
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This topology is also described by a connectivity matrix **C\*** defined below: | ||
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![](<../../.gitbook/assets/image (155).png>) | ||
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## Dual relationships | ||
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The following immage shows the form and the dual diagrams side by side. Both diagrams have the same **number of edges.** | ||
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![](<../../.gitbook/assets/image (116).png>) | ||
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The **faces** of the **force diagram** are related to **internal vertices** in the **form diagram** | ||
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![](../../.gitbook/assets/ags\_sequence-06.jpg) | ||
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With such relations, the equilibrium of each node of the form diagram is related to a **closed polygon in the force diagram**. The following images show these relation for the internal nodes of the form diagram: | ||
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![](../../.gitbook/assets/ags\_sequence-08.jpg) | ||
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![](../../.gitbook/assets/ags\_sequence-09.jpg) | ||
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![](../../.gitbook/assets/ags\_sequence-10.jpg) | ||
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![](../../.gitbook/assets/ags\_sequence-11.jpg) | ||
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![](../../.gitbook/assets/ags\_sequence-12.jpg) | ||
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## Diagram orientation | ||
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As obeserved above, the dual diagram will generate edges that are perpendicular to the original edge sin the form diagram. However, up to a rotation of 90˚ this relationship can be changed, and how instead of perpendicular the edges in equilibrium will be parallel. | ||
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![](../../.gitbook/assets/ags\_sequence-13.jpg) |
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# 3. assigning forces | ||
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## Independent Edges | ||
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The forces can only be freely assigned to certain number of edges in a given form diagram. The number of edges that can be freely loaded corresponds to the number of independent states of self-stress _k_ defined in Van Mele et al. (2014). In a graph the states of self stress are associated with the geometry by the following equation: | ||
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$$ | ||
k - t =m-2n_i | ||
$$ | ||
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where $$t$$ is the number of inextensibles mechanisms, $$m$$ is the number of edges in the form graph and $$n_i$$ is the number of internal vertices of the form diagram. For all the examples in this tutorial no inextensibles mechanisms exist $$t=0$$ , such that the number of independent edges can be computed simply by: | ||
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$$ | ||
k =m-2n_i | ||
$$ | ||
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In the examples below we compute the number of independent edges (or DOF) in the form diagrams. The edges highlighted in purple represent a possible selection of the independent/loaded edges. Note that any combination of edges (including internal edges) can be selected as independent in these problems, however, it is more convenient to select the applied loads as independent edges. Based on the number of independent edges in a pattern we can divide the structures usually studied with IGS in three types: | ||
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![](<../../.gitbook/assets/image (35).png>) | ||
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IGS checks the required number of independent edges via the button `Check DOF`.  | ||
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We will be interested specially in structures of type A (non-funicular) and C (funicular) which can be asociated with the figure below: | ||
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![](<../../.gitbook/assets/image (184).png>) | ||
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with the definition of the independent edges the equilibrium can be solved in the next step. |
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gitbook/documentation/user-manual/4.-solve-equilibrium-matrix.md
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# 4. solve equilibrium matrix | ||
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## Equilibrium through independent edges | ||
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The equations of equilibrium can be rearanged such that the equilibrium matrix **A** is defined as explained in the following chart: | ||
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![](<../../.gitbook/assets/image (13).png>) | ||
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Where **q** represent the force densities in the edges of the form diagram. With the definition of the equilibrium matrix the matrix A can be sliced and the forces in the dependent edges are calculated based on the forces assigned to the independent ones. | ||
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![](<../../.gitbook/assets/image (75).png>) | ||
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With such operations the new coordinates of the force diagram **x\***, **y\*** are computed. The update in the force graph is explained in the following section. |
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# 5. update force graph | ||
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The new coordinates of the force diagram computed through the [previous step](5.-update-force-graph.md) are then assigned to the repective nodes of the dual force graph [created in step ](2.-force-graph.md)2. As a result, the topology created is modified and both diagrams are [reciprocal](6..md). | ||
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![](../../.gitbook/assets/ags\_sequence-15\_reciprocation.gif) |
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# 6. reciprocal diagrams | ||
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Reciprocal diagrams respect the following: | ||
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* All corresponding edges in form and force diagram are parallel. | ||
* The length of the edges in the force diagram correspond to the magnitude of the forces in the form diagram.  | ||
* The nodes of the form diagram are represented by closed polygons in the force diagram. | ||
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![](<../../.gitbook/assets/image (178).png>) |
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# User Manual | ||
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The User Manual goes through the steps of IGS in depth explaining what's happening in the backgroud of the engine at each step.  |
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# Extensions | ||
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Future extensions of IGS will include: | ||
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* Optimisation features | ||
* Additional functions and visualisation setttings | ||
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If you wish to contribute look at our [GitHub](https://github.com/BlockResearchGroup/compas-IGS) page. |
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# Settings | ||
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The following Settings can be modified in IGS, this menu is activated by the button `Settings` in the toolbar. | ||
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![](<../../.gitbook/assets/image (66).png>) | ||
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## General settings | ||
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The general setings can be modified: | ||
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* **autoupdate:** It updates form and force diagrams automatically after a modification is imposed in one of them. The default value is off. | ||
* **bi-directional:** It activates the module to perform modification on both diagrams after constraints are applied. | ||
* **max\_deviation:** Sets the maximum deviation allowed by the program. If the angle deviations are higher than this parameter warnings will show in the screen. | ||
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## Form display settings | ||
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The display settings can be modified for the form diagram, such as: | ||
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*  **colors:** the default colors used can me modified by the user. | ||
* **show:** a series of addititonal visualisation settings can be turned on or off by the user. Options include showing thicker pipes on the edges, displaying edge/vertex labels, etc.  | ||
* **scale of force-pipes:** The scale of the force pipes can be set directly on this FormObject display setting. | ||
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## Force display settings | ||
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The display settings can be modified for the force diagram, such as: | ||
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*  **colors:** the default colors used can me modified by the user. | ||
* **show:** a series of addititonal visualisation settings can be turned on or off by the user. Options such as displaying edge/vertex labels, etc.  | ||
* **rotate:** The force diagram can be rotated of 90 degrees, such that reciprocal edges are perpendicular instead of parallel. |
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