%0 Conference Paper %1 forster2024structural %A Forster, David %A Baker, William F. %A Bischoff, Manfred %B Proceedings of the IASS 2024 Symposium Redefining the Art of Structural Design %D 2024 %E Block, Philippe %E Boller, Giulia %E DeWolf, Catherine %E Pauli, Jacqueline %E Kaufmann, Walter %K RP12-2 ibb %T Structural Analysis Using the Redundancy Matrix and Graph Theory %X Structural engineers often want to have a redundant structure where the loss of a member would not lead to structural collapse. For a truss, adding a bar beyond that required for static determinacy renders the structure redundant, but what is the spatial distribution of the static indeterminacy within the individual elements of a framework? Can an additional bar be redundant with several existing bars? Are there truss topologies and geometries that enhance redundancy? The assessment of structures based on such load-independent quantitative measures can be useful in early design stages to achieve an integrative planning process for designers and engineers. The degree of static indeterminacy and in particular its spatial distribution, quantified with the redundancy matrix can be used for assessing structural integrity of a framework. Focusing on structural properties independent of the individual member stiffness, such as geometry and topology, graph theory offers yet another tool to assess structural performance. This paper explores the integration of the Maxwell-Calladine count with the redundancy matrix from theoretical structural mechanics and with contributions of graph theory to explore a deeper understanding of structural redundancy.

@inproceedings{forster2024structural, abstract = {Structural engineers often want to have a redundant structure where the loss of a member would not lead to structural collapse. For a truss, adding a bar beyond that required for static determinacy renders the structure redundant, but what is the spatial distribution of the static indeterminacy within the individual elements of a framework? Can an additional bar be redundant with several existing bars? Are there truss topologies and geometries that enhance redundancy? The assessment of structures based on such load-independent quantitative measures can be useful in early design stages to achieve an integrative planning process for designers and engineers. The degree of static indeterminacy and in particular its spatial distribution, quantified with the redundancy matrix can be used for assessing structural integrity of a framework. Focusing on structural properties independent of the individual member stiffness, such as geometry and topology, graph theory offers yet another tool to assess structural performance. This paper explores the integration of the Maxwell-Calladine count with the redundancy matrix from theoretical structural mechanics and with contributions of graph theory to explore a deeper understanding of structural redundancy.}, added-at = {2024-10-18T08:41:03.000+0200}, author = {Forster, David and Baker, William F. and Bischoff, Manfred}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/21845cb371da86f36f9f780efb8186ab0/ibb-publication}, booktitle = {Proceedings of the IASS 2024 Symposium Redefining the Art of Structural Design}, editor = {Block, Philippe and Boller, Giulia and DeWolf, Catherine and Pauli, Jacqueline and Kaufmann, Walter}, interhash = {58ecd92b263e87cfb8149308ed98f10a}, intrahash = {1845cb371da86f36f9f780efb8186ab0}, keywords = {RP12-2 ibb}, timestamp = {2024-10-18T08:49:34.000+0200}, title = {Structural Analysis Using the Redundancy Matrix and Graph Theory}, year = 2024 }