External post-tensioning

Structures that behaves according to their shapes are characterized by the close and inseparable relationship between geometry and structural behavior. Therefore, the choice of an appropriate geometry is the indispensable previous step in the conceptual design of these structures.


In this task, the selection of possible antifunicular geometries for the most common permanent load distributions are rather limited and, many times, non-structural criteria (functional adaptability, aesthetics, construction process, etc.) do not allow their use in order to guarantee the maximum use of the material.

In this context, this research studies the possibility of obtaining a structure without bending moments even if the geometry is not antifunicular for its permanent loads.

Indeed, this work presents a procedure, based on graphic statics, which demonstrates how a set of additional loads, introduced through an external prestressing system with post-tension elements, can eliminate the bending moments due to permanent loads at any plane geometry. This results to be an antifunicular structure that provides innovative answers related to architectural versatility and material optimization.

This graphic methodology has been implemented through a freely distributed software (EXOEQUILIBRIUM), where the structural analysis and geometric variation are included in the same interactive and parametric environment. The use of these tools allows more versatility in the research of new efficient forms, which is of great importance in the conceptual design of structures, let the engineer free from the limitation of the calculation and from the misunderstanding of structural behavior.



This research includes the application of these procedures to structures of any geometry and initial load distribution, as well as the study of different possible design criteria to optimize the position of the post-tensioning system. In addition, the methodology has been used in the project of models on a reduced scale and in the construction of a pavilion made entirely of cardboard, which has allowed obtaining a physical validation of the developed procedure.

In essence, this thesis significantly expands the range of possible antifunicular geometries and it opens up enormous possibilities for the design of structures that combine structural efficiency and architectural flexibility.



Todisco, L; Stocks, E; León, J; Corres, H

Enhancing the Structural Performance of Masonry Structures by Post-Tensioning Journal Article

Nexus Network Journal, pp. 1–21, 2018.

Abstract | Links | BibTeX


Todisco, Leonardo; Mueller, Caitlin

Externally post-tensioned structures : Validation through physical models Inproceedings

International Conference on Structures and Architecture, pp. 1144–1151, 2016, ISBN: 9781138026513.


Todisco, Leonardo

Funicularity and Equilibrium for High-Performance Conceptual Design PhD Thesis

Technical University of Madrid, Spain, 2016.

Links | BibTeX

Todisco, Leonardo; Corres-Peiretti, Hugo; Mueller, Caitlin

Funicularity through External Posttensioning : Design Philosophy and Computational Tool Journal Article

Journal of Structural Engineering, 142 (2), pp. 1–9, 2016, ISSN: 978-90-5363-042-6.

Links | BibTeX


Todisco, L; Fivet, C; Corres-Peiretti, H; Mueller, C

Design and exploration of externally posttensioned structures using graphic statics Journal Article

Journal of the International Association for Shell and Spatial Structures, 56 (4), pp. 249–258, 2015.

Abstract | BibTeX