On the thrust line of piecewise-linear-elastic continuous funicular structures

Ranaudo F., Van Mele T. and Block P.
Proceedings of the IASS/APCS 2022 Symposium
Beijing
2022

Thrust Line Analysis (TLA) is a powerful graphical method for the assessment of the stability of compression-only structural systems. TLA can also be used for the design of two-dimensional funicular structures by aligning the centreline of the structure to the trust line of the given loads. Structures designed in such a way are in a state of uniform compressive stresses under the given loads, making full use of the section’s capacity, and therefore very efficient. Nevertheless, TLA only provides the correct solution for structures made of multiple discrete elements (e.g., voussoirs) or for continuous but statically determinate systems. When a continuous structure is statically indeterminate (such as a two-hinged arch, for example, made of concrete), the actual thrust line, sometimes called True Thrust Line and in this paper referred to as Elastic Thrust Line (ETL), deviates from the structure’s centreline, generating bending moments that induce tension and could potentially lead to unwanted cracks. This paper discusses the derivation of the ETL of generic continuous statically indeterminate elastic systems and presents an extension of the traditional TLA method to piecewise-linear-elastic continuous structures. Combining elastic theory and graphic statics, it provides an easy, fast, and insightful method for the design of new funicular structures. Examples of applications to the design of funicular structures are also presented and discussed.