Elastic Stresses in Structures

Abstract

Many of the modern methods of structural analysis based on concepts of virtual work and energy were developed and popularised in Italy in the latter half of the nineteenth century. Building on the work of Luigi Menabrea, the mathematician Carlo Alberto Castigliano (1847–84) provided the first full proof of these methods in his 1873 dissertation while based in Turin. Equally important was his popularisation of the theory in his Théorie de l'équilibre des systèmes élastiques et ses applications (1879), in which he applied his theory to a wide range of important real-world cases. The work is here reissued in its 1919 English translation, by the consulting engineer and lecturer Ewart S. Andrews. Castigliano covers the basic theory of elastic stresses, introducing useful approximations; he then moves on to the analysis of real structures, including roof trusses, arches and bridges in both iron and masonry.

A review of experimental investigations and assessment methods for masonry arch bridges

“…A program known as CTAP was developed at the University of Cardiff starting from the elastic approach initially proposed by Castigliano (1996). In order to determine the thrust line and the loadcarrying capacity, tensile zones in the arch ring are eliminated, which results in progressive development of hinges, and loads are applied until the ultimate limit state is reached, and therefore the actual collapse load cannot be determined exactly as it lies between the last two load increments.…”

Buckling Assessment in the Dynamics Mechanisms, Stewart Platform Case Study: In the Context of Loads and Joints, Deflection Positions Gradient

“…This uncovers that the dynamic arm can exhibit critical deflection and stress at a range of the arm sections. The platform arm is assumed to be a column applying Euler's formula for buckling deflections [21][22][23] as a foundational tool and also aligned with Castigliano's theorem to find a deflection of the elastic structure [24]. This approach provides a transparent stream for designing the Stewart platform multi-element arm concerning the joints' location among the arm and not being at critical deflection sections.…”

Hierarchical Sliding Mode Algorithm for Athlete Robot Walking

“…We introduce the following notations: Behavior of elastic leg is determined by Castigliano's Theorem [24] which provides a good tool for analyzing forces on curved components. AR can be regarded as an equivalent inverted pendulum in Figure 6 where the elastic legs are equivalent to springs.…”