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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 Theorie de l'equilibre des systemes elastiques 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.