Abstract
Virtual Work is a concept which will help us to develop most of the properties and methods pertaining to the theory of structures. In parallel with ‘equilibrium systems’ between external and internal loads (Chap. 1), we independently construct ‘compatible systems’ composed of deformations which result from displacements. It is shown that the virtual work of the external loads through the displacements is equal to the virtual work of the internal forces through the deformations. This is the principle of virtual work. The concept is illustrated with simple examples of discrete particles, and is further developed for a beam segment under continuous and point loads undergoing an arbitrary displacement.
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Notes
- 1.
In what follows we will not construe anything from the fact that this product was called work. We could have called it ‘virtual melody’ and discuss the virtual melody of a force.
- 2.
On the right-hand side we have in fact minus the work of the internal forces, however it is commonly called the internal virtual work.
- 3.
This is in fact minus the work of the internal forces but in line with probably most authors we call it simply ivw.
- 4.
For clarity, the figure depicts only the lateral components, that is, s for the internal forces, and q and Q for the external forces.
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© 2016 Springer International Publishing Switzerland
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Fuchs, M.B. (2016). Virtual Work. In: Structures and Their Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-31081-7_3
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DOI: https://doi.org/10.1007/978-3-319-31081-7_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-31081-7
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