Abstract
In this chapter we will apply virtual work using equilibrium systems and compatible systems taken from a same real structure. For every deformed shape of the structure we can derive an equilibrium system and a compatible system. Taking the equilibrium system from one deformed shape and the compatible system from another deformed shape, and vice versa, will eventually lead to Betti’s reciprocal theorem and to Maxwell’s flexibility coefficients.
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Notes
- 1.
Depending on the nature of v(x), the loads can comprise point forces and couples as well as distributed loads. Also, you can add a rigid-body motion to the imposed displacements without affecting the curvatures and the forces.
- 2.
We also use \(F_{ij}\) for the components of the flexibiliy matrix.
- 3.
JH Argyris, Energy Theorems and Structural Analysis, Part I. General Theory, Structures 347–394, Oct 1954.
- 4.
As we shall see in a statically determinate structure we can compute nsm(x) by means of equilibrium only.
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© 2016 Springer International Publishing Switzerland
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Fuchs, M.B. (2016). Flexibility Coefficients. In: Structures and Their Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-31081-7_10
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DOI: https://doi.org/10.1007/978-3-319-31081-7_10
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Online ISBN: 978-3-319-31081-7
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