Abstract
This chapter deals with forces and couples and recalls the basic laws of static equilibrium. We emphasize the important concept of equivalent forces and show that a system of forces is in static equilibrium if it is statically equivalent to zero. In other words, a system of forces is in static equilibrium if it is equivalent to no forces at all. We also postulate the existence of internal forces, better known as stresses, without which the principles of equilibrium do not make sense. There are a myriad of internal forces which come in pairs; no-one has ever seen them, but these forces are essential for equilibrium.
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Notes
- 1.
S.O. Asplund, Structural Mechanics: Classical and Matrix Methods, Prentice-Hall, Englewood Cliffs, N.J., 1966 (A leading book on contemporary structural analysis).
- 2.
Here and throughout this text we deal with plane structures and forces.
- 3.
A mechanism is a body whose shape can significantly be changed by very small forces, for example a pair of scissors.
- 4.
A free body is a free-floating structure or part of a structure.
- 5.
We differ here from the convention used in continuum mechanics where the positive facet is the one with its outer normal in the direction of x.
- 6.
For the reconstruction of the actual internal stresses from the stress resultants nsm(x) the reader is referred to treatises on Strength of Materials or Solid Mechanics.
- 7.
If \(\text {d}x\) is, for instance, of the order of \(10^{-100}\) then the last term is of the order of \(10^{-200}\), that is, the last term is \(10^{-100}\) smaller than the other terms.
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© 2016 Springer International Publishing Switzerland
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Fuchs, M.B. (2016). Equilibrium. In: Structures and Their Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-31081-7_1
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DOI: https://doi.org/10.1007/978-3-319-31081-7_1
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