Published online by Cambridge University Press: 05 June 2012
At this point, all that is available for the purpose of accomplishing a general structural analysis are the three equilibrium equations, Eqs. (1.6). These equations pertain to the stress state in a general structural body subjected to a general mechanical loading (including dynamic loads) and a temperature change. These three equations are insufficient to deduce the six stresses that define the stress state. Since the reader's ambition and good sense require nothing less than a complete set of equations that are applicable to a structure of any shape or material, as well as any loading, it is necessary to look beyond equilibrium considerations in order to describe fully the response of a general structural body. The two other physical phenomena that need to be investigated in order to obtain additional equations are the geometry of the deformations of the general structure, and the response of materials to mechanical and thermal loadings. Descriptions of the deformations of loaded structures are the focus of this chapter and Chapter 4. Chapters 5 and 6 discuss the response of structural materials to loadings and temperature changes.
The general concept of a displacement is simply that of a movement; a change in position that has been completed or is in progress. The change in position involves both a direction and a distance. Thus a displacement is defined as a vector quantity. For engineering purposes, the displacement concept must be susceptible to precise description and measurement.