If the support at B is removed, the reaction VB cannot occur, and the system becomes statically determinate (or isostatic). Note that the system is completely constrained here. The solution to the problem is
- ,
- ,
- .
If, in addition, the support at A is changed to a roller support, the number of reactions are reduced to three (without HA), but the beam can now be moved horizontally; the system becomes unstable or partially constrained. In order to distinguish between this and the situation when a system under equilibrium is perturbed and becomes unstable, it is preferable to use the phrase partially constrained here. In this case, the 2 unknowns VA and VC can be determined by resolving the vertical force equation and the moment equation simultaneously. The solution yields the same results as previously obtained. However, it is not possible to satisfy the horizontal force equation unless .
Statical indeterminacy is the existence of a non-trivial (non-zero) solution to the homogeneous system of equilibrium equations. It indicates the possibility of self-stress (stress in the absence of an external load) that may be induced by mechanical or thermal action.
Read more about this topic: Statically Indeterminate
Famous quotes containing the words statically and/or determinate:
“The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with cylinder oil, and coat their outsides with sprayed rubber film, and let them statically await the next emergency.”
—Norbert Wiener (1894–1964)
“When an image is said to be singular, it is meant that it is absolutely determinate in all respects. Every possible character, or the negative thereof, must be true of such an image.”
—Charles Sanders Peirce (1839–1914)