The Primary System
For statically indeterminate systems, M > N, and hence, we can augment (3) with I = M-N equations of the form:
The vector X is the so-called vector of redundant forces and I is the degree of statical indeterminacy of the system. We usually choose j, k, ..., and such that is a support reaction or an internal member-end force. With suitable choices of redundant forces, the equation system (3) augmented by (4) can now be solved to obtain:
Substitution into (2) gives:
Equations (5) and (6) are the solution for the primary system which is the original system that has been rendered statically determinate by cuts that expose the redundant forces . Equation (5) effectively reduces the set of unknown forces to .
Read more about this topic: Flexibility Method
Famous quotes containing the words primary and/or system:
“Europe has a set of primary interests, which to us have none, or a very remote relation. Hence she must be engaged in frequent controversies, the causes of which are essentially foreign to our concerns. Hence, therefore, it must be unwise in us to implicate ourselves, by artificial ties, in the ordinary vicissitudes of her politics or the ordinary combinations and collisions of her friendships or enmities.”
—George Washington (1732–1799)
“Television is an excellent system when one has nothing to lose, as is the case with a nomadic and rootless country like the United States, but in Europe the affect of television is that of a bulldozer which reduces culture to the lowest possible denominator.”
—Marc Fumaroli (b. 1932)