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:
“A fact is a proposition of which the verification by an appeal to the primary sources of our knowledge or to experience is direct and simple. A theory, on the other hand, if true, has all the characteristics of a fact except that its verification is possible only by indirect, remote, and difficult means.”
—Chauncey Wright (18301875)
“Our system of government, in spite of Vietnam, Cambodia, CIA, Watergate, is still the best system of government on earth. And the greatest resource of all are the 215 million Americans who still have within us the strength, the character, the intelligence, the experience, the patriotism, the idealism, the compassion, the sense of brotherhood on which we can rely in the future to restore the greatness to our country.”
—Jimmy Carter (James Earl Carter, Jr.)