Flexibility Method - The Primary System

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:

$\mathbf{q}_{M \times 1} = \mathbf{f}_{M \times M} \Big( \mathbf{B}_R \mathbf{R}_{N \times 1} + \mathbf{B}_X \mathbf{X}_{I \times 1} + \mathbf{Q}_{v \cdot M \times 1} \Big) + \mathbf{q}^{o}_{M \times 1} \qquad \qquad \qquad \mathrm{(6)}$

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 .

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