Statically indeterminate structure

Definition

Consider a structure in the linear (small displacement) setting. Let its $n$ unknown static quantities, the support reactions and the internal member forces, form a vector $t \in \R^n$. Let $m$ independent equilibrium equations relate them to the applied loads $f \in \R^m$ in the form $B t = f$, with an $m \times n$ equilibrium matrix $B$. Assume that the structure is not a mechanism, that is, $B$ has rank $m$, so every load can be balanced. The structure is statically determinate if $n = m$, so that $t = B^{-1} f$ is fixed by equilibrium alone. It is statically indeterminate if $n > m$, and its degree of static indeterminacy is $n - m$, the dimension of the kernel of $B$.