TABLE OF CONTENTS We have seen that the degree of statical indeterminacy of a structure is, in fact, the number of forces or stress resultants which cannot be determined using the equations of statical equilibrium. Another form of the indeterminacy of a structure is expressed in terms of its degrees of freedom; this is known as the kinematic indeterminacy, nk, of a structure and is of particular relevance in the stiffness method of analysis where the unknowns are the displacements.
A simple approach to calculating the kinematic indeterminacy of a structure is to sum the degrees of freedom of the nodes and then subtract those degrees of freedom that are prevented by constraints such as support points. It is therefore important to remember that in three-dimensional structures each node possesses 6 degrees of freedom while in plane structures each node possess three degrees of freedom.
Determine the degrees of statical and kinematic indeterminacy of the beam ABC shown in Fig. 16.10(a).
The completely stiff structure is shown in Fig. 16.10(b) where we see that M = 4 and N = 3. The number of releases, r, required to return the completely stiff structure to its original state is 5, as indicated in Fig. 16.10(b); these comprise a moment release at each of the three supports and a translational release at each of the supports B and C. Therefore,...
