TABLE OF CONTENTS In some cases the degree of statical indeterminacy of a structure is obvious from inspection. For example, the portal frame in Fig. 16.1 has a degree of external statical indeterminacy of 3, while the truss of Fig. 4.7(b) has a degree of internal statical indeterminacy of 1. However, in many cases, the degree is not obvious and in other cases the internal and external indeterminacies may not be independent so that we need to consider the complete structure, including the support system. A more formal and methodical approach is therefore required.
The simplest approach is to insert constraints in a structure until it becomes a series of completely stiff rings. The statical indeterminacy of a ring is known and hence that of the completely stiff structure. Then by inserting the number of releases required to return the completely stiff structure to its original state, the degree of indeterminacy of the actual structure is found.
Consider the single ring shown in Fig. 16.2(a); the ring is in equilibrium in space under the action of a number of forces that are not coplanar. If, say, the ring is cut at some point, X, the cut ends of the ring will be displaced relative to each other as shown in Fig. 16.2(b) since, in effect, the internal forces equilibrating the external forces have been removed. The cut ends of the ring will move relative to each other in up to six possible ways until a new...
