Statically Indeterminate Structures : Degree Of Redundancy
The above facts will be made clear through the following three examples of statically indeterminate structures.
The simplest example of such a structure is the so-called propped cantilever shown in Figure 1. You know that a cantilever fixed at A and free at the end B is a stable structure as it provides three support reactions VA, HA and MA at the fixed end A which is capable of supporting any loading on the cantilever and can be determined by using the three equilibrium equations.
Figure: Propped Cantilever
Thus, it is a statically determinate structure. Now, if we provide an additional roller support at B, this causes one further constraint condition on the beam through not allowing it to freely deflect at this end. That induces a vertical reaction VB at the roller end. The propped cantilever has now four constraints. At the fixed end A it is denial of both horizontal and vertical displacements and also of any rotations of the beam (3 constraints) and at the end B it is preventing of any vertical deflection (1 constraint). Thus, we find that there are four corresponding reactions: VA, HA, MA and VB, while the equations of statics are three only, hence they cannot be determined by using these equations only.