Statically Indeterminate Structures : Degree Of Redundancy

The above facts will be made clear through the following three examples of statically indeterminate structures.

Propped Cantilever

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 V_A, H_A and M_A 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 V_B 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: V_A, H_A, M_A and V_B, while the equations of statics are three only, hence they cannot be determined by using these equations only.