Types of Supports and Restraints in Structural Analysis
In order to clearly understand the concept of indeterminacies, let us first discuss on supports and restraints. Most structures are either partly or completely restrained so that they cannot move freely in space. Such restrictions on the free motion of a body are called restraints and are supplied by supports that connect the structure to some external stationary body.
For example, consider a planar structure such as the bar AB shown in Figure (a). This bar would move freely in space with some combined translatory and rotational motion, if this bar were a free body and were acted upon by a force P. If a restraint were introduced in the form of a hinge that connected the bar to some stationary body at point A, then the motion of the body will be only of rotational movement about the hinge (Figure (b)). However, point B would move along an arc with point A as the center. Therefore, another restraint is required at B to prevent completely the free motion of the bar.
The supports at A and B, in restricting the free motion of the bar, are called upon to resist the action that the force P imposes upon them through the bar. The resistances method that is developed to counteract the action of the bar upon them are called as supports. The total effect of these supports may, therefore, be replaced by the reactions that they supply to the structure (Figure (c)). Any support would offer restraint and some degree of freedom; restraints may be replaced by reactions (force/moment) and degree of freedom may be represented by displacements (deflections/rotation).
The figure below shows the support reactions and degree of freedom for certain ideal conditions of structure member support. The constrained degrees of freedom can only develop reactions. For any support, the sum of the degree of freedom and support reactions is always 3 in 2D problems.