Determining the support reactions
Let us consider some examples. Example 1. Determine the support reactions of the cantilever beam (Fig. 5.3 a). Solving. Represent the reaction of the patching up in the form of two forces
a) b) Fig. 5.3.
Compose the beam equilibrium equation. 1. Equal the projection sum of all forces on the axis Z acting on the beam to zero: 2. The same is for
from where we have
The vertical component reaction of the cantilever beam is equal to the force sum applied to the beam. 3. Compose the third equilibrium equation. Equal the moment sum of all forces about the some point to zero, for example, about the point A:
from which
The minus sign indicates that the accepted previously direction of the reaction moment has to be changed in the opposite direction. So, the reaction moment is equal to the moments sum of the external forces about the patching up. Example 2. Determine the support reaction of the simple beam (Fig. 5.3 b). Solving. Since the horizontal load is lacking, then Az = 0.
1. 2.
|
and 
directed as indicated in Fig. 5.3 a and the reaction moment 
.
. We obtain 
. The horizontal component is equal to zero without any horizontal load.
The resultant force 
replaces the uniform load q as applied in the middle of the region 
.
.
.
