The reactions at the two supports of a beam may be found by any one of the following two methods:
1. Analytical Method
2. Graphical Method
Analytical Method for Reactions of a Beam:
Consider a simply supported beam AB of span l, subjected to point loads W1, W1 and W3 at the distances of a, b and c respectively from the support A.
Graphical Method for Reactions of a Beam:
It is a systematic, but long method for finding out the reactions of a beam which is done by the following steps:
1. Construction of space diagram
2. Construction of vector diagram
Construction of Space Diagram:
It means to construct the diagram of the beam to a suitable scale. It also includes the loads, carried by the beam along with the lines of action of the reactions. Now, the name of the different loads including the two reactions according to Bow’s notations.
Construction of Vector Diagram:
After drawing the space diagram of the beam, and naming all the loads or forces according to Bow’s notations as shown in the figure:
The next step is to construct the vector diagram. A vector diagram is drawn in the following steps: