(^220) A Textbook of Engineering Mechanics
12.8.GRAPHICAL METHOD FOR THE 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 :
- Construction of space diagram.
- Construction of vector diagram.
12.9.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 name the different loads
(or forces) including the two reactions according to Bow’s notations.12.10. 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 :Fig. 12.5.- Select some suitable point p, near the space diagram and draw pq parallel and equal to the
load PQ (i.e.,W 1 ) to some scale. - Similarly, through q and r, draw qr and rs parallel and equal to the loads QR and RS (i.e.,
W 2 and W 3 ) to the scale. - Select any suitable point o and join op, oq, or and os as shown in Fig. 12.5 (b).
- Now extend the lines of action of the loads and the two reactions in the space diagram.
- Select some suitable point p 1 on the lines of action of the reaction RA. Through p 1 draw p 1
p 2 parallel to op intersecting the line of action of the load W 1 at p 2. - Similarly, draw p 2 p 3 , p 3 p 4 and p 4 p 5 parallel to oq, or and os respectively.
- Join p 1 with p 5 and through o draw a line ot parallel to this line.
- Now the lengths tp and st, in the vector diagram, give the magnitude of the reactions RA
and RB respectively to the scale as shown in Figs. 12.5 (a) and (b).
12.11. TYPES OF END SUPPORTS OF BEAMS
Though there are many types of supports, for beams and frames, yet the following three types
of supports are important from the subject point of view:- Simply supported beams, 2. Roller supported beams, and 3. Hinged beams.