(^290) A Textbook of Engineering Mechanics
14.2.CONSTRUCTION OF SPACE DIAGRAM
It means the construction of a diagram of the given frame to a suitable linear scale, alongwith
the loads it carries. The magnitude of support reactions is also found out and shown in the space
diagram. Now name the various members and forces according to Bow’s notations as shown in
Fig. 14.1 (a).
In the space diagram of the truss ABC shown in Fig. 14.1 (a), the members AB, BC and CA are
represented by SR (or RS), SQ (or QS) and PS (or SP) respectively. Similarly, load at C and reactions
at A and B are represented by PQ, RP and QR respectively.
Note: The reactions are generally found out by analytical method as discussed in the last
chapter.
14.3.CONSTRUCTION OF VECTOR DIAGRAM
After drawing the space diagram and naming the various members of the frame according to
Bow’s notations, as discussed in the last article, the next step is the construction of vector diagram. It
is done in the following steps :
- Select a suitable point p and draw pq parallel to PQ (i.e., vertically downwards) and equal
to the load W at C to some suitable scale. - Now cut off qr parallel to QR (i.e., vertically upwards) equal to the reaction RB to the
scale. - Similarly, cut off rp parallel to RP (i.e., vertically upwards) equal to the reaction RA to the
scale. Thus we see that in the space diagram, we started from P and returned to P after
going for P-Q-R-P (i.e., considering the loads and reactions only). - Now through p draw a line ps parallel to PS and throgh r draw rs parallel to RS, meeting the
first line at s as shown in Fig. 14.1 (b). Thus psrp is the vector diagram for the joint (A). - Similarly, draw the vector diagram qrsq for the joint (B) and pqsp is the vector diagram
for the joint (C) as shown in Fig. 14.1 (b).
Notes: 1. While drawing the vector diagram, for a joint, care should be taken that the joint
under consideration does not contain more than two members whose forces are unknown. if the joint,
under consideration contains more than two such members whose forces are unknown, then some
other joint which does not contain more than two unknown force members, should be considered
for drawing the vector diagram. - If at any stage (which normally does not arise in a perfect frame) the work of drawing the
vector diagram is held up at some joint, it will be then necessary to determine the force at such a
joint by some other method i.e., method of sections or method of joints.
Fig. 14.1.