Engineering Mechanics

(^294) „„„„„ A Textbook of Engineering Mechanics
Now draw vector diagram as shown in Fig. 14.6 (b) and as discussed below :

1. Select some suitable point 1 and draw a vertical line 1-2 equal to 5 kN to some suitable
   scale to represent the load 5 kN at C. Similarly, draw 2-3 equal to 6 kN to the scale to
   represent the load 6 kN at D.


2. Now cut off 3-4 equal to 5 kN to the scale to represent the reaction RB. Thus 4-1 will
   represent the reaction RA to the scale.


3. Now draw vector diagram for the joint A. For doing so through 1, draw 1-5 parallel to AC
   and through 4, draw 4-5 parallel to AE meeting the first line at 5. Now 1-5-4-1 is the
   vector diagram for joint A, whose directions follow 1-5, 5-4 and 4-1. Similarly, draw
   vector diagrams for the joints B, C, D and E as shown in Fig. 14.6 (b).
   Now measuring the various sides of the vector diagram, the results are tabulated here :
   S. No. Member Magnitude of force in kN Nature of force
   1 AC (1-5) 6.9 Compression
   2 CD (2-6) 7.0 Compression
   3 BD (3-7) 10.0 Compression
   4 AE (4-5) 3.5 Tension
   5 CE (5-6) 5.2 Tension
   6 DE (6-7) 5.2 Compression
   7 BE (4-7) 8.7 Tension

Example 14.3. A king post truss of 8 m span is loaded as shown in Fig. 14.7.

Fig. 14.7.

Find the forces in each member of the truss and tabulate the results.

Solution. Since the truss is symmetrical in geometry and loading, therefore reaction at the

left hand support,

12 2 21

4kN

AE 2

RR

++++

== =

First of all, draw the space diagram and name the members and forces according to Bow’s

notations as shown in Fig. 14.8 (a).

Fig. 14.8.