Engineering Mechanics

Chapter 14 : Analysis of Perfect Frames (Graphical Method) „„„„„ 311

Example 14.16. A truss of 8 m span and 4 m height is loaded as shown in Fig. 14.41.

Fig. 14.41
Find the forces in all the members of the truss and mention their nature in each case.
*Solution. Since the truss is supported on rollers at the right hand support (E), therefore the
reaction at this support will be vertical (because of horizontal support). The reaction at A will be the
resultant of vertical and horizontal forces.
Taking moments about A,
VE × 8 = (2 W × 2) + (W × 2) = 6 W

∴

6

0.75 ( ) and 2 – 0.75 1.25 ( )

8

EA

W

VWVWWW== ↑ = = ↑

and HA = W (←)

First of all, draw the space diagram and name all the members and forces according to Bow’s
notations as shown in Fig. 14.42 (a).

Fig. 14.42
Now draw the vector diagram as shown in Fig. 14.42 (b). 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 AB (1-6) 1.77 Compression

2 BC (2-7) 0.35 Compression

3 CD (2-8) 0.35 Compression

4 DE (3-9) 1.06 Compression

5 AF (4-6) 2.25 Tension

6 BF (6-7) 1.41 Compression

7 CF (7-8) 0.5 Tension

8 FD (8-9) 0.71 Tension

9 FE (4-9) 0.75 Tension

* We have already solved this example analytically in the last chapter.