Engineering Mechanics

Chapter 13 : Analysis of Perfect Frames (Analytical Method) „„„„„ 251

The example may be solved by the method of joints or method of sections. But we shall solve
it by both the methods.

Method of Joints

Fig. 13.9.
First of all, consider the joint A. Let the directions of PAB and PAE be assumed as shown in Fig.
13.9 (a) Resolving the forces vertically and equating the same,

PAB sin 60° = 2.5

∴

2.5 2.5

2.887 kN

sin 60 0.866

PAB===

°

(Compression)

and now resolving the forces horizontally and equating the same,

PAE = PAB cos 60° = 2.887 × 0.5 = 1.444 kN (Tension)
Now consider the joint D. Let the directions of the forces PCD and PED be assumed as shown in
Fig. 13.9 (b).

Resolving the forces vertically and equating the same,

PCD × sin 60° = 3.5

∴

3.5 3.5

4.042 kN

sin 60 0.866

PCD===

°

(Compression)

and now resolving the forces horizontally and equating the same,

PDE = PCD cos 60° = 4.042 × 0.5 = 2.021 kN (Tension)

Fig. 13.10.

Now consider the joint B. We have already found that force in member AB i.e., PAB is 2.887 kN

(Compression). Let the direction of the forces PBC and PBE be assumed as shown in Fig.13.10 (a).