Engineering Mechanics

Chapter 14 : Analysis of Perfect Frames (Graphical Method) „„„„„ 295

Now draw the vector diagram as shown in Fig. 14.8 (b). Measuring various sides of the vector
diagram, the result are tabulated here :

S. No. Member Magnitude of force in kN Nature of force

1 AB, DE 6.0 Compression

2 AF, EH 5.2 Tension

3 FG, GH 5.2 Tension

4 BF, DH 0—

5 BG, DG 2.0 Compression

6 BC, CD 4.0 Compression

7 CG 2.0 Tension

Example 14.4. A horizontal link AB is divided into three equal parts AC, CD and DB and
above each, an equilateral triangle is drawn. The apices E, F and G of the triangles on AC, CD and
DB respectively are also jointed.
The figure is then represented by centre lines, a framework simply at its ends A and B. Vertical
loads each equal to W are carried at E and C as shown in Fig. 14.9.

Fig. 14.9.
Find the nature and magnitude of forces in each of the member and write them upon the
members of your diagram or in a table.

Solution. Taking moments about A and equating the same,

13

31

22

RB×= × + ×=WW W

∴^31

232

B

W

RW=× ×=

and

3

()–

A 22

WW
RWW=+ ⎛⎞⎜⎟=
⎝⎠
First of all, draw the space diagram for the truss and name the various members according to
Bow’s notations as shown in Fig. 14.10 (a).

Now draw the vector diagram as shown in Fig. 14.10 (b). Measuring the various sides of the
vector diagram the results are tabulated here :