Engineering Mechanics

Chapter 14 : Analysis of Perfect Frames (Graphical Method) „„„„„ 293

4. Similarly, draw vector diagram for the joint C, whose directions follow q-r; r-s and s-q
   shown Fig.14.4 (a) and (b). Now check the vector diagram for the joint A, whose
   directions follow p-q ; q-s and s-p.
   Now measuring† the various sides of the vector diagram and keeping due note of the
   directions of the arrow heads, the results are tabulated here :

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

1 AB (PS) 8.7 Compression

2 BC (RS) 4.3 Tension

3 AC (SQ) 5.0 Compression

Example 14.2. A truss of span 10 metres is loaded as shown in Fig. 14.5.

Fig. 14.5.
Find the reactions and forces in the members of the truss.
Solution. From the geometry of the figure, we find the load 5 kN is acting at a distance of 2.5
metres and the load of 6 kN at a distance 6.25 metres from the left hand support.

Fig. 14.6.

Taking moments about the left hand support and equating the same.

RB × 10 = (5 × 2.5) + (6 × 6.25) = 50

∴

50

5kN

B 10

R ==

and RA = (5 + 6) – 5 = 6 kN

First of all, draw space diagram for the truss alongwith loads and reactions as shown in Fig.
14.6 (a). Name the various members of the truss and forces according to Bow’s notations.
† Sometimes, there is a slight variation in the results obtained by the analytical method and graphical
method. The values obtained by graphical method are taken to be correct, if they agree upto the first
decimal point with the values obtained by analytical method, e.g., 8.66 (Analytical) = 8.7 (graphical).
Similarly, 4.32 (Analytical) = 4.3 (graphical).