Engineering Mechanics

Chapter 14 : Analysis of Perfect Frames (Graphical Method) „„„„„ 319

Now, consider (for the time being only) the members OP and PQ as removed and substitute an
imaginary member joining the joints 5 and 6 (as shown by the dotted line) as shown in Fig. 14.54. (a).
Now we find that this substitution reduces the unknown force members at joint 4, from three to two
(i.e., members DI and IN; assuming the letter I in place of P and O) and thus we can draw the vector
diagram for this joint (i.e., No. 4).

Fig. 14.54 (a).

1

2

a b c d e k f g h i j

q

o

m

w

v n r

t u

s

x, l

Fig. 14.54 (b).
Now after drawing the vector diagram for joint 4, proceed to joint 6 at which there are only two
members (i.e., EQ and QI) in which the forces are unknown. The vector diagram, at this joint will
give the forces in EQ by the side eq of the vector diagram.

After drawing vector diagram at joint 6 and determining the forces in EQ (i.e., eq) replace the
imaginary member by the original members PQ and PO and again draw vector diagram for the joint
No. 6 as shown in Fig. 14.54 (b). This will give the force in the member PO.

Now proceed to joint No. 5 as usual and complete the whole vector diagram as shown in Fig.
14.54 (b). Meausring the various sides of the vector diagram, the results are tabulated here :