(^292) A Textbook of Engineering Mechanics
Example 14.1. The truss ABC shown in Fig. 14.3 has a span of 5 metres. It is carrying a load
of 10 kN at its apex.
Fig. 14.3.
Find the forces in the members AB, AC and BC
Solution*. From the geometry of the truss, we find that the load of 10 kN is acting at a
distance of 1.25 m from the left hand support i.e., B and 3.75 m from C. Taking moments about B and
equating the same,
RC × 5 = 10 × 1.25 = 12.5
∴
12.5
2.5 kN
C 5
R ==
and RB = 10 – 2.5 = 7.5 kN
†First of all, draw the space diagram for the truss alongwith the load at its apex and the reac-
tion RB and RC as shown in Fig. 14.4 (b). Name the members AB, BC and AC according to Bow’s
notations as PS, RS and SQ respectively. Now draw the vector diagram as shown in Fig. 14.4 (b) and
as discussed below :
Fig. 14.4.
- Select some suitable point p and draw a vertical line pq equal to 10 kN to some suitable
scale to represent the load PQ at joint A. - Now cut off qr equal to 2.5 kN to the scale to represent the reaction RC at C. This rp will
represent the reaction RB to the scale. - Now draw the vector diagram for the joint B. For doing so, through p draw ps parallel to
PS and through r draw rs parallel to RS meeting the first line at s. Now psrp is the vector
diagram for the joint B, whose directions follow p-s; s-r and r-p.
- We have already solved this example analylically in the last chapter.
† As a matter of fact, this is the advantage of graphical method, that the previous work is checked. If at any
stage some error is noticed, the complete vector diagram should be drawn once again.