(^310) A Textbook of Engineering Mechanics
Exmaple 14.15. Figure 14.39 shows a framed structure of 4 m span and 1.5 m height
subjected to two point loads at B and D.
Fig. 14.39.
Find graphically, or otherwise, the forces in all the members of the structure.
Solution. *Since the structure is supported on rollers at the right hand support (C), therefore
the reaction at this support will be vertical (because of horizontal support). The reaction at the left
hand support (A) will be the resultant of vertical and horizontal forces and inclined with the vertical.
Taking moments about A and equating the same,
VC × 4 = (8 × 1.5) + (12 × 2) = 36
∴
36
9kN( ) and 12–9 3kN( )
CA 4
VV== ↑ = = ↑
and HA = 8 kN (←)
First of all, draw the space diagram and name the members and forces according to Bow’s
notations as shown in Fig. 14.40 (a).
Fig. 14.40.
Now draw the vector diagram as shown in Fig. 14.40 (b). Measuring the various sides of the
vector diagram the results are tabulated here :
S.No. Member Magnitude of force in kN Nature of force
1 AB (1-6) 5.0 Compression
2 BC (2-7) 15.0 Compression
3 AD (4-6) 12.0 Tension
4 BD (6-7) 12.0 Tension
5 DC (3-7) 12.0 Tension
- We have already solved this example analytically in the last chapter.