Chapter 14 : Analysis of Perfect Frames (Graphical Method) 315
Solution. Since the truss is supported on rollers at the right end, therefore the reaction at this
end will be vertical. Moreover, as the truss is hinged at the left end, therefore the reaction at this end
will be inclined with the vertical.
- First of all draw the space diagram for the roof truss and name the various forces and
reactions according to Bow’s notations. - Compound all the forces together and assume them to act through the centre of gravity of
the forces, i.e., along the line of action of 2 kN force. - Produce the line of action of the resultant force (compound together as per item 2) to meet
the line of action of the roller support (which will be vertical due to support on rollers)
at O. - Join OA. From O cut off OM equal to the total compound load (i.e., 1 + 2 + 1 = 4 kN)
according to some scale, along the line of action of the resultant load. - Complete the parallelogram OLMN with OM as diagonal.
- Measure OL and ON. The length ON gives the magnitude and direction of the reaction RA.
The length OL gives the magnitude of the reaction RB. - By measurement, we find that
R 1 = 2.52 kN, R 2 = 1.92 kN and θ = 51° Ans.
Fig. 14.48.
Now draw the vector diagram as shown in Fig. 14.48 (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 EJ 1.3 Tension
2 JC 2.1 Compression
3 HJ 0—
4 HE 1.3 Tension
5 HG 2.3 Compression
6 GB 0.9 Compression
7 FG 1.2 Tension
8 FE 0.7 Compression
9 AF 2.0 Compression