Mechanical Engineering Principles

44 MECHANICAL ENGINEERING PRINCIPLES

A B

E

D C

R 1 R 2

H 2

Joint 1 Joint^2

4 kN

30 ° 60 °

Figure 4.15

In this case, the spaces between the unknown forces
areA,B,C,DandE. It should be noted that the
reaction at joint (1) is vertical because the joint is on
rollers, and that there are two reactions at joint (2)
because it is firmly anchored to the ground and there
is also a horizontal force of 4 kN which must be
balanced by the unknown horizontal reactionH 2.
If this unknown horizontal reaction did not exist,
the structure would ‘float’ into space due to the
4 kN load.
Consider joint ABE, as there are only two
unknown forces here, namely the forces in the mem-
bersBEandEA. Working clockwise around this
joint, the vector diagram for this joint is shown
in Figure 4.16. By measurement,ae= 3 .5kNand
be= 2 .1kN.

30 °^60 °

a

e

4 kN b

Figure 4.16

Joint (2) cannot be considered next, as it has three
unknown forces, namelyH 2 ,R 2 and the unknown
member forceDE. Hence, joint (1) must be consid-
ered next; it has two unknown forces, namelyR 1 and
the force in memberED. As the memberAEand
its direction can be obtained from Figure 4.16, it can
be drawn to scale in Figure 4.17. By measurement,
de=3kN.
AsR 1 is vertical, then the vectordais vertical,
hence, the positiond can be found in the vector
diagram of Figure 4.17, whereR 1 =da (pointing
downwards). By measurement,R 1 = 1 .8kN.
To determineR 2 andH 2 , joint (2) can now be
considered, as shown by the vector diagram for the
joint in Figure 4.18.
The complete diagram for the whole framework
is shown in Figure 4.19, where it can be seen that

3.5 kN

a

d e

30 °

Figure 4.17

c b

d 3 kN e

2.1 kN

Figure 4.18

a,c b

d e

Figure 4.19

this diagram is the sum of the vector diagrams of

Figures 4.16 to 4.18.

The table below contains a summary of all the

measured forces

Member Force (kN)

be −2.1

ae 3.5

de −3.0

R 1 −1.8

R 2 1.8

H 2 4.0

Couple and moment

Prior to solving Problem 7, it will be necessary for

the reader to understand the nature of acouple;this

is described in Chapter 9, page 109.

The magnitude of a couple is called itsmoment;

this is described in Chapter 5, page 57.