Mechanical Engineering Principles

FORCES IN STRUCTURES 53

i.e. F 2 = 9 .96 kN,

F 5 =−4kN

and F 6 =− 7 .5kN

The above answers can be seen to be the same as
those obtained in Problem 10.

Now try the following exercise

Exercise 22 Further problems on the

method of sections

Determine the internal member forces of the

following trusses, by the method of sections:

1. Figure 4.23 (page 46)

[R 1 = 3 .0kN, R 2 = 1 .0kN,

1–2, 1.73 kN, 1–3,−3.46 kN,

2–3,−2.0 kN]

2. Figure 4.24 (page 46)
   ⎡

⎢

⎢

⎣

R 1 =− 2 .61 kN, R 2 = 2 .61 kN,

H 2 =6kN, 1–2,−1.5 kN,

1–3, 3.0 kN, 2–3,−5.2 kN

⎤

⎥

⎥

⎦

3. Figure 4.25 (page 46)
   ⎡

⎢

⎢

⎣

R 1 = 5 .0kN, R 2 = 1 .0kN,

H 1 = 4 .0kN 1–2,1.0kN,

1–3,−7.07 kN, 2–3,−1.41 kN

⎤

⎥

⎥

⎦

4. Figure 4.26 (page 46)
   ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
   R 1 = 5 .0kN, R 2 = 7 .0kN,
   1–3,−10.0 kN, 1–6,−8.7 kN,
   3–4,−8.0 kN, 3–6,−2.0 kN,
   4–6, 4.0 kN, 4–5, 8.0 kN,
   5–6,−6.0 kN, 5–2,−14.0 kN,

6–2, 12.1 kN

⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

Exercise 23 Short answer questions on

forces in structures

1. Where must the loads be applied on a pin-
   jointed truss?
   2. If there are three unknown forces in a
   truss, how many simultaneous equations
   are required to determine these unknown
   forces?
   3. When is a truss said to be statically
   indeterminate?
   4. For a plane pin-jointed truss, what are the
   maximum number of unknowns that can
   exist at a joint to analyse that joint without
   analysing another joint before it?

Exercise 24 Multi-choice questions on

forces in frameworks (Ans-

wers on page 284)

1. Is the truss of Figure 4.42:

F 1

F 2

Figure 4.42

(a) a mechanism

(b) statically determinate

(c) statically indeterminate

2. The value ofF 1 in Figure 4.43 is:

(a) 1 kN (b) 0.5 kN (c) 0.707 kN

1 kN

F (^230) °F 1
Figure 4.43

3. The value ofF 2 in Figure 4.43 is:

(a) 0.707 kN (b) 0.5 kN (c) 0