Mechanical Engineering Principles

FORCES IN STRUCTURES 41

indeterminatepin-jointed trusses, nor can they be
used to determine forces inmechanisms. Statically
indeterminate structures are so called because they
cannot be analysed by the principles of statics alone.
Typical mechanisms are shown in Figure 4.4; these
are not classified as structures because they are not
firm and can be moved easily under external loads.

(a) (b)

Pin-

joints

Figure 4.4 Mechanisms

To make the mechanism of Figure 4.4(a) into a
simple statically determinate structure, it is neces-
sary to add one diagonal member joined to a top
joint and an ‘opposite’ bottom joint. To make the
mechanism of Figure 4.4(b) into a statically deter-
minate structure, it is necessary to add two members
from the top joint to each of the two bottom joints
near the mid-length of the bottom horizontal.
Three methods of analysis will be used in this
chapter — one graphical and two analytical methods.

4.2 Worked problems on mechanisms

and pin-jointed trusses

Problem 1. Show how the mechanism of

Figure 4.4(a) can be made into a statically

determinate structure.

The two solutions are shown by the broken lines of
Figures 4.5(a) and (b), which represent the place-
ment of additional members.

(a) (b)

Figure 4.5

Problem 2. Show how the mechanism of

Figure 4.4(b) can be made into a statically

determinate truss.

The solution is shown in Figures 4.6, where the bro-

ken lines represent the placement of two additional

members.

Figure 4.6

Problem 3. Show how the mechanism of

Figure 4.4(a) can be made into a statically

indeterminate truss.

The solution is shown in Figure 4.7, where the

broken lines represent the addition of two members,

which are not joined where they cross.

A B

Figure 4.7

Problem 4. Why is the structure of

Figure 4.7 said to be statically indeterminate?

As you can only resolve vertically and horizontally

at the joints AandB, you can only obtain four

simultaneous equations. However, as there are five

members, each with an unknown force, you have

one unknown force too many. Thus, using the prin-

ciples of statics alone, the structure cannot be satis-

factorily analysed; such structures are therefore said

to be statically indeterminate.