Mechanical Engineering Principles

4

Forces in structures

At the end of this chapter you should be

able to:

• recognise a pin-jointed truss


• recognise a mechanism


• define a tie bar


• define a strut


• understand Bow’s notation


• calculate the internal forces in a truss by
  a graphical method


• calculate the internal forces in a truss by
  the ‘method of joints’


• calculate the internal forces in a truss by
  the ‘method of sections’

4.1 Introduction

In this chapter it will be shown how the principles
described in Chapter 3 can be used to determine the
internal forces in the members of a truss, due to
externally applied loads. The definition of a truss is
that it is a frame where the joints are assumed to
be frictionless and pin-jointed, and that all external
loads are applied to the pin joints. In countries where
there is a lot of rain, such structures are used to
support the sloping roofs of the building, as shown
in Figure 4.1.

Loads

Pin-joints

Figure 4.1 Pin-jointed truss

The externally applied loads acting on the pin-

jointed trusses are usually due to snow and self-

weight, and also due to wind, as shown in Figure 4.1.

In Figure 4.1, the snow and self-weight loads act

vertically downwards and the wind loads are usually

assumed to act horizontally. Thus, for structures

such as that shown in Figure 4.1, where the exter-

nally applied loads are assumed to act at the

pin-joints, the internal members of the framework

resist the externally applied loads in tension or in

compression.

Members of the framework that resist the exter-

nally applied loads in tension are calledtiesand

members of the framework which resist the exter-

nally applied loads in compression are calledstruts,

as shown in Figure 4.2.

(a) Tie (b) Strut

Figure 4.2 Ties and struts

The internal resisting forces in the ties and struts

will act in the opposite direction to the externally

applied loads, as shown in Figure 4.3.

(a) Tie in tension (b) Strut in compresion

Figure 4.3 Internal resisting forces in ties and struts

The methods of analysis used in this chapter

breakdown if the joints are rigid (welded), or if

the loads are applied between the joints. In these

cases, flexure occurs in the members of the frame-

work, and other methods of analysis have to be

used, as described in Chapters 5 and 6. It must

be remembered, however, that even if the joints of

the framework are smooth and pin-jointed and also

if externally applied loads are placed at the pin-

joints, members of the truss in compression can fail

through structural failure (see references [1] and [2]

on page 54).

It must also be remembered that the methods used

here cannot be used to determine forces instatically