Mechanical Engineering Principles

5

Simply supported beams

At the end of this chapter you should be

able to:

• define a ‘moment’ of a force and state
  its unit


• calculate the moment of a force from
  M=F×d


• understand the conditions for equilibrium
  of a beam


• state the principle of moments


• perform calculations involving the princi-
  ple of moments


• recognise typical practical applications of
  simply supported beams with point load-
  ings


• perform calculations on simply supported
  beams having point loads


• perform calculations on simply supported
  beams with couples

5.1 The moment of a force

When using a spanner to tighten a nut, a force tends

to turn the nut in a clockwise direction. This turning

effect of a force is called themoment of a forceor

more briefly, just amoment. The size of the moment

acting on the nut depends on two factors:

(a) the size of the force acting at right angles to

the shank of the spanner, and

(b) the perpendicular distance between the point
of application of the force and the centre of
the nut.

In general, with reference to Figure 5.1, the moment

M of a force acting about a pointP is force×

perpendicular distance between the line of action

of the force andP, i.e.

M=F×d

P

Moment,M

Turning radius,d

Force, F

Figure 5.1

The unit of a moment is thenewton metre (N m).

Thus, if forceF in Figure 5.1 is 7 N and distance

dis 3 m, then the momentM is 7 N×3 m, i.e.

21 N m.

Problem 1. A force of 15 N is applied to a

spanner at an effective length of 140 mm

from the centre of a nut. Calculate (a) the

moment of the force applied to the nut,

(b) the magnitude of the force required to

produce the same moment if the effective

length is reduced to 100 mm.

M

P

140 mm

15 N

(a)

F

P

100 mm

(b)

M= 2100 N mm

Figure 5.2

From above,M=F×d,whereMis the turning

moment,Fis the force applied at right angles to the

spanner andd is the effective length between the

force and the centre of the nut. Thus, with reference

to Figure 5.2(a):

(a) Turning moment,

M=15 N×140 mm=2100 N mm

=2100 N mm×

1m

1000 mm

= 2 .1Nm