Stress and Strain - Structural and Stress Analysis - page 151

P

m

P

m

(a)

P

m

m

N P

N P

m

P

m

F IGURE 7.1 Structural
member with axial load

(b)

Direct
stress

P

m

F IGURE 7.2 Internal force distribution in a beam
section

m

This direct stress acts in the direction shown in Fig. 7.2 when P is tensile and in the
reverse direction when P is compressive. The sign convention for direct stress is iden-
tical to that for normal force; a tensile stress is therefore positive while a compressive
stress is negative. The SI unit of stress is the pascal (Pa) where 1 Pa is 1N/m 2 . However
this is a rather small quantity in many cases so generally we shall use mega-pascals
(MPa) where 1MPa

1N/mm 2 .

=

In Fig. 7.1 the section mm is some distance from the point of application of the load.
At sections in the proximity of the applied load the distribution of direct stress will
depend upon the method of application of the load, and only in the case where the
applied load is distributed uniformly over the cross section will the direct stress be
uniform over sections in this region. In other cases stress concentrations arise which
require specialized analysis; this topic is covered in more advanced texts on strength
of materials and stress analysis.

We shall see in Chapter 8 that it is the level of stress that governs the behaviour of struc-
tural materials. For a given material, failure, or breakdown of the crystalline structure
of the material under load, occurs at a constant value of stress. For example, in the
case of steel subjected to simple tension failure begins at a stress of about 300N/mm 2 ,
although variations occur in steels manufactured to different specifications. This stress
is independent of size or shape and may therefore be used as the basis for the design
of structures fabricated from steel. Failure stress varies considerably from material to