8
2 Analysis of Stress
Fig. 2.1 Forces acting on a body
2.3 Concept of Direct Stress and Shear Stress
Figure 2.2 shows the rectangular components of the force vector F referred to
corresponding axes. Taking the ratios
F x
A x
,
F y
A x
,
F z
A x
, we have three quantities that
establish the average intensity of the force on the area A x . In the limit as A → 0,
the above ratios define the force intensity acting on the x-face at point O. These
values of the three intensities are defined as the “Stress components” associated with
the x-face at point O. The stress components parallel to the surface are called “shear
stress components” denoted by τ. The shear stress component acting on the x-face
in the y-direction is identified as τ xy. The stress component perpendicular to the face
is called “normal stress” or “direct stress” component and is denoted by σ . This is
identified as σ x along x-direction. From the above discussions, the stress components
on the x-face at point O are defined as follows in terms of force intensity ratios
Fig. 2.2 Force components
of F acting on small area
centred on point O