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2 Analysis of Stress
Fig. 2.5 Types of stress
2.7 Types of Stress
Stresses may be classified in two ways, i.e. according to the type of body on which
they act, or the nature of the stress itself. Thus, stresses could be one-dimensional,
two-dimensional or three-dimensional as shown in Fig. 2.5.
2.8 Two-Dimensional Stress at a Point
A two-dimensional state of stress exists when the stresses and body forces are independent of one of the co-ordinates. Such a state is described by stresses σ x , σ y and
τ xy and the X and Y body forces (here, z is taken as the independent co-ordinate
axis).
We shall now determine the equations for transformation of the stress components
σ x , σ y and τ xy at any point of a body represented by infinitesimal element as shown
in Fig. 2.6.
Consider an infinitesimal wedge cut from the loaded body shown in Fig. 2.6. It
is required to determine the stresses σ x and τ x y , that refer to axes x
, y
making an
angle θ with axes x, y as shown in Fig. 2.7. Let side MN be normal to the x
axis.