Normal and Shear Stresses:

You have been already introduced to the concept, definition and description of normal stress and shear stress. In evaluating shear stress components, we utilize two subscripts, such as t_xy, t_yz, t_zx etc. Here, the first subscript denotes the direction of normal to the plane and the second subscript denotes the direction in which stress (its resulting force) is acting. Therefore t_xy is the stress in y direction on x plane that means plane normal to x direction. Logically, all of the stress components must have double subscripts. However, as direction of the stress and direction of the normal to the plane are identically similar in the case of normal stress component, just a single subscript is utilized, i.e. σ_x really represents σ_xx and so on. In the particular case of a shear stress component, two subscripts are essential to define it correctly. The second subscript also mentions the plane on which its complementary component is working.

We have already explained that among normal stresses, tension is let positive while compression is considered negative. In the particular case of shear stresses, one of the components tends to rotate the element in the positive that means anticlockwise direction and is considered positive, when its complementary component which tends to rotate the element in the clockwise direction is considered negative. Accordingly, in the state of stress, defined in Figure, t_xy is positive, while t_yx is negative. This definition helps us to determine the sign of the shear stress on inclined planes also.