Normal and Shear Stresses:

You have been already introduced to the concept, description and definition of normal stress and shear stress. In expressing shear stress elements, we use two subscripts, such as τ_xy, τ_yz, τ_zx etc. Here, the first subscript implies the direction of general to the plane and the second subscript denotes the direction in that stress (its resulting force) is acting. Therefore τ_xy is the stress in y direction on x plane, i.e. plane normal to x direction. Logically, all the stress components should have double subscripts. Therefore, as direction of the stress and direction of the normal to the plane are identically similar in the case of normal stress elements, only a single subscript is used, i.e. σ_x really represents σ_xx and so on. In the case of a shear stress component, two subscripts are essential to describe it correctly. The second subscript also indicates the plane on that its complementary component is acting.

We have already begun that among normal stresses, tension is considered positive although compression is considered negative. In the case of shear stresses, one of the components tends to rotate the element in the positive, i.e. anticlockwise direction and is considered positive, although its complementary component that tends to rotate the element in the clockwise direction is considered negative. Accordingly, in the state of stress, elaborates in Figure, τ_xy is positive, although τ_yx is negative. This definition helps us to determine the sign of the shear stress on inclined planes also.