Positive and Negative Shear:

In the chapter Plane Stress Constitutive Relations we have seen the significance of positive and negative shear. In the following we revisit that section again. The figures are re-drawn for the sake of completeness of the explanation.

The direction of shear loads applied to a lamina, especially an off-axis lamina, is very important both from shear stiffness as well as strength point of view. This is explained with respect to an off-axis lamina. Here we have illustrated for .

The two cases of pure shear loading of a  lamina are shown in Figure 9.1. In these cases the direction of loading is reversed. The pure shear loading can be shown to be equivalent traction and compression loading along the   diagonals of a square element. This is depicted in Figure 9.1 for both cases. For the first case, the fibres are subjected to tensile normal stress and matrix is subjected to compressive normal stress, whereas for the second case, the fibres are subjected to compressive normal stress and matrix is subjected tensile normal stress. The first case of shear loading shown in Figure 9.1 is called is Positive Shear and the second case is called as Negative Shear.

In the case when fibres are oriented at , either tensile or compressive normal stress is aligned along the fibres, thus resulting in higher shear stiffness at . However, when the lamina is loaded in pure shear in principal material directions (as shown in Figure 9.1), the equivalent stress in fibre is neither pure normal tensile stress nor pure normal compressive stress. Thus, it results in lower shear stiffness, that is .

It is well known that fibres are good in traction and weak in compressive loading. Thus, it is desirable from designing point of view that the shear loading should results in an equivalent loading in which the fibres are subjected to tensile normal stress. This kind of shear loading of an off-axis lamina will ensure the higher shear strength of the lamina. In case of  off-axis lamina the fibres are in pure tensile for their positive shear loading. Thus, it results into the highest shear strength.

The positive and negative shear loading has no effect in case of unidirectional lamina as shown in Figure 9.2.

The loading of an off-axis lamina in pure shear should be, in general, positive shear. This is one of the important design considerations.