In-plane Shear Modulus:

The in-plane or axial shear modulus for an off axis lamina can be obtained when it subjected to a pure shear loading as shown in Figure 4.7. Thus, for this loading condition we have  and ..

For this loading, we define the in-plane shear modulus  as

(4.75)

With the help of Equation (4.5) we rewrite this equation as

(4.76)

And in terms of engineering constants, it becomes

(4.77)

The variation of  with fibre orientation between  to  for AS4/3501-6 Epoxy material is shown in Figure 4.8. From this figure it can be seen that shear modulus is maximum when . At  the value of shear modulus is

(4.78)

Note: When the material is isotropic, that is  and , then the above expression reduces to the familiar relation

(4.79)

The minimum value of shear modulus is seen when the lamina is loaded in shear in principal material directions and its value becomes

(4.80)

Note: It is very important to note that the shear modulus of the lamina is a minimum when lamina is in principal directions and a maximum when fibre orientation is  or . Further, the behavior of a lamina under same pure shear for fibre orientation  is significantly different from that of lamina with fibre orientation of . The physical significance of this phenomenon is explained in greater details in the later section.