General Deformation Behaviour of a Single Ply

The previous section has considered the in-plane deformations of a single ply. In practice, real engineering components are likely to be subjected to this type of loading plus (or as an alternative) bending deformations. It is convenient at this stage to consider the flexural loading of a single ply because this will develop the method of solution for multi-ply laminates. 

Consider a unidirectional sheet of material with the fibres aligned in the x-direction and subjected to a stress, If the sheet has thickness, h, as shown in Fig. 3.15 and we consider unit width, then the normal axial force Nx is given by 

Similarly the bending moment, A/, per unit width is given by 

Now in order to determine [a] as a function of z, consider the strain e(z) at any depth across the section. It will be made up of an in-plane component (e) plus a bending component z/R) which is normally written as z-k, where k is the curvature of bending. 

For this special case of a single ply, [B] = 0 and so the forces are related to the strains by 

for the single ply situation, the moments are related to the curvature 

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