Page 213 - Plastics Engineering

196 Mechanical Behaviour of Composites

Or more generally for all the force components N,, N, and N,,
h
2
[NI = JI.1. (3.27)
_-
h
2
Similarly the bending moment, MI, per unit width is given by

h
-2
Once again, all the moments M,, My and M,,, can be expressed as

h
2
[MI = /[alzdz (3.28)
h
-2
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.
Hence,
E(Z) = E -k Z.K
The stresses will then be given by

dz) = [Ql * [&I + [Ql * Z.[K]
where [Q] is the stiffness matrix as defined earlier.
Now, from equation (3.27), the forces [N] are given by

VI = [AI[&] + [Bl[Kl (3.29)
where [A] is the Extensional Stiffness matrix (= [Qlh) and [B] is a Coupling
Matrix. It may be observed that in the above analysis [B] is in fact zero for