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188 Mechanical Behaviour of Composites

1 - $ 2 2 s2 2 2 292
- = SI1 = -(c - s u12) + -(s - c u21) + -
EX E1 E2 GI2

Thus one may use the above expressions to calculate the stiffness of a uni-
directional lamina when it is loaded at any angle 8 to the fibre direction. If
computer facilities are available for the matrix manipulation then it is not
necessary to work out the individual terms as above - the required information
can be determined directly from the matrices. For example, as indicated above
1 1 1
Ex=:, Ey=:-, Gxy=g (3.26)
s11 s22
3.7 Summary of Approach to Analysis of Unidirectional Composites
1. The strains and stresses in the local (1 -2) axis are related by
[E112 = [Sl[al12
or [a112 = [Ql[~li2 where [Ql = [SI-'
2. The global (n-y) stresses and strains may be related to the local (1-2)
stresses and strains by

[a112 = [Tal[alxy
[E112 = [TEI[EIX),
3. The global stresses and strains are related by
CElxy = [mlxy

[a],, = [Ql[Elxy
where
@I = [ToI-l[Ql[TEI and [SI = [GI-'

[::I and
In each case [a112 and [&I12 are written as shorthand for

TI2 Y12
The following Examples illustrate the use of these equations