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Calculations of effective rigidities continued.
where T is the transformation
matrix which is used to transform the reduced stiffness constants from the
principal material fibre directions to a global (x, y, z) beam
coordinates.
Then, the resulting
transformed reduced stiffness constants for a unidirectional or orthotropic
composite from its principal directions is (Berthelot, 1999):
Both equations (above) can be merged into a single equation commonly known
as the "Constitutive Equation". The constitutive equation describes the
stiffness matrix of a laminate plate. The resultant forces and moments are
functions of the in-plane strains and curvatures (Berthelot, 1999).
where
hk is
the distance from the mid-plane of the laminate (Figure 3).
For a bending-torsion coupling behavior the chord wise moment Mx is
assumed to be zero so that the kx curvature can be eliminated from
(above) and then the matrix equation (11) reduces to the following form:
The EI, GJ
and K represent the effective rigidities of the beam in the global (x,
y, z) coordinate system. EI, GJ, and K represent,
respectively, the bending rigidity, torsion rigidity and bending-torsion
coupled rigidity. The effective rigidities are functions of ply angle,
thickness, and stacking sequence. these rigidities can be interactively calculated using www.compositecalculator.com
Editor's Note: Click here for Part 1 of this series.
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