# Normal and Shear Coupling for Unidirectional Angle Ply

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This Demonstration shows the coupling between normal stress and shear strain for a unidirectional, fiber-reinforced angle ply. By varying the applied stress, the material properties of the composite, and the ply angle , you can observe the degree of coupling between normal stress and shear strain for an angle ply. Note that for plies of 0 and 90 degrees, there is no coupling because they behave as orthotropic materials. The effect of varying the longitudinal and transverse stiffness, along with Poisson's ratio, can also be observed.

Contributed by: Sara McCaslin and Fredericka Brown (March 2011)

Open content licensed under CC BY-NC-SA

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## Details

For continuous fiber-reinforced plies, subscript 1 represents the longitudinal axis of a ply (axis along the length of the fibers) and subscript 2 represents the transverse axis (perpendicular to the length of the fibers). A unidirectional, thin, continuous fiber-reinforced ply can be modeled as an orthotropic material in a state of plane stress. Hooke's law can be represented as , where is the strain vector , is the stress vector , and is the reduced compliance,

.

For an angle ply rotated an angle counterclockwise from the axis, the rotated compliance matrix is given by

The resulting strain is then given by

For more information, see Fiber Reinforced Composites.

Reference

[1] B. D. Agarwal, L. J. Broutman, and K. Chandrashekhara, *Analysis and Performance of Fiber Composites*, 3rd ed., New York: Wiley, 2006.

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