In order to reduce material costs, a composite panel is to be made by placing fibers in the matrix material in an X-pattern of ±α as shown in Figure 6

In order to reduce material costs, a composite panel is to be made by placing fibers in the matrix material in an X-pattern of ±α as shown in Figure 6.46, instead of randomly distributing the fibers over all angles. The X-pattern composite is to be designed so that it has at least 90% of the stiffness of the randomly oriented fiber composite along the longitudinal (L) axis.

Determine the CTE for a randomly oriented fiber composite in terms of the longitudinal and transverse CTEs α1 and α2 of the corresponding unidirectional composite lamina.