Example $2$: Two$-$Ply $[45/0]$ Laminate Subjected to Applied Loads

The top lamina with thickness $3$ mm has a $45$ orientation with respect to reference XY coordinates while the bottom lamina of thickness $5$ mm has a $0$ orientation. Thus the laminate has a total thickness of $8$ mm $.$ The applied loads are $N_x=300\frac{N}{m}m$ and $N_Y=150\frac{N}{m}m.$ Calculate the minimum factor of safety $($FoS$)$ considering the maximum stress criterion. Consider an E$-$glass epoxy material with the properties as follow:

Elastic Moduli:

$E_L=38\mathrm{.}6$GPa

$E_T=8\mathrm{.}27$GPa

$G_{LT}=4\mathrm{.}14$GPa

$v_{LT}=0\mathrm{.}26$

${}_{LU}=1062$MPa

${}_{LU}^{\text{'}}=610$MPa

${}_{TU}=31$MPa

Strength properties:

${}_{TU}^{\text{'}}=118$MPa

${}_{\text{L}\text{T}\text{U}}=72$MPa

Solution:

The minimum FoS is $1\mathrm{.}2439549$ at the top surface of the $45$ lamina.

Scilab code is provided.