A symmetric balanced angle$-$ply laminate $[30,-30]$s made of Carbon$/$Epoxy AS$4/3501-6$ is subjected to the in$-$plane loading of $N_x=0\mathrm{.}2M\frac{N}{m}.$

a$)$ Calculate the on$-$axis strain components at the top of each layer $(z_0$ for layer $1,z_1$ for layer $2,z_3$ for layer $3$ and $z_4$ for layer $4).$

b$)$ Calculate the on$-$axis stress components at the top of each layer $(z_0$ for layer $1,z_1$ for layer $2,z_3$ for layer $3$ and $z_4$ for layer $4).$

c$)$ Using First Ply Failure $($FPF$)$ analysis and Tsai$-$Wu criterion, calculate the laminate safety factor and then the maximum $N_x$ before failure. Consider stress and strain components at the top of each layer $(z_0$ for layer $1,z_1$ for layer $2,z_3$ for layer $3$ and $z_4$ for layer $4).$

A symmetric cross$-$ply laminate $[0,90{]}_s$ made of Carbon$/$Epoxy AS$4/3501-6$ is subjected to the bending moment $M_x=10N\frac{m}{m}.$

a$)$ Calculate the on$-$axis strain components at the top of each layer $(z_0$ for layer $1,z_1$ for layer $2,z_3$ for layer $3$ and $z_4$ for layer $4).$

b$)$ Calculate the on$-$axis stress components at the top of each layer $(z_0$ for layer $1,z_1$ for layer $2,z_3$ for layer $3$ and $z_4$ for layer $4).$

c$)$ Using First Ply Failure $($FPF$)$ analysis and Tsai$-$Wu criterion, calculate the laminate safety factor and then the maximum $M_x$ before failure. Consider stress and strain components at the top of each layer $(z_0$ for layer $1,z_1$ for layer $2,z_3$ for layer $3$ and $z_4$ for layer $4).$

For AS$4/3501-6$:

Layer thickness $=0\mathrm{.}15mm$

${}_1^T=2280$MPa,$E_1=142$GPa

${}_1^c=-1440$MPa,$E_2=10\mathrm{.}3$GPa

${}_2^T=57$MPa,$G_{12}=7\mathrm{.}2$GPa

${}_2^c=-228$MPa,$v_{12}=0\mathrm{.}27$

${}_{12}^F=71$MPa,