A structural element is manufactured from a $[+60/60]$s carbon fibre reinforced laminate.

fibres under $+60$ to global x$-$direction

ply thickness t $=1\mathrm{.}5$ mm

fibres under$-60$ to global x$-$direction

ply thickness t $=1\mathrm{.}5$ mm

$1$

x

y

$60$

$2$

$1$

$2$

The engineering constants and strength limits of the laminae in the principal material

directions are:

E$1=140$ GPa X$1$

T $=1500$ MPa $1$

T $=1\mathrm{.}1\%$

E$2=10$ GPa X$1$

C $=1500$ MPa $1$

C $=0\mathrm{.}7\%$

$12=0\mathrm{.}24$ GPa X$2$

T $=50$ MPa $2$

T $=0\mathrm{.}3\%$

G$12=5\mathrm{.}7$ GPa X$2$

C $=250$ MPa $2$

C $=0\mathrm{.}3\%$

X

S $=70$ MPa $$

S $=4\mathrm{.}0\%$

The component is loaded in biaxial tension with Nx $=$ Ny$/2.$

a$)$ Determine limit loads in $[$kN$]$ for first ply failure using Maximum Stress, Maximum Strain

and Tsai$-$Hill failure criteria. Which ply $($plies$)$ will fail first and what is the critical failure

mode?