A structural element is manufactured from a $[+\frac{60}{-}60{]}_s,$ carbon fibre reinforced laminate.

$1$ fibres under $+60$ to global x$-$direction

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

$2$ fibres under$-60$ to global $x-$direction

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

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

directions are:

$E_1=140$GPa,$x_1^T=1500$MPa,$s_1^T=1\mathrm{.}1\%$

$E_2=10$GPa,$x_1^C=1500$MPa,$s_1^C=0\mathrm{.}7\%$

$v_{12}=0\mathrm{.}24$GPa,$x_2^T=50$MPa,$s_2^T=0\mathrm{.}3\%$

$G_{12}=5\mathrm{.}7$GPa,$x_2=250$MPa,$s_2^C=0\mathrm{.}3\%$

$,x^S=70$MPa,$s^S=4\mathrm{.}0\%$

The component is loaded in biaxial tension with $N_x=\frac{N_y}{2}.$

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?

b$)$ Explain the reason for the difference in the predicted limit loads and the advantages and

disadvantages of the different failure criteria.