Question $1$:

Set $N_x=25k\frac{N}{m},N_y=N_{xy}=M_x=M_y=M_{xy}=0,$ and determine the laminate mid$-$surface

strains and curvatures that result from the prescribed loading condition for the $,$

$0]$ laminate discussed in $Q5$ of Part $1.$ Elastic properties in Table $1.$

Hint: To solve this you should consider the laminate constitutive relations $-$ with the

stress$/$moment resultants prescribed, you can solve for the reference surface strains and

curvatures. This is a fully coupled laminate $-$ so complex behaviour is to be expected.

Question $2$:

Given the results from Question $1$ and assuming that the laminate now represents a

cantilever beam, which has a length of $2m$ and negligible width. What is the deflection of

the beam with no forces applied other than that specified in Question $1?($You can assume

that $k_y$ and $k_{xy}$ are zero.$)$

Hint: To solve this you need to use engineer's bending theory and the equation for the

deflection of a cantilever beam due to a bending moment given by:

$=\frac{M_0{L}^2}{2EI}$

Question $3$:

Calculate and illustrate graphically the through thickness stress distribution in the $[90,45,-$

$45,0$ laminate configuration in the laminate $(x,y)$ coordinate system. Remember that the

laminate stack above is presented top to bottom!

Hint: When assessing your predictions, recall that whilst the strains vary continuously across

the laminate thickness, the stresses vary through the thickness of the plies as well, but

usually display discontinuous jumps across the ply interfaces.

Question $4$:

Calculate and illustrate graphically the through thickness stress distribution in the $[90,45,-$

$45,0$ material in the material $(1,2)$ coordinate system. Remember that the laminate stack

above is presented top to bottom!

Table $1$ Lamina engineering elastic constants

Table $2$ Failure stresses $($strengths$)$ and strains $-$ data sheet values: