Problem 3
A composite panel with layup [±75/0], is subjected to the force resultants of Nx = 500 lb/in, Ny = 300 lb/in, and Nxy = 100 lb/in. The mechanical properties of the composite materials are:
E? = 20 × 10? psi
E? = 2.0 × 10? psi
G?? = 1.5 × 10? psi
??? = 0.3
tply = 0.005 in
F?t = 160 × 10³ psi
F?t = 4000 psi
F? = 6000 psi
F?c = 140 × 10³ psi
F?c = 15000 psi
The [Q] and [Q]?? are given as follows:
$\begin{bmatrix} 20.182 & 0.605 & 0\\ 0.605 & 2.018 & 0\\ 0 & 0 & 1.5 \end{bmatrix}$ × 10? psi,
$\begin{bmatrix} 2.298 & 1.542 & 0.648\\ 1.542 & 18.028 & 3.893\\ 0.648 & 3.893 & 2.437 \end{bmatrix}$ × 10? psi
(a) Calculate the extensional stiffness matrix [A].
(b) Calculate the in-plane strains ?x, ?y, ?xy.
(c) Calculate ??, ??, ??? of -75° layer.
(d) Determine the safety factor S? of -75° layer by Tsai-Hill failure criterion.
(e) If additional moment resultant My = 10 lb.in/in is also imposed on the laminate,
Calculate the strains ?x, ?y, ?xy at location z = 0.0075 in. The inverse [d] of the flexural stiffness matrix [D] is given as follows: [d] = $\begin{bmatrix} 0.1575 & -0.01265 & -0.00977\\ -0.01265 & 0.0285 & -0.019\\ -0.00977 & -0.019 & 0.20 \end{bmatrix}$ 1/lb.in
