The document provides material properties and calculations for a composite material. It lists the tensile strengths of plies 1, 2, and 6 as 1830 MPa, 57 MPa, and 71 MPa, respectively. It also shows safety factor calculations. The appendix then shows MATLAB code for further calculations involving transforming stress and strain between material coordinate systems for laminates with different fiber orientations using compliance and transformation matrices.

1. from table 1.1
F1t = 1830 MPa
F2t = 57 MPa
F6 = 71 MPa
8.4151 < 1830
6.5849 < 57
3.4151 < 71
Safety factor = 57/6.6 = 8.636

5. Appendix
Pb 5.2
clear all
clc
%% 5.2
Sx=10; Sy=5; Sxy=2.5;
theta=60;
sigma=[Sx;Sy;Sxy];
C= cosd(theta) ;
S=sind(theta);
T=[(C^2) (S^2) (2*S*C); (S^2) (C^2) (-2*S*C); (-C*S) (S*C) ((C^2)-(S^2))]
sigma_dash=T*sigma
Pb 5.3
clear all
clc
%% 5.3
theta=45;
E1=35; E2=3.5; G12=1.75; neu12=0.3; neu21=0.3;
C= cosd(theta) ;
S=sind(theta);
T=[(C^2) (S^2) (2*S*C); (S^2) (C^2) (-2*S*C); (-C*S) (S*C) ((C^2)-(S^2))]
delta=1-(((neu12)^2)*(E2/E1));
Q=[(E1/delta) ((neu12*E2)/delta) 0; ((neu12*E2)/delta) (E2/delta) 0; 0 0 G12]
Q_bar=inv(T)*Q*T
Pb 5.5
clear all
clc
%% 5.5
theta=10; w=0.01; l=0.15; t=0.002; F=200;
E1=35; E2=3.5; G12=1.75; neu12=0.3; neu21=0.3;
A1= w*t
A2= l*t
A12=l*w
sigma1=F/A1
sigma2=F/A2
sigma12=F/A12
sigma_dash=[sigma1; sigma2; sigma12]
C= cosd(theta);
S=sind(theta);
T=[(C^2) (S^2) (2*S*C); (S^2) (C^2) (-2*S*C); (-C*S) (S*C) ((C^2)-(S^2))]
delta=1-(((neu12)^2)*(E2/E1));
Q=[(E1/delta) ((neu12*E2)/delta) 0; ((neu12*E2)/delta) (E2/delta) 0; 0 0 G12]
S= inv(Q)
B=inv(T)
S_bar=B*inv(Q)*T
sigma=B*sigma_dash
epslon=S_bar*sigma
epslon_dash=S*sigma_dash