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+// exa 4.10 Pg 116
+clc;clear;close;
+
+// Given Data
+Sut=600;//MPa
+Se=280;//MPa
+sigma_x_min=50;// MPa
+sigma_x_max=100;// MPa
+sigma_y_min=20;// MPa
+sigma_y_max=70;// MPa
+
+sigma_xm=(sigma_x_max+sigma_x_min)/2;// MPa
+sigma_xa=(sigma_x_max-sigma_x_min)/2;// MPa
+sigma_ym=(sigma_y_max+sigma_y_min)/2;// MPa
+sigma_ya=(sigma_y_max-sigma_y_min)/2;// MPa
+
+// distortion energy theory -
+sigma_m=sqrt(sigma_xm**2+sigma_ym**2-sigma_xm*sigma_ym);// MPa
+sigma_a=sqrt(sigma_xa**2+sigma_ya**2-sigma_xa*sigma_ya);// MPa
+theta=atand(sigma_a/sigma_m);// degree
+// Sm/Sut+Sa/Se=1 where Sa=Sm*tan(theta)
+Sm=1/(1/Sut+tand(theta)/Se);// MPa
+Sa=tand(theta)*Sm;// MPa
+n=Sa/sigma_a;// factor of safety
+
+printf('\n factor of safety, n = %.2f',n)