Question

Q4. (a) Calculate the ply reduced stiffness matrix, [Q], for a specially orthotropic ply having the following properties: E = 240 E2 = 12 GPa GPa G12 = 6 GPa V12 = 0.3 [13 marks) (b) Calculate the ply reduced compliance matrix, [S], for a specially orthotropic ply having the following properties: E1 = 69.7 GPa E2 = 59.7 GPa G12 = 7.5 GPa V 12 = 0.3 [12 marks]

Answer 1

1 a given E = 240 GP a - 12 GRA n = 6 G Pa 12 = 0.3 Ply reduced stiffners matrix (Q] Q12 (Q] = Qiz Que where, Qui 1- Vzz zz Now, V = 12Ę 0,3x 12 240 = 0.015 Q11 240 1- (0.3) (0.015 1-V12 V 21 = 241.085 Qq2 Vg2 E = 0,3x12 I-V 22 V 21 1 - (0.32 0.015

[9= 3,62 22 E I - Vg2 23 = 12.05 ) 12 1- (0.3) (0.035 22 Ozz - Biz Qzz = 6 Q12 Diz (@J = Qar 033 o 242,085 3.62 O 3.62 1 2,05 Gpa 6 Anwer given, Eg = 69.7 GPA E = 59,7 Gla Cage = 7.5 Gla V2 = 0,3 Ply Reduced Complonce matsix [5] [s] = Es 1 -V21 o 1

= V2 E = 0.3 x 59,7 697 0,257 1 - V12 EL 1 Is = -V21 Ez 0 1 Gaz o - 03 69.7 69,7 - 0.257 59.7 59.7 1 7.5 ری) 14,3 5x103 4,03 x 103 4.3 X 10? 16,75x10 133.33x103 14.35 - 4.3 [s] -4.3 16.75 0 0 133.33 Ans > ((Pa)