where the reduced stiffnesses,Qcan be expressed in terms of the engineering constants Q1=E1/(1-V12V2) (2.11a) Q12=V12E2/(1-V12V2i)=V2E1/(1-V12V2) (2.11b) Q22=E2/(1-v12V2) (2.11c) Q66=G12 2.11d) 2.1.1 Transformation of Stresses and Strains For a lamina whose principal material axes(1,2)are oriented at an angle,0, with respect to the x,y coordinate system(Figure 2.3),the stresses and strains can be transformed.It may be shown [1-6]that both the stresses and strains transform according to 01 Ox 02 =[T] y (2.12) Ty】 and E2 (2.13) Y2/2 Y/2 z,3 2 8o888 FIGURE 2.3 Positive (counterclockwise)rotation of principal material axes(1,2)from arbitrary x,y axes. ©2003 by CRC Press LLCwhere the reduced stiffnesses, Qij, can be expressed in terms of the engineering constants Q11 = E1/(1 – ν12ν21) (2.11a) Q12 = ν12E2/(1 – ν12ν21) = ν21E1/(1 – ν12ν21) (2.11b) Q22 = E2/(1 – ν12ν21) (2.11c) Q66 = G12 (2.11d) 2.1.1 Transformation of Stresses and Strains For a lamina whose principal material axes (1,2) are oriented at an angle, θ, with respect to the x,y coordinate system (Figure 2.3), the stresses and strains can be transformed. It may be shown [1–6] that both the stresses and strains transform according to (2.12) and (2.13) FIGURE 2.3 Positive (counterclockwise) rotation of principal material axes (1,2) from arbitrary x,y axes. 1 2 12 x y xy T σ σ τ σ σ τ           = [ ]             ε ε γ ε ε γ 1 2 12 / / 2 2           = [ ]           T x y xy TX001_ch02_Frame Page 14 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC