Failure,Analysis,and Design of Laminates 371 D12 D16 K My D12 D2 D26 (5.1b) D16 D26 D66」 This shows that the force and moment terms are uncoupled.Thus,if a laminate is subjected only to forces,it will have zero midplane curvatures. Similarly,if it is subjected only to moments,it will have zero midplane strains. The uncoupling between extension and bending in symmetric laminates makes analyzing such laminates simpler.It also prevents a laminate from twisting due to thermal loads,such as cooling down from processing temper- atures and temperature fluctuations during use such as in a space shuttle,etc. 5.2.2 Cross-Ply Laminates A laminate is called a cross-ply laminate(also called laminates with specially orthotropic layers)if only 0 and 90 plies were used to make a laminate.An example of a cross ply laminate is a [0/902/0/90]laminate: 0 90 90 0 90 For cross-ply laminates,A16=0,A26=0,Bi6=0,B26=0,D16=0,and D26 =0;thus,Equation(4.29)can be written as Nx An A12 0 B11 B12 0 Ny A An 0 B12 B22 0 e a 0 0 A66 0 0 Bos Ya (5.2) M B11 B12 0 D11 D12 0 Kx M, Bxz B 0 D12 Da 0 My」 0 0 Bos 0 0 Do K到 In these cases,uncoupling occurs between the normal and shear forces, as well as between the bending and twisting moments.If a cross-ply lami- nate is also symmetric,then in addition to the preceding uncoupling,the coupling matrix [B]=0 and no coupling takes place between the force and moment terms. 2006 by Taylor Francis Group,LLCFailure, Analysis, and Design of Laminates 371 . (5.1b) This shows that the force and moment terms are uncoupled. Thus, if a laminate is subjected only to forces, it will have zero midplane curvatures. Similarly, if it is subjected only to moments, it will have zero midplane strains. The uncoupling between extension and bending in symmetric laminates makes analyzing such laminates simpler. It also prevents a laminate from twisting due to thermal loads, such as cooling down from processing temper￾atures and temperature fluctuations during use such as in a space shuttle, etc. 5.2.2 Cross-Ply Laminates A laminate is called a cross-ply laminate (also called laminates with specially orthotropic layers) if only 0 and 90° plies were used to make a laminate. An example of a cross ply laminate is a [0/902/0/90] laminate: For cross-ply laminates, A16 = 0, A26 = 0, B16 = 0, B26 = 0, D16 = 0, and D26 = 0; thus, Equation (4.29) can be written as . (5.2) In these cases, uncoupling occurs between the normal and shear forces, as well as between the bending and twisting moments. If a cross-ply lami￾nate is also symmetric, then in addition to the preceding uncoupling, the coupling matrix [B] = 0 and no coupling takes place between the force and moment terms. 0 90 90 0 90 M M M D D D D D D D D x y xy ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ = 11 12 16 12 22 26 16 26 6 D 6 x y xy ⎡ ⎣ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ κ κ κ N N N M M M x A A B y xy x y xy ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ = 11 12 0 11 12 12 22 12 22 66 66 11 12 11 1 0 0 0 0 0 0 0 0 B A A B B A B B B D D 2 12 22 12 22 66 66 0 0 0 0 0 0 0 B B D D B D ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ε ε γ κ κ κ x y xy x y xy 0 0 0 ⎥ 1343_book.fm Page 371 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC