Composite Plate Layup Examples

1. +90,0,+90 (symmetric layup), each lamina thickness=0.01", S-glass/epoxy, Nx=Ny=1,000 lb/in

2. 3/+0, lamina thickness=0.01", Woven glass/epoxy, Nx=Ny=1,000 lb/in

3. +45,0,-45 (antisymmetric layup), each lamina thickness=0.01", graphite/epoxy, Nx=Ny=1,000 lb/in

4. same as 3, but Nx=1,000 lb/in

5. same as 3, but Nxy=500 lb/in

6. same as 3, but Mx=10 in-lb/in

7. 4/+0,+45,-45,4/+0, each lamina thickness=0.01", graphite/epoxy, Nx=Ny=1,000 lb/in

8. same as 7, but Mx=50 in-lb/in

9. same as 7, but My=50 in-lb/in

LAMINATE ANALYSIS (plane stress) – Example 1 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is .03 in. (layup is symmetric) Layer# Material # thickness z-bar theta 1 1 0.0100 -.0100 90.0 2 1 0.0100 0.0000 0.0 3 1 0.0100 0.0100 90.0 Laminate Stiffness MatricesA Matrix follows 9.015E+04 1.061E+04 4.395E-02 1.061E+04 1.410E+05 5.700E-01 4.395E-02 5.700E-01 1.980E+04 B Matrix follows -3.803E-06 2.687E-07 -1.790E-12 2.687E-07 1.586E-06 -1.230E-11 -1.790E-12 -1.230E-11 -2.950E-06 D Matrix follows 3.370E+00 7.956E-01 4.761E-06 7.956E-01 1.397E+01 6.175E-05 4.761E-06 6.175E-05 1.485E+00

Laminate Compliance MatricesA' Matrix follows 1.119E-05 -8.420E-07 -6.017E-13 -8.420E-07 7.155E-06 -2.041E-10 -6.017E-13 -2.041E-10 5.051E-05 B' Matrix follows 1.290E-11 -8.546E-13 -4.957E-19 -1.351E-12 -7.193E-13 -3.131E-16 -1.071E-17 -3.754E-16 1.003E-10 D' Matrix follows 3.008E-01 -1.713E-02 -2.518E-07 -1.713E-02 7.258E-02 -2.963E-06 -2.518E-07 -2.963E-06 6.734E-01 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 29.78E+05 46.59E+05 0.075 0.118 66.00E+04 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 1.00E+03 1.00E+03 0.00E+00Mx,My,Mxy= 0.00E+00 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon 0.01035 0.00631 -.00000 kappa 0.00000 -.00000 -.00000 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) 0.01035 0.00631 -.00000 Stresses (x,y) 15.786E+03 44.036E+03 67.560E-03Middle of layer 1 Strains (1,2) 0.00631 0.01035 0.00000 Stresses (1,2) 44.036E+03 15.786E+03 10.431E-02 Tsai-Hill Criterion 2.231602 Top of layer 1 Strains (x,y) 0.01035 0.00631 -.00000 Stresses (x,y) 15.786E+03 44.036E+03 67.560E-03

Note that curvatures are zero

Bottom of layer 2 Strains (x,y) 0.01035 0.00631 -.00000 Stresses (x,y) 68.427E+03 11.927E+03 -13.512E-02Middle of layer 2 Strains (1,2) 0.01035 0.00631 -.00000 Stresses (1,2) 68.427E+03 11.927E+03 -13.512E-02 Tsai-Hill Criterion 1.713186 Top of layer 2 Strains (x,y) 0.01035 0.00631 -.00000 Stresses (x,y) 68.427E+03 11.927E+03 -13.512E-02 Bottom of layer 3 Strains (x,y) 0.01035 0.00631 -.00000 Stresses (x,y) 15.786E+03 44.036E+03 67.560E-03Middle of layer 3 Strains (1,2) 0.00631 0.01035 0.00000 Stresses (1,2) 44.036E+03 15.786E+03 10.431E-02 Tsai-Hill Criterion 2.231602 Top of layer 3 Strains (x,y) 0.01035 0.00631 -.00000 Stresses (x,y) 15.786E+03 44.036E+03 67.560E-03

LAMINATE ANALYSIS (plane stress) – Example 2 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is .03 in. (layup is symmetric) Layer# Material # thickness z-bar theta 1 2 0.0100 -.0100 0.0 2 2 0.0100 0.0000 0.0 3 2 0.0100 0.0100 0.0 Laminate Stiffness MatricesA Matrix follows 1.331E+05 2.264E+04 0.000E+00 2.264E+04 1.331E+05 0.000E+00 0.000E+00 0.000E+00 2.310E+04 B Matrix follows 1.156E-05 -3.700E-07 0.000E+00 -3.700E-07 1.156E-05 0.000E+00 0.000E+00 0.000E+00 -3.442E-06 D Matrix follows 9.986E+00 1.698E+00 0.000E+00 1.698E+00 9.986E+00 0.000E+00 0.000E+00 0.000E+00 1.732E+00

Laminate Compliance MatricesA' Matrix follows 7.734E-06 -1.315E-06 0.000E+00 -1.315E-06 7.734E-06 0.000E+00 0.000E+00 0.000E+00 4.329E-05 B' Matrix follows -9.583E-12 3.437E-12 0.000E+00 3.437E-12 -9.583E-12 0.000E+00 0.000E+00 0.000E+00 8.601E-11 D' Matrix follows 1.031E-01 -1.753E-02 0.000E+00 -1.753E-02 1.031E-01 0.000E+00 0.000E+00 0.000E+00 5.772E-01 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 43.10E+05 43.10E+05 0.170 0.170 77.00E+04 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 1.00E+03 1.00E+03 0.00E+00Mx,My,Mxy= 0.00E+00 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon 0.00642 0.00642 0.00000 kappa -.00000 -.00000 0.00000 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) 0.00642 0.00642 0.00000 Stresses (x,y) 33.333E+03 33.333E+03 0.000E+00Middle of layer 1 Strains (1,2) 0.00642 0.00642 0.00000 Stresses (1,2) 33.333E+03 33.333E+03 0.000E+00 Tsai-Hill Criterion .6289309 Top of layer 1 Strains (x,y) 0.00642 0.00642 0.00000 Stresses (x,y) 33.333E+03 33.333E+03 0.000E+00

Bottom of layer 2 Strains (x,y) 0.00642 0.00642 0.00000 Stresses (x,y) 33.333E+03 33.333E+03 0.000E+00Middle of layer 2 Strains (1,2) 0.00642 0.00642 0.00000 Stresses (1,2) 33.333E+03 33.333E+03 0.000E+00 Tsai-Hill Criterion .6289309 Top of layer 2 Strains (x,y) 0.00642 0.00642 0.00000 Stresses (x,y) 33.333E+03 33.333E+03 0.000E+00 Bottom of layer 3 Strains (x,y) 0.00642 0.00642 0.00000 Stresses (x,y) 33.333E+03 33.333E+03 0.000E+00Middle of layer 3 Strains (1,2) 0.00642 0.00642 0.00000 Stresses (1,2) 33.333E+03 33.333E+03 0.000E+00 Tsai-Hill Criterion .6289309 Top of layer 3 Strains (x,y) 0.00642 0.00642 0.00000 Stresses (x,y) 33.333E+03 33.333E+03 0.000E+00

LAMINATE ANALYSIS (plane stress) – Example 3 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is .03 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0100 45.0 2 5 0.0100 0.0000 0.0 3 5 0.0100 0.0100 -45.0 Laminate Stiffness MatricesA Matrix follows 6.622E+05 2.084E+05 -2.975E-03 2.084E+05 2.439E+05 4.623E-04 -7.877E-04 4.623E-04 2.233E+05 B Matrix follows 4.852E-05 2.811E-05 -2.091E+03 5.018E-05 -4.991E-06 -2.091E+03 -2.091E+03 -2.091E+03 2.999E-05 D Matrix follows 2.898E+01 2.236E+01 -4.339E-07 2.236E+01 2.550E+01 2.554E-07 -3.042E-07 2.554E-07 2.348E+01

Laminate Compliance MatricesA' Matrix follows 2.139E-06 -8.218E-07 -6.641E-14 -8.218E-07 1.767E-05 -1.834E-12 -2.340E-13 -1.412E-12 2.235E-05 B' Matrix follows 4.127E-12 -1.276E-11 1.173E-04 -6.656E-11 -1.027E-10 1.500E-03 6.134E-04 1.295E-03 -1.779E-10 D' Matrix follows 1.235E-01 -5.804E-02 2.961E-09 -5.804E-02 1.964E-01 -1.899E-08 -4.112E-09 -1.483E-08 1.866E-01 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 15.58E+06 18.87E+05 0.384 0.047 14.91E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 1.00E+03 1.00E+03 0.00E+00Mx,My,Mxy= 0.00E+00 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon 0.00132 0.01685 -.00000 kappa -.00000 -.00000 1.61758 NOTE Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) 0.00132 0.01685 -.02426 Stresses (x,y) -64.523E+03 -42.472E+03 -72.390E+03Middle of layer 1 Strains (1,2) 0.00099 0.01717 0.01553 Stresses (1,2) 46.129E+03 16.025E+03 11.025E+03 Tsai-Hill Criterion 4.060878 Top of layer 1 Strains (x,y) 0.00132 0.01685 -.00809 Stresses (x,y) 10.463E+04 12.668E+04 10.249E+04

Bottom of layer 2 Strains (x,y) 0.00132 0.01685 -.00809 Stresses (x,y) 59.896E+03 15.795E+03 -57.424E+02Middle of layer 2 Strains (1,2) 0.00132 0.01685 -.00000 Stresses (1,2) 59.896E+03 15.795E+03 -11.688E-04 Tsai-Hill Criterion 3.722433 Top of layer 2 Strains (x,y) 0.00132 0.01685 0.00809 Stresses (x,y) 59.896E+03 15.795E+03 57.424E+02 Bottom of layer 3 Strains (x,y) 0.00132 0.01685 0.00809 Stresses (x,y) 10.463E+04 12.668E+04 -10.250E+04Middle of layer 3 Strains (1,2) 0.00099 0.01717 -.01553 Stresses (1,2) 46.129E+03 16.025E+03 -11.025E+03 Tsai-Hill Criterion 4.060874 Top of layer 3 Strains (x,y) 0.00132 0.01685 0.02426 Stresses (x,y) -64.523E+03 -42.472E+03 72.390E+03

NOTEFor this problem, only in-plane loads are applied (Nx & Ny). However, we obtain a non-zero curvature Nxy. This is because the layup is unsymmetric and therefore in-plane loads make the corners of the plate curl up (i.e., due to material non-symmetry about centroidal axis of plate). This does not occur in Example 2 where there is material symmetry.

LAMINATE ANALYSIS (plane stress) Example 4 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is .03 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0100 45.0 2 5 0.0100 0.0000 0.0 3 5 0.0100 0.0100 -45.0 Laminate Stiffness MatricesA Matrix follows 6.622E+05 2.084E+05 -2.975E-03 2.084E+05 2.439E+05 4.623E-04 -7.877E-04 4.623E-04 2.233E+05 B Matrix follows 4.852E-05 2.811E-05 -2.091E+03 5.018E-05 -4.991E-06 -2.091E+03 -2.091E+03 -2.091E+03 2.999E-05 D Matrix follows 2.898E+01 2.236E+01 -4.339E-07 2.236E+01 2.550E+01 2.554E-07 -3.042E-07 2.554E-07 2.348E+01

Laminate Compliance MatricesA' Matrix follows 2.139E-06 -8.218E-07 -6.641E-14 -8.218E-07 1.767E-05 -1.834E-12 -2.340E-13 -1.412E-12 2.235E-05 B' Matrix follows 4.127E-12 -1.276E-11 1.173E-04 -6.656E-11 -1.027E-10 1.500E-03 6.134E-04 1.295E-03 -1.779E-10 D' Matrix follows 1.235E-01 -5.804E-02 2.961E-09 -5.804E-02 1.964E-01 -1.899E-08 -4.112E-09 -1.483E-08 1.866E-01 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 15.58E+06 18.87E+05 0.384 0.047 14.91E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 1.00E+03 0.00E+00 0.00E+00Mx,My,Mxy= 0.00E+00 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon 0.00214 -.00082 -.00000 kappa 0.00000 -.00000 0.11734 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) 0.00214 -.00082 -.00176 Stresses (x,y) -17.783E+02 -59.834E+02 -52.514E+02Middle of layer 1 Strains (1,2) 0.00007 0.00125 -.00296 Stresses (1,2) 33.464E+02 11.625E+02 -21.025E+02 Tsai-Hill Criterion .4022242 Top of layer 1 Strains (x,y) 0.00214 -.00082 -.00059 Stresses (x,y) 10.492E+03 62.871E+02 74.353E+02

Bottom of layer 2 Strains (x,y) 0.00214 -.00082 -.00059 Stresses (x,y) 91.286E+03 -30.373E+01 -41.657E+01Middle of layer 2 Strains (1,2) 0.00214 -.00082 -.00000 Stresses (1,2) 91.286E+03 -30.373E+01 -16.612E-05 Tsai-Hill Criterion 1.072169 Top of layer 2 Strains (x,y) 0.00214 -.00082 0.00059 Stresses (x,y) 91.286E+03 -30.373E+01 41.657E+01 Bottom of layer 3 Strains (x,y) 0.00214 -.00082 0.00059 Stresses (x,y) 10.492E+03 62.871E+02 -74.353E+02Middle of layer 3 Strains (1,2) 0.00007 0.00125 0.00296 Stresses (1,2) 33.464E+02 11.625E+02 21.025E+02 Tsai-Hill Criterion .4022242 Top of layer 3 Strains (x,y) 0.00214 -.00082 0.00176 Stresses (x,y) -17.783E+02 -59.834E+02 52.514E+02

LAMINATE ANALYSIS (plane stress)- Example 5 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is .03 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0100 45.0 2 5 0.0100 0.0000 0.0 3 5 0.0100 0.0100 -45.0 Laminate Stiffness MatricesA Matrix follows 6.622E+05 2.084E+05 -2.975E-03 2.084E+05 2.439E+05 4.623E-04 -7.877E-04 4.623E-04 2.233E+05 B Matrix follows 4.852E-05 2.811E-05 -2.091E+03 5.018E-05 -4.991E-06 -2.091E+03 -2.091E+03 -2.091E+03 2.999E-05 D Matrix follows 2.898E+01 2.236E+01 -4.339E-07 2.236E+01 2.550E+01 2.554E-07 -3.042E-07 2.554E-07 2.348E+01

Laminate Compliance MatricesA' Matrix follows 2.139E-06 -8.218E-07 -6.641E-14 -8.218E-07 1.767E-05 -1.834E-12 -2.340E-13 -1.412E-12 2.235E-05 B' Matrix follows 4.127E-12 -1.276E-11 1.173E-04 -6.656E-11 -1.027E-10 1.500E-03 6.134E-04 1.295E-03 -1.779E-10 D' Matrix follows 1.235E-01 -5.804E-02 2.961E-09 -5.804E-02 1.964E-01 -1.899E-08 -4.112E-09 -1.483E-08 1.866E-01 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 15.58E+06 18.87E+05 0.384 0.047 14.91E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 0.00E+00 0.00E+00 5.00E+02Mx,My,Mxy= 0.00E+00 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon -.00000 -.00000 0.01118 kappa 0.30670 0.64761 -.00000 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) -.00460 -.00971 0.01118 Stresses (x,y) -37.304E+03 -44.565E+03 -28.863E+03Middle of layer 1 Strains (1,2) 0.00082 -.01036 -.00341 Stresses (1,2) 32.697E+03 -93.685E+02 -24.204E+02 Tsai-Hill Criterion .8605383 Top of layer 1 Strains (x,y) -.00153 -.00324 0.01118 Stresses (x,y) 65.473E+03 63.052E+03 70.928E+03

Bottom of layer 2 Strains (x,y) -.00153 -.00324 0.01118 Stresses (x,y) -66.241E+03 -33.073E+02 79.346E+02Middle of layer 2 Strains (1,2) -.00000 -.00000 0.01118 Stresses (1,2) -16.138E-04 -85.181E-05 79.346E+02 Tsai-Hill Criterion 1.117547 Top of layer 2 Strains (x,y) 0.00153 0.00324 0.01118 Stresses (x,y) 66.241E+03 33.073E+02 79.346E+02 Bottom of layer 3 Strains (x,y) 0.00153 0.00324 0.01118 Stresses (x,y) -65.473E+03 -63.052E+03 70.928E+03Middle of layer 3 Strains (1,2) -.00082 0.01036 -.00341 Stresses (1,2) -32.697E+03 93.685E+02 -24.204E+02 Tsai-Hill Criterion 2.266084 Top of layer 3 Strains (x,y) 0.00460 0.00971 0.01118 Stresses (x,y) 37.304E+03 44.565E+03 -28.863E+03

LAMINATE ANALYSIS (plane stress) – Example 6 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is .03 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0100 45.0 2 5 0.0100 0.0000 0.0 3 5 0.0100 0.0100 -45.0 Laminate Stiffness MatricesA Matrix follows 6.622E+05 2.084E+05 -2.975E-03 2.084E+05 2.439E+05 4.623E-04 -7.877E-04 4.623E-04 2.233E+05 B Matrix follows 4.852E-05 2.811E-05 -2.091E+03 5.018E-05 -4.991E-06 -2.091E+03 -2.091E+03 -2.091E+03 2.999E-05 D Matrix follows 2.898E+01 2.236E+01 -4.339E-07 2.236E+01 2.550E+01 2.554E-07 -3.042E-07 2.554E-07 2.348E+01

Laminate Compliance MatricesA' Matrix follows 2.139E-06 -8.218E-07 -6.641E-14 -8.218E-07 1.767E-05 -1.834E-12 -2.340E-13 -1.412E-12 2.235E-05 B' Matrix follows 4.127E-12 -1.276E-11 1.173E-04 -6.656E-11 -1.027E-10 1.500E-03 6.134E-04 1.295E-03 -1.779E-10 D' Matrix follows 1.235E-01 -5.804E-02 2.961E-09 -5.804E-02 1.964E-01 -1.899E-08 -4.112E-09 -1.483E-08 1.866E-01 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 15.58E+06 18.87E+05 0.384 0.047 14.91E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 0.00E+00 0.00E+00 0.00E+00Mx,My,Mxy= 1.00E+01 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon 0.00000 -.00000 0.00613 kappa 1.23539 -.58038 -.00000 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) -.01853 0.00871 0.00613 Stresses (x,y) -63.504E+03 -24.827E+03 -36.425E+03Middle of layer 1 Strains (1,2) -.00021 -.00634 0.01816 Stresses (1,2) -10.241E+03 -58.854E+02 12.892E+03 Tsai-Hill Criterion 1.864844 Top of layer 1 Strains (x,y) -.00618 0.00290 0.00613 Stresses (x,y) 21.594E+03 34.485E+03 32.070E+03

Bottom of layer 2 Strains (x,y) -.00618 0.00290 0.00613 Stresses (x,y) -26.344E+04 13.643E+02 43.551E+02Middle of layer 2 Strains (1,2) 0.00000 -.00000 0.00613 Stresses (1,2) 16.234E-04 -60.429E-05 43.551E+02 Tsai-Hill Criterion .613396 Top of layer 2 Strains (x,y) 0.00618 -.00290 0.00613 Stresses (x,y) 26.344E+04 -13.643E+02 43.551E+02 Bottom of layer 3 Strains (x,y) 0.00618 -.00290 0.00613 Stresses (x,y) -21.594E+03 -34.486E+03 32.070E+03Middle of layer 3 Strains (1,2) 0.00021 0.00634 0.01816 Stresses (1,2) 10.241E+03 58.854E+02 12.892E+03 Tsai-Hill Criterion 2.275187 Top of layer 3 Strains (x,y) 0.01853 -.00871 0.00613 Stresses (x,y) 63.504E+03 24.827E+03 -36.425E+03

LAMINATE ANALYSIS (plane stress) – Example 7 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is 9.999999E-02 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0450 0.0 2 5 0.0100 -.0350 0.0 3 5 0.0100 -.0250 0.0 4 5 0.0100 -.0150 0.0 5 5 0.0100 -.0050 45.0 6 5 0.0100 0.0050 -45.0 7 5 0.0100 0.0150 0.0 8 5 0.0100 0.0250 0.0 9 5 0.0100 0.0350 0.0 10 5 0.0100 0.0450 0.0 Laminate Stiffness MatricesA Matrix follows 3.655E+06 2.232E+05 -2.975E-03 2.232E+05 3.083E+05 4.623E-04 -7.877E-04 4.623E-04 2.730E+05 B Matrix follows

8.166E-03 6.679E-04 -1.046E+03 6.832E-04 8.371E-04 -1.046E+03 -1.046E+03 -1.046E+03 7.685E-04 D Matrix follows 3.542E+03 2.439E+01 -5.806E-06 2.439E+01 8.396E+01 -5.814E-06 -5.950E-06 -5.814E-06 6.590E+01 Laminate Compliance MatricesA' Matrix follows 2.864E-07 -2.028E-07 -2.710E-15 -2.028E-07 3.571E-06 -2.884E-13 -5.333E-15 -2.865E-13 3.848E-06 B' Matrix follows -6.196E-13 -1.800E-14 1.326E-06 1.677E-14 -3.389E-11 5.345E-05 8.078E-07 4.769E-05 -4.523E-11 D' Matrix follows 2.831E-04 -7.216E-05 -2.176E-13 -7.216E-05 1.253E-02 4.073E-12 2.042E-13 4.358E-12 1.604E-02 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 34.92E+06 28.00E+05 0.708 0.057 25.99E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 1.00E+03 1.00E+03 0.00E+00Mx,My,Mxy= 0.00E+00 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon 0.00008 0.00337 -.00000 kappa -.00000 -.00000 0.05477 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) 0.00008 0.00337 -.00274 Stresses (x,y) 42.861E+02 31.201E+02 -19.444E+02

Middle of layer 1 Strains (1,2) 0.00008 0.00337 -.00246 Stresses (1,2) 42.861E+02 31.201E+02 -17.500E+02 Tsai-Hill Criterion .7667747 Top of layer 1 Strains (x,y) 0.00008 0.00337 -.00219 Stresses (x,y) 42.861E+02 31.201E+02 -15.556E+02 Bottom of layer 2 Strains (x,y) 0.00008 0.00337 -.00219 Stresses (x,y) 42.861E+02 31.201E+02 -15.556E+02Middle of layer 2 Strains (1,2) 0.00008 0.00337 -.00192 Stresses (1,2) 42.861E+02 31.201E+02 -13.611E+02 Tsai-Hill Criterion .7509611 Top of layer 2 Strains (x,y) 0.00008 0.00337 -.00164 Stresses (x,y) 42.861E+02 31.201E+02 -11.667E+02 Bottom of layer 3 Strains (x,y) 0.00008 0.00337 -.00164 Stresses (x,y) 42.861E+02 31.201E+02 -11.667E+02Middle of layer 3 Strains (1,2) 0.00008 0.00337 -.00137 Stresses (1,2) 42.861E+02 31.201E+02 -97.222E+01 Tsai-Hill Criterion .7388788 Top of layer 3 Strains (x,y) 0.00008 0.00337 -.00110 Stresses (x,y) 42.861E+02 31.201E+02 -77.778E+01 Bottom of layer 4 Strains (x,y) 0.00008 0.00337 -.00110 Stresses (x,y) 42.861E+02 31.201E+02 -77.778E+01Middle of layer 4 Strains (1,2) 0.00008 0.00337 -.00082 Stresses (1,2) 42.861E+02 31.201E+02 -58.333E+01 Tsai-Hill Criterion .7307128 Top of layer 4 Strains (x,y) 0.00008 0.00337 -.00055 Stresses (x,y) 42.861E+02 31.201E+02 -38.889E+01 Bottom of layer 5 Strains (x,y) 0.00008 0.00337 -.00055 Stresses (x,y) 29.992E+03 34.656E+03 30.174E+03Middle of layer 5 Strains (1,2) 0.00159 0.00186 0.00328 Stresses (1,2) 68.323E+03 20.524E+02 23.322E+02

Tsai-Hill Criterion .978777 Top of layer 5 Strains (x,y) 0.00008 0.00337 -.00000 Stresses (x,y) 35.719E+03 40.383E+03 36.096E+03 Bottom of layer 6 Strains (x,y) 0.00008 0.00337 -.00000 Stresses (x,y) 35.719E+03 40.383E+03 -36.096E+03Middle of layer 6 Strains (1,2) 0.00159 0.00186 -.00328 Stresses (1,2) 68.323E+03 20.524E+02 -23.322E+02 Tsai-Hill Criterion .9787766 Top of layer 6 Strains (x,y) 0.00008 0.00337 0.00055 Stresses (x,y) 29.992E+03 34.656E+03 -30.174E+03 Bottom of layer 7 Strains (x,y) 0.00008 0.00337 0.00055 Stresses (x,y) 42.861E+02 31.201E+02 38.889E+01Middle of layer 7 Strains (1,2) 0.00008 0.00337 0.00082 Stresses (1,2) 42.861E+02 31.201E+02 58.333E+01 Tsai-Hill Criterion .7307127 Top of layer 7 Strains (x,y) 0.00008 0.00337 0.00110 Stresses (x,y) 42.861E+02 31.201E+02 77.778E+01 Bottom of layer 8 Strains (x,y) 0.00008 0.00337 0.00110 Stresses (x,y) 42.861E+02 31.201E+02 77.778E+01Middle of layer 8 Strains (1,2) 0.00008 0.00337 0.00137 Stresses (1,2) 42.861E+02 31.201E+02 97.222E+01 Tsai-Hill Criterion .7388784 Top of layer 8 Strains (x,y) 0.00008 0.00337 0.00164 Stresses (x,y) 42.861E+02 31.201E+02 11.667E+02 Bottom of layer 9 Strains (x,y) 0.00008 0.00337 0.00164 Stresses (x,y) 42.861E+02 31.201E+02 11.667E+02Middle of layer 9 Strains (1,2) 0.00008 0.00337 0.00192 Stresses (1,2) 42.861E+02 31.201E+02 13.611E+02 Tsai-Hill Criterion .7509606 Top of layer 9 Strains (x,y) 0.00008 0.00337 0.00219

Stresses (x,y) 42.861E+02 31.201E+02 15.556E+02 Bottom of layer 10 Strains (x,y) 0.00008 0.00337 0.00219 Stresses (x,y) 42.861E+02 31.201E+02 15.556E+02Middle of layer 10 Strains (1,2) 0.00008 0.00337 0.00246 Stresses (1,2) 42.861E+02 31.201E+02 17.500E+02 Tsai-Hill Criterion .7667741 Top of layer 10 Strains (x,y) 0.00008 0.00337 0.00274 Stresses (x,y) 42.861E+02 31.201E+02 19.444E+02

LAMINATE ANALYSIS (plane stress) – Example 8 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is 9.999999E-02 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0450 0.0 2 5 0.0100 -.0350 0.0 3 5 0.0100 -.0250 0.0 4 5 0.0100 -.0150 0.0 5 5 0.0100 -.0050 45.0 6 5 0.0100 0.0050 -45.0 7 5 0.0100 0.0150 0.0 8 5 0.0100 0.0250 0.0 9 5 0.0100 0.0350 0.0 10 5 0.0100 0.0450 0.0 Laminate Stiffness MatricesA Matrix follows 3.655E+06 2.232E+05 -2.975E-03 2.232E+05 3.083E+05 4.623E-04 -7.877E-04 4.623E-04 2.730E+05 B Matrix follows

8.166E-03 6.679E-04 -1.046E+03 6.832E-04 8.371E-04 -1.046E+03 -1.046E+03 -1.046E+03 7.685E-04 D Matrix follows 3.542E+03 2.439E+01 -5.806E-06 2.439E+01 8.396E+01 -5.814E-06 -5.950E-06 -5.814E-06 6.590E+01 Laminate Compliance MatricesA' Matrix follows 2.864E-07 -2.028E-07 -2.710E-15 -2.028E-07 3.571E-06 -2.884E-13 -5.333E-15 -2.865E-13 3.848E-06 B' Matrix follows -6.196E-13 -1.800E-14 1.326E-06 1.677E-14 -3.389E-11 5.345E-05 8.078E-07 4.769E-05 -4.523E-11 D' Matrix follows 2.831E-04 -7.216E-05 -2.176E-13 -7.216E-05 1.253E-02 4.073E-12 2.042E-13 4.358E-12 1.604E-02 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 34.92E+06 28.00E+05 0.708 0.057 25.99E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 0.00E+00 0.00E+00 0.00E+00Mx,My,Mxy= 5.00E+01 0.00E+00 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon -.00000 0.00000 0.00004 kappa 0.01415 -.00361 0.00000 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) -.00071 0.00018 0.00004 Stresses (x,y) -30.216E+03 16.245E+00 28.678E+00

Middle of layer 1 Strains (1,2) -.00064 0.00016 0.00004 Stresses (1,2) -27.194E+03 14.620E+00 28.678E+00 Tsai-Hill Criterion .3826142 Top of layer 1 Strains (x,y) -.00057 0.00014 0.00004 Stresses (x,y) -24.172E+03 12.996E+00 28.678E+00 Bottom of layer 2 Strains (x,y) -.00057 0.00014 0.00004 Stresses (x,y) -24.172E+03 12.996E+00 28.678E+00Middle of layer 2 Strains (1,2) -.00050 0.00013 0.00004 Stresses (1,2) -21.151E+03 11.371E+00 28.678E+00 Tsai-Hill Criterion .2975996 Top of layer 2 Strains (x,y) -.00042 0.00011 0.00004 Stresses (x,y) -18.129E+03 97.469E-01 28.678E+00 Bottom of layer 3 Strains (x,y) -.00042 0.00011 0.00004 Stresses (x,y) -18.129E+03 97.469E-01 28.678E+00Middle of layer 3 Strains (1,2) -.00035 0.00009 0.00004 Stresses (1,2) -15.108E+03 81.224E-01 28.678E+00 Tsai-Hill Criterion .21259 Top of layer 3 Strains (x,y) -.00028 0.00007 0.00004 Stresses (x,y) -12.086E+03 64.979E-01 28.678E+00 Bottom of layer 4 Strains (x,y) -.00028 0.00007 0.00004 Stresses (x,y) -12.086E+03 64.979E-01 28.678E+00Middle of layer 4 Strains (1,2) -.00021 0.00005 0.00004 Stresses (1,2) -90.647E+02 48.734E-01 28.678E+00 Tsai-Hill Criterion .1275949 Top of layer 4 Strains (x,y) -.00014 0.00004 0.00004 Stresses (x,y) -60.431E+02 32.490E-01 28.678E+00 Bottom of layer 5 Strains (x,y) -.00014 0.00004 0.00004 Stresses (x,y) -86.629E+01 -61.405E+01 -66.611E+01Middle of layer 5 Strains (1,2) -.00001 -.00005 0.00009 Stresses (1,2) -27.361E+01 -44.191E+00 63.057E+00

Tsai-Hill Criterion 1.004882E-02 Top of layer 5 Strains (x,y) 0.00000 -.00000 0.00004 Stresses (x,y) 42.237E+01 42.236E+01 43.669E+01 Bottom of layer 6 Strains (x,y) 0.00000 -.00000 0.00004 Stresses (x,y) -42.237E+01 -42.236E+01 43.669E+01Middle of layer 6 Strains (1,2) 0.00001 0.00005 0.00009 Stresses (1,2) 27.361E+01 44.191E+00 63.057E+00 Tsai-Hill Criterion 1.389681E-02 Top of layer 6 Strains (x,y) 0.00014 -.00004 0.00004 Stresses (x,y) 86.629E+01 61.405E+01 -66.611E+01 Bottom of layer 7 Strains (x,y) 0.00014 -.00004 0.00004 Stresses (x,y) 60.431E+02 -32.490E-01 28.678E+00Middle of layer 7 Strains (1,2) 0.00021 -.00005 0.00004 Stresses (1,2) 90.647E+02 -48.734E-01 28.678E+00 Tsai-Hill Criterion .1063738 Top of layer 7 Strains (x,y) 0.00028 -.00007 0.00004 Stresses (x,y) 12.086E+03 -64.979E-01 28.678E+00 Bottom of layer 8 Strains (x,y) 0.00028 -.00007 0.00004 Stresses (x,y) 12.086E+03 -64.979E-01 28.678E+00Middle of layer 8 Strains (1,2) 0.00035 -.00009 0.00004 Stresses (1,2) 15.108E+03 -81.224E-01 28.678E+00 Tsai-Hill Criterion .1772078 Top of layer 8 Strains (x,y) 0.00042 -.00011 0.00004 Stresses (x,y) 18.129E+03 -97.469E-01 28.678E+00 Bottom of layer 9 Strains (x,y) 0.00042 -.00011 0.00004 Stresses (x,y) 18.129E+03 -97.469E-01 28.678E+00Middle of layer 9 Strains (1,2) 0.00050 -.00013 0.00004 Stresses (1,2) 21.151E+03 -11.371E+00 28.678E+00 Tsai-Hill Criterion .2480594 Top of layer 9 Strains (x,y) 0.00057 -.00014 0.00004

Stresses (x,y) 24.172E+03 -12.996E+00 28.678E+00 Bottom of layer 10 Strains (x,y) 0.00057 -.00014 0.00004 Stresses (x,y) 24.172E+03 -12.996E+00 28.678E+00Middle of layer 10 Strains (1,2) 0.00064 -.00016 0.00004 Stresses (1,2) 27.194E+03 -14.620E+00 28.678E+00 Tsai-Hill Criterion .3189168 Top of layer 10 Strains (x,y) 0.00071 -.00018 0.00004 Stresses (x,y) 30.216E+03 -16.245E+00 28.678E+00

LAMINATE ANALYSIS (plane stress) – Example 9 The following orthotropic materials are now defined (english units: lbf, in)Mat # Material Name E1 E2 Nu12 G12 Vf 1 S-Glass/epoxy 63.00E+05 12.90E+05 .270 66.00E+04 .50 2 Woven-Glass/epo 43.10E+05 43.10E+05 .170 77.00E+04 .45 3 Kevlar/epoxy 12.60E+06 80.00E+04 .340 31.00E+04 .60 4 Carbon/epoxy(AS 20.60E+06 15.00E+05 .270 10.40E+05 .63 5 Graphite/epoxy 42.70E+06 92.00E+04 .230 71.00E+04 .57 6 Boron/epoxy 29.20E+06 31.50E+05 .170 78.00E+04 .50 7 Boron/aluminum 34.10E+06 19.90E+06 .300 68.00E+05 .50 8 SiCarbide/alum 29.60E+06 17.10E+06 .270 59.00E+05 .43 9 SiCarbide/ceram 17.60E+06 16.20E+06 .200 64.00E+05 .39 Summary of layup information. Total thickness is 9.999999E-02 in. (layup is anti-symmetric) Layer# Material # thickness z-bar theta 1 5 0.0100 -.0450 0.0 2 5 0.0100 -.0350 0.0 3 5 0.0100 -.0250 0.0 4 5 0.0100 -.0150 0.0 5 5 0.0100 -.0050 45.0 6 5 0.0100 0.0050 -45.0 7 5 0.0100 0.0150 0.0 8 5 0.0100 0.0250 0.0 9 5 0.0100 0.0350 0.0 10 5 0.0100 0.0450 0.0 Laminate Stiffness MatricesA Matrix follows 3.655E+06 2.232E+05 -2.975E-03 2.232E+05 3.083E+05 4.623E-04 -7.877E-04 4.623E-04 2.730E+05 B Matrix follows

8.166E-03 6.679E-04 -1.046E+03 6.832E-04 8.371E-04 -1.046E+03 -1.046E+03 -1.046E+03 7.685E-04 D Matrix follows 3.542E+03 2.439E+01 -5.806E-06 2.439E+01 8.396E+01 -5.814E-06 -5.950E-06 -5.814E-06 6.590E+01 Laminate Compliance MatricesA' Matrix follows 2.864E-07 -2.028E-07 -2.710E-15 -2.028E-07 3.571E-06 -2.884E-13 -5.333E-15 -2.865E-13 3.848E-06 B' Matrix follows -6.196E-13 -1.800E-14 1.326E-06 1.677E-14 -3.389E-11 5.345E-05 8.078E-07 4.769E-05 -4.523E-11 D' Matrix follows 2.831E-04 -7.216E-05 -2.176E-13 -7.216E-05 1.253E-02 4.073E-12 2.042E-13 4.358E-12 1.604E-02 Approximate values of x,y laminate properties from A' matrix NOTE: ONLY VALID FOR SYMMETRIC LAYUP OR WHERE COUPLING (B') IS SMALL Ex Ey Nuxy Nuyx Gxy 34.92E+06 28.00E+05 0.708 0.057 25.99E+05 Applied mid-surface stress and moment resultants follow (lb/in and in-lb/in)Nx,Ny,Nxy= 0.00E+00 0.00E+00 0.00E+00Mx,My,Mxy= 0.00E+00 5.00E+01 0.00E+00 Laminate mid-surface x-y strains and curvatures follow epsilon -.00000 -.00000 0.00238 kappa -.00361 0.62625 0.00000 Lamina x-y strains and stresses follow (top and bottom of each ply)Lamina 1-2 strains and stresses follow (middle of each ply)Tsai-Hill failure criterion is fraction of failure stress.Stresses in psi, strains are in/inBottom of layer 1 Strains (x,y) 0.00018 -.03131 0.00238 Stresses (x,y) 10.790E+02 -28.802E+03 16.931E+02

Middle of layer 1 Strains (1,2) 0.00016 -.02818 0.00238 Stresses (1,2) 97.111E+01 -25.922E+03 16.931E+02 Tsai-Hill Criterion 1.841982 Top of layer 1 Strains (x,y) 0.00014 -.02505 0.00238 Stresses (x,y) 86.321E+01 -23.042E+03 16.931E+02 Bottom of layer 2 Strains (x,y) 0.00014 -.02505 0.00238 Stresses (x,y) 86.321E+01 -23.042E+03 16.931E+02Middle of layer 2 Strains (1,2) 0.00013 -.02192 0.00238 Stresses (1,2) 75.531E+01 -20.162E+03 16.931E+02 Tsai-Hill Criterion 1.440472 Top of layer 2 Strains (x,y) 0.00011 -.01879 0.00238 Stresses (x,y) 64.741E+01 -17.281E+03 16.931E+02 Bottom of layer 3 Strains (x,y) 0.00011 -.01879 0.00238 Stresses (x,y) 64.741E+01 -17.281E+03 16.931E+02Middle of layer 3 Strains (1,2) 0.00009 -.01566 0.00238 Stresses (1,2) 53.951E+01 -14.401E+03 16.931E+02 Tsai-Hill Criterion 1.042356 Top of layer 3 Strains (x,y) 0.00007 -.01253 0.00238 Stresses (x,y) 43.160E+01 -11.521E+03 16.931E+02 Bottom of layer 4 Strains (x,y) 0.00007 -.01253 0.00238 Stresses (x,y) 43.160E+01 -11.521E+03 16.931E+02Middle of layer 4 Strains (1,2) 0.00005 -.00939 0.00238 Stresses (1,2) 32.370E+01 -86.407E+02 16.931E+02 Tsai-Hill Criterion .6538631 Top of layer 4 Strains (x,y) 0.00004 -.00626 0.00238 Stresses (x,y) 21.580E+01 -57.605E+02 16.931E+02 Bottom of layer 5 Strains (x,y) 0.00004 -.00626 0.00238 Stresses (x,y) -39.228E+03 -48.171E+03 -39.327E+03Middle of layer 5 Strains (1,2) -.00036 -.00275 -.00315 Stresses (1,2) -16.154E+03 -26.091E+02 -22.360E+02

Tsai-Hill Criterion .4197905 Top of layer 5 Strains (x,y) -.00000 0.00000 0.00238 Stresses (x,y) 24.937E+03 24.936E+03 25.782E+03 Bottom of layer 6 Strains (x,y) -.00000 0.00000 0.00238 Stresses (x,y) -24.937E+03 -24.936E+03 25.782E+03Middle of layer 6 Strains (1,2) 0.00036 0.00275 -.00315 Stresses (1,2) 16.154E+03 26.091E+02 -22.360E+02 Tsai-Hill Criterion .7052791 Top of layer 6 Strains (x,y) -.00004 0.00626 0.00238 Stresses (x,y) 39.228E+03 48.171E+03 -39.327E+03 Bottom of layer 7 Strains (x,y) -.00004 0.00626 0.00238 Stresses (x,y) -21.580E+01 57.605E+02 16.931E+02Middle of layer 7 Strains (1,2) -.00005 0.00939 0.00238 Stresses (1,2) -32.370E+01 86.407E+02 16.931E+02 Tsai-Hill Criterion 2.023704 Top of layer 7 Strains (x,y) -.00007 0.01253 0.00238 Stresses (x,y) -43.161E+01 11.521E+03 16.931E+02 Bottom of layer 8 Strains (x,y) -.00007 0.01253 0.00238 Stresses (x,y) -43.161E+01 11.521E+03 16.931E+02Middle of layer 8 Strains (1,2) -.00009 0.01566 0.00238 Stresses (1,2) -53.951E+01 14.401E+03 16.931E+02 Tsai-Hill Criterion 3.35782 Top of layer 8 Strains (x,y) -.00011 0.01879 0.00238 Stresses (x,y) -64.741E+01 17.281E+03 16.931E+02 Bottom of layer 9 Strains (x,y) -.00011 0.01879 0.00238 Stresses (x,y) -64.741E+01 17.281E+03 16.931E+02Middle of layer 9 Strains (1,2) -.00013 0.02192 0.00238 Stresses (1,2) -75.531E+01 20.162E+03 16.931E+02 Tsai-Hill Criterion 4.695138 Top of layer 9 Strains (x,y) -.00014 0.02505 0.00238

Stresses (x,y) -86.321E+01 23.042E+03 16.931E+02 Bottom of layer 10 Strains (x,y) -.00014 0.02505 0.00238 Stresses (x,y) -86.321E+01 23.042E+03 16.931E+02Middle of layer 10 Strains (1,2) -.00016 0.02818 0.00238 Stresses (1,2) -97.111E+01 25.922E+03 16.931E+02 Tsai-Hill Criterion 6.033529 Top of layer 10 Strains (x,y) -.00018 0.03131 0.00238 Stresses (x,y) -10.790E+02 28.802E+03 16.931E+02