MT-1620 al.2002 C11 1≈c0s2901+sinb2 22= sin 0 a11 CoS 0 a22 12=c0ssn6(a22-a only exists if a11≠a22 isotropic→ no shea Isotropic Materials 1 value a is the same in all directions Typical Values for Materials Material C LE Steel 6Uns:×106F Aluminum 125 uinn/°F Titanium strain/°F Uni gr/Ep (along fibers) 0.2 Uni Gr/Ep(perpendicular to fibers) 16= strain/F Paul A Lagace @2001 Unit9-p. 10MIT - 16.20 Fall, 2002 ∗ α˜ 11 = cos2 θ α11 + sin2 θ α∗22 ∗ α˜ 22 = sin2θ α11 + cos2θ α∗22 ∗ ∗ α˜ 12 = cos θ sinθ (α22 − α11) ∗ ∗ only exists if α11 ≠ α22 [isotropic ⇒ no shear] • Isotropic Materials 1 value: α is the same in all directions Typical Values for Materials: Units: x 10-6/°F µin/in/°F strain/°F ⇒ µstrain/°F Paul A. Lagace © 2001 Unit 9 - p. 10 Material C.T.E. Uni Gr/Ep (perpendicular to fibers) Uni Gr/Ep (along fibers) Titanium Aluminum Steel 16 -0.2 5 12.5 6