On the basis of this analysis,it is possible to derive an expression for the apparent axial Young's modulus including end constraint (Ex)a=x/Ex (9.12) where o,and are the stress and strain at the centerline of the constrained off-axis coupon.(E)a may be expressed as Ex (但)。=1 (9.13) in which Ex is the modulus for an unconstrained off-axis specimen.The parameterξis given by 35。 (9.14) Su 356+25.L6/w7 Examination of the above equations reveals that0and(E)E=1/Su when LG/w→o. Similarly,Pindera and Herakovich [3]derived an expression for the apparent Poisson's ratio,(Vxy)a 1- B ). (9.15) 1- 3 2 52 where B is given by [3], (9.16) The apparent shear coupling ratio of the specimen subjected to end con- straint is (nxy)a =Ysy/Ex (9.17) 2003 by CRC Press LLCOn the basis of this analysis, it is possible to derive an expression for the apparent axial Young’s modulus including end constraint (Ex)a = σx/εx (9.12) where σx and εx are the stress and strain at the centerline of the constrained off-axis coupon. (Ex)a may be expressed as (9.13) in which Ex is the modulus for an unconstrained off-axis specimen. The parameter ξ is given by (9.14) Examination of the above equations reveals that ξ → 0 and (Ex)a → when LG/w → ∞. Similarly, Pindera and Herakovich [3] derived an expression for the apparent Poisson’s ratio, (νxy)a (9.15) where β is given by [3], (9.16) The apparent shear coupling ratio of the specimen subjected to end con￾straint is (ηxy)a = γxy/εx (9.17) E E x a x ( ) = 1− ξ ξ = + ( )         1 S S 11 3S 2S L w G 16 2 66 11 2 3 E S x = 1 11 ν ν β β xy a xy S S S S ( ) = −       −       1 3 2 1 3 2 26 11 16 12 β =             +             w L S S w L S S G G 2 16 11 2 66 11 1 3 2 TX001_ch09_Frame Page 135 Saturday, September 21, 2002 5:01 AM © 2003 by CRC Press LLC