The denominator   is given as

(7.194)

with

(7.195)

Thus, the effective axial modulus can be found from Equation (7.187) as

(7.196)

Note: One can determine the effective axial modulus from Equation (7.191). The unknown   can be expressed from this equation in terms of unknown . For this, one has to solve Equations (7.180), (7.183) and (7.189) for  and . Then divide both sides of this equation by cross sectional area of the composite cylinder and . This gives the effective axial modulus. For this case, the unknown constants are given as

(7.197)