The first continuity condition is the first of Equation (7.180). The continuity of radial stresses at the fibre and matrix interface from Equation (7.182) gives

(7.202)

The radial stress free condition on outer surface as in Equation (7.188) gives the relation

(7.203)

The effective axial force as given in Equation (7.190) is written as

(7.204)

Here,  and  are the unknowns. These can be obtained by solving the Equations (7.180) and Equations (7.202) through (7.204). These are given as

(7.205)

where,

(7.206)

and

(7.207)

with

(7.208)

Then the effective axial modulus  can be determined from Equation (7.196) with appropriate substitutions of equations for isotropic assumption of fibre and matrix materials.