The flexural stiffness degradation factor associated with the semirigid stiffness Rc is given by (Monforton et al 1963),
rc = 1/(1 + 3EI / LRC) (10)
where EI/L is the flexural stiffness of the elastic member. The factor rc is interpreted as the ratio of the end rotation of the elastic member to the combined rotation of the elastic member and the connection due to unit end-moment (Xu, 1994).
Similarly, the stiffness degradation factor associated with the inelastic stiffness Rp is given by (Grierson et al 2005),
rp = 1/(1 + 3EI / LRP) (11)
where the factor rp is interpreted as the ratio of the inelastic rotation M/Rp to the total elastic and inelastic rotation M/Rp + ML/3EI under the action of bending moment M applied at the end connected to the compound element in the case when the far end of the elastic member is simply supported (Xu et al 2005).
To evaluate the combined stiffness effect, a stiffness degradation factor associated with the compound stiffness R is introduced and similarly expressed as r = 1/(1+3EI/LR). The factor r is the ratio of the rotation of the compound element to the sum total of the rotation of the compound element plus the rotation of the elastic member when simply supported at the far end. From Eqs (3), (10) and (11), the compound stiffness degradation factor is found as,
which maps R є [0, го] to r є [0, 1]. From Eq. (12), the stiffness degradation factor for the compound element is a function of the degradation factors of the semirigid connection and member inelasticity, such that if any of these factors degrades to zero then the stiffness of the compound element will degrade to zero as well.