Over-strength connections: Mp < Mu
Finally, when the ultimate moment of the connection is greater than the plastic moment of the connected member, and even though the connection influences the stiffness degradation of the compound element due to its nonlinear behavior, the member inelasticity dominates the behaviour of the compound element. An example for an extended end-plate (EEP) connection is illustrated in Figures 4 and 5 (where the dotted moment-rotation curve refers to the EEP connection considered alone). It can be seen from Figure 5 that the moment-rotation behaviour of the compound element (solid curve) is dominated by the plastic capacity of the member. This kind of connection is referred to as an over-strength connection and corresponds to a fully restrained (AISC 2001) or rigid (CISC 2004) connection (i. e., in the limit when the connection stiffness is considered infinite).
It can be seen from the foregoing discussion that a satisfactory design may be achieved if both the connection and the corresponding connected member have the same strength capacity, i. e., Mp = Mu. It is not good to use an over-strength connection, i. e., Mu>Mp, since the over-strength of the connection is not utilized in any way. Lower-strength connections may be used in circumstances where stiffeners can be added to avoid excessive deformation.
In the common case of a pinned connection, i. e., rc = 0, the compound element has zero rotational stiffness regardless of the value of rp. In this case, any connected member does not experience plastic behaviour. If rc = 1, the compound element behaviour is determined by the inelastic behaviour of the member, i. e., r = rp in the case of a rigid connection. It is noted that when the plasticity factor is
smaller than unity (e. g., rp = 0.7), the r value of the compound element is close to the value of rc (Liu 2005). This means that even if the member end has experienced some plasticity (e. g., 100-70 = 30%), the stiffness of the compound element is dominated by the connection. In other words, the level of inelasticity has insignificant effect on the stiffness degradation of the compound element. If the ultimate strength of a connection is close to, or lower than, the initial yield strength of the connected member, the influence of member plasticity on structural response may be ignored.