Singularities in RC Beam Elements with Finite-Length Hinges

Abstract

Several models have been presented in the literature for reinforced concrete (RC) beam elements with finite-length hinges to facilitate analyses of the inelastic response of reinforced-concrete frame structures. Such models are considered an improvement on the conventional zero-length hinge (point hinge) model, which seems an unrealistic representation of RC elements undergoing inelastic deformations and is viewed as theoretically inconsistent. This paper identifies two singularities that could arise in the formulation of member models with finite-length hinges. The singularities are more likely to be encountered in frame analysis under cyclic loads (earthquake), than under monotonically increasing loads. Two singularity points are identified in the formulation of the model. One singularity point is due to the direction dependency of the stiffness, and can be avoided if an additional condition is imposed in the formulation to take care of this factor. The other singularity point has physical significance and corresponds to the critical softening parameter, beyond which a member cannot sustain equilibrium.