Substitute Frame and adapted Fish-Bone model: Two simplified frames representative of RC moment resisting frames. (15th April 2019) - Soleimani, Reza; Khosravi, Horr; Hamidi, Hamed
Graphical abstract: Highlights: The 'Modified Fish-Bone' model is adapted for RC moment frames. A 'Substitute Frame' model is proposed to represent RC moment frames. Both models are evaluated through 4 RC building models and 62 earthquake records. The evaluation results declare the robustness of both simplified models. Abstract: This paper aims to develop simplified frame models applicable for Reinforced Concrete (RC) moment frames. For this purpose, the existing Modified Fish-Bone (MFB) model, which is usually used for steel moment frames, is adapted for RC moment frames using modified Ibarra-Medina-Krawinkler springs with deteriorating peak-oriented behavior. Pre-analysis demonstrates that the MFB model requires some modifications for RC moment frames to (a) eliminate the imposed redundant compressive forces to the single column which was caused by the unbalanced shear forces between two half-beams at each story, and (b) simulate the migration of contraflexure point in the beams of original RC frames. The challenges stem from (a) the different negative and positive moment capacities in RC beams, and (b) the peak-oriented hysteretic behavior of rotational springs representing beam plastic hinges. More detailed investigation indicates that eliminating the redundant compressive force is the most effective modification, but the migration of contraflexure point due to different negative and positive moment capacities and even the single curvature bending condition of original beams is not crucial. The reason is investigated using step-by-step incremental nonlinear analysis and illustrated that the contraflexure point is usually located in the mid-span at each step, except for a transient phase in the reverse loading. This minor effect is fundamentally based upon the peak-oriented hysteretic behavior of RC beams. Hence, two simplified models branch from the Modified Fish-Bone model: (i) the Adapted Fish-Bone (Adapted MFB) model in which the first crucial modification is applied, and (ii) the Substitute Frame in which both modifications are reflected and seems to be more compatible for RC moment frames. In the end, the accuracy of the proposed models is evaluated using two sets of far-fault and one set of near-fault ground motions. The comprehensive nonlinear dynamic analysis demonstrates that the two proposed models can estimate engineering demand parameters with high accuracy, while they greatly simplify the modeling process, computational effort and visualization of results.