Finite-element analysis of HSC. moderately deep beams using plastic-damage model under cyclic loading

This paper presents a numerical investigation of high-strength concrete beams moderately deep subjected to imposed inelastic cyclic deflection. Three cantilever beams having cross section of 200 x 400 mm were selected from the experimental work carried out by I-Kuang Fang , et. Al. Test variables included were shear span to depth ratio, ratio of longitudinal reinforcement at top and bottom faces of the beams and loading histories. The cyclic simulation performance of the selected beams were found using the plastic-damage model for concrete developed by Lubliner and Lee & Fenves. The model adopts the concepts of fracture –energy– based damage and stiffness degradation in continuum–damage mechanics. Two damage variables, one for tensile damage and the others for compressive damage, and yield function with multiple–hardening variable are introduced to different damage states. The uniaxial strength function are factored into two parts, corresponding to the effective stress and the degradation of elastic stiffness. A simple consistent scalar degradation model is introduced to simulate the effect of damage on elastic stiffness and its recovery during crack opening and closing. It was found that the ABAQUS model accurately predicts the experimental response under cyclic loading up to the yielding of the steel bars. The prediction is less accurate at post yielding stages. This difference is due to the severe damage of the concrete in tension and compression during loading cycles. Also the prediction of the region damage within the moderately deep beams matches the experimental results. Cracks propagation (opening & closing) and stress distribution during cycles were very well predicted specially the formation of the compression struts and its development into the concrete beams. The contribution of stirrups with the plastic-hinge zone is about 30 % of the latest half–cycle peak load and the developing of the plastic–hinge zone were about 051 % of the beam height which were well estimated compared to the experimental results. The back bone of load-displacement curve predicted by the ABAQUS model shows a close correlation with the experimental results into the inelastic range. تم في هذا البحث دراسة سلوك العتبات الخرسانيه المسلحة عالية المقاومة المتوسطة العمق المعرضة إلى انحرافات دورية لدنه. اختيرت ثلاثة نماذج من العتبات ذات مقطع بأبعاد 200 ملم * 400 ملم من البحث المختبر الذي أجري من قبل مجموعة Kuang Fang-I. حيث اعتبرت المعاملات التي تمثل كل من نسبة فضاء القص إلى الع