Finite-Element Analysis of HSC. Moderately Deep Beams Using Plastic-Damage Model under Cyclic Loading

Finite-Element Analysis of HSC. Moderately Deep Beams UsingPlastic-Damage Model under Cyclic LoadingI. A. S. al-Shaarbaf L. Kh. K. Al-Hadithy H. M. A. Al-BahadlyAssistant Professor Assistant Professor PhD. StudentDepartment of Civil Engineering, AL-Nahrain University, Baghdad, Iraq,AbstractThis paper presents a numerical investigation of high-strength concrete beams moderately deepsubjected to imposed inelastic cyclic deflection .Three cantilever beams having cross section of200 x 400 mm were selected from the experimental work carried out by I-Kuang Fang , et. al. Testvariables included were shear span to depth ratio, ratio of longitudinal reinforcement at top andbottom faces of the beams and loading histories. The cyclic simulation performance of the selectedbeams 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 stiffnessdegradation in continuum damage mechanics . Two damage variables, one for tensile damageand the others for compressive damage , and yield function with multiple hardening variable areintroduced 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 consistentscalar degradation model is introduced to simulate the effect of damage on elastic stiffness and itsrecovery during crack opening and closing . It was found that the ABAQUS model accuratelypredicts the experimental response under cyclic loading up to the yielding of the steel bars . Theprediction is less accurate at post yielding stages .This difference is due to the severe damage ofthe concrete in tension and compression during loading cycles . Also the prediction of the regiondamage within the moderately deep beams matches the experimental results . Cracks propagation(opening & closing ) and stress distribution during cycles were very well predicted specially theformation of the compression struts and its development into the concrete beams . Thecontribution of stirrups with the plastic-hinge zone is about 30% of the latest half cycle peakload and the developing of the plastic hinge zone were about 051% of the beam height whichwere well estimated compared to the experimental results . The back bone of load-displacementcurve predicted by the ABAQUS model shows a close correlation with the experimental resultsinto the inelastic range .Keywords : ; Crack; Cyclic loading; High concrete strength; Moderately deep beams; Numericalanalysis; Plastic damage; Stiffness degradation . . . / / : .I- 011 * 011 . Kuang Fang . Lee , Lubliner . . Fenves . . . . . ABAQUS . . .