Mechanical Behavior Of Reinforced Concrete Beams Subjected To Both Dynamic And Static Loading

Currently, reinforced concrete(RC) is one of the main structure and engineering materials in civil and industry buildings. Particularly, some modern special-purpose structures, including offshore structures, protective shelters, nuclear reactor containments, dams, and so on, may be subjected to all kinds of loads and structural forms. To better design and analyze these structures, it is imperative to simulate the RC structural dynamic response by computer programs. The problem of modeling the mechanical behavior of RC remains one of the most difficult changes in the field of structural concrete engineering. RC is a nonhomogeneity material. Due to difficulties in identifying the influence of such nonhomogeneities, it is often ignored, and the observed load-deformation relations of large scale specimens are “translated” as stress-strain relations. In this paper, an investigation is experimentally and theoretically carried out on the constitutive behavior of RC and the structural response of RC beams subjected to static and dynamic loading.A digitally controlled closed-loop servohydraulic test system(MTS) and a drop-weight system(DHR-9401) are utilized in the research on mechanical behavior of six type RC beams subjected to static and dynamic loading. The specimens are simply supported and are tested in a three-point bending configuration. Here, the time histories of the impact load, deflection and strain are measured. The experimental results show that: 1) under the static loading, the stiffness and load-carrying capacity of beams increase with an increasing reinforcement ratio and strength of concrete; the static maximum deflections of the beams decrease with an increasing reinforcement ratio and strength of concrete. The relationship shown in load-deflection curves can be divided into three stages: the uncracked elastic stage, crack propagation stage, and the plastic stage by the critical points of cracking, yield and maximum load. An equivalent constitutive relationship for reinforced concrete is obtained by considering the tension stiffening and the transformed section approach. 2) Under the dynamic loading, for a given drop-weight mass, there exists a certain threshold velocity after which the flexural load capacity of RC beams could not increase anymore, and increases in strain rate can not increase their load carrying capacity; the impulse resulting from the impact is proportional to the momentum of the impacting mass, the scale factors are significantly different when the drop-weight moves with the beam or rebounded; the maximum and residual deflections are almost proportional with respect to the input impact energy, and the gradient could be empirically formulated using the inverse of the static flexural load-carrying capacity of the beam. Two empirical formulas are proposed to estimate the maximum and residual deflection of the beam based on the static flexural load-carrying capacity and the input impact energy.Considering the strain softening of RC, an elastoplastic model with damage is proposed. Material behaviour is considered as a mixture of two interacting components, one termed elastoplastic(undamaged) and the other termed damaged. The model is divided into four intervals: the elastic stage, the based elastoplastic stage on concrete, the based elastoplastic stage on reinforcement and the strain softening stage. The damage variable is responsible for the softening in strength, for the degradation of the elastic shear modulus, and for induced anisotropy. The parameters of reinforcing steel and concrete are calibrated by the softened truss mod proposed by Abdeldjelil & Hsu and the modified compression field theory proposed by Vecchio & Collins. The model is applied to analyze the load-deflection relationships of RC beams and shows very good agreement with the experimental results.Two single degree of freedom models(SDOF) are proposed to predict the response of the beam. The first model(denoted as “energy model”) is developed from the law of energy balance and assumes that the deformed shape of the beam is represented by its first vibration mode. In the second model(named “dynamic model”), the dynamic behavior of the beam is simulated by a spring-mass oscillator. The damage visco-elastic constitutive model of concrete and the strain rate dependencies of the constitutive properties of the reinforcing steel are considered in both formulations. The energy model is based on energy balance, which requires that the external work on the beam equal the sum of the kinetic energy and the strain energy of the beam at each instant of time. The dynamic model is based on the equations of motion.The efficiency of each model is evaluated by comparing the theoretical results with experimental data in this paper. The comparison shows that the dynamic model gives a good estimation of the deflection of the beam when the drop height is lower, and vice versa. The reinforced concrete is regarded as a steel reinforced concrete material, in which concrete phase is main ingredient. A reinforced multiplier and damage variable are adopted to modify the visco-elastic constitutive model. The model is considered in the dynamic bend beam theory, and the relationship between the deflection and time is obtained.A numerical simulation is carried out on the RC beam under impact loading by LS-DYNA code. Results from the simulations show acceptable accuracy of CSCM model and the conode between concrete and reinforcing steel. A combination of appropriate parameters is obtained by comparing the simulation and experimental results, which provides a solid foundation for the future study.