SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects

In this paper, reinforced concrete beams subjected to blast and impact loads are examined. Two single degree of freedom models 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. In both formulations, the strain rate dependencies of the constitutive properties of the beams are considered by varying the parameters of the models at each time step of the computation according to the values of the strain rates of the materials (i.e. concrete and reinforcing steels). The efficiency of each model is evaluated by comparing the theoretical results with experimental data found in literature. The comparison shows that the energy model gives a good estimation of the maximum deflection of the beam at collapse, defined as the attainment of the ultimate strain in concrete. On the other hand, the dynamic model generally provides a smaller value of the maximum displacement. However, both approaches yield reliable results, even though they are based on some approximations. Being also very simple to implement, they may serve as an useful tool in practical applications.