In this paper, the structural responses of reinforced concrete (RC) beams subjected to blast loading are investigated. In particular, RC beams with a low reinforcement ratio are examined, which are more likely to fail in flexure than in shear. In order to assess the response of the beam, two analytical approaches are developed. In the first one, the beam is modeled as a continuous element by means of Euler-Bernoulli’s theory, which neglects the contributions of shear deformation and rotary inertia. The nonlinear behaviour of the beam in the elastic-plastic range is approximated by a single smooth relationship between bending moment and curvature, which allows to derive an original expression of the differential equation of motion of the beam. The parameters appearing in the latter are easily determined from the geometric and constitutive properties of the beam. The second approach described in this paper consists in evaluating the response of the beam through an equivalent single degree of freedom (SDOF) system. The latter is a mass-spring oscillator, and its constitutive behaviour is expressed through a bilateral relationship between force and displacement. The main drawback of this simplified approach is the need to introduce empirical quantities, such as the equivalent mass and the length of the plastic hinge. In both approaches, strain rate effects are taken into account. In fact, these effects should not be ignored in problems concerning blast loads, since the mechanical properties of both concrete and steel strongly depend on the rate of deformation. In this paper, strain rate effects are considered by changing the parameters related to the material properties during time, in accordance with the rules provided by the CEB Information Bulletin n. 187 and the fib Bulletin n. 55. Finally, in order to test the validity of the two approaches, the theoretical results are compared with some experimental data found in literature. In particular, the time-histories of the maximum deflections of several simply supported RC beams under uniformly distributed loads generated by explosions are analyzed. It is shown that the first approach is capable of predicting both the maximum displacement time-history and the deflection at collapse of any beam accurately. On the other hand, the second approach gives a less precise assessment of the structural response of the beam; nonetheless, the method based on the equivalent SDOF model is simpler to use and its differential equation of motion is faster to integrate.
Evaluation of the structural response of reinforced concrete beams failing in flexure under blast loads
STOCHINO, FLAVIO;CARTA G.
2013-01-01
Abstract
In this paper, the structural responses of reinforced concrete (RC) beams subjected to blast loading are investigated. In particular, RC beams with a low reinforcement ratio are examined, which are more likely to fail in flexure than in shear. In order to assess the response of the beam, two analytical approaches are developed. In the first one, the beam is modeled as a continuous element by means of Euler-Bernoulli’s theory, which neglects the contributions of shear deformation and rotary inertia. The nonlinear behaviour of the beam in the elastic-plastic range is approximated by a single smooth relationship between bending moment and curvature, which allows to derive an original expression of the differential equation of motion of the beam. The parameters appearing in the latter are easily determined from the geometric and constitutive properties of the beam. The second approach described in this paper consists in evaluating the response of the beam through an equivalent single degree of freedom (SDOF) system. The latter is a mass-spring oscillator, and its constitutive behaviour is expressed through a bilateral relationship between force and displacement. The main drawback of this simplified approach is the need to introduce empirical quantities, such as the equivalent mass and the length of the plastic hinge. In both approaches, strain rate effects are taken into account. In fact, these effects should not be ignored in problems concerning blast loads, since the mechanical properties of both concrete and steel strongly depend on the rate of deformation. In this paper, strain rate effects are considered by changing the parameters related to the material properties during time, in accordance with the rules provided by the CEB Information Bulletin n. 187 and the fib Bulletin n. 55. Finally, in order to test the validity of the two approaches, the theoretical results are compared with some experimental data found in literature. In particular, the time-histories of the maximum deflections of several simply supported RC beams under uniformly distributed loads generated by explosions are analyzed. It is shown that the first approach is capable of predicting both the maximum displacement time-history and the deflection at collapse of any beam accurately. On the other hand, the second approach gives a less precise assessment of the structural response of the beam; nonetheless, the method based on the equivalent SDOF model is simpler to use and its differential equation of motion is faster to integrate.
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