Flexural models of reinforced concrete beams under blast load

Nowadays, the issue of structural safety under blast loading has become a dramatic problem. The tragic news of the terrorist attacks of recent years (9/11/2001, New York; 7/7/2005, London; 7/23/2005, Sharm El Sheik; 1/24/2011, Moscow; etc), raise important, urgent questions regarding the real safety and reliability of our buildings. Extreme loads such as impacts, explosions, etc., can occur in everyday life with unexpectedly high frequency. Actually, the problem of terrorist attacks, so important for strategic and military building design, has been linked to residential and industrial building explosion accidents. The present thesis deals with the flexural failure of Reinforced Concrete beams under blast loads. The main aim is firstly to develop dynamic and energy models capable of evaluating the response of R.C. under explosive load. Then a sensitivity analysis is obtained by means of the above mentioned models in order to determine what are the key parameters in the beam response. In this way it is possible to attain simple predictive polynomial formulations and, finally, simple table for early structural assessment of beams under blast load during the design procedure. The thesis is composed of three sections. Various dynamic models are developed in Section 1, taking into account the strain-rate sensitivity of both steel and concrete, as well as other nonlinearities in structural behaviour. Models with different levels of complexity are presented, from the simplest Single Degree Of Freedom (SDOF) system to Continuous Beam and Finite Element models. The characteristics, advantages and disadvantages of each approach are stated and discussed. The author compares his models with some experimental findings available in the scientific literature. The principal innovation that can be inferred from this section is the hypothesis of distributed plasticity along the beam (in the continuous model), represented by a non-linear smooth relationship between bending moment and curvature. This relationship, in addition to the Euler-Bernoulli beam equation, yields a non-linear Partial Differential Equation solved by means of the Finite Difference Method. In Section 2, the same problem is solved in a different way: starting from the principle of energy conservation, the innovative procedure, developed by the author, can calculate the displacement field of a R.C. beam under blast load. This procedure, less accurate than the previous one, produces very good results regarding midspan displacement, especially as it requires less computation time. In order to better understand the phenomenon, with the aim of identifying the key parameters in structural response, a sensitivity analysis is developed in Section 3. To this end, the author has performed a numerical investigation referring to the SDOF model presented in Section 1. Several numerical simulations are performed, with random variation of beam and load characteristics. Results are expressed in terms of maximum deflection and maximum velocity for each case. Then a least-squares interpolation has produced various polynomial curves and surfaces representing both a simplified tool to estimate structural response and a sensitivity analysis of the key parameters involved. One of the possible developments of this useful work is represented by simple tables that provide the response of the beam under blast load for early assessment in design procedures.