Response of reinforced concrete elements to high-velocity impact load

Seyed Hamid Changiz Rezaei, Purdue University

Abstract

Previous studies showed that reinforced concrete (RC) elements designed to fail in flexure under static load can fail in shear under dynamic loads. An experimental program was conducted to investigate the effect of transverse reinforcement on the resistance of small-scale RC beams to shear forces caused by high-velocity impact loads. A total of 26 beams were tested. Beams subjected to impact had transverse reinforcement ratios of 0.41%, 0.54% and 0.8%, and were proportioned to fail in flexure under static loading. The beams were impacted by water-filled containers moving at velocities ranging from 63 m/s to 104 m/s. It was observed that beams were able to form flexural failure mechanisms and resist nominal shear stresses during their initial phases of response equal to at least 1.5 times the static shear capacity of comparable specimens which failed in shear. In tests of beams with the same dimensions and subject to similar impact loads, it was observed that an increase of 30% in the nominal capacity to resist static shear forces was sufficient to prevent shear failure under impact. Single-degree-of-freedom (SDOF) models of the test specimens were built based on the following assumptions: (a) The mass of an equivalent SDOF system representing a continuous beam is 0.37 times the total mass of the beam for the elastic range of response and 0.33 times the total mass of the beam for the plastic range of response. (b) The resistance function of the equivalent SDOF model is elasto-plastic. The stiffness and resistance defining this function were means of values extracted from measured load-deflection curves. (c) The loading history was a rectangular pulse with duration equal to the ratio of projectile length to impact velocity and amplitude proportional to the density of the impacting fluid, the area of the projection of the projectile onto the beam, and the square of the measured impact velocity. (d) Strain-rate effects caused an increase in the unit yield stress of the longitudinal reinforcing steel of 60%. (e) The damping ratio was 5%. Using these assumptions, the obtained mean ratio of computed to measured permanent midspan displacement was 1.1 with a standard deviation of 0.38. For detailed finite element analysis (FEA), this ratio was 0.9 and the standard deviation 0.2. The duration of each of the analysis for SDOF models was in the order of seconds whereas the duration of each FEA was approximately 2 hours on a machine with a 3-GHz CPU and a 3-GB of RAM. Available analysis methods were also evaluated using field evidence. SDOF models representing columns of the Pentagon building were used to simulate the aircraft impact that took place in 2001. The columns were idealized as SDOF systems using the following assumptions: (a) The columns were impacted at mid-height by a prismatic mass of fluid with a density of 800 kg/m 3. (b) Impact velocity decayed either as a quadratic function or as a linear function of the distance to the façade of the building. (c) Column failure took place when the strain in the longitudinal reinforcement reached 30%. (d) Plastic hinge length was equal to the effective depth of the column. (e) The columns had fixed-end supports and an elasto-plastic resistance function. (f) Strain-rate effects caused an increase in the unit yield stress of the longitudinal reinforcing steel of 50%. (g) The mass of an equivalent SDOF system representing a continuous column is 0.35 times the total column mass. (h) The loading history was a rectangular pulse with duration equal to the ratio of projectile length to impact velocity and amplitude proportional to the density of the impacting fluid, the area of the projection of the projectile onto the column, and the square of the impact velocity. (i) The damping ratio was 5%. The quality of the results obtained from nonlinear dynamic analysis of SDOF systems conceived using these assumptions was comparable to the quality of the results obtained from a detailed FEA reported by Hoffmann et al. (2004).

Degree

Ph.D.

Advisors

Pujol, Purdue University.

Subject Area

Civil engineering

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