Finite Element Modeling of Tornado Missile Impact on Reinforced Concrete Wall Panels
This study describes a finite element model for the impact of large tornado missiles on reinforced concrete wall panels. The analysis predicts the dynamic response of wall panels when impacted by a missile with a large contact area such as an automobile. The development and current status of tornado-generated missiles and their impact effects on concrete wall panels are summarized along with the failure criteria for concrete material in the theory of plasticity. Quadratic finite elements are used to discretize the domain of the wall panel. Fundamental assumptions are based on the Mindlin and Reinsser's plate theories. An "embedded" model is employed to account for the reinforcing bars. The nonlinear behaviors of concrete and of steel bars are analyzed by means of rate-dependent constitutive relationships. A new strain rate-stress relationship is proposed, and the relationship between the fluid parameter 7 and the coefficient a is set up. A model is proposed to describe the initial and subsequent yield surfaces of concrete material, which avoids underestimation of the effect of high hydrostatic stresses on the yielding behavior of concrete. Ottosen's four-parameter failure criterion is used to define the failure surface of concrete. A crack monitoring algorithm accounts for post-cracking and post-crushing behavior of concrete. An explicit time integration scheme is used to solve the nonlinear dynamic equations carried out using the finite element discretization of a concrete wall panel. A computer program is developed in accordance with the above conditions. Several impact tests were conducted in the Civil Engineering Testing Laboratory. A steel pipe 3-in diameter by 10-ft long was fired by Texas Tech missile cannon. The missile struck at the center of a .5 in thick by 12-in square steel plate which is attached to the center of the reinforced concrete panel so that the impact contact pressure is spread over the whole steel plate. Dynamic displacements of the concrete panel were measured with a linear variable displacement transducer (LVDT). The calculated results from the computer program were compared with the test results. The computer program for dynamic analysis of reinforced concrete wall panels is verified by the impact test results. The new relationship between stress and strain rate for viscoplastic analysis that is proposed is proven to be correct, and the formula for the critical time step is successfully derived. As a practical application of the analysis technique, the contact failure pressure for a particular panel geometry is calculated. The contact failure pressure and the elapsed time to failure after missile contact define an impulse loading to produce failure of the panel. Since automobile crashes tend to produce triangular impulse loads, the two pulses (failure and impact) can be compared to determine if a particular impact will fail a panel. Thus, a particular concrete panel can be analyzed to determine if it will fail under a postulated automobile impact.