DYNAMIC RESPONSES OF REINFORCED CONCRETE BEAMS WITH VISCOUS-SPRING SUPPORTS SUBJECTED TO LOW VELOCITY IMPACT

The normal force-displacement relations for local contact of block impacting on beam are presented based on Hertz contact theory. Calculation methods of dynamic responses for reinforced concrete beams with viscous-spring supports subjected to low velocity impacts are developed according to the theory of Euler-Bernoulli beam. The main factors such as the impact velocity, stiffness or damping of supports which has influences on the dynamic responses of the beams are analyzed. It is indicated that the values of total displacements of the beams increased with impact velocities being increased, and the plastic deformations occur during contact if impact velocities are high enough. The supports have significant effects on the dynamic responses of the beams. When the stiffness values of supports are increased, the maximal values of total displacements of the beams decreased, but the maximal values of relative displacements and vibration frequences increased obviously. When the damping values of supports are increased, the maximal values of total displacements of the beams decreased, but the damping values do not have any effects on the maximal values of relative displacements. The attenuation values of displacements increase with the damping values being increased, but the damping values do not have any effects on the vibration frequences of the beams. Results show that the impact resistances of the reinforced concrete beams are enhanced for the relative displacements being decreased and the attenuation values of displacements being accelerated by viscous-spring supports.