粘弹性支座RC梁在低速冲击下的动力响应计算

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

给出了基于Hertz接触理论的冲击体与梁结构之间的局部接触力-接触变形关系。根据弯曲理论,建立了具有粘弹性支座钢筋混凝土梁在低速冲击作用下的弹塑性动力响应计算方法,并通过算例分析了冲击速度、支座刚度和支座阻尼对动力响应的影响。分析发现:梁的总位移随冲击速度增大而增大,当冲击速度足够大时梁将出现塑性变形。支座条件对梁的动力响应有较大影响,梁的总位移最大值随支座刚度增大而减小,而相对位移最大值随支座刚度增大而增大,振动频率随支座刚度增大而明显增大;梁的总位移最大值随支座阻尼增大而减小,相对位移最大值随支座阻尼变化不明显,位移幅值衰减值随支座阻尼增大而增大,但振动频率不受支座阻尼影响。结果表明:采用粘弹性支座既能减小钢筋混凝土梁的相对位移幅值,又能加速梁的位移幅值衰减,提高了梁结构的抗冲击能力。

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.