移动荷载下考虑钢筋作用的混凝土裂缝梁动力响应分析

Dynamic response analysis of cracked concrete beams subjected to moving load considering the effect of reinforcement

由于钢筋的约束作用,混凝土梁裂缝截面的局部柔度与无筋时不同。建立了移动荷载作用下考虑钢筋影响的混凝土裂缝梁动力方程,基于力平衡和钢筋与混凝土变形协调对裂缝截面的局部柔度进行修正,采用无质量弹簧模拟裂缝,得到计入钢筋作用的裂缝梁自振特性,通过Newmark方法求解控制方程获取钢筋混凝土梁的动力响应。以受移动车辆荷载的简支梁为例,分析不同荷载速度、裂缝深度、裂缝位置、配筋率等条件下的钢筋混凝土裂缝梁响应。研究结果表明,裂缝处钢筋的约束作用可以显著地影响梁的动力响应,计入钢筋提供的刚度后裂缝梁的位移响应总体减小,且随着开裂损伤程度的增加钢筋的影响呈现变大的趋势。移动荷载下裂缝梁的共振现象较无损梁更为不利,考虑钢筋作用后裂缝梁的共振速度有所提高,共振响应则有一定程度的降低。由于钢筋混凝土裂缝梁和无损梁的共振速度存在差异,在某些荷载速度下无损梁的位移响应大于裂缝梁。

Due to the restraint effect of steel reinforcing bars,the local flexibility of cracked cross-sections of the concrete beam is different from that without reinforcement.Considering the influence of reinforcement,the dynamic equation of cracked concrete beams under moving load was established.Based on the force balance and deformation compatibility between the reinforcement and concrete,the local flexibility of cracked cross-sections was modified.The massless spring was used to simulate the crack,and natural vibration characteristics of the cracked beam were obtained taking into account the effect of the reinforcement.Dynamic responses of the reinforced concrete beam were acquired by solving the governing equation with the Newmark method.Taking the simply-supported beam subjected to moving vehicle load as an example,responses of the cracked reinforced concrete beam under different load speeds,crack depths,crack locations,and reinforcement ratios were analyzed.The results show that the restraint effect of the steel reinforcing bars at the crack location can significantly affect dynamic responses of the beam.The displacement response of the cracked beam will generally decrease after considering the stiffness provided by the reinforcement.Moreover,the effect of the reinforcement shows an increasing trend as the severity of the cracking damage grows.The resonance phenomenon of the cracked beam under moving load is more detrimental compared to that of the undamaged beam.Resonance speeds of the cracked beam increase and resonance responses decrease to a certain extent after considering the effect of the reinforcement.Owing to the difference in the resonance speeds of the cracked and intact reinforced concrete beam,the displacement response of the intact beam is larger than that of the cracked beam under certain load speeds.