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本报告诱导出了求解高速列车与桥梁间动力作用的运动方程式;以新干线车辆及桥梁的实际数据,利用运动方程式进行了数值求解;将模型试验与实桥的实测结果进行了对照;对高速铁路上列车运行引起桥梁的动力效应特性进行了研究讨论。其要点归纳如下: (1)提出了在新干线的高速铁路中,列车运行荷载引起的桥梁动力效应的主要原因;并提出了列车有规则的车轴排列引起梁的共振现象是显著的。 (2)由列车有规则的车轴排列所引起的梁的共振现象,约在速度参数α〔车辆运行速度/(2×桥梁跨度×桥梁基本固有振动频率)〕与轴距参数β〔半个车辆长度/桥梁跨度〕之间的关系式α?β/i_a(i_a=1,2,3,……)得到满足时才产生。 (3)α?β/i_a产生共振时,桥梁动力效应的增大系数,取决于一定荷载列的基本输入振幅Ai_a;i_b及桥梁的衰减常数ζ_(bo)Ai_a,i_b对常数部分A_0,i_b的比值,随跨度的长短而不同,因跨度越短时比值越大,从而桥梁的冲击系数也是短跨的较长跨的为大。 (4)车辆的质量、弹簧常数与衰减常数,虽对梁的动力效应有影响,但以等效参数α_e(f_(b.e)),ζ_(b;e),以代替参数α(f_b),ζ_b,则以上影响大部分就被考虑到了。f_(b,e)/f_b与ζ_(b,e)ζ_b在钢梁中较大;在混凝土梁中接近于1。特别在长跨度的钢梁中,车辆的衰减常数能使梁的冲击系数降低。 (5)本报告的理论计算结果,很好地说明了1:5的模型线路和新干线的实测结果,特别对固有频率小的短跨度钢筋混凝土梁的实测冲击系数比较大这一点,由列车有规律的车轴排列引起的共振作了理论方面的解释。 (6)对于新干线的高速铁路中桥梁的挠曲刚度,希望能使其基本固有频率较图29所示的下限值还高。此下限值是从防止梁在列车运行时引起共振而使梁疲劳和产生大的裂纹这点出发提出的。但在梁高受到限制不能确保此限值时,可按本报告推导的计算法求出其冲击系数。当计算桥梁的基本固有频率时,必须考虑到混凝土的杨氏弹性模量的取法、混凝土的裂纹以及桥梁截面的挠曲刚度等给予的影响。
This report induces the equation of motion for solving the dynamic interaction between high-speed trains and bridges. The actual data of Shinkansen vehicles and bridges are numerically solved by the equations of motion. The model tests are compared with those of actual bridges. The dynamic characteristics of bridges caused by train operation are discussed and discussed. The main points are summarized as follows: (1) The main reasons for the dynamic effect of the bridge on the Shinkansen high-speed railway caused by the train running load are proposed. It is also pointed out that the regular resonance of the train caused by the arrangement of the train axles is significant. (2) The resonance phenomenon of the beam caused by the train’s regular axle arrangement is approximately the same as the speed parameter α (vehicle running speed / (2 × bridge span × bridge basic natural frequency)) and wheelbase parameter β Length / span of bridge] α α β / i_a (i_a = 1, 2, 3, ...) is satisfied. (3) The coefficient of augmenting of the bridge dynamic effect depends on the basic input amplitude Ai_a; i_b and the attenuation constant ζ_ (bo) Ai_a, i_b of a certain load column when αα / β_i_a resonates. For the constants A_0, i_b Of the ratio, with the length of the span of different, because the shorter the span ratio greater, so that the impact coefficient of the bridge is also a short span of the larger span. (4) The mass, spring constant and damping constant of the vehicle have influence on the dynamic effect of the beam, but the equivalent parameters α_e (be) and ζ_ (b; e) ζ_b, then most of the above effects are taken into account. f_ (b, e) / f_b and ζ_ (b, e) ζ_b are larger in the steel beam and close to 1 in the concrete beam. Especially in long-span steel beams, the attenuation constant of the vehicle can reduce the impact coefficient of the beam. (5) The theoretical calculation results in this report illustrate well the measured results of the 1: 5 model line and the Shinkansen. In particular, the measured impact coefficient of short-span RC beams with small natural frequency is relatively large, A theoretical explanation of the resonance caused by the regular arrangement of the axles is made. (6) For the flexural rigidity of bridges in the high-speed railway of the Shinkansen, it is hoped that the basic natural frequency will be higher than the lower limit shown in Figure 29. The lower limit is set forth from the point of preventing the beam from causing fatigue and generating a large crack when the train causes resonance during running of the train. However, when the beam height is limited and can not ensure this limit value, the impact coefficient can be calculated according to the calculation method deduced in this report. When calculating the basic natural frequency of a bridge, it is necessary to take into account the influence of the Young’s modulus of concrete, the crack of concrete and the flexural rigidity of the cross-section of the bridge.