考虑复合边界条件的中、下承式拱桥吊杆张力计算公式

Computational Formula for the Suspender Tension of Half-Through and Through Arch Bridge under Combined Boundary Conditions

基于Euler-Bernoulli梁理论,建立考虑吊杆两端拱肋、系杆梁弹性支承和减振垫影响的吊杆张力计算模型,推导中、下承式拱桥吊杆张力计算公式。对于吊杆两端铰支情况,导出以横向振动频率表达的吊杆张力解析式;对于吊杆两端固支情况,运用Newton-Raphson法迭代求解,采用统一函数形式分段拟合得出分别以吊杆前4阶横向振动频率显式表达的吊杆张力计算公式。依据京港澳高速公路郑州黄河二桥现场施工数据对给出的吊杆张力计算公式进行验证。结果表明,运用给出的吊杆张力公式计算得到的结果与实测值相近,误差在4%以内。说明给出计算公式适用于中、下承式拱桥的吊杆张力计算。

Based on Euler-Bernoulli beam theory, a computational model for suspender tension was established, considering the influences of the arch ribs at both ends of suspender, the elastic supports of tie beams and the damping effect of shock pads. The computational formulas for the suspender tension of half-through and through arch bridge were deduced. For hinged suspender, an analytic expression of suspender tension expressed by transverse vibration frequency was established. For clamped support suspender, by means of Newton-Raphson iterative solution and using a uniform function for piecewise fitting, the computational formula for suspender tension was obtained, which was explicitly expressed by the first 4-step transverse vibration frequency of suspender respectively. The proposed formula was validated by the field construction data of the Second Yellow River Bridge in Zhengzhou on Beijing-Hongkong-Macao expressway. The results show that the computed values of the tension obtained by the proposed formula are similar to measured values, and the errors are less than 4%, which shows that the proposed computational formulas are applicable to the suspender tensions of half-through and through arch bridge.