中、下承式拱桥吊索的模态分析与张力测定

【作者】 董建华；

【导师】 陈淮；

【作者基本信息】 郑州大学 ， 结构工程， 2004， 硕士

【摘要】 中、下承式拱桥由于桥型优美是我国城市桥梁中应用发展很快的一种桥型，据有关资料介绍，我国现在已建成的中、下承式拱桥有300余座，目前仍在向更大跨径、更大规模的方向发展，应用区域和范围也在不断扩大。但是，近年来也连续出现了若干起中、下承式拱桥的垮塌事故，造成了严重的人员伤亡与经济损失。从这些事故分析中可以得出这样的结论：中、下承式拱桥的断桥与垮塌事故大多与吊索的健康状态有关，若能对拱桥吊索的健康状态进行经常及时地或实时在线地监测与诊断，多数中、下承式拱桥的重大事故是可以避免的。 中、下承式拱桥主要由拱肋、桥面系(系杆梁)及吊索系3部分组成，其中吊索系不但是主要的传力(承力)构件，也是易损构件，主要的损伤包括：吊索中部分钢丝断裂、钢丝锈蚀、锚固失效等。无论哪一种损伤，都会引起吊索拉伸刚度的变化，而拱桥桥面系可视为由吊索弹性支承于拱肋上的一个超静定结构，部分吊索刚度的变化必然引起吊索系承受荷载的重新分配，即必然引起吊索系静张力的变化。因此，吊索的静张力是拱桥健康状况的敏感指标，可以根据吊索系静张力的实际测量值与拱桥健康档案中的吊索系静张力值之比较，来对拱桥的健康状况进行诊断与评估。 当前，中、下承式拱桥吊索的张力测定方法主要有2种：直接法和间接法，在工程实际中主要使用间接法，振动法是间接法中最经常使用的一种方法。振动法测定吊索张力可以分为2个方面：张力计算公式；吊索振动频率的测试。目前，振动测试技术已经比较成熟，可以由振动信号十分精确地提取出吊索的振动频率。目前，振动法中测定吊索张力公式所用理论主要借助于斜拉桥斜拉索的张力测定理论。在斜拉索的张力测定中，由于斜拉索长度较大，其弯曲刚度和边界条件影响较小，一般可以忽略不计。中、下承式拱桥不同于斜拉桥，在中、下承式拱桥中，由于拱肋主要承受压力，失稳问题比较突出，矢高不可能太大，所以中、下承式拱桥吊索的长度一般较小。如果将斜拉索张力测定理论直接应用于吊索，特别是短吊索，则会产生较大误差，不能满足实际工程使用要求。吊索的张力测定必须考虑弯曲刚度和边界条件的影响。基于这一背景，本文的主要工作就是提出适合于中、下承式拱桥吊索张力测定的张力计算实用公式。 在中、下承式拱桥吊索张力测定的理论研究中，当不考虑吊索弯曲刚度的影响时，吊索可以看成是一根张紧的弦，由于没有考虑弯曲刚度的影响，其张力与振动频率存在着简单的关系，张力计算十分方便。当只考虑吊索弯曲刚度的影响而将吊索两端的边界条件视为简支时，通过理论分析也可以直接推导出吊索张力与其横向振动频率关系的计算公式。当同时考虑吊索弯曲刚度和吊索两端固定支承的边界条件影响时，吊索的张力与吊索横向振动频率关系的方程是超越方程，无法直接导出张力计算显式公式。本文研究通过振动微郑州大学硕士学位论文分方程导出频率方程，引入无量纲参数化简吊索的张力与其横向振动频率之间关系的超越方程，采用数值计算和曲线拟合方法，在不同的无量纲参数杏取值范围内得到吊索张力与吊索横向振动频率简单的函数关系，文中给出了吊索张力计算的显式公式。 本文给出的当采用吊索第1阶横向振动频率时，吊索张力计算的实用计算公式为:一‘五Z，2[。·82犯一:贪)2」，(。·、一) .，一、，「一______‘。、，飞‘’一4m(了】‘，‘「。’“吕‘一‘Z”‘，j’(了{」’(”<““。，一(厂/，2「1·l一4 .3r4二 厂{ (20<睿)式中，;=z擂，一篇，二为吊索的弯曲刚度，脚为吊索的线质量密度，z为吊索的计算长度，石为实测的吊索第1阶横向振动频率，T为吊索的计算张力。本文还给出了采用吊索第3阶横向振动频率的张力实用计算公式。本文利用京珠国道郑州黄河特大桥主桥的吊索参数，将本文提出的2组吊索张力计算实用公式的计算结果和采用考虑杆件几何刚度(考虑张力影响)的有限元法的计算结果进行了对比，计算结果表明该实用公式具有很高的计算精度。 在基于振动法具体进行吊索张力测定时，可首先对吊索进行振动测试，通过对振动信号的处理，提取出吊索的振动频率，代入相应的张力计算公式，即可得到实测张力值。由于参数咨中含有未知的吊索张力T，在吊索张力测定时要进行迭代计算:可以先假设杏的范围，由对应计算公式计算得到吊索张力，然后计算新的咨值。如果咨值在假设的范围内，得到的吊索张力值是准确的;如果咨值不在假设范围内，根据咨值选用新的计算公式进行迭代计算。一般进行2次迭代计算，就可以得到准确的吊索张力计算值。 为了检验本文提出的中、下承式拱桥吊索张力测定实用计算公式的准确性，作者在京珠国道郑州黄河特大桥主桥施工现场进行了吊索张力测定试验。在吊索的振动频率测试中，采用了环境随机激励方式，利用功率谱峰值法处理振动信号，得到吊索的第1阶横向振动频率，代入本文实用计算公式，得出了吊索张力，通过与现场吊索的张拉力值比较，验证了本文公式的正确性。 本文通过有限元法的数值验证和下承式拱桥施工现场的实践检验，证明了本文提出更多还原

【Abstract】 Because of its graceful bridge type, through and half through arch bridges are a kind of bridge with quicker development and application among all of the city bridges in our country. According to related documents and materials, there have been more than 300 through and half through arch bridges built in our country, which develop in the direction of larger span and scale, and the area of use is expanding gradually. However, in recent years, some accidents of through and half through arch bridges’ collapses engendered severe casualties and economic loss related. Such a conclusion can be derived from these accidents’ analyses breaking up and collapse of through and half through arch bridges mostly relating with the health condition of suspenders; if timely and real time online monitoring and diagnoses are conducted, a majority of serious accidents can be avoided.Through and half through arch bridges are mostly made up of arch ribs and floor systems ( tied beams ) and systems of suspenders. Suspender is not only a primary carrying member, but also a member vulnerable to rained. The primary damages of suspenders are rupture of some steel wires, corrosion of steel wires, lapse of anchors, and the like. Every kind of damages will bring variance of suspender’s stretch stiffness. The floor system is regarded as an indeterminate structure elastically supported on arch ribs. The stiffness variance of some suspenders certainly induces the redistribution of loads. In other words, it causes the variance of static tensile forces of suspenders. The static tensile force of suspenders is a sensitive index of health condition of arch bridge. The health condition of arch bridge can be diagnosed and evaluated by comparison of the values of tension measurement of suspenders and the values of static tensile forces in the health archive of arch bridge.Currently, two methods of tension measurement, direct method and indirect method, are used in the tension measurement of suspender of through and half through arch bridges. Indirect method is mainly used in practical engineering applications. Vibration method is one of the indirect methods, which is mostly put into use. Two respects of tension measurement of suspenders by using vibration method might be involved: tension formula and measurement of vibration frequency. Now the vibration measuring technique has been already developed successfully. The vibration frequency of the suspender can be accurately obtained from the vibration signals. Theory of tension measurement of suspenders mainly depends on the theory of tension measurement of cables of cable-stayed bridge by using vibration method. Since the length of cables is relatively large, the effect of the flexural stiffness and boundary conditions is small on the tension measurement of cable-stayed bridge and can be neglected. Through and half through arch bridges are different from cable-stayed bridge. As the arch ribs of through and half through arch bridges bear compression, the bucking problem is comparatively obvious, and the value of rise of arch can not be too large. Generally the length of suspenders of through and half through arch bridges are relatively small. If the theory of tension measurement of cable-stayed bridge is directly applied to the tension measurement of suspenders, especially short suspenders,a larger error will be produced and it can not satisfy the requirements of practical engineering applications. The effect of the flexural stiffness and boundary conditions must be taken into account during tension measurement of suspenders. On the basis of this background, the raise of practical calculating formulae of suspender’s tension suitable for the tension measurement of suspenders in through and half through arch bridges is the major contents of this dissertation.In the theoretical research of tension measurement of suspenders of through and half through arch bridges, when the influence of the flexural stiffness of suspenders is not taken into account, the suspenders can be regarded as a tensioned string. Sin更多还原