Cable-stayed cable system reliability evaluation method considering broken cable

Abstract

The present application relates to a kind of cable-stayed cable system reliability evaluation method considering broken cable, comprising the following steps: the reliability of the remaining cable-stayed cable unit after broken cable is calculated;Failure path analysis is carried out to the remaining cable-stayed cable after broken cable;The reliability of the remaining cable-stayed cable system is evaluated using PENT method.The method proposed in the present application can be used for the design of cable-stayed cable under the accidental working condition with broken cable risk.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of cable-stayed cable system reliability evaluation, in particular to a cable-stayed cable system reliability evaluation method considering broken cable. BACKGROUND

[0002] In the use process of cable-stayed bridges, accidents such as vehicle impact and terrorist attacks that can produce great impact loadings may occur, and cable-stayed bridges may have broken cables. Although the current specification stipulates that accidental design conditions should be considered in the design of cable-stayed bridges, there is no provision for the reliability of the remaining cable-stayed cables after the cable is broken, and relevant research is also less.

[0003] The present application uses the general finite element software ANSYS to simulate the whole process of cable breaking of a cable-stayed bridge, and analyzes the failure path of the remaining cable-stayed cables, and establishes a reliability evaluation method for the remaining cable-stayed cable system. SUMMARY

[0004] In view of the defects in the prior art, the present application aims to provide a cable-stayed cable system reliability evaluation method considering broken cables, which can solve the problem of lack of cable-stayed cable system reliability evaluation method after cable breaking in the prior art.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is:

[0006] The present application provides a cable-stayed cable system reliability evaluation method considering broken cables, comprising the following steps:

[0007] S1: Calculate the reliability of the remaining cable-stayed cable unit after cable breaking:

[0008] According to the ultimate bearing capacity of the cable-stayed cable unit i and the actual cable force requirement value of the remaining cable-stayed cable unit , the bearing capacity limit state of the remaining cable-stayed cable unit is defined as i

[0009]

[0010] In the above formula, the ultimate bearing capacity of the cable-stayed cable unit i can be expressed as

[0011]

[0012] In the formula, G ki is the design value of the main girder segment weight allocated to the cable-stayed cable unit i . is the intersection angle of the cable-stayed cable and the main girder.

[0013] ​​​After the cable breaks, the remaining cable units i Actual cable force requirement It can be represented as,

[0014]

[0015] In the formula, G bi For the remaining cable units after the cable breaks i The actual weight of the main beam segments allocated.

[0016] Based on the ultimate limit state of the remaining cable elements, the remaining cable elements i failure probability It can be written as,

[0017]

[0018] By establishing The probability model is calculated using the formula above. For the same cable-stayed bridge, Size and remaining cable unit i Horizontal distance from the broken rope l Relevant. Assuming the median of This can be expressed by the following equation:

[0019]

[0020] In the formula, a and b These are the regression parameters.

[0021] assumed If it follows a log-normal distribution, then They follow a normal distribution. After the cable breaks, the remaining cable units... i failure probability It can be written as,

[0022]

[0023] In the formula, for The logarithmic standard deviation; N is the number of data points obtained.

[0024] S2: Failure path analysis of the remaining stay cables after cable breakage:

[0025] The initial design stress of the stay cable is generally controlled at about 40% of the ultimate strength, and since the redundancy of the cable force is high, the present application only considers the case of failure of two stay cables, i.e. there are two nodes in the failure path. According to the grouping of the failure path according to the position of the first node: the failure paths with the same first node are regarded as the same failure path, and each different failure path group is independent of each other, and the number of groups is determined according to the total number of stay cables. In addition, for the same failure path, the failure of the stay cable at the most unfavorable position is taken as the second node in the failure path. According to the above principles, the main failure paths of the stay cable system can be established.

[0026] S3: The reliability of the remaining stay cable system is evaluated by using the PENT method:

[0027] The probability of occurrence of the failure path is calculated by using the conditional probability, and the occurrence probability of any failure path j can be written as,

[0028]

[0029] In the formula, A j,i represents the event of failure of the j th stay cable in the failure path i ; n is the number of failed stay cables in a failure path; is the j th stay cable failure event in the failure path i-1 ; A j,i-1 Under the condition of A j,i event, is the event of failure of the j th stay cable in the failure path 1 ; A j,1 Under the condition of A j,2 event, is the event of failure of the j th stay cable in the failure path 1 ; A j,1 occurrence probability;

[0030] According to the PENT method, the failure probability of the structural system can be written as,

[0031]

[0032] In the formula, m is the number of groups of failure paths. ​

[0033] This invention provides a reliability assessment method for cable-stayed bridge systems considering cable breakage. It uses the general-purpose finite element software ANSYS to simulate the entire process of cable breakage in a cable-stayed bridge and analyzes the failure paths of the remaining cables to establish a reliability assessment method for the remaining cable-stayed bridge system. This invention can solve the problem of the lack of a reliability assessment method for cable-stayed bridge systems after cable breakage in the prior art. Attached Figure Description

[0034] Figure 1 This is an overall flowchart of an embodiment of the present invention—a reliability assessment method for a cable-stayed system considering cable breakage;

[0035] Figure 2 This is a schematic diagram of the stress on a stay cable according to an embodiment of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0037] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0038] like Figure 1 As shown: This invention provides a reliability assessment method for a cable-stayed system considering cable breakage, comprising the following steps:

[0039] S1: Calculate the reliability of the remaining stay cable elements after cable breakage:

[0040] According to the cable-stayed unit i ultimate bearing capacity and remaining cable-stayed units i Actual cable force requirement Define the ultimate limit state of the remaining cable-stayed element as follows:

[0041]

[0042] like Figure 2 As shown, it is assumed that the bridge towers are perpendicular to the main girder. In the above formula, the cable-stayed unit... i ultimate bearing capacity It can be represented as,

[0043]

[0044] In the formula, Gki For cable-stayed units i The design value of the weight allocated to the main beam segment. It is the angle between the stay cable and the main beam.

[0045] like Figure 2 As shown, after the cable breaks, the remaining cable units... i Actual cable force requirement It can be represented as,

[0046]

[0047] In the formula, G bi For the remaining cable units after the cable breaks i The actual weight of the main beam segments allocated.

[0048] Based on the ultimate limit state of the remaining cable elements, the remaining cable elements i failure probability It can be written as,

[0049]

[0050] By establishing The probability model in the above formula Calculations are performed. For the same cable-stayed bridge, Size and remaining cable unit i Horizontal distance from the broken rope l Relevant. Assuming the median of This can be expressed by the following equation:

[0051]

[0052] In the formula, a and b These are the regression parameters.

[0053] assumed If it follows a log-normal distribution, then They follow a normal distribution. After the cable breaks, the remaining cable units... i failure probability It can be written as,

[0054]

[0055]

[0056] In the formula, for The logarithmic standard deviation; N is the number of data points obtained.

[0057] S2: Failure path analysis of the remaining cable after cable breakage:

[0058] The design initial stress of the cable is generally controlled at about 40% of the ultimate strength. Since the redundancy of the cable force is high, the present application only considers the case of failure of two cables, i.e. there are two nodes in the failure path. According to the grouping of the first node position of the failure path: the same failure path of the first node is regarded as the same failure path, and each different failure path group is independent of each other, and the number of groups is determined according to the total number of cables. In addition, for the same failure path, the failure of the cable at the most unfavorable position is taken as the second node in the failure path. According to the above principles, the main failure paths of the cable system can be established.

[0059] S3: Reliability evaluation of the remaining cable system by PENT method:

[0060] According to the failure path of the remaining cable, the reliability index of the remaining cable system is calculated by PENT method. The probability of occurrence of the failure path is calculated by conditional probability, and the occurrence probability of any failure path j is which can be written as,

[0061]

[0062] In the formula, A j,i represents the event of failure of the first cable in the failure path j ; i is the number of failure cables in a failure path. n

[0063] Probabilistic Network Evaluation Technique (PENT) is one of the structure system failure probability point estimation methods. According to the correlation between each failure path, the failure paths are grouped, and the most important failure path in each group is selected as the representative failure path, and the failure probability of the system is calculated by assuming that each representative failure path is independent. According to PENT method, the failure probability of the structure system can be written as,

[0064]

[0065] In the formula, m is the number of groups of failure paths.​

Claims

1.A method for evaluating the reliability of a cable-stayed cable system considering broken cables, comprising the following steps: S1: calculating the reliability of the remaining cable-stayed cable units after the cables are broken: According to the cable-stayed unit i ultimate bearing capacity and the actual cable force demand value of the remaining cable-stayed unit i The bearing capacity limit state of the remaining cable-stayed unit is defined as,​ ， In the above equation, the ultimate load-carrying capacity of the cable-stayed unit i may be expressed as, may be expressed as, ， wherein G ki for a stay cable unit i a design value of the weight of the main girder segment to which the stay cable is assigned; for an intersection angle of the stay cable and the main girder remaining cable unit after cable breakage i the actual cable force requirement value may be expressed as, ， In the formula, G bi After the broken cable, the remaining cable-stayed unit i Actual assigned girder segment weight; According to the load-carrying capacity limit state of the residual cable-stayed unit, the failure probability of the residual cable-stayed unit i can be written as, can be written as, ， The calculation is made by establishing a probability model of the formula The size of the same cable-stayed bridge The size of the remaining cable-stayed unit i The horizontal distance from the broken cable l Related; assuming The median Is expressed by the following equation,​ ， wherein a and b are regression parameters; Assume Subject to lognormal distribution, then Subject to normal distribution; failure probability of remaining cable element after cable breakage i is written as is written as ， ， wherein is the log standard deviation; N is the number of data points calculated. S2: performing failure path analysis on the remaining cable-stayed cables after the cables are broken: According to the failure of two cable-stayed cables, that is, there are two nodes on the failure path, the grouping of the failure path according to the position of the first node: the failure paths with the same first node are regarded as the same failure path, and each different failure path group is independent of each other, and the number of groups is determined according to the total number of cable-stayed cables; In addition, for the same failure path, the failure of the cable-stayed cable at the most unfavorable position is taken as the second node in the failure path; According to the above principles, the main failure path of the cable-stayed cable system is established; S3: using the PENT method to evaluate the reliability of the remaining cable-stayed cable system: The probability of occurrence of any failure path is calculated using conditional probabilities j The probability of occurrence of any failure path is calculated using conditional probabilities is written as, ， wherein A j,i the event of the failure of the root cable in the failure path j i the event of the failure of the root cable in the failure path n the number of failed cables in a failure path the event of the failure of the root cable in the failure path j i-1 the event of the failure of the root cable in the failure path A j,i-1 under the event condition, A j,i the probability of the event, the event of the failure of the root cable in the failure path j 1 the event of the failure of the root cable in the failure path A j,1 under the event condition, A j,2 the probability of the event, the event of the failure of the root cable in the failure path j 1 the event of the failure of the root cable in the failure path A j,1 the probability of the event;​​​​ According to the PENT method, the structural system failure probability is written as, ， In the formula, m Number of packets for failed paths.

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