A calculation method for mid-span vertical displacement of beam bridges as a function of temperature

A technology of vertical displacement and calculation method, applied in the direction of calculation, computer-aided design, elasticity test, etc., can solve the problems of troublesome application of the three-bending moment equation, difficult to meet the field application of engineers, poor versatility, etc., to avoid finite element numerical value Effects of simulation, avoidance of structural mechanics analysis, ease of parametric analysis

Active Publication Date: 2021-09-07
UNIV OF SCI & TECH BEIJING
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  • Abstract
  • Description
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  • Application Information

AI Technical Summary

Problems solved by technology

The application of the three-bending moment equation is cumbersome, and the structures with different span arrangements need to be analyzed separately, which has poor versatility
Numerical simulation is also a time-consuming and labor-intensive process. It is not easy to reveal the mechanism behind the phenomenon, and there are certain technical thresholds, so it is difficult to meet the needs of engineers for field application.
Regarding the mid-span vertical displacement of girder bridges under the action of the temperature difference between the top surface and the bottom surface, there has not been a unified calculation formula with strong versatility, simple form, and clear parameter relationships

Method used

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  • A calculation method for mid-span vertical displacement of beam bridges as a function of temperature
  • A calculation method for mid-span vertical displacement of beam bridges as a function of temperature
  • A calculation method for mid-span vertical displacement of beam bridges as a function of temperature

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Embodiment 1

[0212] A girder bridge is a 6-span continuous girder structure, each span is 110m long, the main girder is made of steel, and the girder height is 4.5m. Due to direct sunlight, the temperature difference between the top and bottom of the girder is 20°C. The vertical displacement of the bridge deck in the mid-spans of the first and third spans needs to be determined.

[0213] It can be seen from the above conditions that the number of spans n=6 is the case of a continuous beam with even spans, and the number of unknown independent joint angles u=3. The span diameters of the main span and the side span are equal, l 0 = l 1 =110m, the linear expansion coefficient of the main girder is α=1.2×10 -5 ℃ -1 , the beam height h=4.5m, the temperature difference between the top surface and the bottom surface of the main beam is ΔT=20℃. Substituting the above parameters into formula (36), it can be obtained that when k=1, ΔS 1 =-0.0295m; when k=3, ΔS 3 =-0.0016m. It can be seen tha...

Embodiment 2

[0215] Assuming that the number of spans of the girder bridge is n, the span of each span is 110m, the material of the main girder is steel, the girder height is 4.5m, and the temperature difference between the top and bottom of the main girder is 20°C. Calculate the mid-span vertical displacement of the main girder of the outermost side span of the girder bridge when n=1,2,...,10.

[0216] The following parameters can be known from the above conditions: l 0 = l 1 =110m, α=1.2×10 -5 ℃ -1 , h=4.5m, ΔT=20°C, k=1. Depending on whether n is odd or even, these parameters are substituted into formula (35) or formula (36), respectively, and let (that is, take the smallest one of the integers not less than n / 2), so as to obtain the mid-span vertical displacement of the main girder of the outermost side span of the girder bridge with different total spans n (in order of increasing number of spans): -0.0807m , -0.0202m, -0.0323m, -0.0288m, -0.0297m, -0.0295m, -0.0295m, -0.0295m, -...

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Abstract

The invention provides a calculation method for the mid-span vertical displacement of a girder bridge changing with temperature, and belongs to the technical field of bridge structure analysis and monitoring. In this method, the node rotation angle of the main beam at each support is set as an unknown quantity, and the equation is established according to the moment balance condition of the node, and then the sequence is introduced to establish the quantitative relationship between the unknown quantities, and the relationship is brought into Equation, the analytical formula of the rotation angle of each node is solved, and then the analytical formula of the bending moment of each node is obtained by the superposition principle, and finally the analytical formula of the mid-span vertical displacement of the main beam of each span is obtained by the principle of virtual work. This method is aimed at equal-section beam bridges with equal side spans and arbitrary spans. The analytical formula given is an accurate solution, which is convenient to calculate and has strong versatility. It also reveals the behavior of beam bridges under temperature changes from the mechanism level, which can be used to guide The measuring point layout of the bridge monitoring system provides prior knowledge for the establishment of the temperature deformation benchmark model.

Description

technical field [0001] The invention relates to the technical field of bridge structure analysis and monitoring, in particular to a calculation method for the mid-span vertical displacement of a girder bridge changing with temperature. Background technique [0002] Simply supported beams and continuous beams are the most commonly used bridge forms in transportation networks, which are collectively referred to as girder bridges in the present invention. Structural deformation of girder bridges is the focus of structural health monitoring during the bridge operation period. It is usually characterized by the telescopic displacement of the girder end and the vertical displacement of the main girder mid-span. The expansion and contraction displacement of the girder of girder bridges has been well studied and can be estimated by the one-dimensional thermal expansion and contraction formula. In contrast, there are much less studies on the variation of mid-span vertical displaceme...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F30/13G06F30/20G06F119/14
CPCG06F30/13G06F30/20G06F2119/14G01M5/0008G01M5/0041G06F2119/08G06F2111/10
Inventor 周毅
Owner UNIV OF SCI & TECH BEIJING
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