CN111651927B - Method for calculating vertical worst temperature gradient of box girder - Google Patents

Abstract

The invention discloses a method for calculating the worst vertical temperature gradient of a box girder, which considers a concrete temperature field with transient characteristics, rapidly processes temperature data of each part of the box girder obtained by field monitoring through an RBTMAS method to obtain real-time vertical temperature difference data of the box girder, establishes a theoretical calculation formula of temperature load borne by the box girder under the action of temperature rise and temperature drop based on a semi-theoretical semi-empirical formula and a generalized extreme value statistical theory, and calculates a positive and negative temperature gradient distribution mode and the worst positive and negative temperature difference possibly occurring in a reappearance period by adopting an extreme value statistical method. And (4) checking the reliability of the result by using a Pearson correlation coefficient method. The method for solving the vertical temperature gradient of the box girder established by the invention can simply, conveniently and accurately calculate the mode of the worst vertical temperature gradient of the box girder in the temperature rising and reducing environment, thereby calculating the temperature load, and obviously improving the accuracy compared with the traditional method.

Description

A Method for Calculating the Most Unfavorable Vertical Temperature Gradient of Box Girder

technical field

The invention relates to the technical field of calculating the most unfavorable temperature gradient of a bridge superstructure under the action of temperature effect in bridge engineering, in particular to a method for calculating the most unfavorable vertical temperature gradient of a box girder.

Background technique

Concrete bridges that have been in the atmospheric environment for a long time have to bear not only their own weight and loads such as vehicles, but also the influence of solar radiation and atmospheric temperature changes. The temperature stress generated by the temperature action in the concrete box girder can reach more than 3MPa, which exceeds the allowable tensile stress of the concrete, and sometimes exceeds the section stress generated by the live load of the bridge, causing serious cracks and even collapse accidents. The number of damaged bridges caused by these temperature effects has attracted the attention of many domestic and foreign experts and scholars on the most unfavorable temperature gradient of bridges.

Through the investigation of bridge diseases caused by temperature effect, it is found that there have been many serious accidents caused by concrete cracking caused by temperature effect at home and abroad. The Jagst concrete bridge in Germany suffered severe cracks in its fifth year of operation. It is estimated that the tensile stress caused by the temperature effect is as high as 2.6MPa. The Champigny concrete box girder bridge in the United States produces a tensile stress of up to 3.92 MPa on the lower flange of the box girder due to the temperature difference between the box girder top plate and the box girder bottom plate. A prestressed concrete viaduct in New Zealand suffered severe cracks shortly after operation due to temperature effects from sunlight. A concrete-steel box girder bridge in Canada collapsed due to thermal stress and deformation. In recent years, many concrete bridge disease accidents caused by temperature effects have also occurred in China. For example, a curved continuous box girder overpass in Shenzhen in China has a lateral displacement of nearly 50cm at the moment when the temperature difference between the beams is the largest; the box girder roof and main pier body of the Guanghua Hanjiang Bridge in Hubei have cracks caused by temperature stress; The simply supported box girder of the approach bridge of Jiujiang Bridge and the continuous box girder of Tonghui River have suffered severe cracking caused by temperature load. These temperature effects caused by the temperature gradient can cause cracks in the bridge, causing huge economic losses in the process of repair;

Experts and scholars at home and abroad have conducted experimental research on a large number of concrete structural diseases and have shown that the most unfavorable temperature gradient is the main reason for the failure of bridges. Therefore, the accurate calculation of the most unfavorable temperature gradient will help to improve the design theory of concrete bridge box girder, and will have very important theoretical and practical significance to improve the safety, durability and economy of concrete bridge structures.

SUMMARY OF THE INVENTION

Aiming at the defects of the prior art, the present invention provides a method for calculating the most unfavorable vertical temperature gradient of a box girder, and solves the defects existing in the prior art.

In order to realize the above purpose of the invention, the technical scheme adopted by the present invention is as follows:

A method for calculating the vertical most unfavorable temperature gradient of a box girder, comprising the following steps:

S1: Screen and process temperature monitoring data, clear wrong data and fill in vacant monitoring data.

The sub-steps of S1 are as follows:

S11: Use the following erroneous data identification criteria to clear erroneous data:

Criterion 1: Use the Grubbs criterion to identify erroneous data with a 95% confidence probability.

Criterion 2: According to the analysis of long-term temperature monitoring data, two empirical criteria are obtained: the temperature change of the same monitoring point at a certain moment exceeds the temperature at the previous moment ±10 degrees Celsius, the temperature data at this moment is judged to be wrong, and the red processing is performed. If the temperature of all measuring points is higher than the daily average temperature +15 degrees Celsius or lower than the daily average temperature -18 degrees Celsius, it will be judged that the temperature data at this moment is wrong and will be marked in red.

S12: Due to the monitoring system, the temperature of some measuring points cannot be measured at a certain time or the measured temperature is judged to be wrong data, so the following formula is used as the identification criterion of supplementary data to supplement the monitoring data;

In the formula, T _at is the temperature that is not measured at time t at measurement point a during the monitoring time, _Tav is the average temperature at measurement point a on the day, _Tam is the temperature difference at measurement point a on the day, and t ₀ is the time when the highest temperature occurs at measurement point a.

S2: According to the completed temperature monitoring data, through the bridge temperature real-time monitoring and analysis method (Real-time BridgeTemperature Monitoring Analysis System), hereinafter referred to as: RBTMAS method, this method is the method proposed by the applicant, and this method is used to screen the most unfavorable daily positive Temperature gradients and worst negative temperature gradients, and plot temperature gradients.

S3: The calculation formula of the vertical temperature gradient can be written as:

T _y =T ^{me ay} ₍ 2)

where T _m is the maximum positive temperature difference in the beam height direction, y is the distance from the calculation point to the top surface of the box girder, T _y is the temperature difference at the calculation point position, and a is the index.

S4: The two parameters T _m and a in the formula (1) are constants, which are determined by the environment where the bridge is located and the structural form of the box girder. They are obtained by fitting the long-term temperature monitoring data. The fitting principle is as follows:

where (x; μ, σ, ξ) is the distribution function of x, μ is the position parameter, σ is the scale parameter, and ξ is the shape parameter.

where (x; μ, σ, ξ) is the density function of x.

The temperature probability p=1/P (0<p<1) once in P year, when the return period is p, the extreme value of the temperature difference is x _p :

x _p = μ-σ(1-(-log p) ^-ξ )/ξ (5)

To perform generalized extreme value statistical analysis on non-independent random variables, μ, σ, and ξ need to be corrected:

In the formula, θ is the extreme value index, which can be calculated by the run-length method.

S5: Fit the most unfavorable positive temperature gradient data through the maximum likelihood estimation of the generalized extreme value distribution, and obtain the three parameters μ, σ, ξ of the most unfavorable positive temperature gradient T _m and a respectively.

S6: Correct the parameters through the formula (6), and then obtain the modified _Tm ' and a' of the most unfavorable positive temperature gradient. Similarly, T _m ' and a' of negative temperature gradient can be obtained.

S7: The formula to finally get the most unfavorable vertical temperature gradient is:

T _y =T _m 'e ^a'y (7)

S8: Use P-P graph, Q-Q graph and Pearson correlation coefficient method to test the accuracy of fitting with this method. If the P-P graph and Q-Q graph are straight lines and the Pearson correlation coefficient r≥0.8, use this method to fit the The vertical most unfavorable temperature gradient has high accuracy and meets the requirements.

S9: Establish the finite element model of the bridge, load the most unfavorable temperature gradient into the finite element calculation model, and calculate the influence of the most unfavorable vertical temperature gradient mode of the box girder on the bridge.

Further, the calculation steps of the RBTMAS method in S2 are as follows:

S21: Import the monitoring data table, filter and sort out the temperature data measured by the vertical temperature measuring point channel;

S22: Use W _i S _j to express the temperature of the Wth day, time i, and the temperature of the vertical jth measuring point (unit °C), then the temperature of the vertical measuring point at the same time can be expressed as

S23: At the same time (W _i ) in one day, all the measuring points in the vertical direction are subtracted from each other and then compare their sizes to obtain the maximum and minimum temperature differences at this time of the day;

S24: Step S23 is expressed by the following formula:

Let _Wi x ₁₂ = _Wi (S ₁ -S ₂ ), then

The maximum value in this determinant is represented by W _m x _max , that is, the Wth day, at time m, the most unfavorable positive temperature difference on the day of occurrence is x _max , and the minimum value is represented by W _n x _min , that is, the Wth day, at time n, the day of occurrence The most unfavorable negative temperature difference is x _min . Note: If W _m x _max ≤ 0, there is no most unfavorable positive temperature difference on that day; if W _m x _min ≥ 0, then there is no most unfavorable negative temperature difference on that day;

表示，该行列式最小值为W_mx_min,则第W日最不利正温度梯度为

i＝m；S25: Filter out the temperature of the vertical temperature measuring point at the time of W _m , use

means that the minimum value of the determinant is W _m x _min , then the most unfavorable positive temperature gradient on the W-th day is

i = m;

i＝n表示，该行列式最小值为W_nS_max,则第W日最不利负温度梯度为

i＝n；S26: Screen the temperature of the vertical temperature measuring point at time W _n , use

i=n means that the minimum value of the determinant is W _n S _max , then the most unfavorable negative temperature gradient on the Wth day is

i=n;

S27: According to steps S25 and S26, the daily most unfavorable positive temperature gradient Z _ij and the most unfavorable negative temperature gradient F _ij in the monitoring date are obtained.

S28: Draw images of the most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient.

Compared with the prior art, the advantages of the present invention are:

Considering the concrete temperature field with transient characteristics, the "RBTMAS" method is used to quickly process the temperature data of each part of the box girder obtained by on-site monitoring, and obtain the real-time vertical temperature difference data of the box girder. Based on semi-theoretical and semi-empirical formulas and generalized extreme value statistics The theoretical calculation formula of the temperature load of the box girder under the action of heating and cooling is established, and the extreme value statistics method is used to count the distribution patterns of positive and negative temperature gradients, as well as the most unfavorable positive and negative temperature gradients that may occur in the recurrence period. negative temperature difference. The reliability of the results was tested using the Pearson correlation coefficient method. The method for solving the vertical temperature gradient of the box beam established by the present invention can simply and accurately calculate the most unfavorable vertical temperature gradient mode of the box beam in the environment of heating and cooling, thereby calculating the temperature load, which is more accurate than the previous method. Significantly improved. According to the box girder temperature measured at the specific site, the most unfavorable positive and negative temperature differences that may occur during the recurrence period can be fitted, and the most unfavorable positive and negative temperature gradient patterns in the region can be deduced. It has guiding significance for bridge design and construction.

Description of drawings

Fig. 1 is the whole process calculation flow chart of the inventive method;

Fig. 2 is the algorithm flow chart of the " RBTMAS " method that the present invention relates to screening and complementing measured temperature data;

Fig. 3 is the vertical temperature gradient map drawn after screening and complementing the measured temperature data by the proposed method of the present invention;

Fig. 4 is the PP map and the QQ map of the accuracy of using the method of the present invention to fit and obtain _Tm and a;

FIG. 5 is a graph of the results obtained by fitting the temperature gradient with the specification by the method of the present invention.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below according to the accompanying drawings and examples.

As shown in Figure 1, a method for calculating the most unfavorable vertical temperature gradient of a box girder includes the following steps:

S1: Screen and process temperature monitoring data, clear wrong data and fill in vacant monitoring data.

S11: Use the following erroneous data identification criteria to clear erroneous data:

Criterion 1: Use the Grubbs criterion to identify erroneous data with a 95% confidence probability.

Criterion 2: According to the analysis of long-term temperature monitoring data, two empirical criteria are obtained: the temperature change of the same monitoring point at a certain moment exceeds the temperature at the previous moment ±10 degrees Celsius, the temperature data at this moment is judged to be wrong, and the red processing is performed. If the temperature of all measuring points is higher than the daily average temperature +15 degrees Celsius or lower than the daily average temperature -18 degrees Celsius, it will be judged that the temperature data at this moment is wrong and will be marked in red.

S12: Due to the monitoring system, the temperature of some measuring points cannot be measured at a certain time or the measured temperature is judged to be wrong data, so the following formula is used as the identification criterion of supplementary data to supplement the monitoring data;

In the formula, T _at is the temperature that is not measured at time t at measurement point a during the monitoring time, _Tav is the average temperature at measurement point a on the day, _Tam is the temperature difference at measurement point a on the day, and t ₀ is the time when the highest temperature occurs at measurement point a.

S2: According to the completed temperature monitoring data, through the bridge temperature real-time monitoring and analysis method (Real-time BridgeTemperature Monitoring Analysis System), hereinafter referred to as: RBTMAS method, this method is the method proposed by the applicant, and this method is used to screen the most unfavorable daily positive Temperature gradients and worst negative temperature gradients, and plot temperature gradients.

As shown in Figure 2, the calculation steps of the RBTMAS method are as follows:

S21: Import the monitoring data table, filter and sort out the temperature data measured by the vertical temperature measuring point channel;

S22: Use W _i S _j to express the temperature of the Wth day, time i, and the temperature of the vertical jth measuring point (unit °C), then the temperature of the vertical measuring point at the same time can be expressed as

S23: At the same time (W _i ) in one day, all the measuring points in the vertical direction are subtracted from each other and then compare their sizes to obtain the maximum and minimum temperature differences at this time of the day;

S24: Step S23 is expressed by the following formula:

Let _Wi x ₁₂ = _Wi (S ₁ -S ₂ ), then

The maximum value in this determinant is represented by W _m x _max , that is, the Wth day, at time m, the most unfavorable positive temperature difference on the day of occurrence is x _max , and the minimum value is represented by Q _n x _min , that is, the Wth day, at time n, the day of occurrence The most unfavorable negative temperature difference is x _min . Note: If W _m x _max ≤ 0, there is no most unfavorable positive temperature difference on that day; if W _m x _min ≥ 0, then there is no most unfavorable negative temperature difference on that day;

i＝m表示，该行列式最小值为W_mS_min,则第W日最不利正温度梯度为

i＝m；S25: Filter out the temperature of the vertical temperature measuring point at the time of W _m , use

i=m means that the minimum value of the determinant is W _m S _min , then the most unfavorable positive temperature gradient on the Wth day is

i = m;

i＝n表示，该行列式最小值为W_nS_max,则第W日最不利负温度梯度为

i＝n；S26: Screen the temperature of the vertical temperature measuring point at time W _n , use

i=n means that the minimum value of the determinant is W _n S _max , then the most unfavorable negative temperature gradient on the Wth day is

i=n;

S27: According to steps S25 and S26, the daily most unfavorable positive temperature gradient Z _ij and the most unfavorable negative temperature gradient F _ij in the monitoring date are obtained.

S28: Draw images of the most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient, as shown in FIG. 3 .

S3: The calculation formula of the vertical temperature gradient can be written as:

T _y =T ^{me ay} ₍ 2)

where T _m is the maximum positive temperature difference in the beam height direction, y is the distance from the calculation point to the top surface of the box girder, T _y is the temperature difference at the position of the calculation point, and a is the index.

S4: The two parameters T _m and a in the formula (1) are constants, which are determined by the environment where the bridge is located and the structural form of the box girder. They are obtained by fitting the long-term temperature monitoring data. The fitting principle is as follows:

where (x; μ, σ, ξ) is the distribution function of x, μ is the position parameter, σ is the scale parameter, and ξ is the shape parameter.

where (x; μ, σ, ξ) is the density function of x.

The temperature probability p=1/P (0<p<1) once in P year, when the return period is p, the extreme value of the temperature difference is x _p :

x _p = μ-σ(1-(-log p) ^-ξ )/ξ (5)

To perform generalized extreme value statistical analysis on non-independent random variables, μ, σ, and ξ need to be corrected:

In the formula, θ is the extreme value index, which can be calculated by the run-length method.

S5: Fit the most unfavorable positive temperature gradient data through the maximum likelihood estimation of the generalized extreme value distribution, and obtain the three parameters μ, σ, ξ of the most unfavorable positive temperature gradient T _m and a respectively.

S6: Correct the parameters through the formula (6), and then obtain the modified _Tm ' and a' of the most unfavorable positive temperature gradient. Similarly, T _m ' and a' of negative temperature gradient can be obtained.

S7: The formula to finally get the most unfavorable vertical temperature gradient is:

T _y =T _m 'e ^a'y (7)

S8: Use P-P graph, Q-Q graph and Pearson correlation coefficient method to test the accuracy of fitting with this method. If the P-P graph and Q-Q graph are straight lines and the Pearson correlation coefficient r≥0.8, use this method to fit the The vertical most unfavorable temperature gradient has high accuracy and meets the requirements.

S9: Establish the finite element model of the bridge, load the most unfavorable temperature gradient into the finite element calculation model, and calculate the influence of the most unfavorable vertical temperature gradient mode of the box girder on the bridge.

Example 1

In order to verify the accuracy of the proposed method for calculating the vertical temperature gradient of the box girder, the method is used to process the long-term monitoring temperature data of the single box double chamber box girder, and the generalized extreme value distribution method is used to fit the QQ plot and the PP plot. The result is judged. Figure 4 shows the PP and QQ plots for testing the accuracy of _Tm .

The data in Fig. 4 are all approximated by a straight line distribution, which shows that the result of fitting the temperature gradient of the box girder by this method is accurate. Equation (8) was used to calculate the Elson correlation coefficient between the fitting results and the measured results by this method. The correlation coefficients of the three sets of fitting results are 0.98, 0.92, and 0.87, respectively, and |r|≥0.8, indicating that the fitting results are highly correlated with the measured results. To sum up, the results of the two judgment methods show that the results calculated by this method have high accuracy. This method can calculate the most unfavorable temperature gradient of the box girder.

Example 2

In order to further verify the superiority of the proposed method, the method proposed in the present invention is compared with the method for calculating the vertical temperature gradient of the box girder proposed by the specification.

As shown in Fig. 5, the calculation results are in good agreement with the calculation results of the code. The calculated temperature difference curve of the middle web is very close to the curve style of the code, but the maximum positive temperature difference in the railway code is lower than the maximum positive temperature difference of the web calculation curve in this case; The temperature difference calculation curves of the east and west webs of the box girder are basically the same, but the maximum positive temperature difference is different. Compared with the standard positive temperature difference curve, the temperature difference calculation curve of the east and west webs changes faster at the top of the box girder. It shows that the temperature gradients at different positions of the box girder are not the same, and the difference is large. If only the method of calculating the temperature gradient proposed by the code is used, the calculated temperature load may be too large, and the safety factor may be too high, resulting in Construction costs increase. Through this method, the magnitude of the vertical temperature gradient at different positions of the box girder can be calculated, and the temperature gradient can be loaded into the finite element model, and the magnitude of the temperature load can be calculated more accurately. The design provides a good reference.

Those of ordinary skill in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation method of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to the technical teaching disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.

Claims (1)

1. A method for calculating the worst vertical temperature gradient of a box girder is characterized by comprising the following steps:

s1: screening and processing temperature monitoring data, eliminating error data and completing vacant monitoring data;

the substeps of S1 are as follows:

s11: error data is cleared using the following error data identification criteria:

criterion 1: under the condition that the confidence probability is 95%, adopting Grubbs criterion to identify error data;

criterion 2: two empirical criteria were derived from long-term temperature monitoring data analysis: when the temperature change of the same monitoring point at a certain moment exceeds the temperature of the previous moment by +/-10 ℃, judging that the temperature data at the moment are wrong, and performing red marking treatment; if the temperature of all the measuring points is higher than the daily average temperature by plus 15 ℃ or lower than the daily average temperature by minus 18 ℃, judging that the temperature data at the moment are wrong, and performing red marking treatment;

s12: because of the monitoring system, the temperature of some measuring points can not be measured at a certain moment or the measured temperature is judged to be error data, the following formula is adopted as the identification criterion of the supplementary data to complement the monitoring data;

in the formula T_atIs the temperature not measured at the moment of the point a and the point T in the monitoring time, T_avIs the average temperature of the point a on the day, T_amThe temperature difference of the point a in the day, t₀The time when the highest air temperature appears at the point a is measured;

s2: screening the most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient of the day by an RBTMAS method according to the supplemented temperature monitoring data, and drawing a temperature gradient graph;

the RBTMAS method comprises the following calculation steps:

s21: importing a monitoring data table, and screening and arranging temperature data measured by the vertical temperature measuring point channels;

s22: by W_iS_jExpressing the temperature of the jth vertical measuring point on the W th day and the i momentDegree, in degrees C, the temperature at the vertical measuring point at the same time can be expressed as

S23: the same time of day (W)_i) Sequentially subtracting all the measuring points in the vertical direction and then comparing the measuring points to obtain the maximum value and the minimum value of the temperature difference at the moment of the day;

s24: step S23 is expressed by the following equation:

let W_ix₁₂＝W_i(S₁-S₂) Then, then

Maximum value in the determinant is W_mx_maxIndicating that the worst positive temperature difference of the appearance day is x at the moment of m on the W th day_maxW for minimum value_nx_minIndicating that the worst negative temperature difference of the appearance day is x at the time of n on the W day_min(ii) a Note: if W_mx_maxNo more than 0, no most unfavorable positive temperature difference exists in the day; if W_mx_minIf the temperature is more than or equal to 0, the day has no most unfavorable negative temperature difference;

s25: screening out W_mMeasuring the temperature of the point at a time vertical temperature, using

Expressed in that the minimum value of the determinant is W_mS_minThen the most unfavorable positive temperature gradient of day W is

S26: screening of W_nMeasuring the temperature of the point at a time vertical temperature, using

Expressed in that the minimum value of the determinant is W_nS_maxThe worst negative temperature gradient on day W is

S27: monitoring the most adverse daily positive temperature gradient Z within the date according to steps S25 and S26_ijAnd the most unfavorable negative temperature gradient F_ij；

S28: drawing images of the most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient;

s3: the formula for the calculation of the vertical temperature gradient can be written as:

T_y＝T_me^ay (2)

in the formula T_mIs the maximum positive temperature difference in the beam height direction, y is the distance from the calculated point to the top surface of the box beam, T_yIs the temperature difference value at the position of the calculation point, a is an index;

s4: (1) two parameters T in the formula_mAnd a is a constant which is determined by the environment of the bridge and the structural form of the box girder and is obtained by fitting long-term temperature monitoring data, and the fitting principle is as follows:

in the formula, H (x; mu, sigma, xi) is a distribution function of x, mu is a position parameter, sigma is a scale parameter, and xi is a shape parameter;

wherein h (x; mu, sigma, xi) is a density function of x;

the probability P of the temperature of the year meeting is 1/P, 0<p<1, x is the extreme value of the temperature difference when the reproduction period is p_p：

x_p＝μ-σ(1-(-log p)^-ξ)/ξ (5)

If the generalized extreme value statistical analysis is to be performed on the dependent random variables, the correction needs to be performed on μ, σ and ξ:

in the formula, theta is an extreme value index and can be calculated by using a run-length method;

s5: fitting the most unfavorable positive temperature gradient data through the maximum likelihood estimation of the generalized extremum distribution to respectively obtain the most unfavorable positive temperature gradient T_mAnd three parameters μ, σ, ξ for a;

s6: and then the parameters are corrected by the formula (6), and the corrected T with the most unfavorable positive temperature gradient is obtained_m'and a'; the negative temperature gradient T can be obtained in the same way_m'and a';

s7: the formula for finally obtaining the vertical worst temperature gradient is as follows:

T_y＝T_m′e^a′y (7)

s8: the accuracy of the fitting of the method is checked by using a P-P diagram, a Q-Q diagram and a Pearson correlation coefficient method, if the P-P diagram and the Q-Q diagram are lifting straight lines and the Pearson correlation coefficient r is more than or equal to 0.8, the accuracy of the vertical worst temperature gradient fitted by the method is higher and meets the requirement;

s9: and establishing a finite element model of the bridge, loading the worst temperature gradient to the finite element calculation model, and calculating the influence of the worst vertical temperature gradient mode of the box girder on the bridge.

Images