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

Method for calculating vertical worst temperature gradient of box girder Download PDF

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CN111651927B
CN111651927B CN202010535393.1A CN202010535393A CN111651927B CN 111651927 B CN111651927 B CN 111651927B CN 202010535393 A CN202010535393 A CN 202010535393A CN 111651927 B CN111651927 B CN 111651927B
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黄博
颜挺毅
任青阳
崔晓璐
万通
祝兵
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Chongqing Jiaotong University
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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

Method for calculating vertical worst temperature gradient of box girder
Technical Field
The invention relates to the technical field of calculation of the worst temperature gradient of a bridge superstructure in bridge engineering under the action of a temperature effect, in particular to a method for calculating the vertical worst temperature gradient of a box girder.
Background
Concrete bridges which are in atmospheric environment for a long time are not only required to bear loads such as self weight and vehicles, but also required to be subjected to influences such as solar radiation and atmospheric environment temperature change. The temperature stress generated by the temperature action in the concrete box girder can reach more than 3MPa, exceeds the allowable tensile stress of concrete, sometimes exceeds the section stress generated by the live load of a bridge, and causes serious cracks and even collapse accidents. The number of damaged bridges caused by the temperature effect influences arouses the attention of numerous experts and scholars at home and abroad to the most adverse temperature gradient of the bridges.
The investigation of bridge diseases caused by the temperature effect discovers that a plurality of serious accidents caused by concrete cracking caused by the temperature effect occur at home and abroad. The Jagst concrete bridge in Germany generates serious cracks in the fifth year of traffic, and the tensile stress caused by the temperature effect is estimated to be as high as 2.6 MPa. The champgny concrete box girder bridge in the united states generates a tensile stress of up to 3.92MPa in the bottom flange of the box girder due to the temperature difference between the top plate and the bottom plate of the box girder. A prestressed concrete viaduct in new zealand suffers severe cracking of the bridge shortly after operation due to the temperature effects caused by sunlight. A concrete-steel box combined beam bridge in canada has a collapse accident due to temperature stress and deformation. In recent years, many concrete bridge disease accidents caused by temperature effects occur in China. For example, a certain curve continuous box girder overpass located in Shenzhen in China has lateral displacement of nearly 50cm when the temperature difference of the girder body is maximum; cracks caused by temperature stress are generated on the box girder top plate and the main pier body of the photochemical Hanjiang bridge in Hubei; the nine-river bridge approach simply supported box girder and the Tonghui continuous box girder all have severe cracking caused by temperature load. The temperature effect caused by the temperature gradient is light, so that the bridge is cracked, and huge economic loss is caused in the repairing process; the major structure of the bridge is directly damaged, and the serious accident of bridge collapse is caused.
The expert and scholars at home and abroad test and research a large number of concrete structure diseases, and the most unfavorable temperature gradient is the main cause of the damage of the bridge. Therefore, the accurate calculation of the worst temperature gradient is helpful for perfecting the design theory of the concrete bridge box girder, and has very important theoretical and practical significance for improving the safety, durability and economy of the concrete bridge girder structure.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for calculating the worst vertical temperature gradient of a box girder, and solves the defects in the prior art.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a method for calculating the worst vertical temperature gradient of a box girder comprises the following steps:
s1: and screening and processing the temperature monitoring data, eliminating error data and completing the vacant monitoring data.
The substeps of S1 are as follows:
s11: error data is cleared using the following error data identification criteria:
criterion 1: in the case of a 95% confidence probability, the Grubbs criterion is used to identify erroneous data.
Criterion 2: two empirical criteria were derived from long-term temperature monitoring data analysis: and 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. And if the temperature of all the measuring points is higher than the daily average air temperature by +15 ℃ or lower than the daily average air temperature by-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;
Figure BDA0002536878200000021
in the formula TatIs the temperature not measured at the moment of the point a and the point T in the monitoring time, TavIs the average temperature of the point a on the day, TamThe temperature difference of the point a in the day, t0The time at which the highest air temperature occurs at point a is shown.
S2: according to the compensated Temperature Monitoring data, the Bridge Temperature Real-time Monitoring analysis method (Real-time Bridge Temperature Monitoring analysis System) is used, and the following is abbreviated as follows: the RBTMAS method, which is proposed by the applicant, screens the daily most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient, and plots the temperature gradients.
S3: the formula for the calculation of the vertical temperature gradient can be written as:
Ty＝Tmeay (2)
in the formula TmIs 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, TyIs the value of the temperature difference at the location of the calculation point, and a is an index.
S4: (1) two parameters T in the formulamAnd 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:
Figure BDA0002536878200000031
where (x; mu, sigma, xi) is the distribution function of x, mu is the position parameter, sigma is the scale parameter, and xi is the shape parameter.
Figure BDA0002536878200000032
Where (x; mu, sigma, xi) is a function of the density of x.
The probability P of the temperature of the year meeting is 1/P (0)<p<1) When the reproduction period is p, the extreme value of the temperature difference is xp：
xp＝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:
Figure BDA0002536878200000033
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 TmAnd three parameters of aμ，σ，ξ。
S6: and then the parameters are corrected by the formula (6), and the corrected T with the most unfavorable positive temperature gradient is obtainedm'and a'. The negative temperature gradient T can be obtained in the same waym'and a'.
S7: the formula for finally obtaining the vertical worst temperature gradient is as follows:
Ty＝Tm′ea′y (7)
s8: and (3) checking the fitting accuracy of the method by using a P-P diagram, a Q-Q diagram and a Pearson correlation coefficient method, wherein 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 using the method is higher, and the requirement is met.
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.
Further, the calculation procedure of the RBTMAS method in S2 is as follows:
s21: importing a monitoring data table, and screening and arranging temperature data measured by the vertical temperature measuring point channels;
s22: by WiSjExpressing the temperature (unit ℃) of the jth vertical measuring point at the time of day W and i, and then the temperature of the vertical measuring point at the same time can be expressed as
Figure BDA0002536878200000041
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:
Figure BDA0002536878200000051
let Wix12＝Wi(S1-S2) Then, then
Figure BDA0002536878200000052
Maximum value in the determinant is WmxmaxIndicating that the worst positive temperature difference of the appearance day is x at the moment of m on the W th daymaxW for minimum valuenxminIndicating that the worst negative temperature difference of the appearance day is x at the time of n on the W daymin. Note: if WmxmaxNo more than 0, no most unfavorable positive temperature difference exists in the day; if WmxminIf the temperature is more than or equal to 0, the day has no most unfavorable negative temperature difference;
s25: screening out WmMeasuring the temperature of the point at a time vertical temperature, using
Figure BDA0002536878200000053
Expressed in that the minimum value of the determinant is WmxminThen the most unfavorable positive temperature gradient of day W is
Figure BDA0002536878200000054
i＝m；
S26: screening of WnMeasuring the temperature of the point at a time vertical temperature, using
Figure BDA0002536878200000055
i is n and the minimum value of the determinant is WnSmaxThe worst negative temperature gradient on day W is
Figure BDA0002536878200000056
i＝n；
S27: monitoring the most adverse daily positive temperature gradient Z within the date according to steps S25 and S26ijAnd the most unfavorable negative temperature gradient Fij。
S28: and drawing images of the most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient.
Compared with the prior art, the invention has the advantages that:
the concrete temperature field with transient characteristics is considered, temperature data of all parts of the box girder obtained by field monitoring are rapidly processed through a RBTMAS method, real-time vertical temperature difference data of the box girder are obtained, a theoretical calculation formula of temperature load borne by the box girder under the action of temperature rise and temperature drop is established based on a semi-theoretical semi-empirical formula and a generalized extreme value statistical theory, and a positive and negative temperature gradient distribution mode and the most unfavorable positive and negative temperature difference possibly occurring in a recurrence period are counted through 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 environment of temperature rise and temperature drop, thereby calculating the temperature load, and obviously improving the accuracy compared with the traditional method. The worst positive and negative temperature differences which may occur in the recurrence period can be fitted according to the box girder temperature actually measured on a specific site, and the worst positive and negative temperature gradient mode of the area can be deduced. Has guiding significance for bridge design and construction.
Drawings
FIG. 1 is a flow chart of the overall process calculation of the method of the present invention;
FIG. 2 is a flow chart of the algorithm of the RBTMAS method of the present invention involving screening and complementing measured temperature data;
FIG. 3 is a vertical temperature gradient plot drawn after screening and complementing measured temperature data by the method of the present invention;
FIG. 4 is a graph of a test of T obtained by fitting using the method of the present inventionmAnd a P-P and Q-Q plots of accuracy;
FIG. 5 is a graph of the results of a temperature gradient fit compared to a specification by the method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail below with reference to the accompanying drawings by way of examples.
As shown in fig. 1, a method for calculating the worst vertical temperature gradient of a box girder comprises the following steps:
s1: and screening and processing the temperature monitoring data, eliminating error data and completing the vacant monitoring data.
S11: error data is cleared using the following error data identification criteria:
criterion 1: in the case of a 95% confidence probability, the Grubbs criterion is used to identify erroneous data.
Criterion 2: two empirical criteria were derived from long-term temperature monitoring data analysis: and 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. And if the temperature of all the measuring points is higher than the daily average air temperature by +15 ℃ or lower than the daily average air temperature by-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;
Figure BDA0002536878200000071
in the formula TatIs the temperature not measured at the moment of the point a and the point T in the monitoring time, TavIs the average temperature of the point a on the day, TamThe temperature difference of the point a in the day, t0The time at which the highest air temperature occurs at point a is shown.
S2: according to the compensated Temperature Monitoring data, the Bridge Temperature Real-time Monitoring analysis method (Real-time Bridge Temperature Monitoring analysis System) is used, and the following is abbreviated as follows: the RBTMAS method, which is proposed by the applicant, screens the daily most unfavorable positive temperature gradient and the most unfavorable negative temperature gradient, and plots the temperature gradients.
As shown in fig. 2, the RBTMAS method includes the following steps:
s21: importing a monitoring data table, and screening and arranging temperature data measured by the vertical temperature measuring point channels;
s22: by WiSjExpressing the temperature (unit ℃) of the jth vertical measuring point at the time of day W and i, and then the temperature of the vertical measuring point at the same time can be expressed as
Figure BDA0002536878200000072
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:
Figure BDA0002536878200000081
let Wix12＝Wi(S1-S2) Then, then
Figure BDA0002536878200000082
Maximum value in the determinant is WmxmaxIndicating that the worst positive temperature difference of the appearance day is x at the moment of m on the W th daymaxMinimum value QnxminIndicating that the worst negative temperature difference of the appearance day is x at the time of n on the W daymin. Note: if WmxmaxNo more than 0, no most unfavorable positive temperature difference exists in the day; if WmxminIf the temperature is more than or equal to 0, the day has no most unfavorable negative temperature difference;
s25: screening out WmMeasuring the temperature of the point at a time vertical temperature, using
Figure BDA0002536878200000083
i is m, and the minimum value of the determinant is WmSminThen the most unfavorable positive temperature gradient of day W is
Figure BDA0002536878200000084
i＝m；
S26: screening of WnMeasuring the temperature of the point at a time vertical temperature, using
Figure BDA0002536878200000085
i is n and the minimum value of the determinant is WnSmaxThe worst negative temperature gradient on day W is
Figure BDA0002536878200000086
i＝n；
S27: monitoring the most adverse daily positive temperature gradient Z within the date according to steps S25 and S26ijAnd the most unfavorable negative temperature gradient Fij。
S28: the most adverse positive temperature gradient and the most adverse negative temperature gradient images were plotted as shown in fig. 3.
S3: the formula for the calculation of the vertical temperature gradient can be written as:
Ty＝Tmeay (2)
in the formula TmIs 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, TyIs the value of the temperature difference at the location of the calculation point, and a is an index.
S4: (1) two parameters T in the formulamAnd 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:
Figure BDA0002536878200000091
where (x; mu, sigma, xi) is the distribution function of x, mu is the position parameter, sigma is the scale parameter, and xi is the shape parameter.
Figure BDA0002536878200000092
Where (x; mu, sigma, xi) is a function of the density of x.
The probability P of the temperature of the year meeting is 1/P (0)<p<1) When the reproduction period is p, the extreme value of the temperature difference is xp：
xp＝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:
Figure BDA0002536878200000093
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 TmAnd a, and three parameters μ, σ, ξ.
S6: and then the parameters are corrected by the formula (6), and the corrected T with the most unfavorable positive temperature gradient is obtainedm'and a'. The negative temperature gradient T can be obtained in the same waym'and a'.
S7: the formula for finally obtaining the vertical worst temperature gradient is as follows:
Ty＝Tm′ea′y (7)
s8: and (3) checking the fitting accuracy of the method by using a P-P diagram, a Q-Q diagram and a Pearson correlation coefficient method, wherein 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 using the method is higher, and the requirement is met.
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.
Example 1
In order to verify the accuracy of the method for calculating the vertical temperature gradient of the box girder, the method is used for processing long-term monitoring temperature data of the single-box double-chamber box girder, and a fitting result is judged by using a Q-Q diagram and a P-P diagram of a generalized extreme value distribution method. Shown in FIG. 4 as test TmP-P and Q-Q plots of accuracy.
The data in fig. 4 are all distributed approximately along a straight line, which shows that the result of the method for fitting the box girder temperature gradient is accurate. The heson correlation coefficient of the fitting result and the measured result by the method is calculated by using formula (8). The correlation coefficients of the three groups of fitting results are respectively 0.98, 0.92 and 0.87, | r | > 0.8, which indicates that the fitting results are highly correlated with the actual measurement results. In conclusion, the results of the two judgment methods show that the result calculated by the method has higher precision. The method can calculate the worst temperature gradient of the box girder.
Figure BDA0002536878200000101
Example 2
In order to further verify the superiority of the proposed method, the proposed method of 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 result is more consistent with the calculation result of the specification, wherein the calculated temperature difference curve of the middle web is very close to the curve pattern of the specification, but the maximum positive temperature difference in the railway specification is lower than the maximum positive temperature difference of the calculated curve of the web in the present case; the model of the temperature difference calculation curves of the east web and the west web of the box girder is basically the same, only the maximum positive temperature difference is different, and compared with the standard positive temperature difference curve, the temperature difference calculation curves of the east web and the west web are faster in change of the temperature difference at the top of the box girder. The temperature gradients at different positions of the box girder are different and are greatly different, and if the temperature gradients are calculated by only using the method for calculating the temperature gradients provided by the specification, the calculated temperature load is overlarge, the safety coefficient is overhigh, and the construction cost is increased. By the method, the size of the vertical temperature gradient at different positions of the box girder can be calculated, and the temperature gradient is loaded into the finite element model, so that the size of the temperature load can be calculated more accurately, and a good reference is provided for the design of the upper structure of the bridge under the action of the temperature gradient.
It will be appreciated by those of ordinary skill in the art that the examples described herein are intended to assist the reader in understanding the manner in which the invention is practiced, and it is to be understood that the scope of the invention is not limited to such specifically recited statements and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the 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;
Figure FDA0003556018280000011
in the formula TatIs the temperature not measured at the moment of the point a and the point T in the monitoring time, TavIs the average temperature of the point a on the day, TamThe 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 WiSjExpressing 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
Figure FDA0003556018280000012
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:
Figure FDA0003556018280000021
let Wix12＝Wi(S1-S2) Then, then
Figure FDA0003556018280000022
Maximum value in the determinant is WmxmaxIndicating that the worst positive temperature difference of the appearance day is x at the moment of m on the W th daymaxW for minimum valuenxminIndicating that the worst negative temperature difference of the appearance day is x at the time of n on the W daymin(ii) a Note: if WmxmaxNo more than 0, no most unfavorable positive temperature difference exists in the day; if WmxminIf the temperature is more than or equal to 0, the day has no most unfavorable negative temperature difference;
s25: screening out WmMeasuring the temperature of the point at a time vertical temperature, using
Figure FDA0003556018280000023
Expressed in that the minimum value of the determinant is WmSminThen the most unfavorable positive temperature gradient of day W is
Figure FDA0003556018280000024
S26: screening of WnMeasuring the temperature of the point at a time vertical temperature, using
Figure FDA0003556018280000025
Expressed in that the minimum value of the determinant is WnSmaxThe worst negative temperature gradient on day W is
Figure FDA0003556018280000026
S27: monitoring the most adverse daily positive temperature gradient Z within the date according to steps S25 and S26ijAnd the most unfavorable negative temperature gradient Fij；
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:
Ty＝Tmeay (2)
in the formula TmIs 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, TyIs the temperature difference value at the position of the calculation point, a is an index;
s4: (1) two parameters T in the formulamAnd 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:
Figure FDA0003556018280000031
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;
Figure FDA0003556018280000032
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 pp：
xp＝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:
Figure FDA0003556018280000033
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 TmAnd 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 obtainedm'and a'; the negative temperature gradient T can be obtained in the same waym'and a';
s7: the formula for finally obtaining the vertical worst temperature gradient is as follows:
Ty＝Tm′ea′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.
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