Main Girder Deflection Variations in Cable-Stayed Bridge with Temperature over Various Time Scales

+e cable-stay bridge is a complex hyperstatic structure with large span and slender proportions, making it highly sensitive to temperature, especially in terms of deformation. A cable-stayed bridge with a steel tower and steel box girder was taken as an example in this study to explore the temperature effects on the deflection of the main girder under different time scales. +e temperature gradient characteristics of the girder and tower were observed; then, the daily and annual variations of girder deflection were investigated. Finally, the main influencing factors of deflection variations with temperature were verified by finite element simulation. +e results show that the girder/pylon temperature gradient under current Chinese code is not applicable to cable-stayed bridges, and the measured values are usually underestimated. In terms of diurnal variations, the deflection is greatly affected by the temperature difference between the cable and beam and the temperature gradient of the girder. +e annual variation law of deflection data and temperature at 1 : 00am shows obvious linear characteristics. +e daily deflection at 1 : 00am., after removing the temperature effect, can thus be used as an index to evaluate the long-term degradation of bridges. +is is a workable approach for efficient and rapid mining of large sets of monitoring data.


Introduction
Cable-stayed bridges are components of many transportation systems across the globe. ey are popular as they are aesthetically pleasing and have strong mechanical and economic performance. Transportation infrastructure construction projects are booming in China, and at present, China has the world's largest number of cable-stayed bridges: approximately 60 with a total span of more than 200 meters [1]. Long-span cable-stayed bridges are often located in traffic throat positions and serve as important transportation hubs. Most are equipped with health monitoring systems to control their operation states; the deflection of the main girder is an important health monitoring parameter [2] as it reflects deformation in the bridge, which can indirectly reveal any abnormal displacement of the cable force, pylon, expansion joint, bearing, and other parts of the structure. Main girder deflection is of great significance for damage identification [3,4]. e influence of temperature on bridge deformation is usually greater than that of traffic or wind loads. A benchmark model of temperature and deformation effects can be used to monitor changes in the structure's performance, which makes research on bridge temperature effects very valuable [5][6][7]. e temperature effects of high-order statically indeterminate structures are highly complex. Measurement results vary throughout the literature [8][9][10][11][12]. Five-day monitoring data of the Zhanjiang Bay Bridge in the summer of 2008 showed that the mid-span deflection of the main girder increased during the high-temperature period [13]. Lee et al. [14] found that the elevation of the Seohae Bridge girder in South Korea is higher in summer than in winter but did not explain the reason for this phenomenon. Monitoring data of the Donghai Bridge from March to September 2007 showed that mid-span deflection decreased with an increase in the average temperature over the main girder; a time lag emerged between the deformation and the temperature as well [7]. Monitoring data for the Dafosi Yangtze River Bridge and Masongxi Yangtze River Bridge over an approximately 10-day period showed that the deck of the midspan bridge dropped when temperature increased [15]. e relationship between main girder vertical displacement and temperature is not consistent in cable-stayed bridges, though this is the case in suspension bridges [16].
Many previous scholars have explored temperature actions via finite element analysis. Zhou et al. [17] investigated the effects of seasonal as well as diurnal temperature variations on thermally induced changes in the mid-span vertical displacement of steel bridges; they assessed the effects of the distance between the two tower tops and cable tensions based on monitoring data for steel box girder and twintower cable-stayed bridges. ey found that the correlations between temperature and structural responses can be classified into two modes. Lucas et al. [18] processed temperature data for the steel box girder of the Normandy Bridge to determine the daily change rule of the girder temperature. Xia et al. [19] analyzed the factors influencing the temperature distributions of the Tsing Ma suspension bridge based on numerical simulation. Miao and Shi [20] proposed a temperature gradient for the hexagonal flat steel box girder. Zhou et al. [21] investigated the mechanisms of temperature effects on the mid-span vertical displacement of the Shanghai Yangtze River Bridge via plane geometric and finite element analyses.
Previous scholars have conducted in-depth analyses of the temperature effects of deflection in cable-stayed bridges of different materials, but there are few reports on temperature effects in cable-stayed bridges with steel towers and steel girders specifically. Additionally, there is no suitable evaluation index for the long-term deflection degradation of cable-stayed bridges. A cable-stayed bridge with a steel tower and steel main girder, the Nanjing No. 3 Yangtze River Bridge, was taken as an example in this study. e temperature field and girder deflection monitoring data were utilized to determine the temperature distribution patterns as per British and Chinese temperature gradient design specifications. e diurnal and annual variations in girder deflection with temperature were monitored accordingly, then verified according to a finite element simulation. Finally, the appropriate index was established to efficiently and accurately reflect the long-term structural degradation. e conclusions of this work may not only deepen our understanding of the temperature effects of steel cable-stayed bridges but also provide an approach for efficient and rapid mining of large quantities of monitoring data.

Temperature Characteristics Analysis of the Girder and Pylon
2.1. Introduction to the Monitoring System. e research object discussed in this paper is the Nanjing No. 3 Yangtze River Bridge, which is located in Nanjing City, Jiangsu Province, China ( Figure 1). e bridge opened in October 2005. Its main structure is a cable-stayed bridge with a main span of 648 meters plus a tower 215 meters in height. It is a five-span, 1288 m long cable-stayed bridge structure with a span arrangement of 63 + 257+648 + 257 + 63. It is equipped with steel pylon, steel box girder, and reinforced concrete pier components. It was the first cable-stayed bridge with steel towers completed in China and the world's first cablestayed bridge with an arc-shaped steel tower. e bridge health monitoring system (BHMS) was put into use in May 2006. e system includes a sensor subsystem, data acquisition and transmission subsystem, data processing and control subsystem, structural safety evaluation subsystem, center database subsystem, user interface subsystem, and electronic inspection and maintenance management subsystem. e sensor subsystem continuously measures a number of bridge parameters related to the structures' response and environment (e.g., strain, cable force, geometric deformation, dynamic characteristics, and structural temperature). e system contains a total of 548 types of sensors. e specific number of relevant sensors targeting temperature and girder deflection is given in Table 1.

Temperature Distribution of Steel Box Girder.
e vertical temperature gradient is an important temperature effect in the steel box girder, as it significantly affects the stress of the structure. e temperature gradient distribution assessed in this study is discussed in this section. e main girder of the target bridge is a streamlined flat steel box girder 3.2 m in height and 37.2 m in width, comprised of Q345-D steel. e thickness of the bridge deck pavement is 50 mm. e standard girder (15 m length) contains four solid diaphragm plates spaced 3.75 m apart. e temperature mode of each section in the longitudinal direction of a given bridge is basically consistent [21], so only one position is necessary for an effective analysis. Consider the mid-span monitoring points of the target bridge as an example; the temperature monitoring point arrangement is as shown in Figure 2.
ere are seven monitoring points in the top plate (GT1-GT7), four in the web plate (GW1-GW4), and five in the bottom plate (GB1-GB5). e steel box girder provides temperature sensor data to the system every 30 min with 0.5°C precision. e transverse temperature distribution of the bottom plate and top plate is basically consistent, while there is a pronounced vertical temperature gradient. To obtain the maximum temperature gradient distribution for subsequent calculation of temperature effects, temperature data from days with the strongest solar radiation were collected. Monitoring data statistics for temperature differences throughout 2007 showed that July 26 was best-suited to this analysis; data from this day was abstracted accordingly. GT1 (top plate) and GW1-2 (web plate) data were selected for analysis. e differences between them and the mean temperature of the bottom plate are shown in Figure 3. e maximum temperature difference occurred between 14 : 00 and 15 : 30. e mean values of temperature difference during this period can be considered as the data reference value of the maximum vertical temperature gradient, as marked with a "△" in Figure 4.      e British standard BS5400 provides detailed regulation over bridge girder temperature effects [22]. e general specifications for the design of highway bridges and culverts (JTG D60-2015) in China have relatively simple regulation for calculating temperature effects in the T-section continuous beam [23]. Figure 4 also shows the temperature gradient distributions under both sets of specifications.
As shown in Figure 4, the main girder temperature gradient specified in China's codes cannot be directly applied to steel box girders in cable-stayed bridges. e monitoring value of this bridge basically conforms to the temperature gradient in the British code, however. e girder temperature gradient of British standard BS 5400 can thus be reasonably applied for finite element simulation purposes.

Temperature Distribution of Steel Pylon.
e design codes of various countries lack information regarding the temperature gradient of the steel pylon. e temperature difference is 5°C in the codes given by China and Europe. e location of the pylon temperature monitoring point used in this study is given in Figure 5. e upstream and downstream measuring points are symmetrically arranged. Two measuring points are arranged at four corners in the box cell and numbered P1 to P8, respectively, across the monitoring points 40 m above the bridge deck.
Since the two temperature measuring points at each corner are almost entirely consistent, only one was chosen as a reference here. Figure 6 shows the temperature changes of the four measuring points of upstream P8, P4, P1 and P5. e resolution of the temperature sensor is 0.5 o C, so the curve has a stepped shape. P1 and P4 belong to the south side and P5 and P8 to the north side of the structure. Due to the angle at which solar radiation strikes the bridge, the temperature rises more quickly on the south side than the north; the maximum temperature difference of the steel tower occurs around 10 : 30, which is 3-5 hours ahead of the maximum temperature difference of the steel box girder. e maximum temperature difference is 6°C, which is slightly higher than the value given in the code.
We also found that the maximum negative temperature difference of the pylon occurred in winter, at 9.94 between 16 : 00 and 17 : 00 on January 7. is is much larger than the value given in the code of China or Europe. erefore, the measurement data should be used to define the temperature gradient of the tower.

Variation Law Analysis of Girder
Deflection under Different Time Scales e deflection of the main girder of the cable-stayed bridge reflects the stress condition and potential damage to the entire structure. e deck alignment should generally be detected separately in the annual inspection. rough several years of monitoring data analysis, we discovered that changes in deflection have multiscale features with temperature variations. We divided these results into two scales to create a daily temperature model and annual temperature model, as discussed in detail in the following.

Diurnal Variations.
e main girder deflection monitoring process was conducted via a closed connected pipe method using a ROSEMOUNT 3051S, which has high precision, fast reaction, good synchronism, and high-frequency acquisition capability. e horizontality of the liquid surface in the connected pipe was exploited to connect the pipe along the beam, transfer the changes in liquid level over the pressure wave, and reveal fluctuations in liquid pressure by a high-performance pressure transmitter that could be converted into a numerical bridge deflection value. We found that the correlation between each measurement point was very high, so we focused only on the deflection of the mid-span. e variations in mid-span deflection and temperature over a five-day period in 2007 are shown in Figure 7.
Negative values indicate down-deflection and girder deflection at the pylon (0). As shown in Figure 7, the mid-span deflection fluctuated along with temperature and produced a "hysteresis loop" [24]. e temperature changes in one day  were divided into three stages: temperature fall, temperature rise, and a secondary temperature fall. e three corresponding stages of mid-span deflection were labeled as A, B, and C, respectively. Stage A occurred from 0 : 00 to sunrise; as the structure was in a dark environment, the deflective effects of temperature were relatively small. e deflective effects of vehicle loads were larger at this time, likely due to the relatively high proportion of heavy vehicles in the nighttime hours. During Stage B, which occurred from sunrise to the sunset, the mid-span deflection decreased as temperature increased. e mid-span deflection gradually increased throughout Stage C, which occurred from sunset to 24 : 00. e hysteresis loops gathered in this analysis also appear to be different sizes. We reached several conclusions regarding the typical temperature and deflection curves of the five-day period observed here: (a) When the maximum temperature difference is large over the course of one day, the corresponding deflection change is large and the hysteresis loop is relatively large (and vice versa). When the maximum temperature difference over one day is small (which is common in summer and winter months), the relationship between deflection and temperature is nearly linear due to the limited range of solar radiation during the day. When the temperature difference in spring and autumn is large, the deflection shows a distinct and nonstationary change. (b) e deflection change rate grows gradually stable at a certain value in Stage B. e fitting result based on monitoring data was approximately 4 cm/°C in this case. e mechanism behind this observation was determined via finite element simulation, as discussed in the following section. (c) e mid-span deflection is relatively stable due to the stable ambient temperature during the period from 0 : 00 to sunrise. e red dotted line in Figure 7 roughly indicates that there is a negative correlation between the deflection and temperature at 1 : 00. e mid-span deflection at 1 : 00 can be used as the basic data for long-term trend analysis. Annual deflection variations can be obtained by collecting the data at 1 : 00, as discussed in detail in the following.

Annual Variations. Data from January 2007
to December 2009 (one day per month) were extracted to investigate annual variations. We collected the average mid-span deflection and temperature from 0 : 00 to 1 : 00 per day and plugged the data into a linear simulation. Figure 8 shows the changes in mid-span deflection with temperature, which have a strong negative correlation with a Pearson coefficient of −0.87. e linear fitting results were calculated as follows:where D is the average monitored mid-span deflection from 0 : 00 to 1 : 00 in a day in millimetres; T is the average monitored temperature from 0 : 00 to 1 : 00 in a day in degrees Celsius.
e slope in the formula is −1.721, which indicates that the variation in mid-span deflection caused by unit temperature is −1.721. ( is was also simulated by finite element analysis, as discussed below.) e girder deflection was unified to the same temperature during the completion of the bridge (24°C) through a linear fitting. e data accumulated and the damage appears to be easily verifiable. e maintenance department was recommended to conduct targeted inspections based on this damage data.

Finite Element Model Establishment.
eoretically, a model with relative accuracy can simulate the actual mechanical behavior of a given structure. e reliability of monitoring data can be verified through changes in cable forces and deflection as-acquired by exerting a corresponding temperature load in a finite element model. We built a spatial "fishbone-typed beam" model ( Figure 9)   Table 2 [25][26][27][28][29][30].
A spatial beam element was adopted for the steel box girder, main pylon, and pier; a tension-only truss element was employed for the stay cable. Rigid arm connection was adopted between the node and stay cable. e mass of the diaphragm plate and deck pavement was defined by nodal loads. e constraint conditions of the whole bridge included consolidation of the main tower bottom, the auxiliary pier bottom, and the transition pier bottom in this case. e vertical and horizontal supports between the main beam and the tower column were simulated by a spring element with a certain rigidity. e effect of cable sag cannot be considered in a simulation of a cable with a truss element, so we imposed an equivalent elastic modulus method on the cable with an Ernst formula. Our ABAQUS initial finite element model of the whole cable-stayed bridge contains 5,515 nodes and 3,805 elements. e cable sag effect was considered in the nonlinear analysis.
is bridge was modified with a combined static and dynamic model. A loading test was conducted on the completed bridge to validate the model by comparison against the simulation results. Eighteen trucks (63 kN front axle, 222 kN back axle weight) were placed in the mid-span area resulting in a load arrangement as shown in Figures 10(a) and 10(b) for the actual bridge and the model, respectively. Table 3 gives measurement and calculation results. e statistical items included 19-21# cable forces at the river side of the south pylon, mid-span deflection, and vertical oneorder frequency. Among them, the average relative error of the three cable forces is −1.7%.

Comparison of Finite Element Simulation and Monitoring
Results. Accurate temperature simulation was crucial in this study for an effective contrast between the calculated and measured values. e unit temperature action was imposed on the model according to the actual measured temperature gradient of the girder as shown in Table 4; Table 4 also gives the calculated values of the mid-span deflection under different temperature actions. Figure 11 shows the girder deflection variations under four types of thermal actions. ey indicate that the positive temperature gradient of the  Mathematical Problems in Engineering girder and temperature difference between the cable and girder appear to be the strongest influence on the mid-span deflection among all the factors observed here. e overall temperature change of the whole structure is relatively large and changes in a manner opposite to these two effects. e influence of the temperature gradient of the pylon on the mid-span deflection is negligible.
It is worth noting that uniform temperature variations were input to the model for analysis. at is to say, the spatial variations in temperature and effects of sunlight radiation were not considered (as was the case in a previous study [26]).
is is not especially problematic for steel bridge analyses but may affect the results for concrete bridges or members. e results of finite element simulation and actual monitoring for the deflection change behavior on different time scales are as follows.

Diurnal Variations.
In the diurnal deflection variations, the monitoring data is greatly affected by one-day temperature differences and solar radiation. e bridge is mainly affected by the temperature difference between the cable and beam and the temperature gradient of the girder under solar radiation. e calculated sum of these two is 37.73 mm per degree Celsius; the monitoring fitting data is roughly 40 mm per degree Celsius. e finite element results accurately fit the changes in monitoring data. e influence   of solar radiation fluctuates in severity, so the hysteresis loops are different sizes and the changes are nonlinear.

Annual Variations.
e annual variations in deflection are mainly affected by the increases and decreases in overall temperature across the structure. e monitored deflection rate with temperature is −1.721 mm per degree Celsius and the finite element simulation result is −1.6 mm per degree Celsius; these values are very similar.
e above results suggest that the finite element simulation we conducted effectively describes the deflection changes under different temperatures in the target bridge. Detailed analysis of such results can provide bridge maintainers with accurate, comprehensive bridge deformation information to make effective judgments regarding damage in the bridge.

Conclusions
Our conclusions based on time multiscale effect analysis of deflection in a steel cable-stayed bridge with temperature variations can be summarized as follows: (1) e girder temperature gradient and the tower temperature gradient in current Chinese codes cannot be reasonably applied to steel box girders in steel cable-stayed bridges. However, the monitoring value of the bridge analyzed in this study conforms to the temperature gradient under British code. e girder temperature gradient of British standard BS 5400 can thus be reasonably applied for finite element simulation. e tower temperature gradient must be fitted with measurement data.
(2) e time scale variations in girder deflection are both diurnal and annual. Diurnally, the deflection is greatly affected by the temperature difference between the cable and beam and the temperature gradient of the girder. e annual variation law of deflection data and temperature at 1 : 00 am presents obvious linear characteristics. ese phenomena were corroborated by finite element simulation.
(3) e daily deflection at 1 : 00 am can be unified to a certain reference temperature. is deflection index reflects the long-term degradation law of the structure, which provides an approach for efficient and rapid mining of massive sets of monitoring data. (4) is work remits a deeper understanding of the multiscale behavior characteristics of deflection in steel cable-stayed bridges. However, our conclusions are limited to steel box girder cable-stayed bridges with steel towers and are not necessarily applicable to other types of cable-stayed bridges or bridges at alternate sites.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.