Solar Radiation Parameters for Assessing Temperature Distributions on Bridge Cross-Sections

applied sciences

Article Solar Radiation Parameters for Assessing Temperature Distributions on Bridge Cross-Sections

Junqing Xue 1,* ID , Jianhui Lin 1, Bruno Briseghella 1 ID , Habib Tabatabai 2 ID and Baochun Chen 1 1 College of Civil Engineering, Fuzhou University, Fuzhou, Fujian 350108, China; [email protected] (J.L.); [email protected] (B.B.); [email protected] (B.C.) 2 Department of Civil and Environmental Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211, USA; [email protected] * Correspondence: [email protected]; Tel.: +86-591-2286-5375 Received: 20 March 2018; Accepted: 12 April 2018; Published: 17 April 2018

Abstract: Solar radiation is one of the most important factors influencing the temperature distribution on bridge girder cross-sections. The bridge temperature distribution can be estimated using estimation models that incorporate solar radiation data; however, such data could be cost- or time-prohibitive to obtain. A review of literature was carried out on estimation models for solar radiation parameters, including the global solar radiation, beam solar radiation and diffuse solar radiation. Solar radiation data from eight cities in Fujian Province in southeastern China were obtained on site. Solar radiation models applicable to Fujian, China were proposed and verified using the measured data. The linear Ångström–Page model (based on sunshine duration) can be used to estimate the daily global solar radiation. The Collares-Pereira and Rabl model and the Hottel model can be used to estimate the hourly global solar radiation and the beam solar radiation, respectively. Three bridges were chosen as case study, for which the temperature distribution on girder cross-sections were monitored on site. Finite element models (FEM) of cross-sections of bridge girders were implemented using the Midas program. The temperature–time curves obtained from FEM showed very close agreement with the measured values for summertime. Ignoring the solar radiation effect would result in lower and delayed temperature peaks. However, the influence of solar radiation on the temperature distribution in winter is negligible.

Keywords: global solar radiation; beam solar radiation; diffuse solar radiation; estimation model; temperature distribution; bridge girder; cross-section; ﬁnite element model; monitoring

1. Introduction Temperature distribution in bridge structures built in the outdoor environment are appreciably influenced by solar radiation and ambient temperature variations [1]. The thermal energy associated with solar radiation can result in an increase in temperature at the top surfaces of the structure beyond the ambient temperature. Solar radiation is one of the most important factors affecting the temperature distribution in bridge structures [2]. Heat conduction can further affect the temperature distribution. Although there are many experimental studies that address temperature distribution in bridges [3–8], few consider and measure solar radiation when assessing bridge temperature distributions. When carrying out a dynamic heat transfer analysis on bridge structures, the geometry of cross-section, initial thermal state, varying boundary conditions, thermal properties of materials, etc. should be input into any Finite Element Method (FEM) software used. The solar radiation levels on different parts of bridge structures represent one of the time-varying boundary conditions, which can be estimated by considering the various model parameters. Taking box girder bridges as example, the external surface of the top flange is influenced by both the beam and diffuse solar radiation, while the external surface of the web is influenced by a combination of the beam solar radiation, diffuse

Appl. Sci. 2018, 8, 627; doi:10.3390/app8040627 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 627 2 of 27 solar radiation and reflection from the ground. The undersides of the top and bottom flanges are influenced by ground reflection. The geometry of the cross-section, thermal parameters of materials, and bridge location are all determined or known at the beginning of the design process; however, the solar radiation must be estimated or measured. The accuracy of heat transfer analysis using FEM is influenced by the precision of solar radiation estimates. At present, there is a lack of measured solar radiation data in most parts of China. There are 756 meteorological stations in China, but only 122 of those stations monitor solar radiation data [9]. In Fujian, there are more than 60 meteorological stations, with only the Fuzhou and Jian’ou stations monitoring the solar radiation levels. Therefore, engineers usually establish estimation models of solar radiation for engineering applications or scientific research. However, choosing the appropriate estimation models for solar radiation from among those proposed by researchers is a key problem. Some are empirical models based on different meteorological parameters, while others are established using numerical simulation involving different types of artificial intelligence methodologies. In this paper, the similarities and differences of various estimation models for solar radiation are summarized, including models for global, beam, and diffuse solar radiation, all of which should be considered in the analyses of temperature distribution on bridge girder cross-sections. Based on the solar radiation data obtained from eight cities in Fujian, China, estimation models of solar radiation applicable for Fujian, China were proposed. The monitoring of some bridges was carried out to obtain the temperature distribution on bridge girder cross-sections. The FEM of cross-sections of bridge girders were built using the Midas software. The influence of solar radiation on bridge temperature distribution in different seasons was analyzed. The results can be considered as a model for future development of specifications and estimation models for solar radiation in different regions in China and elsewhere.

2. State of Art of Estimation Models for Solar Radiation 2.1. Estimation Models for Global Solar Radiation The global solar radiation is the sum of beam solar radiation and diffuse solar radiation. Most of the research on global solar radiation is based on two different time scales: daily and hourly.

2.1.1. Estimation Models for Daily Global Solar Radiation The global solar radiation is mainly related to meteorological factors such as the duration of sunshine, extent of cloud cover, ambient temperature and so on. Accordingly, empirical regression analyses or artiﬁcial intelligence techniques are used by researchers to establish the estimation models of daily global solar radiation based on different meteorological factors. • Sunshine duration fraction models In 1924, a linear equation relating the clearness index and the sunshine duration fraction was proposed by Ångström [10], as shown below:

H/HC = a + b(S/S0) (1) where H/HC is the clearness index, H is the daily global solar radiation (averaged over one month), HC is the average clear-day global solar radiation, S/S0 is the sunshine duration fraction, S is the daily sunshine duration (averaged over one month), S0 is the maximum daily sunshine duration (averaged over one month), and a and b are empirical coefficients. However, it is difficult to properly define the concept of “clear day” in the equation proposed by Ångström. Therefore, a daily extraterrestrial solar radiation on a horizontal surface (averaged over one month) (H0) was proposed by Page to be used instead of HC, resulting in the Ångström–Page equation as follows [11]: H/H0 = a’ + b’(S/S0) (2) where a’ and b’ are empirical coefficients in Ångström–Page equation. Appl. Sci. 2018, 8, 627 3 of 27

The Ångström–Page equation is one of the classical equations for estimation of the daily global solar radiation. Different mathematical expressions have been proposed by other researchers to improve its accuracy, including using quadratic [12], cubic [13], logarithmic [14], exponential [15] and power expressions [16]. However, the improvement in the accuracy of equations using these expressions is not obvious when comparing with the linear expression [17]. Therefore, the linear Ångström–Page equation is generally used due its sufficient accuracy and lower computational effort. In China, research on global solar radiation models began in the 1960s, and was based on the Ångström–Page equation with empirical coefficients for different geographic zones [18]. However, China is vast in territory, and environmental conditions in different regions are obviously different. Thus, it is difficult to establish a common set of empirical coefficients applicable to all regions. Some researchers have used other meteorological and geographic parameters such as the ambient temperature, altitude, longitude and latitude information, relative humidity, and cloud cover to improve the accuracy of the Ångström–Page equation [19–21]. It is noted that sunshine duration has the greatest influence on the daily global solar radiation compared with other meteorological factors. Moreover, considering other meteorological factors may reduce the accuracy of the estimated values [22].

• Non-sunshine duration models

The ambient temperature was chosen by some researchers to establish an estimation model for global solar radiation. The difference between the daily maximum and minimum temperatures was used to predict the daily global solar radiation by Hargreaves and Samani (H-S model) in 1982 [23]. To improve the accuracy of the H-S model, some meteorological factors such as the altitude [24], and precipitation [25–27] were considered. Based on the H-S model, an exponential equation considering the daily temperature range was proposed by Bristow and Campbell (B-C model) in 1984 [28]. Grillone et al. compared the results of these empirical models with measured data from the Mediterranean region and concluded that the H-S model had the highest accuracy [29]. However, Liu et al. suggested using the B-C model after comparing various empirical models with measured data from 15 meteorological stations in Northern China due to better accuracy and ease of determining the empirical factors [30]. It should be noted that the estimation error for models based on ambient temperature is larger than for those based on sunshine duration [22]. The extent of cloud cover was chosen by some researchers to establish estimation models for global solar radiation due to the lack of measured sunshine duration in some regions, especially in the oceans, mountains and deserts, where few meteorological stations exist. However, cloud cover is usually noted visually, which may have great uncertainty and error. An increase in cloud cover would reduce the beam solar ration and increase the diffuse solar radiation. A linear equation for the clearness index and average total cloud cover was proposed by Kimball based on the measured data from many meteorological stations in the U.S. [31]. The relationships between the clearness index and the sunshine duration fraction, and between the clearness index and the extent of cloud cover, were discussed by Bennett in 1965 [32]. It is reported that the relationship between the clearness index and the sunshine duration fraction is more evident compared to other parameters. Three types of estimation models were presented by Wang based on the sunshine duration fraction, the extent of cloud cover, and the combination of the two [33]. Results indicated that the model considering the sunshine duration fraction had the highest accuracy.

• Artiﬁcial intelligence approach

The artificial intelligence approach has been utilized by some researchers to predict the global solar radiation [22,34–37]. However, more factors are involved in the artificial intelligence techniques compared to empirical models. Consequently, the computational effort is significantly higher, making them less convenient for engineering applications. Overall, the empirical model for daily global solar radiation based on the sunshine duration fraction is preferred for engineering applications. Appl. Sci. 2018, 8, 627 4 of 27

2.1.2. Estimation Model for Hourly Global Solar Radiation Hourly global solar radiation data are needed for research on temperature distribution on bridge girder cross-sections. Research on hourly global solar radiation is less frequent than its daily counterpart. A linear relationship between hourly and daily global solar radiation was proposed by Liu and Jordan in 1960 using the following Equation [38]:

rT = I/H = (π(cosω − cosωs))/(24(sinωs − ωscosωs)) (3) where rT is the proportionality coefﬁcient, I is the hourly global solar radiation, H is the daily global solar radiation, ω is the solar hour angle, and ωs is the sunset hour angle. However, some researchers have reported that a linear relationship only exists in a clear day [39]. The equation proposed by Liu and Jordan was modiﬁed by Collares-Pereira and Rabl as follows [40]:

rT = I/H = ((a + bcosω)(π(cosω − cosωs)))/(24(sinωs − ωscosωs)) (4) where a = 0.409 + 0.5016sin(ωs − 60) and b = 0.6609 − 0.4767sin(ωs − 60). The validity of this equation was veriﬁed by measured data [41,42]. Although some modiﬁcations were proposed by other researchers [42–44], the Collares-Pereira and Rabl equation is the most frequently used model for estimating the hourly global solar radiation. The Gaussian function was considered by some researchers to estimate the hourly global solar radiation, which assumes that the meteorological parameters are all stochastic and the variation of hourly global solar radiation follows a normal distribution. However, this approach can only be used for a clear day [45,46].

2.2. Estimation Model for Beam and Diffuse Solar Radiation The beam solar radiation is related to the solar altitude, atmospheric transparency, cloud cover, altitude and so on [39]. The diffuse solar radiation is related to the incident angle of solar radiation, atmospheric condition and so on [39]. Literature on the beam or diffuse solar radiation are less frequent compared to the global solar radiation. Most of the research is focused on estimation models for beam and diffuse solar radiation under clear conditions. Moreover, most such estimation models are based on the hourly time scale. The model suggested by American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE model) is a widely used estimation model for beam and diffuse solar radiation in a clear day [47]. Some modiﬁcations have been proposed to improve its accuracy [48–50]. A relationship between the transmission ratio of beam solar radiation τb and the transmission ratio of diffuse solar radiation τd was proposed by Liu and Jordan in 1960 [38] under the assumption that the atmosphere is transparent.

τd = 0.2710 − 0.2939τb (5) where τd = Id/I0, τb = Ib/I0, Id is the hourly diffuse solar radiation, Ib is the hourly beam solar radiation, and I0 is the hourly extraterrestrial solar radiation on a horizontal surface. The following equation was proposed by Hottel in 1976 for estimating the transmission ratio of beam solar radiation based on the solar altitude angle and geographic altitude [51].

τb = a0 + a1exp(−k/sinh) (6) where a0, a1 and k are empirical coefﬁcients considering the altitude and meteorological conditions, and h is the solar altitude angle. Other meteorological factors, such as ambient temperature and relative humidity, as well as the artiﬁcial intelligence approach, were considered by some researchers to establish a numerical relationship for beam solar radiation and diffuse solar radiation [35,52,53]. However, a combination of the Liu and Jordan equation and Hottel equation has been used by researchers to estimate the hourly beam and diffuse solar radiation values. Appl. Sci. 2018, 8, 627 5 of 27 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 27

33.. Appl.Monitoring Sci. 2018, 8 ,of x FORSolar PEER Radiation REVIEW 5 of 27 The maximum solar radiation in a clear day is generally considered to provide the maximum 3. MonitoringThe maximum of Solar solar Radiation radiation in a clear day is generally considered to provide the maximum sunshine effect on the temperature distribution in bridge structures. In In this this paper, paper, the hourly global The maximum solar radiation in a clear day is generally considered to provide the maximum solar radiation radiation and and hourly hourly diffuse diffuse solar solar radiation radiation for for eight eight cities cities in inFuj Fujianian were were measured measured using using an sunshine effect on the temperature distribution in bridge structures. In this paper, the hourly global automatedan automated meteorological meteorological station, station, as asshown shown in inFigure Figure 1.1 .The The cities cities (from (from north north to south) andand thethe solar radiation and hourly diffuse solar radiation for eight cities in Fujian were measured using an corresponding measurement dates are shown in Figure2 2:: Fu’anFu’an (10(10 AugustAugust 2016),2016), Jian’ouJian’ou (7(7 AugustAugust automated meteorological station, as shown in Figure 1. The cities (from north to south) and the 2016), Fuzhou ( (22 August 2010), NinghuaNinghua ( (44 August 2016), Zhangping (27(27 July 2016). Anxi ( (22 August corresponding measurement dates are shown in Figure 2: Fu’an (10 August 2016), Jian’ou (7 August 2015), Hua’an ( (3030 July 2016) and Zhangzhou (31(31 July 2014).2014). 2016), Fuzhou (2 August 2010), Ninghua (4 August 2016), Zhangping (27 July 2016). Anxi (2 August 2015), Hua’an (30 July 2016) and Zhangzhou (31 July 2014).

Figure 1. Automated meteorological station. FigureFigure 1.1.Automated Automated meteorological station. station.

FigureFigure 2. 2. Map Map of of eight eight cities inin FujianFujian Fujian.. . Appl. Sci. 2018, 8, x 627 FOR PEER REVIEW 6 of 27

The measured hourly global and diffuse solar radiation curves for the eight cities on a clear day are illustratedThe measured in Figure hourly 3a,b global, respectively. and diffuse The solar hourly radiation beam solarcurves radiation for the eight can be cities calculated on a clear by subtractingday are illustrated the measured in Figure hourly3a,b, respectively.diffuse solar Theradiation hourly fro beamm the solar corresponding radiation can hourly be calculated global solar by radiation.subtracting The the calculated measured hourly hourly beam diffuse solar solar radiation radiation curves from are the correspondingshown in Figure hourly 3c. The global variation solar trendradiation. for all The hourly calculated solar hourlyradiation beam curves solar are radiation similar, curveswith the are solar shown radiation in Figure appearing3c. The variation at about 0trend6:00, forreaching all hourly the peak solar value radiation at about curves 12:00, are similar, and disappearing with the solar at about radiation 18:00 appearing. at about 06:00, reachingThe theglobal peak solar value radiation at about is 12:00, related and to disappearing parameters such at about as latitude, 18:00. altitude and atmospheric quality.The The global influence solar radiationof latitude is on related the global to parameters solar radiation such in as Fujian latitude, is neg altitudeligible,and because atmospheric all cities quality.are located The between inﬂuence 23 of° and latitude 28° northern on the global latitude. solar The radiation maximum in Fujian measured is negligible, global solar because radiation all cities for ◦ ◦ Ninghuaare located (about between 1100 23 W/mand2) was 28 northernthe highest latitude. among The all cities, maximum because measured this city global has the solar highest radiation altitude for 2 (asNinghua shown (about in Figure 1100 3a W/m). However,) was the the highest difference among between all cities, maximum because global this city solar has radiation the highest values altitude for (asdifferent shown cities in Figure was not3a). large However, (about the 10 difference0 W/m2). The between maximum maximum measured global diffuse solar radiation solar radiation values and for 2 thedifferent calculated cities beam was not solar large radiation (about 100were W/m in Fu’an). The (about maximum 250 W measured/m2) and Ninghua diffuse solar (about radiation 900 W/m and2), 2 2 respectively,the calculated as beam illustrated solar radiation in Figure were 3b,c in. The Fu’an difference (about 250 between W/m )maximum and Ninghua diffuse (about or 900beam W/m solar), radiationrespectively, values as illustratedfor different in cities Figure was3b,c. about The 15 difference0 W/m2. between maximum diffuse or beam solar radiation values for different cities was about 150 W/m2.

(a) (b)

(c)

Figure 3.3. Hourly solar radiationradiation:: ( (aa)) measured measured global global solar radiation radiation;; ( (b)) measured diffuse solar radiationradiation;; and (c) calculated beam solar radiation.radiation.

4. Estimation Model for Solar Radiation in Fujian 4. Estimation Model for Solar Radiation in Fujian

44.1..1. Estimation Model for Daily Global Solar Radiation As discussed earlier, the Ångström–PageÅ ngström–Page equation [[10,1110,11]] was chosen in this study to predict the daily global solar radiation for different cities in Fujian. The daily global solar radiation (averaged over one month) for the entire Fujian cannot be determined determined because only two meteorological meteorological stations in Fuzhou Fuzhou and and Ji Jian’ouan’ou provide provide such such data. data. Instead, Instead, the the daily daily global global solar solar radiation radiation (averaged (averaged over over one month) from 1983 to 2005 provided in a U.S. NASA database was used in this analysis, since the Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 27 Appl. Sci. 2018, 8, 627 7 of 27 NASA database is used by many researchers when meteorological data are lacking [54–56]. The NASA database divides the map of China into grids based on the longitude and latitude and provides dataone month)for each from grid 1983point to. The 2005 validity provided of inthe a data U.S. in NASA NASA database database was has used been in verified this analysis, by comparing since the withNASA solar database radiation is used data by from many 88 researchersmeteorological when stations meteorological in China data measured are lacking before [54 2010–56]. [57 The]. NASA databaseThe divides daily astronomical the map of China solar into radiation grids based can be on thecalculated longitude using and latitudeearth–sun and distance, provides solar data elevation,for each grid duration point. of The sunlight validity and of theso dataon [11 in]. NASA The historical database average has been sunshine verified duration by comparing (averaged with oversolar one radiation month) data since from 1951 88 for meteorological four cities in stations Fujian (Nanping, in China measured Fuzhou, Yong’an before 2010 and [ 57Xiamen)]. can be obtainedThe daily from astronomical the National solar radiation Meteorological can be calculated Information using earth–sun Center, distance,China Meteorological solar elevation, Administrationduration of sunlight [58]. The and average so on [11 maximum]. The historical possible average sunshine sunshine duration duration (averaged (averaged over one over mon oneth) canmonth) be calculated since 1951 using for four the citiesfollowing in Fujian equation: (Nanping, Fuzhou, Yong’an and Xiamen) can be obtained from the National Meteorological Information Center, China Meteorological Administration [58]. The average maximum possible sunshineS0 duration = (2ωs/15) (averaged × (180/π) over one month) can be calculated using(7) wherethe following ωs is the equation: sunset hour angle. The empirical coefficients a’ and b’ for different cities in Fujian can be calculated by using a linear regressionS0 =analysis (2ωs/15) between× (180/ theπ )clearness index H/HC and the sunshine (7) duration fraction S/S0. where ωs is the sunset hour angle. The empirical coefficients a’ and b’ for different cities in Fujian can be calculated by using a linear regression analysis between the clearness index H/HC and the sunshine 4.1.1. Influence of Time Scale on Empirical Coefficients duration fraction S/S0. The daily clearness index and the sunshine duration fraction (both averaged over one month) were4.1.1. Influence chosen by of ÅTime ngström Scale onand Empirical Page [10,11 Coefficients]. The daily solar radiation data measured by 36 meteorologicalThe daily clearness stations index in China and the were sunshine compared duration with fraction the calculated (both averaged daily solar over one radiation month) using were differentchosen by time Ångström scales. T andhe accuracy Page [10 ,of11 ].estimated The daily solar solar radiation radiation using data the measured monthly by time 36 meteorologicalscale is higher thanstations those in Chinausing daily were comparedor yearly time with scales the calculated [59]. Fuzhou daily was solar chosen radiation as an using example different to analyze time scales. the influenceThe accuracy of different of estimated time solar scales radiation (daily, monthly using the and monthly yearly) time on the scale empirical is higher coefficients than those in using the Ådaily ngström or yearly–Page timeequation. scales The [59 results]. Fuzhou are listed was chosenin Table as 1 anand example illustrated to in analyze Figure the 4, in influence which the of hollowdifferent points time scales denote (daily, the data monthly and theand solid yearly) line on denotes the empirical the linear coefficients regression. in the The Ångström–Page coefficient of correlationequation. The(γxy) results for the arelinear listed regression in Table analysis1 and illustrated using the in monthly Figure4 time, in whichscale is the the hollow largest pointsamong diffdenoteerent the time data scales. and Moreover, the solid the line root denotes-mean the-square linear error regression. (RMSE) using The the coefficient monthly of time correlation scale is the(γxy smallest.) for the As linear a result, regression the monthly analysis time using scale the was monthly chosen time to calculate scale is the em largestpirical among coefficients different in thetime Å ngström scales.– Moreover,Page equation. the root-mean-square error (RMSE) using the monthly time scale is the smallest. As a result, the monthly time scale was chosen to calculate the empirical coefficients in the Ångström–PageTable 1. Linear equation. regression analysis of clearness index and sunshine duration fraction using different time scales. Table 1. Linear regression analysis of clearness index and sunshine duration fraction using different time scales. Time Scale Types Data Points a’ b’ γxy RMSE Daily 8030 0.213 0.505 0.86 0.10 Time Scale Types Data Points a’ b’ γ RMSE Monthly 264 0.196 0.553 0.92 xy 0.03 DailyYearly 803022 0.2130.242 0.422 0.505 0.79 0.86 0.01 0.10 Monthly 264 0.196 0.553 0.92 0.03 Yearly 22 0.242 0.422 0.79 0.01

(a) (b)

Figure 4. Cont. Appl. Sci. Sci. 20182018,, 88,, x 627 FOR PEER REVIEW 88 of of 27 27

(c)

FigureFigure 4 4.. LinearLinear regression regression using using different different time time scales scales:: (a) (dailya) daily time time scale scale;; (b) monthly (b) monthly time timescale scale;; and (andc) yearly (c) yearly time timescale scale..

44.1.2..1.2. Influence Influence of of Sunshine Sunshine Duration Duration on on the Empirical Coefficients Coefficients Aside from the time scale, the actual sunshine duration would also affect the empirical coefficients Aside from the time scale, the actual sunshine duration would also affect the empirical in the Ångström–Page equation. The measured average sunshine duration (averaged over one month) coefficients in the Å ngström–Page equation. The measured average sunshine duration (averaged since 1951 for four cities in Fujian can be obtained from National Meteorological Information Center, over one month) since 1951 for four cities in Fujian can be obtained from National Meteorological China Meteorological Administration [58]. Hua’an was chosen as an example to illustrate the influence Information Center, China Meteorological Administration [58]. Hua’an was chosen as an example to of sunshine duration on the empirical coefficients. The results listed in Table2 show that the coefficient illustrate the influence of sunshine duration on the empirical coefficients. The results listed in Table of correlation obtained using the sunshine duration are largest for Xiamen, which is nearest to Hua’an. 2 show that the coefficient of correlation obtained using the sunshine duration are largest for Xiamen, Moreover, the root-mean-square error obtained by using the sunshine duration of Xiamen is the which is nearest to Hua’an. Moreover, the root-mean-square error obtained by using the sunshine smallest. Consequently, the empirical coefficients for cities in the Fujian that did not have measured duration of Xiamen is the smallest. Consequently, the empirical coefficients for cities in the Fujian sunshine duration data can be predicted using the available sunshine duration for the nearest city that did not have measured sunshine duration data can be predicted using the available sunshine (Nanping, Fuzhou, Yong’an, or Xiamen). duration for the nearest city (Nanping, Fuzhou, Yong’an, or Xiamen). Table 2. Linear regression analysis of clearness index and sunshine duration fraction using sunshine Tableduration 2. Linear for four regression cities. analysis of clearness index and sunshine duration fraction using sunshine duration for four cities.

Solar Radiation Data Source Sunshine Duration Data Source a’ b’ γxy RMSE Solar Radiation Data Source Sunshine Duration Data Source a’ b’ γxy RMSE Hua’anHua’an NanpingNanping 0.2160.216 0.4670.467 0.810.81 0.05 0.05 Hua’an Fuzhou 0.217 0.519 0.82 0.06 Hua’anHua’an Yong’anFuzhou 0.2120.217 0.5190.519 0.850.82 0.06 0.06 Hua’anHua’an XiamenYong’an 0.1780.212 0.5220.519 0.900.85 0. 0.0406 Hua’an Xiamen 0.178 0.522 0.90 0.04 4.1.3. Veriﬁcation of Ångström–Page Equation 4.1.3. Verification of Å ngström–Page Equation To verify the applicability and accuracy of the Ångström–Page equation in Fujian, the accuracy of linearTo verify regression the applicability estimates forand all accuracy eight cities of the are Å ngströmlisted in– TablePage 3equation. For all in cities, Fujian, the the coefﬁcients accuracy ofof linear correlation regression are larger estimates than for 0.84, all andeight the cities root-mean-square are listed in Table errors 3. For are all less cities, than the 0.05. coefficients Therefore, of correlationthe accuracy are of larger the Ångström–Page than 0.84, and model the root is considered-mean-square good, errors and are this less model than can 0.05. be usedTherefore, to predict the accuracythe global of solar the Å radiation ngström– forPa differentge model cities is considered in the Fujian. good, and this model can be used to predict the global solar radiation for different cities in the Fujian. Table 3. Linear regression analysis of clearness index and sunshine duration fraction for eight cities. Table 3. Linear regression analysis of clearness index and sunshine duration fraction for eight cities. City Solar Radiation Data Source Sunshine Duration Data Source a’ b’ γxy RMSE Solar Radiation Sunshine Duration Fu’anCity Fu’an Fuzhoua’ b 0.211’ 0.546γxy 0.84RMSE 0.05 Jian’ouData Source Jian’ou Data Source Nanping 0.180 0.537 0.84 0.05 FuzhouFu’an Fu’an Fuzhou Fuzhou Fuzhou0.211 0.546 0.196 0.5530.84 0.920.05 0.03 NinghuaJian’ou Jian’ou Ninghua Nanping Yong’an0.180 0.537 0.179 0.5710.84 0.850.05 0.05 ZhangpingFuzhou Fuzhou Zhangping Fuzhou Yong’an0.196 0.553 0.213 0.5200.92 0.840.03 0.05 NinghuaAnxi Ninghua Anxi Yong’an Xiamen0.179 0.571 0.197 0.4790.85 0.880.05 0.04 ZhangpingHua’an Zhangping Hua’an Yong’an Xiamen0.213 0.520 0.178 0.5220.84 0.900.05 0.04 ZhangzhouAnxi Anxi Zhangzhou Xiamen Xiamen0.197 0.479 0.196 0.5060.88 0.890.04 0.04 Hua’an Hua’an Xiamen 0.178 0.522 0.90 0.04 Zhangzhou Zhangzhou Xiamen 0.196 0.506 0.89 0.04 Appl. Sci. 2018, 8, 627 9 of 27 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 27

4.2.4 Estimation.2. Estimation Model Model for for Hourly Hourly Global Global SolarSolar Radiation AsAs discussed discussed in in Section Section 2.1.2 2.1.2,, the the Collares-PereiraCollares-Pereira and and Rabl Rabl equation equation was was chosen chosen to estimate to estimate the the hourlyhourly global global solar solar radiation radiation for for different different cities cities in in Fujian Fujian based based on on the the corresponding corresponding daily daily global global solar radiation.solar radiation. The sunshine The sunshine duration duration for the for eight the eight cities cities were were measured measured on on site. site. FuzhouFuzhou was was chosen chosen as exampleas example to estimate to estimate the hourlythe hourly global global solar solar radiation. radiation. The measured measured and and estimated estimated hourly hourly global global solarsolar radiation radiation curves curves for for different different citiescities areare compared in in Figure Figure 5,5 ,with with the the hollow hollow point point denoting denoting the measured values and the solid line showing the estimated results. The minimum coefficients of the measured values and the solid line showing the estimated results. The minimum coefﬁcients of correlation for all eight cities is 0.989. Therefore, the hourly global solar radiation for different cities correlation for all eight cities is 0.989. Therefore, the hourly global solar radiation for different cities in in Fujian can be accurately predicted by the Collares-Pereira and Rabl equation. Fujian can be accurately predicted by the Collares-Pereira and Rabl equation.

(a) (b)

(e) (f)

Figure 5. Cont. Appl.Appl. Sci. 2018Sci. 2018, 8, 627, 8, x FOR PEER REVIEW 10 of 1027 of 27 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 27

(g) (h) (g) (h) FigureFigure 5. Comparison 5. Comparison between between measured measured andand estimated hourly hourly global global solar solar radiation radiation curves curves for eight for eight citiesFigurecities in Fujian:in 5 Fujian. Comparison (a: ()a Fu’an) Fu’an between(10 (10 August measured 2016) 2016); ;and (b ()b Jian’ouestimated) Jian’ou (7 August hourly (7 August global2016) 2016);; (solarc) Fuzhou (radiationc) Fuzhou (2 August curves (2 August 2010) for eight; (d 2010);) cities in Fujian: (a) Fu’an (10 August 2016); (b) Jian’ou (7 August 2016); (c) Fuzhou (2 August 2010); (d) (d) Ninghua (4 (4 August August 2016) 2016);; (e) Zhangping (e) Zhangping (27 July (27 2016) July; ( 2016);f) Anxi (f(2) August Anxi (2 2015) August; (g) Hua’an 2015); ( 30g) July Hua’an Ninghua (4 August 2016); (e) Zhangping (27 July 2016); (f) Anxi (2 August 2015); (g) Hua’an (30 July (30 July2016) 2016);; and (h and) Zhangzhou (h) Zhangzhou (31 July (31 2014) July. 2014). 2016); and (h) Zhangzhou (31 July 2014). 4.3. Estimation Model for Hourly Beam and Diffuse Solar Radiation 4.3.4 Estimation.3. Estimation Model Model for for Hourly Hourly Beam Beam andand DiffuseDiffuse Solar Radiation Radiation 4.3.1.4.3 Estimation.1. Estimation Model Model for for Hourly Hourly Beam Beam SolarSolar Radiation 4.3.1. Estimation Model for Hourly Beam Solar Radiation GlobalGlobal solar solar radiation radiation should should be beseparated separated into beam beam and and diffuse diffuse solar solar radiation radiation to analyze to analyze the the Global solar radiation should be separated into beam and diffuse solar radiation to analyze the temperaturetemperature distribution distribution on on bridge bridge girdergirder cross-sections.cross-sections. As As discussed discussed earlier, earlier, the the Hottel Hottel equation equation temperaturewas chosen to distribution predict the hourlyon bridge beam girder solar cross radiation-sections. for dif Asferent discussed cities inearlier, Fujian. the The Hottel measured equation and was chosen to predict the hourly beam solar radiation for different cities in Fujian. The measured and wasestimated chosen hourly to predict beam the solar hourly radiation beam solarcurves radiation for the eightfor dif citiesferent in cities Fujian in areFujian. compared The measured in Figure and 6, estimated hourly beam solar radiation curves for the eight cities in Fujian are compared in Figure6, estimatedin which thehourly hollow beam points solar denoteradiation the curves measured for the values eight andcities the in solidFujian line are denotescompared the in estimated Figure 6, in which the hollow points denote the measured values and the solid line denotes the estimated results. inresults. which The the mini hollowmum pointscoefficients denote of correlation the measured for all values eight and cities the is 0.974. solid lineTherefore, denotes the the hourly estimated beam Theresults.solar minimum radiation The mini coefﬁcients formum different coefficients of correlationcities in of Fujiancorrelation for can all be eightfor accurately all citieseight cities is predicted 0.974. is 0.974. Therefore, by Therefore, the Hottel the the equation hourly hourly beam. beam solar radiationsolar radiation for different for different cities in cities Fujian in Fujian can be can accurately be accurately predicted predicted by the by the Hottel Hottel equation. equation.

(a) (b) (a) (b)

Figure 6. Cont. Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 27

Appl.Appl. Sci. 2018Sci. 2018, 8, 627, 8, x FOR PEER REVIEW 11 of 1127 of 27

(e) (f)

(g) (h)

Figure 6. Comparison between(g) measured and estimated hourly beam solar(h) radiation curves for eight cities in Fujian: (a) Fu’an (10 August 2016); (b) Jian’ou (7 August 2016); (c) Fuzhou (2 August 2010); (d) FigureFigure 6. Comparison 6. Comparison between between measured measured andand estimated hourly hourly beam beam solar solar radiation radiation curves curves for eight for eight Ninghuacitiescities in (4 Fujian: in August Fujian (a:) 2016)(a Fu’an) Fu’an; ( (10e ()10 Zhangping August August 2016);2016) (27; ((b July) Jian’ou 2016) (7 (7 ;August August(f) Anxi 2016) 2016); (2 ;August (c) ( Fuzhouc) Fuzhou 2015) (2 August (2; (g August) Hua’an 2010) 2010);; ( d(30) (Julyd) 2016)Ninghua; andNinghua (h (4) Zhangzhou August(4 August 2016); 2016) (31 (;e ()Julye Zhangping) Zhangping 2014). (27(27 JulyJuly 2016) 2016);; ( (ff) )Anxi Anxi (2 (2 August August 2015) 2015);; (g) (Hua’ang) Hua’an (30 July (30 July 2016);2016) and; and (h) ( Zhangzhouh) Zhangzhou (31 (31 July July 2014). 2014). 4.3.2. Estimation Model for Hourly Diffuse Solar Radiation 4.3.2. Estimation Model for Hourly Diffuse Solar Radiation 4.3.2.The Estimation hourly diffuse Model solar for Hourly radiation Diffuse can Solar be calculatedRadiation by subtracting the hourly beam solar The hourly diffuse solar radiation can be calculated by subtracting the hourly beam solar radiationradiationThe from hourly fromthe diffusecorresponding the corresponding solar radiation hourly hourly can global global be calculated solar solar radiation. by subtracting The The measured measured the hourly and and beamestimated estimated solar hourly radiation hourly diffusefromdiffuse solar the corresponding solarradiation radiation curves hourlycurves for for globalthe the eight eight solar cities cities radiation. inin Fujian The are are measured co comparedmpared and in Figure estimatedin Figure 7, in hourly7,which in which the diffuse the hollowsolarhollow radiationpoints points denote curves denote the for the measured measuredeight cities values values in Fujian and and are the the compared solid solid line line in denotes denotes Figure the7, inthe estimated which estimated the results. hollow results. The points The minimumdenoteminimum thecoefficients measured coefficients of values correlation of correlation and the for solid for all all lineeight eight denotes cities cities is the 0.948.0.948. estimated Therefore, Therefore, results. the the estimated The estimated minimum hourly hourly coefﬁcientsdiffuse diffuse solarof correlationradiationsolar radiation curve for allcurves eightares closeare cities close to is theto 0.948. the measured measured Therefore, valuesvalues the estimated.. hourly diffuse solar radiation curves are close to the measured values.

(a) (b)

Figure 7. Cont. Appl.Appl. Sci. Sci.20182018, 8, ,x8 FOR, 627 PEER REVIEW 1212 of of 27 27

(e) (f)

(g) (h)

Figure 7. Comparison between measured and estimated hourly diffuse solar radiation curves for eight Figure 7. Comparison between measured and estimated hourly diffuse solar radiation curves for eight citiescities in Fujian in Fujian:: (a) (Fu’ana) Fu’an (10 (10August August 2016) 2016);; (b) ( Jian’oub) Jian’ou (7 August (7 August 2016) 2016);; (c) (Fuzhouc) Fuzhou (2 (2August August 2010) 2010);; (d) Ninghua(d) Ninghua (4 August (4 August 2016); 2016); (e) Zhangping (e) Zhangping (27 July (27 July2016) 2016);; (f) Anxi (f) Anxi (2 August (2 August 2015) 2015);; (g) (Hua’ang) Hua’an (30 (30July 2016)July; and 2016); (h) and Zhangzhou (h) Zhangzhou (31 July (31 2014) July. 2014).

5. Solar Radiation in Fujian The maximum values of the global, beam and diffuse solar radiation (for summer solstice, 21 June) for 56 cities in Fujian were calculated using the models described in Section 3, and are illustrated in Figure 8. The maximum global solar radiation for Xiapu (about 1210 W/m2) is the highest and the maximum global solar radiation for Anxi (about 970 W/m2) is the lowest among all cities, as shown in Figure 8a. The biggest difference among the global solar radiation maxima in different cities is about 240 W/m2. The maximum beam solar radiation for Zhouning (about 909 W/m2) is the highest, and the maximum beam Appl. Sci. 2018, 8, 627 13 of 27 solar radiation for Ningde (about 821 W/m2) is the lowest among all cities, as shown in Figure 8b. The biggest difference among the beam solar radiation maxima for different cities is about 88 W/m2. The as shown in Figure8b. The biggest difference among the beam solar radiation maxima for different maximum diffuse solar radiation for Xiapu (about 388 W/m2) is the highest and the maximum diffuse cities is about 88 W/m2. The maximum diffuse solar radiation for Xiapu (about 388 W/m2) is the 2 solar radiationhighest andfor theDehua maximum (about diffuse 102 W/m solar radiation) is the lowest for Dehua among (about all 102 cities, W/m as2) isshown the lowest in Figure among 8c. The biggest differencall cities, ase among shown in the Figure diffuse8c. The solar biggest radiation difference maxima among for the different diffuse solar cities radiation is about maxima 286 W/m for 2. different cities is about 286 W/m2.

(a)

(b)

(c)

Figure 8Figure. Maximum 8. Maximum solar solarradiation radiation for for56 cities 56 cities in inFujian Fujian:: (a (a) )maximum maximum globalglobal solar solar radiation; radiation; (b) maximum(b) maximumbeam solar beam radiation solar radiation;; and (c and) maximum (c) maximum diffuse diffuse solar solar radiation radiation. . Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 27

Appl. Sci. 2018, 8, 627 14 of 27 6. Influence of Solar Radiation on Temperature Distribution on Bridge Girder Cross-Sections

6.16.. Box Inﬂuence Girder ofBridge Solar Radiation on Temperature Distribution on Bridge Girder Cross-Sections

6.16.1..1. Finite Box Girder Element Bridge Model 6.1.1.One Finite 8-span Element continuous Model prestressed concrete box girder bridge in Fuzhou was chosen as case study. TheOne dimensions 8-span continuous of girder prestressed cross-section concrete and boxthe girderinstallation bridge locations in Fuzhou of wastemperature chosen as sensors case arestudy. illustrated The dimensions in Figure 9. of The girder thickness cross-section of the and concrete the installation overlay locationsis 80 mm. of Four temperature temperature sensors sensors are wereillustrated installed in near Figure the9. Theexternal thickness surfaces of the of concrete the top overlay flange is(A 80–T), mm. east Four web temperature (A–E), west sensors web were(A–W) andinstalled bottom near flange the external(A–B) to surfaces measure of the the top air flange temperature (A–T), east at web different (A–E), parts west webof the (A–W) box and girder. bottom One temperatureflange (A–B) sensor to measure was hu theng air in temperature the box girder at different (A–I) to parts measure of the boxthe girder.air temperature One temperature inside sensorthe box girder.was hungSix temperature in the box girder sensors (A–I) were to measure installed the airin temperaturethe concrete inside within the the box east girder. web, Six west temperature web and bottomsensors flange, were installedof which in three the concrete were near within the theexternal east web, surface west (EW web- and1, WW bottom-1 and flange, B-1) ofand which three three were nearwere the near internal the external surface surface of each (EW-1, component WW-1 and (EW B-1)- and2, WW three-2 were and near B-2). the The internal meteorological surface of each data, includingcomponent hourly (EW-2, global WW-2 solar and B-2). radiation, The meteorological hourly diffuse data, solar including radiation hourly and global wind solar speed, radiation, were measuredhourly diffuse by an solarautomated radiation meteorological and wind speed, station. were measuredThe monitori by anng automated period was meteorological from 1 April station. 2010 to 31 TheMarch monitoring 2011 and period the time was increment from 1 April between 2010 measurements to 31 March 2011 was and one the hour. time increment between measurementsThe software was Midas one hour.was chosen to establish the finite element model of the cross-section of box girder (TheFigure software 9) based Midas on wasa heat chosen-conduction to establish model the. A finite 2D elementplane strain model element of the cross-sectioncan used for of steady box - stategirder or transient (Figure9) basedanalyses. on a heat-conductionThe ambient air model. temperature A 2D plane data strain were element obtained can from used forthe steady-state temperature sensorsor transient installed analyses. near the The external ambient surfaces air temperature of the box data girder were. The obtained solar radiation from the temperature was calculated sensors using installed near the external surfaces of the box girder. The solar radiation was calculated using the the estimation models described earlier. The effects of solar radiation and convective and radiative estimation models described earlier. The effects of solar radiation and convective and radiative heat heat transfer were considered at the external surfaces of the box girder. The surface heat transfer transfer were considered at the external surfaces of the box girder. The surface heat transfer coefficient coefficient and the temperature of the surrounding fluid medium were input as boundary conditions and the temperature of the surrounding fluid medium were input as boundary conditions for the for the finite element model. The influence of the solar radiation on different parts of the box girder finite element model. The influence of the solar radiation on different parts of the box girder was wasconsidered considered by usingby using the followingthe following rules andrules assumptions: and assumptions: (a) The external(a) The surfaceexternal of surface the top flangeof the istop flangeinfluenced is influenced by both by the both beam the and beam diffuse and solar diffuse radiation. solar radiation (b) The external. (b) The surfaces external of surfaces the two websof the are two websin the are shadow in the dueshadow to the due top to flange. the top Therefore, flange. theyTherefore, are influenced they are by influenced the diffuse solarby the radiation diffuse andsolar radiationground and reflection ground only. reflection (c) The undersidesonly. (c) The of undersides the top and bottomof the top flanges and bottom are influenced flanges by are the influenced ground by reflectionthe ground alone. reflection The boundary alone. The condition boundary of the condition internal surface of the of internal the box surface girder in of the the finite box elementgirder in themodel finite waselement set based model on was the set measured based on temperature the measured obtained temperature from the obtained temperature from sensorthe temperature hung in sensorthe box hung girder in the (A-I). box For girder the thermal(A-I). For parameters the thermal of the parameters concrete, specificof the concrete, heat of 960 specific J/(kg heat◦C), heatof 960 J/(kgconductivity °C ), heat conductivity of 1.5 W/(m ◦ofC), 1.5 and W/(m density °C ), of and 2400 density kg/m3 ofwere 2400 used kg/m [603]. were The finiteused element[60]. The mesh finite elementsize was mesh set assize 0.02 was m. set There as 0.02 were m 21,000. There and were 19,337 21,000 nodes and and 19 elements,,337 nodes respectively, and elements as illustrated, respectively, in as Figureillustrated 10. Each in Figure node had10. Each a single node temperature had a single degree temperature of freedom. degree of freedom.

FigFigureure 9 9.. LayoutLayout of of cross cross-section-section of boxbox girdergirder (cm). (cm). Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 27

Appl. Sci. 2018, 8, 627 15 of 27 Appl. Sci. 2018, 8, x FOR PEER REVIEW 15 of 27

Figure 10. Finite element model of cross-section of box girder. Figure 10. Finite element model of cross-section of box girder. 6.1.2. Influence of SolarFigure Radiation 10. Finite on Temperature element model Distribution of cross-section on ofCross box girder.-Section of Box Girder 6During.1.2. Influence the monitoring of Solar Radiation period, on 2 Temperature August 2010 Distribution was a sunny on Cross day-Section with highof Box solar Girder radiation. 6.1.2. Influence of Solar Radiation on Temperature Distribution on Cross-Section of Box Girder ComparisonsDuring of tempe the monitoringrature–time period, curves 2 August obtained 2010 experimentally was a sunny or day from with finite high element solar radiation. model with or withoutComparisonsDuring the the consideration of monitoring temperature of period, –solartime curvesradiation 2 August obtained are 2010illustrated experimentally was ain sunny Figure or from day 11 ( finite2 with August element high 2010). solar model The radiation. with hollow pointsComparisonsor withoutdenote ofthe temperature–time considerationmeasured data, of solar the curves solidradiation obtained line are denotes illustrated experimentally the calculatedin Figure or 11 from cur (2 Augustves finite with 2010). element the Theconsideration model hollow with ofor solar withoutpoints radiation, denote the consideration the and measured the dashed of data, solar linethe radiation solid denotes line are denotesthe illustrated calculated the calculated in Figurecurves cur 11 without ves(2 Augustwith the the 2010). considerationconsideration The hollow of solarpointsof radiation. solar denote radiation, the The measured temperature and the data, dashed contour the line solid denotesplots line denotes obtained the calculated the from calculated finitecurves element curveswithout with modelthe theconsideration with consideration or without of of thesolar considerationsolar radiation, radiation. and of The solar the temperature dashed radiation line contourare denotes compared plots the obtained calculated in Figure from curves12 finite (15:00, withoutelement 2 August themodel consideration2010). with or without of solar radiation.theIn Figureconsideration The 11, temperature it ofcan solar be radiaobserved contourtion are plotsthat compared the obtained variation in Figure from trends finite12 (15:00, and element 2the August times model 2010). at with which or withoutthe highest the temperaturesconsiderationIn Figure occurredof solar 11, it radiation canare be similar observed are compared for that measured the in variation Figure and 12 calculatedtrends (15:00, and 2 Augustthe results times 2010). on at 2which August the highest 2010. The temperatures occurred are similar for measured and calculated results on 2 August 2010. The differencesIn Figure between 11, it the can highest be observed measured that and the variationcalculated trends temperatures and the when times considering at which the the highest effect differences between the highest measured and calculated temperatures when considering the effect oftemperatures solar radiation occurred were are very similar small for (maximum measured and 0.2 calculated°C for the results two webs on 2 August and 1.1 2010. °C for The the differences bottom of solar radiation were very small (maximum 0.2 °C for the two webs and 1.1 °C for the bottom between the highest measured and calculated temperatures when considering the effect of solar flange).flange). However, However, the the highest highest calculated calculated temperatures temperatures without the the considerati considerationon of ofsolar solar radiation radiation radiation were very small (maximum 0.2 ◦C for the two webs and 1.1 ◦C for the bottom flange). werewere lower lower (maximum (maximum 1.7 1. °C7 °C for for the the two two webs webs and and 1.1.3 °C forfor the the bottom bottom flange) flange) and and had had a time a time delay delay (3However, h (3for h two for the two webs highest webs and and calculatedthe the bottom bottom temperatures flange). flange). The The withoutaccuracy accuracy the of the considerationthe solar solar radiation radiation of solarcalculated calculated radiation by byusing were using the lower the ◦ ◦ estimation(maximumestimation models 1.7 modelsC for can thecan meet twomeet the webs the en engineering andgineering 1.3 C requirements. requirements. for the bottom Moreover,Moreover, flange) and when when had solar asolar time radiation radiation delay (3was hwas fornot twonot considered,websconsidered, and the the bottom thedifferences differences flange). between between The accuracy the the highest highest of themeasured measured solar radiation andand calculated calculated calculated temperatures temperatures by using at the theat the external estimation external surfacesmodelssurfaces canof the meetof thebox thebox girder engineering girder (1. (1.7 °C7 °C requirements.for for EW EW-1,-1, 1. 1.55 °C Moreover,°C forfor WW- when-11 andand solar1. 1.3 3°C °C radiation for for B -B1)- 1)were was were signif not signif considered,icantlyicantly largerthe differenceslarger than than the thedifferences between differences the at highestatthe the internal internal measured surfaces surfaces and ofof calculated the box girdergirder temperatures (0. (0.7 7°C °C for for EW at EW the-2,- 0.2, external2 0. °C2 °Cfor forWW surfaces WW- - ◦ ◦ ◦ 2of and the2 and0. box5 °C0. girder5 for°C forB (1.7-2). B- 2).ThisC This for is EW-1,becauseis because 1.5 the theC influence forinfluence WW-1 ofof and solar 1.3 radiationradiationC for B-1) on on the werethe temperature temperature significantly distribution distribution larger than ◦ ◦ ◦ decreasesthe differencesdecreases as the as at thedistance the distance internal from from surfacesexternal external ofs urfacessurfaces the box increases. increases. girder (0.7 FromFromC Figure forFigure EW-2, 12, 12, it 0.2 itcan can Cbe forbe observed observed WW-2 that and that the 0.5 theC differences between the highest calculated temperatures with or without the consideration of solar differencesfor B-2). This between is because the highest the influence calculated of solar temperatures radiation on with the temperatureor without the distribution consideration decreases of solar as radiation were significant at 15:00 on 2 August 2010 (maximum 12.5 °C ). The vertical temperature radiationthe distance were from significant external at surfaces 15:00 on increases. 2 August From 2010 Figure (maximum 12, it can 12.5 be °C observed). The vertical that the temperatu differencesre variation on the cross-section of box girder when considering the effect of solar radiation (19.2 °C ) variationbetween theon highestthe cross calculated-section of temperatures box girder when with or considering without the the consideration effect of solar of solarradiation radiation (19.2 were °C ) was significantly larger than that without the consideration◦ of solar radiation (7.0 °C ). Therefore, the wassignificant significantly at 15:00 larger on 2 than August that 2010 without (maximum the consideration 12.5 C). The of solar vertical radiation temperature (7.0 °C ). variation Therefore, on the the influence of solar radiation should be considered in the analyses of the temperature◦ distribution on influencecross-sectionbox girder of solar ofs. box radiation girder whenshould considering be considered the in effect the ofanalyses solar radiation of the temperature (19.2 C) was distribution significantly on ◦ boxlarger girder thans.that without the consideration of solar radiation (7.0 C). Therefore, the influence of solar radiation should be considered in the analyses of the temperature distribution on box girders.

(a) (b)

Figure 11. Cont. Appl. Sci. 20182018,, 8,, x 627 FOR PEER REVIEW 1616 of 27

Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 27

(e()e ) (f()f )

FigureFigure 11 .11 Influence. Influence of of solar solar radiation radiation on on temperature temperature distribution onon cross cross-section-section of of box box girder girder in in Figure 11. Influence of solar radiation on temperature distribution on cross-section of box girder in summersummer (2 (August2 August 2010 2010): )(: a()a )east east web web (EW (EW--1)1);; ((bb)) east web (EW(EW--2)2); ; ((cc) )west west web web (WW (WW-1)-1); (;d ()d west) west summer (2 August 2010): (a) east web (EW-1); (b) east web (EW-2); (c) west web (WW-1); (d) west web web (WW-2); (e) bottom flange (B-1); and (f) bottom flange (B-2). web(WW-2); (WW (e-2)) bottom; (e) bottom flange flange (B-1); (B and-1); (andf) bottom (f) bottom flange flange (B-2). (B-2).

(a) (a)

(b)

Figure 12. Temperature contour plots of box girder(b )at 15:00 on 2 August 2010: (a) with solar radiation; Figure 12. Temperature contour plots of box girder at 15:00 on 2 August 2010: (a) with solar radiation; and (b) without solar radiation. Figandure (b )12 without. Temperature solar radiation. contour plots of box girder at 15:00 on 2 August 2010: (a) with solar radiation; and (b) without solar radiation. Appl. Sci. 2018, 8, x FOR PEER REVIEW 17 of 27

Appl. Sci. 2018, 8, x FOR PEER REVIEW 17 of 27 During the monitoring period, 16 December 2010 was a cloudy day with low solar radiation. ComparisonsDuring of the temperature monitoring– timeperiod, curves 16 December obtained 2010experimentally was a cloudy or fromday with finite low element solar radiation.model with or Comparisonswithout the consideration of temperature of–time solar curves radiat obtainedion are experimentallyillustrated in Figure or from 13 finite (16 Decemberelement model 2010). with The hollowor without points the denote consideration the measured of solar data,radiat ion the are solid illustrated line denotes in Figure the 13 calculated (16 December curves 2010). with The the considerationhollow points of denote solar radiation, the measured and thedata, dashed the solid line line denotes denotes the the calculated calculated curves curves without with the the consideraconsiderationtion of ofsolar solar radiation. radiation, The and temperature the dashed contour line denotes plots obtained the calculated from curvesfinite element without model the withconsidera or withouttion ofthe solar consideration radiation. The of solar temperature radiation contour are compared plots obtained in Figure from 14 finite (24:00, element 16 December model 2010).with or without the consideration of solar radiation are compared in Figure 14 (24:00, 16 December Appl.2010). Sci.In Figure2018 , 8, 62713, it can be found that the variation trends, lowest temperatures and the times17 of at 27 which theIn Figure lowest 13 temperatures, it can be found occurred that the were variation similar trends, for measured lowest temperatures and calculated and values the times without at thewhich consideration the lowest of temperatures solar radiation occurred on 16 Decemberwere similar 2010 for (maximum measured and 0.3 °Ccalculated for two values webs andwithout 0.2 °C forthe theDuring consideration bottom the flange). monitoring of solar In Figureradiation period, 14, on 16 it 16 December can December be observed 2010 2010 was (maximum that a cloudy the differences 0.3 day °C for with two between low webs solar and the radiation. 0. highest2 °C calculatedComparisonsfor the bottomtemperatures of temperature–time flange). with In Figure or without curves 14, it obtainedthe can consideration be observed experimentally thatof solar the or differencesradiation from ﬁnite were between element negligible model the highest at with 24:00 or calculated temperatures with or without the consideration of solar radiation were negligible at 24:00 withouton 16 December the consideration 2010 (maximum of solar radiation0.1 °C ). The are illustratedvertical temperature in Figure 13 variation (16 December on the 2010). cross The-section hollow of on 16 December 2010 (maximum 0.1 °C ). The vertical temperature variation on the cross-section of boxpoints girder denote were the similar measured for data,calculated the solid values line denoteswith or thewithout calculated the consideration curves with the of considerationsolar radiation. of box girder were similar for calculated values with or without the consideration of solar radiation. Therefore,solar radiation, the influence and the dashedof solar lineradiation denotes on thethe calculatedtemperature curves distribution without on the the consideration cross-section of of solar the Therefore, the influence of solar radiation on the temperature distribution on the cross-section of the boxradiation. girder is The negligible temperature in winter. contour plots obtained from ﬁnite element model with or without the considerationbox girder is of negligible solar radiation in winter. are compared in Figure 14 (24:00, 16 December 2010).

(a()a ) (b(b) ) Figure 13. Influence of solar radiation on temperature distribution on cross-section of box girder in FigFigureure 13.13. InfluenceInﬂuence of solar radiation on temperature distribution on on cross cross-section-section of box girder in winter (16 December 2010): (a) east web (EW-1); and (b) bottom flange (B-1). winter (16(16 December 2010):2010): ( a) east web (EW-1);(EW-1); and ((b)) bottom ﬂangeflange (B-1).(B-1).

Appl. Sci. 2018, 8, x FOR PEER REVIEW 18 of 27

(a) (a)

(b)

FigureFigure 14. 14Temperature. Temperature contour contour plots plots of box girder at at 24:00 24:00 on on 16 16 December December 2010 2010:: (a) ( awith) with solar solar radiation;radiation and; and (b ()b without) without solar solar radiation. radiation.

6.2. Side-by-Side Box Girder Bridge In Figure 13, it can be found that the variation trends, lowest temperatures and the times at which6.2.1. the Finite lowest Element temperatures Model occurred were similar for measured and calculated values without the consideration of solar radiation on 16 December 2010 (maximum 0.3 ◦C for two webs and 0.2 ◦C One 6-span concrete continuous bridge in Zhangzhou with a cross-section consisting of 11 side- by-side box girders was chosen as case study. The thickness of the concrete overlay is 100 mm. The dimensions of girder cross-sections and the installation locations of temperature sensors are illustrated in Figure 15. Six temperature sensors were installed in the concrete within the top flanges (1-T and 11-T), webs (1-W and 11-W) and bottom flanges (1-B and 11-B) of box girders #1 and #11. The meteorological data, including ambient air temperature, hourly global solar radiation, hourly diffuse solar radiation and wind speed, were measured by an automated meteorological station. The monitoring period was from 30 July 2014 to 3 August 2014 and the time increment between measurements was set as one hour. The 2D plane strain element in Midas-FEA was chosen to establish the finite element model of the cross-sections of side-by-side box girders (Figure 15). The ambient air temperature data were obtained from the automated meteorological station. The solar radiation was calculated using the estimation models described earlier. The effects of solar radiation and convective and radiative heat transfer were considered at the external surfaces of the side-by-side box girders. The surface heat transfer coefficient and the temperature of the surrounding fluid medium were input as boundary conditions for the finite element model. The influence of the solar radiation on different parts of the side-by-side box girders was considered by using the following rules and assumptions: (a) The external surfaces of the top flanges are influenced by the beam solar radiation and diffuse solar radiation. (b) The webs in the shadow are influenced by the diffuse solar radiation and ground reflection. (c) The webs not in the shadow are influenced by the beam solar radiation, diffuse solar radiation and ground reflection. (d) The undersides of the top and bottom flanges are not influenced by the solar radiation or ground reflection, because the space below the side-by-side box girders is small obtained by the field observation. No temperature gauge was hung inside the side-by-side box girders. Therefore, the boundary condition of the internal surfaces of the side-by-side box girders was simulated using the 2D plane strain element with the thermal parameters of the air (0 °C and 100 °C ) for the finite element model. The thermal parameters of the concrete were discussed earlier. For the air (at 0 °C), a specific heat of 714.8 J/(kg °C ), heat conductivity of 0.023 W/(m °C ) and density of 1.293 kg/m3 was used. For the air (at 100 °C ), a specific heat of 716.9 J/(kg °C ), heat conductivity of 0.030 W/(m °C ) and density of 0.946 kg/m3 were used [61]. It can be found observed that the influence of temperature on the thermal parameters of the air is small. Therefore, the thermal parameters of the air (at 100 °C and air 0 °C) were input into the finite element models in summer and winter, respectively. The finite element mesh size was set as 0.02 m. There were 27,370 and 27,190 nodes and elements, respectively, as illustrated in Figure 16. Each node had a single temperature degree of freedom. Appl. Sci. 2018, 8, 627 18 of 27 for the bottom ﬂange). In Figure 14, it can be observed that the differences between the highest calculated temperatures with or without the consideration of solar radiation were negligible at 24:00 on 16 December 2010 (maximum 0.1 ◦C). The vertical temperature variation on the cross-section of box girder were similar for calculated values with or without the consideration of solar radiation. Therefore, the inﬂuence of solar radiation on the temperature distribution on the cross-section of the box girder is negligible in winter.

6.2. Side-by-Side Box Girder Bridge

6.2.1. Finite Element Model One 6-span concrete continuous bridge in Zhangzhou with a cross-section consisting of 11 side-by-side box girders was chosen as case study. The thickness of the concrete overlay is 100 mm. The dimensions of girder cross-sections and the installation locations of temperature sensors are illustrated in Figure 15. Six temperature sensors were installed in the concrete within the top flanges (1-T and 11-T), webs (1-W and 11-W) and bottom flanges (1-B and 11-B) of box girders #1 and #11. The meteorological data, including ambient air temperature, hourly global solar radiation, hourly diffuse solar radiation and wind speed, were measured by an automated meteorological station. The monitoring period was from 30 July 2014 to 3 August 2014 and the time increment between measurements was set as one hour. The 2D plane strain element in Midas-FEA was chosen to establish the finite element model of the cross-sections of side-by-side box girders (Figure 15). The ambient air temperature data were obtained from the automated meteorological station. The solar radiation was calculated using the estimation models described earlier. The effects of solar radiation and convective and radiative heat transfer were considered at the external surfaces of the side-by-side box girders. The surface heat transfer coefficient and the temperature of the surrounding fluid medium were input as boundary conditions for the finite element model. The influence of the solar radiation on different parts of the side-by-side box girders was considered by using the following rules and assumptions: (a) The external surfaces of the top flanges are influenced by the beam solar radiation and diffuse solar radiation. (b) The webs in the shadow are influenced by the diffuse solar radiation and ground reflection. (c) The webs not in the shadow are influenced by the beam solar radiation, diffuse solar radiation and ground reflection. (d) The undersides of the top and bottom flanges are not influenced by the solar radiation or ground reflection, because the space below the side-by-side box girders is small obtained by the field observation. No temperature gauge was hung inside the side-by-side box girders. Therefore, the boundary condition of the internal surfaces of the side-by-side box girders was simulated using the 2D plane strain element with the thermal parameters of the air (0 ◦C and 100 ◦C) for the finite element model. The thermal parameters of the concrete were discussed earlier. For the air (at 0 ◦C), a specific heat of 714.8 J/(kg ◦C), heat conductivity of 0.023 W/(m ◦C) and density of 1.293 kg/m3 was used. For the air (at 100 ◦C), a specific heat of 716.9 J/(kg ◦C), heat conductivity of 0.030 W/(m ◦C) and density of 0.946 kg/m3 were used [61]. It can be found observed that the influence of temperature on the thermal parameters of the air is small. Therefore, the thermal parameters of the air (at 100 ◦C and air 0 ◦C) were input into the finite element models in summer and winter, respectively. The finite element mesh size was set as 0.02 m. There were 27,370 and 27,190 nodes and elements, respectively, asAppl. illustrated Sci. 2018, 8, in x FOR Figure PEER 16 REVIEW. Each node had a single temperature degree of freedom. 19 of 27

FigureFigure 15.15. Layout of cross cross-section-section of side-by-sideside-by-side box girder (cm).(cm).

Figure 16. Finite element model of cross-section of side-by-side box girder.

6.2.2. Influence of Solar Radiation on Temperature Distribution on Cross-Section of Side-by-Side Box Girder The monitoring period on 31 July 2014 was a sunny day with high solar radiation. Comparisons of temperature–time curves obtained experimentally or from finite element model with or without the consideration of solar radiation are illustrated in Figure 17 (31 July 2014). The hollow points denote the measured data, the solid line denotes the calculated curves with the consideration of solar radiation, and the dashed line denotes the calculated curves without consideration of solar radiation. The temperature contour plots obtained from finite element model with or without the consideration of solar radiation are compared in Figure 18 (16:00, 31 July 2014). In Figure 17, it can be observed that the variation trends and the times at which the highest temperatures occurred are similar for measured and calculated results on 31 July 2014. The differences between the highest measured and calculated temperatures when considering the effect of solar radiation were very small (maximum 0.5 °C for top flanges and 1.8 °C for webs). However, the highest calculated temperatures without the consideration of solar radiation were lower (maximum 9.3 °C for top flanges and 1.8 °C for webs) and had a time delay (2 h for top flanges). For bottom flanges, the differences between the highest measured and calculated temperatures with and without the consideration of solar radiation were very small (maximum 0.6 °C ). The accuracy of the solar radiation calculated by using the estimation models can meet the engineering requirements. In Figure 18, it can be observed that the differences between the highest calculated temperatures with or without the consideration of solar radiation were significant at 16:00 on 31 July 2014 (maximum 10.3 °C ). The vertical temperature variation on the cross-section of side-by-side box girder when considering the effect of solar radiation (15.5 °C ) was significantly larger than that without the consideration of solar radiation (5.3 °C ) in summer. Therefore, the influence of solar radiation should be considered in the analyses of the temperature distribution on side-by-side box girders, especially for top flanges.

(a) (b) Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 27

Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 27

Appl. Sci. 2018, 8, 627 19 of 27 Figure 15. Layout of cross-section of side-by-side box girder (cm).

Figure 15. Layout of cross-section of side-by-side box girder (cm).

FigureFigure 16. 16.FiniteFinite element element model model of of cross cross-section-section of of side-by-side side-by-side box box girder. girder.

6.2.2.6.2.2. Influence Influence of Solar ofFig Solar ureRadiation Radiation16. Finite elementon on Temperature Temperature model of cross DistributionDistribution-section of side on- byon Cross-Section-side Cross box -girderSection. of Side-by-Side of Side-by-Side Box GirderBox Girder 6.2.2. Influence of Solar Radiation on Temperature Distribution on Cross-Section of Side-by-Side The monitoring period on 31 July 2014 was a sunny day with high solar radiation. Comparisons TheBox monitoring Girder period on 31 July 2014 was a sunny day with high solar radiation. Comparisons of temperatof temperature–timeure–time curves curves obtained obtained experimentally experimentally or fromfrom finite finite element element model model with with or without or without the considerationThe monitoring of solar period radiation on 31 July are 2014 illustrated was a sunny in Figureday with 17 high (31 solar July radiation. 2014). The Comparisons hollow points the consideration of solar radiation are illustrated in Figure 17 (31 July 2014). The hollow points denoteof temperat the measuredure–time data, curves the obtained solid line experimentally denotes the calculatedor from finite curves element with model the consideration with or without of solar denote thethe considerationmeasured data, of solar the radiationsolid line are denotes illustrated the in calculated Figure 17 (31curves July with2014). the The consideration hollow points of solar radiation, and the dashed line denotes the calculated curves without consideration of solar radiation. denote the measured data, the solid line denotes the calculated curves with the consideration of solar radiation,The temperature and the dashed contour line plots denotes obtained the from calculated finite element curves model without with consideration or without the of consideration solar radiation. The temperatureradiation, and contour the dashed plots line obtained denotes the from calculated finite elementcurves without model consideration with or without of solar the radiation. consideration of solarThe temperature radiation arecontour compared plots obtained in Figure from 18 finite (16:00, element 31 July model 2014). with In or Figure without 17 the, it consideration can be observed of solar radiation are compared in Figure 18 (16:00, 31 July 2014). In Figure 17, it can be observed that thatof thesolar variation radiation trendsare compared and the in timesFigure at 18 which (16:00, the31 July highest 2014). temperatures In Figure 17, it occurred can be observed are similar that for the variationmeasuredthe variation and trendscalculated trends and and the results the times times on 31 at at July which which 2014. the the The highest highest differences temperatures temperatures between occurred the occurred highest are similarmeasured are similarfor and for measuredcalculatedmeasured and temperaturescalculated and calculated results when results on considering on 31 31 July July 2014.2014. theeffect TheThe di ofdifferencesfferences solar radiation between between the were highest the very highest measured small (maximummeasured and and ◦ ◦ calculated0.5calculatedC fortemperatures top temperatures flanges andwhen when 1.8 considering Cconsidering for webs). thethe However, effecteffect of of thesolar solar highest radiation radiation calculated were were very temperatures smallvery (maximumsmall without(maximum ◦ ◦ 0.5 °Cthe for0. consideration5 top°C for flanges top flanges ofand solar and 1.8 radiation 1.°C8 °Cfor for webs). werewebs). lowerHowever, However, (maximum the the highest highest 9.3 calculatedC forcalculated top temperatures flanges temperatures and 1.8withoutC for without the webs) the consideration of solar radiation were lower (maximum 9.3 °C for top flanges and 1.8 °C for webs) and considerationand had a o timef solar delay radiation (2 h for were top flanges). lower (maximum For bottom 9. flanges,3 °C for the top differences flanges and between 1.8 °C the for highest webs) and measuredhad a time and delay calculated (2 h for temperatures top flanges). with For and bottom without flanges, the the consideration differences between of solar theradiation highest were had a time delay (2 h for top flanges). For bottom flanges, the differences between the highest verymeasured small (maximum and calculated 0.6 ◦ temperaturesC). The accuracy with ofand the without solar radiation the consideration calculated of bysolar using radiation the estimation were measured and calculated temperatures with and without the consideration of solar radiation were modelsvery small can meet (maximum the engineering 0.6 °C ). The requirements. accuracy of the In solar Figure radiation 18, it cancalculated be observed by using that the theestimation differences very betweensmallmodels (maximum the can highest meet the 0. calculated6 engineering °C ). The temperatures accuracy requirements. of with the In or Figuresolar without radiation18, it the can consideration be calculated observed that of by solar theusing differences radiation the estimation were between the highest calculated temperatures with or without the consideration of solar radiation modelssignificant can meet at 16:00the engineering on 31 July 2014 requirements. (maximum 10.3In Figure◦C). The 18, verticalit can be temperature observed variationthat the differences on the were significant at 16:00 on 31 July 2014 (maximum 10.3 °C ). The vertical temperature variation on betweencross-section the highest of side-by-side calculated box temperatures girder when withconsidering or without the effect the of consideration solar radiation of (15.5 solar◦C) radiation was the cross-section of side-by-side box girder when considering the effect of solar radiation (15.5 °C ) were significant at 16:00 on 31 July 2014 (maximum 10.3 °C ). The vertical◦ temperature variation on significantlywas significantly larger thanlarger that than without that without the consideration the consideration of solar of radiation solar radiation (5.3 C) (5.3 in summer.°C ) in summer. Therefore, the crosstheTherefore, influence-section the ofof solar influenceside radiation-by -ofside solar shouldbox radiation girder be considered should when be considering inconsidered the analyses in the the of effect theanalyses temperature of ofsolar the temperatureradiation distribution (15.5 on °C ) was side-by-sidesignificantlydistribution box onlarger girders,side- bythan-side especially that box girders,without for top esp the flanges.ecially consideration for top flanges. of solar radiation (5.3 °C ) in summer. Therefore, the influence of solar radiation should be considered in the analyses of the temperature distribution on side-by-side box girders, especially for top flanges.

(a) (b)

Figure 17. Cont.

(a) (b) Appl.Appl. Sci. Sci.2018 2018, 8, 8 627, x FOR PEER REVIEW 20 of 2027 of 27 Appl. Sci. 2018, 8, x FOR PEER REVIEW 20 of 27

(c()c ) (d)

(e()e ) (f)

FigureFigFigure 17.ure 17 Influence.17 Influence. Influence of of solarof solar solar radiationradiation radiation on on temperature temperaturetemperature distribution distribution distribution onon on crosscross cross-section-section of sideside of side-by-side--byby--sideside box girder in summer (31 July 2014): (a) top flange (1-T); (b) top flange (11-T); (c) web (1-W); (d) web boxbox girder girder in in summer summer (31 (31July July 2014):2014): ( a)) top top flange flange (1 (1-T);-T); (b ()b top) top flange flange (11 (11-T);-T); (c) web (c) web (1-W) (1-W);; (d) web (d) web (11-W); (e) bottom flange (1-B); and (f) bottom flange (11-B). (11-W);(11-W) (e; )(e bottom) bottom flange flange (1-B); (1-B); andand ((ff)) bottom flange flange (11 (11-B).-B).

Appl. Sci. 2018, 8, x FOR PEER REVIEW 21 of 27

(a) (a)

(b)

FigureFig 18.ureTemperature 18. Temperature contour contour plots plots of of side-by-side side-by-side box girder girder at at 16:00 16:00 on on 31 31July July 2014 2014:: (a) with (a) withsolar solar radiation;radiation and; and (b) without(b) without solar solar radiation. radiation.

6.3. T-Shaped Girder Bridge

6.3.1. Finite Element Model One 4-span concrete continuous bridge in Yongchun with a cross-section consisting of 4 T- shaped girders was chosen as case study. The thickness of the concrete overlay is 190 mm. The dimensions of girder cross-section and the installation locations of temperature sensors are illustrated in Figure 19. Four temperature sensors were installed in the concrete within the top flanges (T-1), webs (1-W and 2-W) and bottom flanges (4-B) of the T-shaped girders. The meteorological data, including ambient air temperature, hourly global solar radiation, hourly diffuse solar radiation and wind speed, were measured by an automated meteorological station. The monitoring period were from 15 August 2012 to 25 August 2012 and the time increment between measurements was set as one hour. The 2D plane strain element in Midas-FEA was chosen to establish the finite element model of the cross-sections of T-shaped girders (Figure 19). The ambient air temperature data were obtained from the automated meteorological station. The solar radiation was calculated using the estimation models described earlier. The effects of solar radiation and convective and radiative heat transfer were considered at the external surfaces of the T-shaped girders. The surface heat transfer coefficient and the temperature of the surrounding fluid medium were input as boundary conditions for the finite element model. The influence of the solar radiation on different parts of the T-shaped girders was considered by dividing the cross-section into four zones, as shown in Figure 20. (a) The external surfaces of the top flanges are considered as Zone 1, which are influenced by the beam solar radiation and diffuse solar radiation. (b) The external surfaces of the webs of the girders #1 and #4 are considered as Zone 2, of which the parts in shadow are influenced by the diffuse solar radiation and ground reflection, and the parts not in shadow are influenced by the beam solar radiation, diffuse solar radiation and ground reflection. (c) The undersides of the top and bottom flanges are set as Zone 3, which are considered as the inner surfaces in the T-shaped girders and are not influenced by the solar radiation or ground reflection. Moreover, the convective heat transfer coefficient of the inner surfaces in the T-shaped girders was set as 5 W/(m2 °C), which is larger than that in the box girders (3.5 W/(m2 °C )) [62]. The finite element mesh size was set as 0.02 m. There were 16,165 and 15,149 nodes and elements, respectively, as illustrated in Figure 20. Each node had a single temperature degree of freedom. Appl. Sci. 2018, 8, 627 21 of 27

6.3. T-Shaped Girder Bridge

6.3.1. Finite Element Model One 4-span concrete continuous bridge in Yongchun with a cross-section consisting of 4 T-shaped girders was chosen as case study. The thickness of the concrete overlay is 190 mm. The dimensions of girder cross-section and the installation locations of temperature sensors are illustrated in Figure 19. Four temperature sensors were installed in the concrete within the top flanges (T-1), webs (1-W and 2-W) and bottom flanges (4-B) of the T-shaped girders. The meteorological data, including ambient air temperature, hourly global solar radiation, hourly diffuse solar radiation and wind speed, were measured by an automated meteorological station. The monitoring period were from 15 August 2012 to 25 August 2012 and the time increment between measurements was set as one hour. The 2D plane strain element in Midas-FEA was chosen to establish the finite element model of the cross-sections of T-shaped girders (Figure 19). The ambient air temperature data were obtained from the automated meteorological station. The solar radiation was calculated using the estimation models described earlier. The effects of solar radiation and convective and radiative heat transfer were considered at the external surfaces of the T-shaped girders. The surface heat transfer coefficient and the temperature of the surrounding fluid medium were input as boundary conditions for the finite element model. The influence of the solar radiation on different parts of the T-shaped girders was considered by dividing the cross-section into four zones, as shown in Figure 20. (a) The external surfaces of the top flanges are considered as Zone 1, which are influenced by the beam solar radiation and diffuse solar radiation. (b) The external surfaces of the webs of the girders #1 and #4 are considered as Zone 2, of which the parts in shadow are influenced by the diffuse solar radiation and ground reflection, and the parts not in shadow are influenced by the beam solar radiation, diffuse solar radiation and ground reflection. (c) The undersides of the top and bottom flanges are set as Zone 3, which are considered as the inner surfaces in the T-shaped girders and are not influenced by the solar radiation or ground reflection. Moreover, the convective heat transfer coefficient of the inner surfaces in the T-shaped girders was set as 5 W/(m2 ◦C), which is larger than that in the box girders (3.5 W/(m2 ◦C)) [62]. The finite element mesh size was set as 0.02 m. There were 16,165 and 15,149 nodes and elements, Appl.respectively, Sci. 2018, 8, x asFOR illustrated PEER REVIEW in Figure 20. Each node had a single temperature degree of freedom. 22 of 27

Figure 19. Layout of cross-section of T-shaped girder (cm). Figure 19. Layout of cross-section of T-shaped girder (cm).

Figure 20. Finite element model of cross-section of T-shaped girder.

6.3.2. Influence of Solar Radiation on Temperature Distribution on Cross-Section of T-Shaped Girder During the monitoring period, 23 August 2012 was a sunny day with the high solar radiation. Comparisons of temperature–time curves obtained experimentally or from finite element model with or without the consideration of solar radiation are illustrated in Figure 21 (23 August 2012). The hollow points denote the measured data, the solid line denotes the calculated curves with the consideration of solar radiation, and the dash line denotes the calculated curves without the consideration of solar radiation. The temperature contour plots obtained from finite element model with or without the consideration of solar radiation are compared in Figure 22 (15:00, 23 August 2012). In Figure 21, it can be observed that the variation trends and the times at which the highest temperatures occurred are similar for measured and calculated results on 23 August 2012. The differences between the highest measured and calculated temperatures when considering the effect of solar radiation were very small (maximum 1.7 °C for top flanges and 1.0 °C for webs). However, the highest calculated temperatures without the consideration of solar radiation were lower (maximum 7.6 °C for top flanges and 3.1 °C for webs) and had a time delay (2 h for top flanges). For bottom flanges, the differences between the highest measured and calculated temperatures with and without the consideration of solar radiation were very small (maximum 0.3 °C ). The accuracy of the solar radiation calculated by using the estimation models can meet the engineering requirements. In Figure 22, it can be observed that the differences between the highest calculated temperatures with or without the consideration of solar radiation were significant at 15:00 on 23 August 2012 (maximum 13.5 °C). The vertical temperature variation on the cross-section of T-shaped girder when considering the effect of solar radiation (19.7 °C) was significantly larger than that without the consideration of solar radiation (6.5 °C ) in summer. Therefore, the influence of solar radiation should be considered in the analyses of the temperature distribution on T-shaped girders, especially for top flanges and webs. Appl. Sci. 2018, 8, x FOR PEER REVIEW 22 of 27

Appl. Sci. 2018, 8, 627 22 of 27 Figure 19. Layout of cross-section of T-shaped girder (cm).

FigFigureure 20.20. FiniteFinite element element model model of of cross cross-section-section ofof T-shapedT-shaped girder. girder.

6.3.26.3.2.. Influence Influence of Solar of Solar Radiation Radiation on on Temperature Temperature Distribution on on Cross-Section Cross-Section of T-Shapedof T-Shaped Girder Girder During the monitoring period, 23 August 2012 was a sunny day with the high solar radiation. ComparisonsDuring the monitoring of temperature–time period, curves23 August obtained 2012 experimentally was a sunny orday from with finite the element high solar model radiation. with Comparisonsor without of the temperat considerationure–time of solar curves radiation obtained are illustrated experimentally in Figure or 21 fro (23m August finite element 2012). The model hollow with or withoutpoints denote the consideration the measured ofdata, solar the radiationsolid line denotes are illustrated the calculated in Figure curves 21 with (23 theAugust consideration 2012). The hollowof solar points radiation, denote and the the measured dash line denotes data, the the solidcalculated line curves denotes without the calculated the consideration curves of with solar the radiation. The temperature contour plots obtained from finite element model with or without the consideration of solar radiation, and the dash line denotes the calculated curves without the consideration of solar radiation are compared in Figure 22 (15:00, 23 August 2012). In Figure 21, it can consideration of solar radiation. The temperature contour plots obtained from finite element model be observed that the variation trends and the times at which the highest temperatures occurred are withsimilar or without for measured the consideration and calculated of resultssolar radiation on 23 August are 2012.compared The differences in Figure between22 (15:00, the 23 highest August 2012).measured In Figure and 21 calculated, it can be temperatures observed that when the considering variation thetrends effect and of solar the times radiation at which were very the smallhighest temperatures(maximum occurred 1.7 ◦C for top are flanges similar and for 1.0 measured◦C for webs). and However, calculated the results highest calculatedon 23 August temperatures 2012. The differenceswithout between the consideration the highest of solar measured radiation and were calculated lower (maximum tempera 7.6tures◦C for when top flanges considering and 3.1 the◦C foreffect of solarwebs) radiation and had awere time very delay small (2 h for (maximum top flanges). 1.7 For °C bottom for top flanges, flanges the and differences 1.0 °C betweenfor webs). the highestHowever, the measured highest calculated and calculated temperatures temperatures without with and the without consideration the consideration of solar of radiation solar radiation were were lower (maximumvery small 7.6(maximum °C for top 0.3flanges◦C).The and accuracy 3.1 °C for of thewebs) solar and radiation had a time calculated delay by (2 usingh for thetop estimationflanges). For bottommodels flanges, can meetthe differences the engineering between requirements. the highest In Figure measured 22, it and can calculated be observed temperatures that the differences with and withoutbetween the consideration the highest calculated of solar radiation temperatures were very with small or without (maximum the consideration 0.3 °C ). The ofaccura solarcy radiation of the solar ◦ radiationwere significantcalculated by at 15:00using on the 23 estimation August 2012 models (maximum can meet 13.5 theC). engineering The vertical requirements. temperature In variation Figure 22, ◦ it canon be the observed cross-section that the of T-shapeddifferences girder between when the considering highest calculated the effect temperatures of solar radiation with (19.7 or withoutC) was the significantly larger than that without the consideration of solar radiation (6.5 ◦C) in summer. Therefore, consideration of solar radiation were significant at 15:00 on 23 August 2012 (maximum 13.5 °C). The the influence of solar radiation should be considered in the analyses of the temperature distribution on vertical temperature variation on the cross-section of T-shaped girder when considering the effect of solar T-shaped girders, especially for top flanges and webs. radiation (19.7 °C) was significantly larger than that without the consideration of solar radiation (6.5 °C ) in summer. Therefore, the influence of solar radiation should be considered in the analyses of the temperature distribution on T-shaped girders, especially for top flanges and webs. Appl.Appl. Sci. Sci.2018 2018, 8,, 8 627, x FOR PEER REVIEW 2323 of of27 27 Appl. Sci. 2018, 8, x FOR PEER REVIEW 23 of 27

(a) (b) (a) (b)

(c) (d) (c) (d) FigureFigure 21. 21Influence. Influence of of solar solar radiation radiation onon temperature distribution distribution on on cross cross-section-section of of T- T-shapedshaped girder girder Figure 21. Influence of solar radiation on temperature distribution on cross-section of T-shaped girder in summer: (a) top flange (T-1); (b) web (1-W); (c) web (2-W); and (d) bottom flange (4-B). inin summer: summer (:a ()a top) top flange flange (T-1); (T-1); ( b(b)) web web (1-W);(1-W); ((cc)) webweb (2-W);(2-W); and ( (dd)) bottom bottom flange flange (4 (4-B).-B).

(a) (a)

(b) (b) Figure 22. Temperature contour plots of T-shaped girder at 15:00 on 23 August 2012: (a) with solar Figure 22. Temperature contour plots of T-shaped girder at 15:00 on 23 August 2012: (a) with solar Figureradiation; 22. Temperature and (b) without contour solar radiation. plots of T-shaped girder at 15:00 on 23 August 2012: (a) with solar radiation;radiation; and and (b ()b without) without solar solar radiation. radiation. Appl. Sci. 2018, 8, 627 24 of 27

7. Discussion The following discussions can be drawn based on the results and within the limitations of the research presented in this paper:

(1) The variation trends for all hourly solar radiation curves are similar, with the solar radiation appearing at about 6:00 a.m., reaching the maxima at about 12:00 p.m. and disappearing at about 6:00 p.m. The maximum measured global solar radiation for Ninghua (about 1100 W/m2) was the highest and the difference between maximum global solar radiation for different cities was about 100 W/m2. The maximum measured diffuse solar radiation for Fu’an (about 250 W/m2) and the calculated beam solar radiation for Ninghua (about 900 W/m2) was the highest. The difference between the maximum diffuse or beam solar radiation for different cities were both about 150 W/m2. (2) The linear regression of Ångström–Page equation using the monthly time scale of data sample can predict the global solar radiation for different cities in Fujian. For the cities in Fujian that did not have actual data on sunshine duration, the empirical coefficients can be estimated using the available sunshine duration for the nearest city. (3) The Collares-Pereira and Rabl equation can estimate the hourly global solar radiation for different cities in Fujian based on the daily global solar radiation. The hourly beam solar radiation for different cities in Fujian can be predicted well using the Hottel equation. The hourly diffuse solar radiation for different cities in Fujian can be calculated by subtracting the hourly beam solar radiation from the corresponding hourly global solar radiation. (4) The maximum global solar radiation, beam solar radiation and diffuse solar radiation (for 21 June, the summer solstice) for 56 cities in Fujian were calculated. The maximum global solar radiation for Xiapu (about 1210 W/m2) is the highest and the maximum global solar radiation for Anxi (about 970 W/m2) is the lowest. The biggest difference among the global solar radiation maxima in different cities is about 240 W/m2. The maximum beam solar radiation for Zhouning (about 909 W/m2) is the highest and the maximum beam solar radiation for Ningde (about 821 W/m2) is the lowest. The biggest difference among the beam solar radiation maxima in different cities is about 88 W/m2. The maximum diffuse solar radiation for Xiapu (about 388 W/m2) is the highest and the maximum diffuse solar radiation for Dehua (about 102 W/m2) is the lowest. The biggest difference among the diffuse solar radiation maxima in different cities is about 286 W/m2. (5) Comparisons of the measured and calculated temperature–time responses for the concrete box girder, side-by-side box girder and T-shaped girder with or without the consideration of solar radiation indicates that the influence of solar radiation should be considered in the analyses of the temperature distribution on the bridge girder cross-sections in summer. The accuracy of the solar radiation calculated using the estimation models can meet the engineering requirements. The highest calculated temperatures without the consideration of solar radiation were lower and had a time delay, especially for top flanges in the summertime. The vertical temperature variation when considering the effect of solar radiation was significantly larger than that without the consideration of solar radiation. The influence of solar radiation on the temperature distribution decreases as the distance from external surfaces. The influence of solar radiation on the temperature distribution of the bridge girder cross-sections is negligible in winter. (6) The solar radiation parameters for other cities and regions in China and elsewhere, as well as different bridge superstructure types, can be similarly developed based on more case studies to establish the relevant estimation models. This can serve as a prelude for future development of specifications related to temperature effects in bridge engineering.

Acknowledgments: The research was supported by National Natural Science Foundation of China (51508103), National Natural Science Foundation of China (51778148), Fujian Provincial Education Department Research Foundation for Young Teacher (JA15074) and Recruitment Program of Global Experts Foundation (TM2012-27). The authors would also like to acknowledge the Sustainable and Innovative Bridge Engineering Research Center Appl. Sci. 2018, 8, 627 25 of 27

(SIBERC) of the College of Civil Engineering, Fuzhou University (Fuzhou, China) and National Meteorological Information Center, China Meteorological Administration. Author Contributions: All authors substantially contributed to this work. Junqing Xue, Bruno Briseghella and Jianhui Lin conceived and performed the monitoring of solar radiation. Junqing Xue, Habib Tabatabai and Jianhui Lin conceived and designed the estimation model for solar radiation. Junqing Xue and Baochun Chen performed the monitoring of temperature distribution on bridge girder cross-sections. Junqing Xue and Jianhui Lin performed the finite element simulation and analyzed the temperature distribution on bridge girder cross-sections. All authors helped with the writing of the paper. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Kehlbeck, F. Einfluss der Sonnenstrahlung bei Bruckenbauwerken; Werner: Dusseldorf, Germany, 1975. 2. Peng, Y.S.; Qiang, S.Z. Analytical solution to temperature variations in highway concrete bridges due to solar radiation. In Proceedings of the First International Conference on Transportation Engineering, Chengdu, China, 22–24 July 2007; American Society of Civil Engineers: Reston, VA, USA, 2017; pp. 1536–1541. 3. Emerson, M. Bridge Temperatures Estimated from the Shade Temperature; TRRL Laboratory Report 696; TRRL: Berkshire, UK, 1976. 4. Imbsen, R.A.; Vandershaf, D.E.; Schamber, R.A.; Nutt, R.V. Thermal Effects in Concrete Bridge Superstructures; NCHRP Report 276; Transportation Research Board: Washington, DC, USA, 1985. 5. Shiu, K.N.; Russell, H.G.; Tabatabai, H. Instrumentation of the Red River Bridge at Boyce; Report No. FHWA/LA-91/223; Louisiana Transportation Research Center: Baton Rouge, LA, USA, 1991. 6. Shiu, K.N.; Tabatabai, H. Measured Thermal Response of Concrete Box-Girder Bridge; Transportation Research Record No. 1460; Transportation Research Board: Washington, DC, USA, 1994; pp. 94–105. 7. Qin, Y.; Lin, L.; Tie, M.; Zhang, L. Observation and research on temperature distribution of concrete box girder in diurnal change of temperature. In Proceedings of the International Conference on Transportation, Mechanical, and Electrical Engineering, Changchun, China, 16–18 December 2011. 8. Avossa, A.M.; Giacinto, D.D.; Malangone, P.; Rizzo, F. Seismic retrofit of a multispan prestressed concrete girder bridge with friction pendulum devices. Shock Vib. 2018, 2018, 1–22. [CrossRef] 9. Zang, H.X.; Xu, Q.S.; Bian, H.H. Generation of typical solar radiation data for different climates of China. Energy 2012, 38, 236–248. [CrossRef] 10. Angstrom, A. Solar and terrestrial radiation. Quart. J. R. Meteorol. Soc. 1924, 50, 121–126. [CrossRef] 11. Page, J.K. The estimation of monthly mean values of daily total short wave radiation on-vertical and inclined surfaces from sun shine records for latitudes 40◦ N-40◦ S. In Proceedings of the United Nations Conference on New Sources of Energy, Rome, Italy, 21–31 August 1961; pp. 378–387. 12. Ögelman, H.; Ecevit, A.; Tasdemiroglu,ˇ E. A new method for estimating solar radiation from bright sunshine data. Sol. Energy 1984, 33, 619–625. [CrossRef] 13. Bahel, V.; Bakhsh, H.; Srinivasan, R. A correlation for estimation of global solar radiation. Energy 1987, 12, 131–135. [CrossRef] 14. Bakirci, K. Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey. Energy 2009, 34, 485–501. [CrossRef] 15. Duzen, H.; Aydin, H. Sunshine-based estimation of global solar radiation on horizontal surface at Lake Van region (Turkey). Energy Convers. Manag. 2012, 58, 35–46. [CrossRef] 16. Li, H.S.; Ma, W.B.; Lian, Y.W.; Wang, X.L.; Zhao, L. Global solar radiation estimation with sunshine duration in Tibet, China. Renew. Energy 2011, 36, 3141–3145. [CrossRef] 17. Katiyar, A.K.; Pandey, C.K. Simple correlation for estimating the global solar radiation on horizontal surfaces in India. Fuel Energy Abstr. 2010, 35, 5043–5048. [CrossRef] 18. Weng, D.M. Radiation Climate in China; China Meteorological Press: Beijing, China, 1997. 19. Chen, R.S.; Kang, E.S.; Yang, J.P.; Lu, S.H.; Zhao, W.Z. Validation of five global radiation models with measured daily data in China. Energy Convers. Manag. 2004, 45, 1759–1769. [CrossRef] 20. Chen, R.S.; Lu, S.H.; Kang, E.S.; Yang, J.P.; Ji, X.B. Estimating daily global radiation using two types of revised models in China. Energy Convers. Manag. 2006, 47, 865–878. 21. Zhao, N.; Zeng, X.F.; Han, S.M. Solar radiation estimation using sunshine hour and air pollution index in China. Energy Convers. Manag. 2013, 76, 846–851. [CrossRef] Appl. Sci. 2018, 8, 627 26 of 27

22. Zhang, J.Y.; Zhao, L.; Deng, S.; Xu, W.C.; Zhang, Y. A critical review of the models used to estimate solar radiation. Renew. Sustain. Energy Rev. 2017, 70, 314–329. [CrossRef] 23. Hargreaves, G.H.; Samani, Z.A. Estimating potential evapotranspiration. J. Irrig. Drain. Div. 1982, 108, 225–230. 24. Annandale, J.; Jovanovic, N.; Benadé, N.; Allen, R. Software for missing data error analysis of Penman-Monteith reference evapotranspiration. Irrig. Sci. 2002, 21, 57–67. 25. De, J.R.; Stewart, D.W. Estimating global solar radiation from common meteorological observations in western Canada. Can. J. Plant Sci. 1993, 73, 509–518. 26. Hamby, A.L. Estimation of solar radiation for use in crop modeling. Agric. For. Meteorol. 1998, 91, 293–300. 27. Wu, G.F.; Liu, Y.L.; Wang, T.J. Methods and strategy for modeling daily global solar radiation with measured meteorological data—A case study in Nanchang Station, China. Energy Convers. Manag. 2007, 48, 2447–2452. [CrossRef] 28. Bristow, K.L.; Campbell, G.S. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agric. For. Meteorol. 1984, 31, 159–166. [CrossRef] 29. Grillone, G.; Agnese, C.; D’asaro, F. Estimation of daily solar radiation from measured air temperature extremes in the Mid-Mediterranean area. J. Irrig. Drain. Eng. 2012, 138, 939–947. [CrossRef] 30. Liu, X.Y.; Mei, X.R.; Li, Y.Z.; Wang, Q.S.; Jens, R.J.; Zhang, Y.Q.; Johnroy, P. Evaluation of temperature-based global solar radiation models in China. Agric. For. Meteorol. 2009, 149, 1433–1446. [CrossRef] 31. Kimball, H.H. Solar and sky radiation measurements during June. Mon. Weather Rev. 1928, 56, 230. [CrossRef] 32. Bennett, I. Monthly maps of mean daily insolation for the United States. Sol. Energy 1965, 9, 145–158. [CrossRef] 33. Wang, B.Z.; Zhang, F.G.; Li, L.X. Solar energy resources in China. Acta Energ. Sol. Sin. 1980, 1, 229–241. 34. Alsina, E.F.; Bortolini, M.; Gamberi, M.; Regattieri, A. Artificial neural network optimisation for monthly average daily global solar radiation prediction. Energy Convers. Manag. 2016, 120, 320–329. [CrossRef] 35. Zou, L.; Wang, L.C.; Lin, A.W.; Zhu, H.J.; Peng, Y.L.; Zhao, Z.Z. Estimation of global solar radiation using an artificial neural network based on an interpolation technique in southeast China. J. Atmos. Sol. Terr. Phys. 2016, 146, 110–122. [CrossRef] 36. Mehdizadeh, S.; Behmanesh, J.; Khalili, K. Comparison of artificial intelligence methods and empirical equations to estimate daily solar radiation. J. Atmos. Sol. Terr. Phys. 2016, 146, 215–227. [CrossRef] 37. Voyant, C.; Notton, G.; Kalogirou, S.; Nivet, M.L.; Paoli, C.; Motte, F.; Fouilloy, A. Machine learning methods for solar radiation forecasting: A review. Renew. Energy 2017, 105, 569–582. [CrossRef] 38. Liu, B.Y.H.; Jordan, R.C. The interrelationship and characteristic distribution of direct, diffuse and total solar radiation. Sol. Energy 1960, 4, 1–19. [CrossRef] 39. Duffie, J.A.; Beckman, W.A. Solar Engineering of Thermal Processes, 4th ed.; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2013. 40. Collares-Pereira, M.; Rabl, A. The average distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values. Sol. Energy 1979, 22, 155–164. [CrossRef] 41. Kalogirou, S.A.; Pashiardis, S.; Pashiardi, A. Statistical analysis and inter-comparison of the global solar radiation at two sites in Cyprus. Renew. Energy 2017, 101, 1102–1123. [CrossRef] 42. Yao, W.X.; Li, Z.G.; Xiu, T.B.; Lu, Y.; Li, X.B. New decomposition models to estimate hourly global solar radiation from the daily value. Sol. Energy 2015, 120, 87–99. [CrossRef] 43. Newell, T.A. Simple models for hourly to daily radiation ratio correlations. Sol. Energy 1983, 31, 339–342. [CrossRef] 44. Zhang, S.N.; Tian, S.Y. The institution of the hourly solar radiation model. Acta Energy Sol. Sin. 1997, 18, 273–277. 45. Jain, P.C. Comparison of techniques for the estimation of daily global irradiation and a new technique for the estimation of hourly global irradiation. Sol. Wind Technol. 1984, 1, 123–134. [CrossRef] 46. Baig, A.; Akhter, P.; Mufti, A. A novel approach to estimate the clear day global radiation. Renew. Energy 1991, 1, 119–123. [CrossRef] 47. American Society of Heating. Refrigerating, and Air Conditioning Engineers. In ASHRAE Handbook of Fundamentals; ASHRAE: New York, NY, USA, 1972. 48. Nijegorodov, N. Improved ASHRAE model to predict hourly and daily solar radiation components in Botswana, Namibia, and Zimbabwe. Renew. Energy 1996, 9, 1270–1273. [CrossRef] Appl. Sci. 2018, 8, 627 27 of 27

49. Song, A.G.; Wang, F.R. Preliminary study on clear-day solar radiation model of Beijing region. Acta Energ. Sol. Sin. 1993, 14, 251–255. 50. Al-Sanea, S.A.; Zedan, M.F.; Al-Ajlan, S.A. Adjustment factors for the ASHRAE clear-sky model based on solar-radiation measurements in Riyadh. Appl. Energy 2004, 79, 215–237. [CrossRef] 51. Hottel, H.C. A simple model for estimating the transmittance of direct solar radiation through clear atmospheres. Sol. Energy 1976, 18, 129–134. [CrossRef] 52. Jiang, Y.N. Correlation for diffuse radiation from global solar radiation and sunshine data at Beijing, China. J. Energy Eng. 2009, 135, 363–372. [CrossRef] 53. Janjai, S.; Praditwong, P.; Moonin, C. A new model for computing monthly average daily diffuse radiation for Bangkok. Renew. Energy 1996, 9, 1283–1286. [CrossRef] 54. Bai, J.S.; Chen, X.P.; Dobermann, A.; Yang, H.S.; Kennethg, C.; Zhang, F.S. Evaluation of NASA Satellite- and Model-Derived weather data for simulation of Maize yield potential in China. Agron. J. 2010, 102, 9–16. [CrossRef] 55. Kaplanis, S.; Kumar, J.; Kaplani, E. On a universal model for the prediction of the daily global solar radiation. Renew. Energy 2016, 91, 178–188. [CrossRef] 56. Bakirci, K. Prediction of global solar radiation and comparison with satellite data. J. Atmos. Sol. Terr. Phys. 2017, 152, 41–49. [CrossRef] 57. Ma, X.Q. Estimation of Solar Radiation Using Nasa/Power Data. Master’s Thesis, Southwest University, Chongqing, China, 2015. 58. National Meteorological Information Center, China Meteorological Administration. Available online: http://data.cma.cn/site/index.html (accessed on 15 March 2018). 59. Zhang, J.F. Estimation Models of Solar Radiation at Different Time Scales. Master’s Thesis, Southwest University, Chongqing, China, 2013. 60. Elbadry, M.M.; Ghali, A. Temperature Variations in Concrete Bridges. J. Struct. Eng. 1983, 109, 2355–2374. [CrossRef] 61. Zhang, X.Y. Practical Handbook of Chemistry; National Defense Industry Press: Beijing, China, 2011. 62. Chen, X.Y. Research on Sunlight Thermal Effect of Integral Abutment Bridge. Master’s Thesis, Fuzhou University, Fuzhou, China, 2012.

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).