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The Top 20 Most-Cited Papers from 2022 to 2023
2022 Vol. 37, No. 4
Display Method:
2022, 37(4): 1-13.
doi: 10.13206/j.gjgs21121901
Abstract
PDF (22578KB)
Abstract:
Orthotropic steel decks(OSDs) have obvious advantages and are the preferred deck structure for long-span bridges. However, the fatigue problem of the OSDs is prominent. In recent years, driven by the construction of national major engineering projects, the manufacturing concept and mode of OSDs in China have made continuous progress, the manufacturing technological equipment and process level have been greatly improved, providing a whole-process, multi-dimensional and professional solution to improve the fatigue performance of OSDs. Computer numerical control laser cutting machine is introduced to realize the high quality machining of transverse rib tooth plate in cutting parts. In the welding of U-rib unit, the special welding machines for U-rib internal and external welds are adopted based on submerged arc welding technology to realize the high quality and efficient welding of U-rib double-sided welds. A welding robot based on off-line programming and three-direction sensing technology is used to weld stereo units of bridge decks. Ultrasonic phased array detection technique is used to achieve accurate identification and detection of internal defects in U-rib welds.
Recent advances in OSDs manufacturing technology include the following:1) From the manual welding-based manufacturing mode to the mechanization and automation-based manufacturing mode, various types of automated manufacturing equipment have been developed, which have greatly improved the welding quality and production efficiency. The intelligent welding technology represented by machine vision technology has been used in the manufacture of OSDs. 2) Successfully developed the U-rib internal welding technology of OSDs and developed the U-rib double-sided welding technology on this basis, which fundamentally solved the problem of fatigue cracking at the root of the traditional single-sided weld of the U-rib, which greatly improves the fatigue resistance of key welds of OSDs, and strongly supports the further development of OSDs. 3) In order to solve the problem of internal quality inspection of U-rib welds, the ultrasonic phased array inspection technology was introduced into the non-destructive testing of U-rib welds of OSDs, which played an important role in the quality control of U-rib welds. 4) The stereo unit robot welding technology of OSDs was developed, which realized the automatic welding of the U-rib and the transverse rib connection weld of OSDs, and improved the fatigue resistance of the weld at this part. Through the research and development, promotion and application of key technologies, the manufacturing quality and fatigue performance of OSDs have been effectively improved, and the new generation technology system of OSDs manufacturing that integrates intelligent manufacturing technology, efficient welding technology and advanced detection technology has been established. In this paper, the development of OSDs manufacturing technology is summarized and commented on the aspects of manufacturing concept and mode, U-rib welding technology development and stereo unit robot welding technology of OSDs.
Orthotropic steel decks(OSDs) have obvious advantages and are the preferred deck structure for long-span bridges. However, the fatigue problem of the OSDs is prominent. In recent years, driven by the construction of national major engineering projects, the manufacturing concept and mode of OSDs in China have made continuous progress, the manufacturing technological equipment and process level have been greatly improved, providing a whole-process, multi-dimensional and professional solution to improve the fatigue performance of OSDs. Computer numerical control laser cutting machine is introduced to realize the high quality machining of transverse rib tooth plate in cutting parts. In the welding of U-rib unit, the special welding machines for U-rib internal and external welds are adopted based on submerged arc welding technology to realize the high quality and efficient welding of U-rib double-sided welds. A welding robot based on off-line programming and three-direction sensing technology is used to weld stereo units of bridge decks. Ultrasonic phased array detection technique is used to achieve accurate identification and detection of internal defects in U-rib welds.
Recent advances in OSDs manufacturing technology include the following:1) From the manual welding-based manufacturing mode to the mechanization and automation-based manufacturing mode, various types of automated manufacturing equipment have been developed, which have greatly improved the welding quality and production efficiency. The intelligent welding technology represented by machine vision technology has been used in the manufacture of OSDs. 2) Successfully developed the U-rib internal welding technology of OSDs and developed the U-rib double-sided welding technology on this basis, which fundamentally solved the problem of fatigue cracking at the root of the traditional single-sided weld of the U-rib, which greatly improves the fatigue resistance of key welds of OSDs, and strongly supports the further development of OSDs. 3) In order to solve the problem of internal quality inspection of U-rib welds, the ultrasonic phased array inspection technology was introduced into the non-destructive testing of U-rib welds of OSDs, which played an important role in the quality control of U-rib welds. 4) The stereo unit robot welding technology of OSDs was developed, which realized the automatic welding of the U-rib and the transverse rib connection weld of OSDs, and improved the fatigue resistance of the weld at this part. Through the research and development, promotion and application of key technologies, the manufacturing quality and fatigue performance of OSDs have been effectively improved, and the new generation technology system of OSDs manufacturing that integrates intelligent manufacturing technology, efficient welding technology and advanced detection technology has been established. In this paper, the development of OSDs manufacturing technology is summarized and commented on the aspects of manufacturing concept and mode, U-rib welding technology development and stereo unit robot welding technology of OSDs.
2022, 37(4): 14-24.
doi: 10.13206/j.gjgs21070501
Abstract:
The closed section of steel frame column has the advantages of high bearing efficiency and large torsional modulus. The problem that steel beam and Hollow Square Column(HSC) cannot be directly connected by ordinary high-strength bolts can be solved by using thread-fixed one-side bolt(TOB). TOB is to directly tighten the high-strength bolt on the threaded hole of the column wall by machining the threaded bolt hole on the column wall, instead of the traditional nut, so as to realize the installation and tightening on the outside of the steel tube column. Based on the study of the thread-fixed one-side bolted double T-joint model, the stress mechanism and failure mode of thread-fixed one-side bolted T-stub with steel tube are further studied. The tensile tests of 10 thread-fixed one-side bolted T-stub with steel tube joints were carried out. The failure modes, bearing capacity mechanisms, displacement-load curves, yield capacity and ultimate bearing capacity of different joints were analyzed and compared.
It is found that there are four kinds of failure modes, which are thread shear failure, tube wall local yield with thread shear failure, bolt rod tensile failure and tube wall yield failure. When the thickness of the steel tube wall is small, the thread shear failure in the bolt hole occurs. When the tube wall is thick and the bolt diameter is relatively small, the bolt rod is broken and the internal thread of the threaded hole remains intact, indicating that when the internal thread length of the bolt hole is sufficient, the internal thread of the bolt hole of the steel tube wall has sufficient bearing capacity and the thread anchoring method is feasible.
At the same time, the effects of bolt spacing, bolt diameter and tube wall thickness on the bearing capacity of the joint are compared and analyzed. The test results show that the bearing capacity of the joint can be improved by increasing the bolt diameter, tube wall thickness and bolt spacing. The influence of bolt spacing on the bearing capacity of the joint is related to the shape of the yield line of the steel tube wall under the bolt tension. When the bolt spacing is small, the yield lines of tensile bolts on the steel tube wall are superimposed. With the increase of bolt spacing, the bearing capacity of the joint is significantly improved. However, when the bolt spacing is large, the yield line of each tensile bolt to the steel tube wall is oblong. With the increase of bolt spacing, the bearing capacity of the joint will remain unchanged. With the increase of the bolt diameter, the failure mode of the joint gradually changes from the bolt rod tensile failure to the thread shear failure or tube wall yield failure, and the bearing capacity of the joint increases. The increase of tube wall thickness significantly increases the yield capacity of steel tube wall, and the growth rate is approximately square with the growth rate of wall thickness.
In order to avoid the problem of insufficient anchoring force in the bolt hole of the steel tube wall when the steel tube wall is thin, the influence of the steel tube with a backing plate on the mechanical performance of the thread-fixed one-side bolted T-stub with steel tube joint is further studied. The test results show that the anchor length of the thread is increased, the bearing capacity of the strengthened joint is significantly improved, and the shear failure of the thread is effectively avoided, but the initial stiffness changes little.
The closed section of steel frame column has the advantages of high bearing efficiency and large torsional modulus. The problem that steel beam and Hollow Square Column(HSC) cannot be directly connected by ordinary high-strength bolts can be solved by using thread-fixed one-side bolt(TOB). TOB is to directly tighten the high-strength bolt on the threaded hole of the column wall by machining the threaded bolt hole on the column wall, instead of the traditional nut, so as to realize the installation and tightening on the outside of the steel tube column. Based on the study of the thread-fixed one-side bolted double T-joint model, the stress mechanism and failure mode of thread-fixed one-side bolted T-stub with steel tube are further studied. The tensile tests of 10 thread-fixed one-side bolted T-stub with steel tube joints were carried out. The failure modes, bearing capacity mechanisms, displacement-load curves, yield capacity and ultimate bearing capacity of different joints were analyzed and compared.
It is found that there are four kinds of failure modes, which are thread shear failure, tube wall local yield with thread shear failure, bolt rod tensile failure and tube wall yield failure. When the thickness of the steel tube wall is small, the thread shear failure in the bolt hole occurs. When the tube wall is thick and the bolt diameter is relatively small, the bolt rod is broken and the internal thread of the threaded hole remains intact, indicating that when the internal thread length of the bolt hole is sufficient, the internal thread of the bolt hole of the steel tube wall has sufficient bearing capacity and the thread anchoring method is feasible.
At the same time, the effects of bolt spacing, bolt diameter and tube wall thickness on the bearing capacity of the joint are compared and analyzed. The test results show that the bearing capacity of the joint can be improved by increasing the bolt diameter, tube wall thickness and bolt spacing. The influence of bolt spacing on the bearing capacity of the joint is related to the shape of the yield line of the steel tube wall under the bolt tension. When the bolt spacing is small, the yield lines of tensile bolts on the steel tube wall are superimposed. With the increase of bolt spacing, the bearing capacity of the joint is significantly improved. However, when the bolt spacing is large, the yield line of each tensile bolt to the steel tube wall is oblong. With the increase of bolt spacing, the bearing capacity of the joint will remain unchanged. With the increase of the bolt diameter, the failure mode of the joint gradually changes from the bolt rod tensile failure to the thread shear failure or tube wall yield failure, and the bearing capacity of the joint increases. The increase of tube wall thickness significantly increases the yield capacity of steel tube wall, and the growth rate is approximately square with the growth rate of wall thickness.
In order to avoid the problem of insufficient anchoring force in the bolt hole of the steel tube wall when the steel tube wall is thin, the influence of the steel tube with a backing plate on the mechanical performance of the thread-fixed one-side bolted T-stub with steel tube joint is further studied. The test results show that the anchor length of the thread is increased, the bearing capacity of the strengthened joint is significantly improved, and the shear failure of the thread is effectively avoided, but the initial stiffness changes little.
2022, 37(4): 25-32.
doi: 10.13206/j.gjgS21111701
Abstract:
Wind-resistance performance of super high transmission tower during construction has been studied by wind tunnel tests and finite element methods(FEM). The effectiveness of measures against strong wind for the tower and crane has been analyzed and validated. Wind tunnel tests for the 385 m height tower and its construction facility had been conducted. Wind force coefficients of the crane structure were obtained by sectional model tests for the standard crane structure and high-frequency force balance tests for the scaled crane model, and compared with the code values of Load Code for the Design of Building Structures(GB 50009-2012). Two FEM models were established respectively for the crane structure with soft connection to the tower and the tower-crane coupled system to investigate the different wind-resistant performance between two models. FEM analysis had been performed to calculate the maximum crane displacement and the maximum tension of main cables for different cases of balance or unbalance lifting with varying wind angles, and the unfavorable factors in the process of crane construction were analysed. In strong wind conditions, detail evaluations of the proposed wind-resistance measures, i.e., free rotations of double flat arms and lowering the cantilever height of crane, were carried out, which could provide a reference for super high transmission tower during construction.
It was found there exist noticeable difference between wind tunnel results and the code values for wind force coefficients of the crane structure. While the code values may underestimate wind force, wind tunnel tests yield the maximum x or y directional wind force coefficients up to 2.40 and 2.51, respectively. The unfavorable conditions of unbalance lifting and the critical wind angle of 45° have been identified and should be avoided during the construction if possible. The maximum displacement from the tower-crane coupled model is greater than that of a single crane model. On the other hand, the maximum tension of main cables of the coupled model is smaller than the single crane model. The analysis result of the coupled model shows the decreasing of tower lateral stiffness to support the crane due to the smaller tower section at a high altitude during the later stage of tower construction. Correspondingly, a sharp increase of the maximum cable tension was observed from the coupled model at a lower position. In strong wind conditions, the maximum tension of the main cable could be reduced by 30%~40% by free rotations of flat double arms. Therefore, it is suggested to take effective wind-resistance measures, i.e., free rotations of double flat arms or lowering the cantilever height of crane structure to ensure the construction safety of the super high transmission tower under strong wind conditions.
Wind-resistance performance of super high transmission tower during construction has been studied by wind tunnel tests and finite element methods(FEM). The effectiveness of measures against strong wind for the tower and crane has been analyzed and validated. Wind tunnel tests for the 385 m height tower and its construction facility had been conducted. Wind force coefficients of the crane structure were obtained by sectional model tests for the standard crane structure and high-frequency force balance tests for the scaled crane model, and compared with the code values of Load Code for the Design of Building Structures(GB 50009-2012). Two FEM models were established respectively for the crane structure with soft connection to the tower and the tower-crane coupled system to investigate the different wind-resistant performance between two models. FEM analysis had been performed to calculate the maximum crane displacement and the maximum tension of main cables for different cases of balance or unbalance lifting with varying wind angles, and the unfavorable factors in the process of crane construction were analysed. In strong wind conditions, detail evaluations of the proposed wind-resistance measures, i.e., free rotations of double flat arms and lowering the cantilever height of crane, were carried out, which could provide a reference for super high transmission tower during construction.
It was found there exist noticeable difference between wind tunnel results and the code values for wind force coefficients of the crane structure. While the code values may underestimate wind force, wind tunnel tests yield the maximum x or y directional wind force coefficients up to 2.40 and 2.51, respectively. The unfavorable conditions of unbalance lifting and the critical wind angle of 45° have been identified and should be avoided during the construction if possible. The maximum displacement from the tower-crane coupled model is greater than that of a single crane model. On the other hand, the maximum tension of main cables of the coupled model is smaller than the single crane model. The analysis result of the coupled model shows the decreasing of tower lateral stiffness to support the crane due to the smaller tower section at a high altitude during the later stage of tower construction. Correspondingly, a sharp increase of the maximum cable tension was observed from the coupled model at a lower position. In strong wind conditions, the maximum tension of the main cable could be reduced by 30%~40% by free rotations of flat double arms. Therefore, it is suggested to take effective wind-resistance measures, i.e., free rotations of double flat arms or lowering the cantilever height of crane structure to ensure the construction safety of the super high transmission tower under strong wind conditions.
2022, 37(4): 33-39.
doi: 10.13206/j.gjgS21121902
Abstract:
Assembled cable supported steel-concrete composite floor is a new type of long-span prestressed composite structure. In order to explore the mechanical properties of the floor part of the composite floor, the standard floor element formed by the connection and combination of four slot laminated plates through inter plate connectors was selected from assembled cable supported steel-concrete composite floor. Taking this as the research object, the mechanical performance of it in the normal use stage was simulated and analyzed by finite element method.
The simulation results show that due to the existence of rib beam and post cast strip, in the initial stage of loading, the single slot composite plate element takes the lead in two-way bending deformation, and the mid span deflection is the largest. With the continuous increase of load, the overall bending deformation of composite floor unit occurs, and the deflection deformation at the middle of the span is the largest. When the loading is completed, the deflection value at the middle of the span is 59 mm. Under the action of external load, the concrete of composite slab element appears obvious plastic damage along the span direction, which indicates that the bending stiffness of simply supported composite slab element at both ends is related to the section perpendicular to the span direction. In order to explore in detail the effects of concrete strength, thickness of composite layer, height of rib beam and height of connectors between plates on the flexural stiffness and other mechanical properties of composite floor slab, thirteen finite element models were established to analyze the variable parameters of the laminated plate and the connection between plates of the grooved reinforced truss. By comparing the mid-span load-displacement curves under the same load and boundary conditions, the effects of different factors on the flexural performance of composite floors were explored.
The results show that when other conditions remain unchanged, with the increase of the height of the rib beam, the flexural stiffness increases sharply and the displacement decreases rapidly. The height of the rib beam increases from 400 mm to 700 mm, the flexural stiffness increases by 322.6% and the displacement decreases by 99%. As the thickness of composite layer increases, the bending stiffness increases and the midspan displacement decreases. When the thickness of composite layer increases from 40 mm to 70 mm, the bending stiffness increases by 24.2% and the displacement decreases by 54.7%. With the increase of concrete strength, the bending stiffness increases slightly but the midspan displacement has no obvious change. When the concrete strength increases from C25 to C40, the bending stiffness increases by 10.1% and the displacement fluctuates between 55 mm and 60 mm. Only changing the height of the inter-plate connector does not change its central position which has little effect on the bending stiffness and deflection. When the height of the inter-plate connector increases from 300 mm to 360 mm, the bending stiffness increases by 8.0% and the displacement decreases by less than 10%. In summary, the rib beam height has the greatest impact on the overall bending stiffness and mid-span displacement of the composite slab, followed by the thickness of the composite layer, and the concrete strength and the height of the connection between the slabs have little impact.
Assembled cable supported steel-concrete composite floor is a new type of long-span prestressed composite structure. In order to explore the mechanical properties of the floor part of the composite floor, the standard floor element formed by the connection and combination of four slot laminated plates through inter plate connectors was selected from assembled cable supported steel-concrete composite floor. Taking this as the research object, the mechanical performance of it in the normal use stage was simulated and analyzed by finite element method.
The simulation results show that due to the existence of rib beam and post cast strip, in the initial stage of loading, the single slot composite plate element takes the lead in two-way bending deformation, and the mid span deflection is the largest. With the continuous increase of load, the overall bending deformation of composite floor unit occurs, and the deflection deformation at the middle of the span is the largest. When the loading is completed, the deflection value at the middle of the span is 59 mm. Under the action of external load, the concrete of composite slab element appears obvious plastic damage along the span direction, which indicates that the bending stiffness of simply supported composite slab element at both ends is related to the section perpendicular to the span direction. In order to explore in detail the effects of concrete strength, thickness of composite layer, height of rib beam and height of connectors between plates on the flexural stiffness and other mechanical properties of composite floor slab, thirteen finite element models were established to analyze the variable parameters of the laminated plate and the connection between plates of the grooved reinforced truss. By comparing the mid-span load-displacement curves under the same load and boundary conditions, the effects of different factors on the flexural performance of composite floors were explored.
The results show that when other conditions remain unchanged, with the increase of the height of the rib beam, the flexural stiffness increases sharply and the displacement decreases rapidly. The height of the rib beam increases from 400 mm to 700 mm, the flexural stiffness increases by 322.6% and the displacement decreases by 99%. As the thickness of composite layer increases, the bending stiffness increases and the midspan displacement decreases. When the thickness of composite layer increases from 40 mm to 70 mm, the bending stiffness increases by 24.2% and the displacement decreases by 54.7%. With the increase of concrete strength, the bending stiffness increases slightly but the midspan displacement has no obvious change. When the concrete strength increases from C25 to C40, the bending stiffness increases by 10.1% and the displacement fluctuates between 55 mm and 60 mm. Only changing the height of the inter-plate connector does not change its central position which has little effect on the bending stiffness and deflection. When the height of the inter-plate connector increases from 300 mm to 360 mm, the bending stiffness increases by 8.0% and the displacement decreases by less than 10%. In summary, the rib beam height has the greatest impact on the overall bending stiffness and mid-span displacement of the composite slab, followed by the thickness of the composite layer, and the concrete strength and the height of the connection between the slabs have little impact.
2022, 37(4): 40-62.
doi: 10.13206/j.gjgS20112501
Abstract:
Steel bridges are built in a complex natural environment, and thus their temperature varies with solar radiation and air temperature.Such temperature variation includes not only a uniform temperature rise or temperature fall but also non-uniform distribution in the transverse direction of a bridge in the vertical direction of the main girder.Temperature variation and non-uniform distribution inside the bridge may result in thermal expansion and contraction in the structure, which leads to structural displacement or deformation.When this displacement or deformation is constrained, large secondary internal force and secondary thermal stresses will be generated in the structure, and under some unfavorable conditions, the secondary thermal stress developed in some parts of the structure may be greater than the stress produced by vehicles or other live loads.If such temperature loads are ignored or not properly predicted in the design stage, it may result in bridge damage or even collapse.
To investigate the magnitude and distribution characteristics of the vertical temperature gradient of a closed steel box girder under solar radiation, specifications in four major codes on the vertical temperature gradient of a main girder or steel box girder in China and other countries are compared.The comparison reveals that only Eurocode 1 specifies the vertical temperature gradient pattern of a steel box girder with a steel bridge deck.Then, temperature measurement is carried out inside the steel box girder of the Sanchaji Bridge across the Xiangjiang River in Changsha with two temperature measuring sections set up on the same diaphragm in the transverse direction of the bridge.Under strong solar radiation and high ambient temperature in summer, the temperature at the measurement points on different sections was measured several times to obtain the temperature of the top surface of the deck overlay, the deck, interior air, and bottom plate of the steel box, as well as the ambient temperature in 24 h.The change laws of vertical temperature with time at different measurement points on the diaphragm are analyzed.
It was found that under the effect of hot weather and strong solar radiation, the temperature variations at the top surface of the deck overlay and the deck, interior air, and bottom plate of the steel box girder shared the same trends with air temperature.Under solar radiation, the temperature rose rapidly on the deck overlay and reached its maximum at around 14:00, while the maximum temperature of the deck was recorded at around 16:00.Great temperature differences between the deck and bottom plate occurred from 14:00 to 18:00, with the maximum value of 16.8℃ presented at around 14:30.It was also found that the positive vertical temperature gradient showed nonlinear distribution, and the girder top had a larger positive temperature difference but a significantly smaller negative temperature difference.On the basis of the maximum temperature difference obtained between the deck and the bottom plate, a suggested pattern of vertical temperature gradient was fitted using a four-broken-line, where the five reference points are 0, 100 mm, 300 mm, 650 mm, and the girder depth h away from the deck, with their corresponding temperature gradient values of ΔT1=17℃, ΔT2=13℃, ΔT3=8℃, ΔT4=4.5℃, and 0℃, respectively.Studies showed that the four-broken-line mode specified in the Eurocode 1 is applicable to the vertical temperature gradient of steel box girders of this steel bridge.
Steel bridges are built in a complex natural environment, and thus their temperature varies with solar radiation and air temperature.Such temperature variation includes not only a uniform temperature rise or temperature fall but also non-uniform distribution in the transverse direction of a bridge in the vertical direction of the main girder.Temperature variation and non-uniform distribution inside the bridge may result in thermal expansion and contraction in the structure, which leads to structural displacement or deformation.When this displacement or deformation is constrained, large secondary internal force and secondary thermal stresses will be generated in the structure, and under some unfavorable conditions, the secondary thermal stress developed in some parts of the structure may be greater than the stress produced by vehicles or other live loads.If such temperature loads are ignored or not properly predicted in the design stage, it may result in bridge damage or even collapse.
To investigate the magnitude and distribution characteristics of the vertical temperature gradient of a closed steel box girder under solar radiation, specifications in four major codes on the vertical temperature gradient of a main girder or steel box girder in China and other countries are compared.The comparison reveals that only Eurocode 1 specifies the vertical temperature gradient pattern of a steel box girder with a steel bridge deck.Then, temperature measurement is carried out inside the steel box girder of the Sanchaji Bridge across the Xiangjiang River in Changsha with two temperature measuring sections set up on the same diaphragm in the transverse direction of the bridge.Under strong solar radiation and high ambient temperature in summer, the temperature at the measurement points on different sections was measured several times to obtain the temperature of the top surface of the deck overlay, the deck, interior air, and bottom plate of the steel box, as well as the ambient temperature in 24 h.The change laws of vertical temperature with time at different measurement points on the diaphragm are analyzed.
It was found that under the effect of hot weather and strong solar radiation, the temperature variations at the top surface of the deck overlay and the deck, interior air, and bottom plate of the steel box girder shared the same trends with air temperature.Under solar radiation, the temperature rose rapidly on the deck overlay and reached its maximum at around 14:00, while the maximum temperature of the deck was recorded at around 16:00.Great temperature differences between the deck and bottom plate occurred from 14:00 to 18:00, with the maximum value of 16.8℃ presented at around 14:30.It was also found that the positive vertical temperature gradient showed nonlinear distribution, and the girder top had a larger positive temperature difference but a significantly smaller negative temperature difference.On the basis of the maximum temperature difference obtained between the deck and the bottom plate, a suggested pattern of vertical temperature gradient was fitted using a four-broken-line, where the five reference points are 0, 100 mm, 300 mm, 650 mm, and the girder depth h away from the deck, with their corresponding temperature gradient values of ΔT1=17℃, ΔT2=13℃, ΔT3=8℃, ΔT4=4.5℃, and 0℃, respectively.Studies showed that the four-broken-line mode specified in the Eurocode 1 is applicable to the vertical temperature gradient of steel box girders of this steel bridge.
