Experimental study on composite mechanical properties of a double-deck prestressed concrete box girder

Abstract

A series of tests were carried out on a scaled (1:8) double-deck prestressed concrete box girder in this study, aiming to study the structural response and failure mechanism of the box girder under prestressed axial compression, transverse bending, and torsion. The test results, such as the twist angle, crack development, and distortion of the box girder, were analyzed in detail. The results show that (1) the box girder eventually suffered lateral bending damage, and the cross-section of the support distorted severely; (2) torsional cracking occurred in the pure torsion region at the mid-span, but the longitudinal and transverse rebars did not yield, indicating that the pure torsion section of the box girder was still in the early stage of torsion failure; and (3) after the cracking of the box girder, stress redistribution phenomenon occurred, resulting in obvious nonlinear strain variations. Comparison of the longitudinal and transverse steel strains showed that transverse steel withstood the most shear stress during the early stage of torsion.

Keywords

box girder concrete distortion double-deck failure mechanism torsion

Introduction

With the rapid economic development in recent years, urban construction has also developed rapidly. In developed and even developing countries, the availability of land is becoming more and more limited. In order to meet the traffic demand and utilize urban lands more effectively, large-span prestressed concrete (PC) box-girder bridges have increasingly become a viable option, as they have a good combined capability of bending, shearing, and torsion (Guo et al., 2010; Zhu et al., 2015). To accommodate public utilities (e.g. pipelines), combined with the concept of double-deck traffic and the advantages of PC box sections, a single girder unit with the three-cell cross section is proposed in this study. Compared with the traditional box girder, this new section eliminates cross diaphragms and uses transverse stiffeners to enhance the lateral stiffness. The overall stiffness is ensured to meet the mechanical performance requirements, while the necessary headroom within the box is maintained. Till date, studies on the overall damage of such systems subjected to complex loading and working conditions are limited. As a result, the relatively new girder system has experienced various degrees of damage. This warrants an investigation of its mechanical properties and failure modes in order to better understand the system and possibly extend its practical applications.

In recent years, with the development of prestressing technology, various large-span PC box bridges have been extensively constructed, which are especially adaptable to on-site construction conditions. Due to the wide applications of the box girder in bridges, the analysis of its mechanical properties has attracted widespread attention from many researchers and engineers. Fang et al. (2000) conducted an experimental study on the distribution of shear lags and performed the finite element (FE) analysis on a reinforced concrete (RC) single-cell continuous beam model with a scale of 1:6. Xu et al. (2000) proposed a calculation method for the torsional resistance of a concrete box girder under composite stress conditions. Sheng and Xin (2005) studied the relevant characteristics of a model PC diagonal box girder of scale 1:8 considering the entire loading process and analyzed the girder nonlinearly using the FE method. Cao and Fang (2006) tested a continuous RC box-girder model with uniform loads, and studied the deflection and crack resistance at various girder sections, and the effective distribution width of flanges. Galal and Yang (2009) conducted stress tests on a thin-walled RC box girder under eccentric loading. Yuan et al. (2017) designed and conducted fatigue tests on a PC box girder and studied the shear crack propagation process of the girder under cyclic loading. Vu et al. (2018) studied the bearing capacity of a steel–concrete composite box girder and developed a three-dimensional (3D) FE model for the girder using the ABAQUS software. They also investigated the effect of intermediate diaphragms on the bearing capacity of the girder spanning 30–60 m analytically. Ding et al. (2012) established a 3D FE model of a PC box girder with corrugated steel webs and studied its behavior under pure torsion. Through a parametric study, their results show that the ultimate torsional resistance of the test model is linearly proportional to shear modulus, the thickness of corrugated steel web, and the compressive strength of concrete. Zhou et al. (2016) proposed a theoretical model based on assimilating orthotropic plates and performed a 3D FE analysis, focusing on the differences of the mechanical properties of corrugated steel webs in different directions. He et al. (2012) conducted a model test on a three-span continuous PC box girder with a tilt angle of 45°. Displacements, stress, natural frequency, mode shape, and damping ratio, were obtained. Kristek et al. (1990) proposed a shear lag analysis for composite steel box girders with various cross sections. Li et al. (2018) analyzed the distortional effect of a non-prismatic composite box girder with corrugated steel web under the action of eccentric loads in the elastic stage and derived the deformation-control differential equations for the girder. Mo et al. (2003) conducted a series of tests on four PC box-girder bridges with corrugated steel webs. They found that the thickness of end diaphragms and the position of prestressing strands at both ends of the test model had little influence on the force–deflection relationship. Ding et al. (2018) and Huang et al. (2018) studied the seismic performance of simply supported composite I-beams and box girders through quasi-static experiments. Ryu et al. (2004) conducted static tests on a PC continuous composite box-girder bridge, and proposed a simple method for calculating the ultimate bending capacity of the continuous bridge. Akl et al. (2017) studied the deflection of a PC box-girder bridge using the post-tensioning method under the actual construction process. Park et al. (2016) studied the influence of high-strength prestressing strand on the compressive and tensile strengths of PC box girders. Wu et al. (2013) proposed a new type of steel–concrete composite beams for railway bridges, and the bending capacity, stiffness, stress distribution, and crack pattern were studied through static tests. Wen (2011) analyzed the long-term effect of PC box-girder bridges and proposed a correction method based on the energy principle of incremental method for shrinkage and creep. According to this method, a calculation program was compiled and verified by the test results. Chung and Kim (2011) conducted dynamic tests on a 20 m-long full-size spliced PC beam. Zhang and Li (2018) proposed an improved truss simulation method for estimating the shear lag effect of RC walls with any lateral load distribution. Tong et al. (2016) studied the long-term deflection and deflection damage growth of long-span bridges. They considered the viscoelastic behavior of concrete and the coupling effect of tensile cracking and plastic softening of concrete and developed a uniform constitutive model for estimating the performance of bridges. Xu et al. (2011) attached additional concrete to the bottom flange of the continuous composite steel girder to increase the local buckling strength, and concluded that the use of composite materials would slow the development of concrete cracks. In view of the limited research on the mechanical properties of PC box girders with double-deck traffic, technical guide or specification is still lacking. This new complex girder system possesses a practical significance, and deserves further study.

The proposed concrete box girder for double-deck traffic uses the modern PC technology to improve the structural system of conventional concrete box girders, to ensure the necessary clearance height inside the box allowing the traffic, and to accommodate the upper and lower decks of traffic. At present, there are few related tests done for such girder systems and studies of its composite mechanical properties are limited. This article focuses on the performance and failure of this new type of box girder under bending and torsion.

Experimental studies

Test overview

According to the current design codes in China (Ministry of Transport of the People’s Republic of China, 2015, 2018), the trapezoidal section of box girder with wider top flange has been commonly used in bridge structures. A plan view of the model box girder (scale 1:8) is shown in Figure 1. Two types of cross sections were considered: open 3-bay box section (Figure 2(a)) and closed 3-cell box section (Figure 2(b)), whose reinforcement arrangements are shown in Figure 2(c) and (d), respectively.

Figure 1.

Plan of the model box girder (scale 1:8; unit: mm).

Figure 2.

Cross-sectional dimensions and reinforcement of the girder (unit: mm). (a) Dimensions of open 3-bay box section. (b) Dimensions of closed 3-cell box section. (c) Reinforcement of open 3-bay box section. (d) Reinforcement of closed 3-cell box section reinforcement.

The rebars with a diameter of 20.0 and 6.5 mm were adopted for the longitudinal and transverse reinforcements, respectively, as shown in Figure 2. The yield strengths of longitudinal and transverse reinforcements were 439.3 and 414.5 MPa, respectively. The cubic compressive strength of concrete was 46.24 MPa for the top slab and web, and 48.92 MPa for the bottom slab. The elastic modulus of all the concrete was determined to be about 3.25 × 10⁴ MPa.

Test program

The test program is summarized as follows:

Record the actual loading values used in the test for all load levels, calculate the bending moments of the box girder under external forces, and compute the applied torques by measuring the positions of load points and load magnitudes for all load levels. The bearing stiffener of the box girder is considered equivalent to a statically indeterminate structural model. The bending moment distribution for the stiffener can be determined using the basic principle of structural mechanics, from which the maximum bending moment of the stiffener can then be obtained. The torque T is simply calculated as

T = F \cdot L

(1)

where F is the end reaction of the load distribution beam and L is the distance between the center of force F and the center of girder bearing taken as 1.13 m, as shown in Figure 3.

Measure the magnitudes and variations of steel and concrete strains at the key measuring points on the control sections under composite forces. Measure the deflections and torsional conditions at each control section and at both the end bearings. The deflections and strains (concrete and steel) were measured using DH3821 dynamic data measurement system and the twist angle of each section was read from a digital inclinometer.

Measure the distortions at the end and mid-span girder sections for each load level during the test using with the dial gauges and the layout of deformation measurement.

Observe the appearance of cracks and the development of cracks on girder’s components under various loads and further record the crack width and the corresponding loads during the test.

Measure the stress changes in the eight prestressing tendons under various loads and ensure the stress does not exceed the capacity of the tendons during the test, so that accidents related to the fracture of prestressing tendons are prevented. Finally, record the settlement and deflection of the rubber bearings at both the ends under each level of loads.

Figure 3.

Illustration of test device and bearing arrangement. (a) Side view of the loading device. (b) Support layout.

Test device and measurement scheme

The test device consists of a loading beam, 300 t pressure sensor, rigid cushion, 250 t hydraulic jack, load distribution beam, rubber bearings, and rigid pad, as shown in Figure 3. The loading point is at the junction between the bearing stiffener and the exterior girder web. Four rectangular rubber bearings were installed at each loading point on the load distribution beam to form a flexible bearing to prevent the loading device from excessive deformation due to the tilting of the box girder. The hydraulic jack and sensor were placed at the mid-span of the load distribution beam, thus distributing the load evenly to both the beam ends (load points). At the same time, the load was applied at both the end bearings of the box girder to maintain a balanced and stable loading for the girder.

In order to capture the force evolutions of the components in the test model during the test, resistive strain gauges were used in the test. For illustrative purposes, Figures 4 and 5 show the strain gauge layouts for reinforcements at Section 3-3 (mid-span) and that around web openings. Figure 6 shows the strain gauge layout for concrete at Section 3-3.

Figure 4.

Stain gauge layout for reinforcements at Section 3-3.

Figure 5.

Stain gauge layout for reinforcements around web openings.

Figure 6.

Stain gauge layout for concrete at Section 3-3.

Loading procedure

The concentrated force was applied at the junction between the stiffener and the exterior web and two loading points were set symmetrically through a secondary distribution beam, as shown in Figure 7. The self-weight of the loading device was predetermined at 24 kN, with 12 kN distributed to each loading point. Prior to the test, preloading test was carried out for each component to ensure its normal working condition and stability. There were 15 levels of loading with the load increment of 10 kN for each load point, and the total applied load was 184 kN at each load point.

Figure 7.

Schematic diagram of loading device. (a) Top view of the loading device. (b) Side view of the loading device.

Test results and analysis

Damage pattern and sectional torsion angle

Three representative girder sections were studied experimentally: Sections 1-1, 2-2, and 3-3 (see Figure 1). Specifically, the torsion angles of these sections were measured along with those at the bearings. The relationships between the torque (T) and torsion angle (δ) are shown in Figure 8. As shown in Figure 8, when T is less than 150 kN m, the T-δ relationship is almost linear for each section. When T = 81 kN m, the initial linear line turns to another less steep line. It was found that cracks appeared at the bottom of bearing stiffeners (BBS) and approached the bearing rubber pads at that moment, which affected the torsional performance of the box-girder section slightly. When T = 149 kN m, oblique cracks appeared at the top of bearing stiffeners (TBS); and oblique cracks that are approximately 45° from longitudinal direction of the girder began to appear on the webs and both the top and bottom of the box girder. Actually, it is found that the theoretical cracking torque is very close to 149 kN m when a single cell of the box girder is assumed to be twisted. When T = 150–210 kN m, the T-δ relationship for each section becomes nonlinear, indicating the failure stage of the box girder. When T = 208 kN m, the bending moment M = 73.63 kN m at the BBS, crack width increased there, and concrete spalled off the rebars. At the last loading level, the concrete at the top of the box girder was still not crushed and the box girder showed good overall ductility. There was no apparent torsional failure found during the test. Local bending failure was observed at the BBS. The final damage to the tested PC box girder is shown in Figure 9.

Figure 8.

Relationships between torque and torsion angle for the support sections.

Figure 9.

Final damage of the box girder.

The relationships between the torque (T) and the line torsional angle relative to Section 3-3, that is, relative line angle δ′, are shown in Figure 10. As shown in Figure 10, when T is less than 81.36 kN m, the T-δ′ relationships are almost the same for Sections 0-0, 1-1, and 2-2 relative to Section 3-3, indicating that these sections have virtually the same torsional stiffness (about 5×10⁻⁴ rad/m). When T is larger than 81.36 kN m, the torsional stiffness for Section 0-0 decreases, which is due to the flexural cracks at the BBS. When T is larger than 149.16 kN m, the T-δ′ relationship becomes nonlinear for all the three sections, which is due to the appearance of torsional cracks, reducing the torsional stiffness of each section and causing the torsion bars of the box girder to enter the yielding stage.

Figure 10.

Relationships between torque and relative line angle.

Distortion of box girder

Under torsion, the cross section of the box girder will also experience distortional deformation in addition to the sectional twisting, which is represented by the distortion angle Δθ, as shown in Figure 11. In this study, it was assumed that the edges of the box-girder section were not compressed nor stretched during the loading process, that is, the length of each edge remains unchanged. Using a dial indicator to measure the change in the diagonal length of the box cell (Δl) and according to the Cosine theorem, Δθ can be obtained as (Figure 11)

Δ θ = \cos^{- 1} (\frac{{(l + Δ l)}^{2} - a^{2} - b^{2}}{2 ab}) - θ

(2)

Figure 11.

Schematic diagram showing the loaded and unloaded box-girder cells.

The T-Δθ relationships for the bearing and mid-span sections are shown in Figure 12. As shown in the figure, the distortion angle at the loaded cell was larger than that at the unloaded cell for the support sections. The effect of the Δθ of the unloaded cell on the overall torsional performance of the section was negligible. While the effect of Δθ of the loaded cell affected the torsional performance at the bearings, the Δθ caused primarily due to the transverse bending at the BBS reduced the torsional stiffness of the section. The Δθ value at the mid-span section was generally small and its effect could be neglected.

Figure 12.

T-Δθ curves of box-girder cells at the bearing and mid-span sections. (a) Distortions of unloaded and loaded cells at the support sections. (b) Distortions of left and cells at the mid-span section.

Crack development

The crack development of the box girder during loading is shown in Figure 13. The first vertical microcrack appeared at the BBS when F = 72 kN (Figure 13(a) and (b)). With the increasing load, the vertical cracks started to extend obliquely toward the openings (Figure 13(c) and (d)).

Figure 13.

Crack pattern of the box girder. (a) West side. (b) East side. (c) South side. (d) North side. (e) Top view. (f) Bottom view.

When F = 132 kN, 45^° diagonal cracks with width of 0.025 mm appeared on the web and at the top and bottom of the box girder at the mid-span, and began to extend to the girder edge, and oblique cracks at the TBS were observed. When F = 184 kN (final), the concrete spalled off at the BBS and the cracks penetrated to the bearing pads showing visible through-cracks.

Based on the deformation and cracking characteristics of the girder, the entire test process went through three stages. The first stage was from the start of loading to the cracking at the BBS and the overall mechanical properties of the test components were still within the elastic range in this stage. The second stage was between the cracking at the BBS and the occurrence of 45^° diagonal cracks in the vicinity of girder mid-span. In this stage, the bottom of bearing stiffeners experienced plastic deformation and the stressed rebars started yielding, while the vicinity of girder mid-span was still in the elastic torsion stage. The third stage was caused by the occurrence from the appearance of 45^°diagonal cracks in the vicinity of girder mid-span to the failure at the BBS. In this stage, the bearing stiffeners experienced local bending failure, causing the loss of load and reducing the overall girder stiffness, while the mid-span area did not experience a torsional failure. Clearly, bearing stiffeners contribute more to the girder stiffness and hence strengthening measures for them should be taken in future practical applications, if necessary.

Variation of strains

1. Concrete strain

Both compressive and tensile strains were measured in this experiment. When F = 132 kN (T = 149.16 kN m), the mid-span of the test girder experienced torsional cracking, resulting in stress redistribution. The specific variations of concrete strains are shown in Figure 14. As seen from Figure 14, when T is less than 140 kN m, there is an almost linear relationship between T and the principal strain, indicating that the components of the test model were still in the elastic torsion range. When F = 144 kN (T = 162.72 kN m), the strain at each position increased significantly and entered the nonlinear stage. This is due to the stress redistribution caused by torsional cracking of the girder occurring prior to the applied load. Moreover, some concrete strain gauges broke after the concrete cracking. When F = 174 kN (T = 196.62 kN m), the strain increment became more apparent. In comparison, the principal compressive stress was greater in the girder web than at the girder top or bottom slab, but this trend was reversed for the principal tensile stress. The main reason is that the top and bottom slabs are thinner than the web, thus weaker in torsional resistance at the mid-span. It is suggested to thicken the top and bottom slabs of the box girder in practice to enhance its overall stiffness.

Figure 14.

Variations of concrete strains at different positions at the mid-span. (a) Principal compressive strain of concrete. (b) Principal tensile strain of concrete.

Figure 15 shows the variations of concrete principal strain angles (θ_cp) with respect to girder’s longitudinal direction at the mid-span. As shown in the figure, prior to concrete cracking, θ_cp is approximately 45^°. When concrete cracked, some concrete strains fractured and the variation of θ_cp became irregular.

Figure 15.

Variations of concrete principal strain angles at the mid-span.

In the early loading stage, T and θ_cp were virtually in linear relationship and the components of the test box girder did not exhibit torsional cracks, implying that the components were still in the elastic torsion stage. In the later loading stage, the strain values increased significantly and rapidly, its variation turned irregular, and the T-θ_cp relationship was nonlinear.

2. Rebar strain

The strains of both longitudinal rebars (ε_sl) and transverse rebars (ε_st) were measured, as shown in Figure 16. It was found that the maximum (absolute value) compressive and tensile strain of longitudinal rebars were 130 and 777 με, respectively (Figure 16(a)), and the maximum (absolute value) compressive and tensile strain of transverse rebars were 1095 and 902 με, respectively (Figure 16(b)). All these strains were less than the yield strain of 1974 με.

Figure 16.

Strains of longitudinal and transverse rebar. (a) Strains of longitudinal rebar εsl. (b) Strains of transverse rebar εst.

In comparison, ε_st developed earlier and more dramatically than ε_sl under the same load. This indicates that in the early torsion stage the transverse steel withstood most of the torsion-induced stress.

The strains of rebar at the openings and stiffeners are shown in Figure 17. As shown, these strains varied with rebar positions and were smaller than the ε_sl and ε_st values of the girder components. Prior to the concrete cracking, the steel strain was small and the concrete and steel worked together. After the concrete cracking, the strain of the strengthening steel around the openings changed more rapidly, with the top and bottom steel mainly in tension and the left and right steel in compression. The development of the steel strains at the stiffeners was slower and followed a straight line basically. This is because the stiffening steel plays a role in enhancing the overall lateral stiffness for the girder as it is larger and stronger than the steel at the top and bottom of the girder and the concrete there is thicker. Therefore, the stiffeners remained in the elastic stage prior to the failure of the top or bottom slab.

Figure 17.

Strains of rebar at the openings and stiffeners. (a) Strains of rebar at the openings. (b) Strains of rebar at the stiffeners.

Conclusion

Based on the experimental study, the following conclusions could be drawn:

The torsional rigidity of the box girder was virtually the same for each section within the elastic range. When the torsion bars yielded and obvious torsional cracks appeared, the torsional stiffness for each section started to decrease. To minimize the cracks, it is recommended that the top and bottom of the box girder and the stiffeners should be thickened to increase the torsional stiffness of the girder.

Based on the test, the failure characteristics of the box girder can be divided into three stages. The first stage is the elastic torsion resistance stage, which slightly affects the girder’s torsional performance. The second stage is the yielding of some components in which the bottom of concrete bearing stiffeners undergoes plastic deformation and the tension rebar begins to yield, while the mid-span section remains in the elastic stage. The third stage begins when the box girder experiences local failure and the test shows the unfound results. Therefore, it is suggested to further improve the loading system, the layout of bearings, and the strengthening measures for local failure locations.

The failure characteristics of the box girder observed from this experiment differ from the conventional torsion failure mode. For example, the bottom of bearing stiffeners experienced local bending failure and was cut off during the loading process, while the mid-span section did not enter the stage of torsion failure. This suggests that bearing stiffener designs should be further improved to enhance the lateral stiffness of the box girder in the future.

Stress redistribution occurs after cracking, resulting in obvious nonlinear strain distribution. Comparing the steel strains of the tested box girder, the transverse steel develops strain earlier and more significantly than the longitudinal one under the same load level. This means that the transverse steel withstands most of the shear stress during the early torsional stage of the girder.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors are grateful for the financial support provided by the National Natural Science Foundation of China (Grant Nos 51378202, 51578236, and 51608191).

ORCID iD

Zefeng Yan

References

Akl

Saiid Saiidi

Vosooghi

(2017) Deflection of in-span hinges in prestressed concrete box girder bridges during construction. Engineering Structures 131: 293–310.

Cao

Fang

(2006) Mechanical behaviors test of RC continuous box girder with wide flange. China Journal of Highway and Transport 19(5): 46–52.

Chung

Kim

(2011) Comparison of dynamic properties of spliced and monolithic prestressed concrete box railway girders. Engineering Structures 33(5): 1773–1780.

Ding

Liu

, et al. (2018) Experimental investigation on hysteretic behavior of simply supported steel-concrete composite beam. Journal of Constructional Steel Research 144: 153–165.

Ding

Jiang

Liu

(2012) Nonlinear analysis for PC box-girder with corrugated steel webs under pure torsion. Thin-Walled Structures 51: 167–173.

Fang

Cao

Wang

(2000) Experimental study on shear lag effect of rc continuous box girder. Bridge Construction 2000(4): 1–3.

Galal

Yang

(2009) Experimental and analytical behavior of haunched thin-walled RC girders and box girders. Thin-Walled Structures 47(2): 202–218.

Guo

Yao

, et al. (2010) Experiment on reinforced concrete box-girder strengthened by steel stranded wire mesh and polymer mortar. China Journal of Highway and Transport 23(02): 36–42.

Sheng

Scanlon

, et al. (2012) Skewed concrete box girder bridge static and dynamic testing and analysis. Engineering Structures 39: 38–49.

10.

Huang

Jiang

Chen

, et al. (2018) Experimental study on the seismic performance of concrete filled steel tubular laced columns. Steel and Composite Structures 26(6): 719–731.

11.

Kristek

Evans

Ahmad

MKM

(1990) A shear lag analysis for composite box girders. Journal of Constructional Steel Research 16(1): 1–21.

12.

Zhou

Wang

(2018) Distortion analysis of non-prismatic composite box girders with corrugated steel webs. Journal of Constructional Steel Research 147: 74–86.

13.

Ministry of Transport of the People’s Republic of China (2015) General Specifications for Design of Highway Bridges and Culverts (JTG D60–2015). Beijing, China: China Communications Press.

14.

Ministry of Transport of the People’s Republic of China (2018) Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts (JTG3362–2018). Beijing, China: China Communications Press.

15.

Jeng

Krawinkler

(2003) Experimental and analytical studies of innovative prestressed concrete box-girder bridges. Materials and Structures 36(2): 99–107.

16.

Park

Jeong

Lee

, et al. (2016) Flexural behavior of post-tensioned prestressed concrete girders with high-strength strands. Engineering Structures 112: 90–99.

17.

Ryu

Shim

Chang

, et al. (2004) Inelastic behaviour of externally prestressed continuous composite box-girder bridge with prefabricated slabs. Journal of Constructional Steel Research 60(7): 989–1005.

18.

Sheng

Xin

(2005) Nonlinear analysis of the prestressed concrete skew box continuous girder. China Railway Science 26(2): 67–71.

19.

Tong

Liu

Zhang

, et al. (2016) Long-term performance of prestressed concrete bridges under the intertwined effects of concrete damage, static creep and traffic-induced cyclic creep. Engineering Structures 127: 510–524.

20.

Thai

Kim

(2018) Effect of intermediate diaphragms on the load – Carrying capacity of steel – concrete composite box girder bridges. Thin-Walled Structures 122: 230–241.

21.

Wen

(2011) Long-term effect analysis of prestressed concrete box-girder bridge widening. Construction and Building Materials 25(4): 1580–1586.

22.

Nie

, et al. (2013) A new type of steel–concrete composite channel girder and its preliminary experimental study. Journal of Constructional Steel Research 85: 163–177.

23.

, et al. (2011) Experimental study on double composite action in the negative flexural region of two-span continuous composite box girder. Journal of Constructional Steel Research 67(10): 1636–1648.

24.

Liu

(2000) Calculating method and experimental study of torsion strength of concrete box beams under combing loading. China Journal of Highway and Transport 13(3): 38–42.

25.

Yuan

Yan

Zhong

, et al. (2017) Experimental investigation of high-cycle fatigue behavior for prestressed concrete box-girders. Construction and Building Materials 157: 424–437.

26.

Zhang

(2018) Effects of the shear lag on longitudinal strain and flexural stiffness of flanged RC structural walls. Engineering Structures 156: 130–144.

27.

Zhou

Liu

Zhang

, et al. (2016) Equivalent computational models and deflection calculation methods of box girders with corrugated steel webs. Engineering Structures 127: 615–634.

28.

Zhu

Wang

(2015) A landscape bridge as the example introduction to the application of double traffic. Natural Science Journal of Xiangtan University 37(4): 24–28.