Flexural Behavior of a 30-Meter Full-Scale Simply Supported Prestressed Concrete Box Girder

: Compared with scaled-model testing, full-scale destructive testing is more reliable since the test has no size e ﬀ ect and can truly record the mechanical performance of the structure. However, due to the high cost, only very few full-scale destructive tests have been conducted on the ﬂexural behavior of prestressed concrete (PC) box girders with girders removed from decommissioned bridges. Moreover, related destructive testing on the ﬂexural behavior of a new precast box girder has been rarely reported. To investigate the ﬂexural behavior and optimize the design, destructive testing of a 30-meter full-scale simply supported prestressed box girder was conducted at the construction site. It is illustrated that the failure mode of the tested girder was fracture of the prestressing tendon, and the corresponding maximum compressive strain in the top ﬂange was only 1456 µε , which is far less than the ultimate compressive strain (3300 µε ). Therefore, the concrete in the top ﬂange was not fully utilized. A nonlinear analysis procedure was performed using the ﬁnite strip method (FSM). The validity of the analysis was demonstrated by comparing the analytical results with those of the full-scale test in the ﬁeld and a scaled model test in a laboratory. Using the developed numerical method, parametric analyses of the ratio of reinforcement were carried out. The prestressing tendon of the tested girder was increased from four strands to six strands in each duct. After the optimization of the prestressed reinforcement, the girder was ductile and the bearing capacity could be increased by 44.3%.


Introduction
Many civil infrastructures are operated under adverse service conditions [1], such as corrosion [2][3][4], vibration [5,6], overload [7,8], and impact [9], which may cause structural damages at different levels, including loosened connections [10], cracks [11,12], reduced bending stiffness [13,14], and decreased or even lost load carrying capacity [15,16]. Structural damages have received much attention in recent years from different directions [17,18]. On one hand, structural health monitoring (SHM) [19][20][21] and damage detection technologies [22,23] have been developed to report structural health status and damage situations by using various integrated sensors [24][25][26] and advanced algorithms with the goal of issuing early warnings in the presence of structural damage. On the other hand, destructive tests are conducted on various structures to better understand the structural behavior under failure [27,28]. However, civil infrastructures often involve large-sized structural components, making destructive tests of such large components difficult. A good example is the prestressed concrete (PC) box girder, which has the advantage of long span capacity at relatively low cost. A large number of studies have been conducted on the mechanical behavior and failure mode of PC box girders using small-scale models [29,30]. It is known that full-scale experiments, without the influence of size effects, are more intuitive and reliable. However, due to them consuming a lot of human, financial, and material resources, only very few studies have been carried out with full-scale model tests on the flexural behavior of PC box girders from decommissioned bridges around the world.
McClure, R.M. and West, H.H. conducted a full-scale experiment on a segmental PC box girder bridge with a length of 36.88 meters (m) [31]. They found that the structure was 15% more stiff than theoretical predictions suggested. The failure mode was that a wide crack occurred at a segmental joint and the strand was broken in the tensile zone, while the concrete was crushed in the compression area. Shenoy and Frantz carried out a destruction experiment on two PC box girders removed from a 27-year-old bridge with a span length of 16.5 m [32]. It was illustrated that the PC girders were ductile and behaved as predicted. The load-deflection curve performance was as anticipated, while the flexural strength was more than that required. Miller, R. and Parekh K. carried out a destructive experiment on a deteriorated PC girder with a length of 21.32 m [33,34]. The tested PC girder failed suddenly just after the yielding of the prestressing strand. The cracking moment could be predicted using the American Association of State Highway and Transportation Officials (AASHTO) Standard, while the specification was not suitable for the ultimate moment. Labia, Y. et al. tested two PC box girders with a length of 21.34 m [35]. Due to a low amount of prestress, both PC girders experienced an unexpected brittle failure. Chung, W. and Kang, D tested the static and dynamic behavior of a 20 m PC box girder subjected to four-point bending load until failure with an fibre Bragg grating (FBG) sensing system [36]. It was observed that at the failure stage, the bending moment of the girder was lost abruptly after the prestressing tendon yielded. Huffman, J.M. conducted destructive testing of a three-span PC box girder bridge to determine the mechanical behavior of the bridge under varying magnitudes of damage [37]. The bridge behaved well as a system, and the shear keys and transverse tie rods were able to transfer load to adjacent beams. Su, J.Z. et al. tested a 30 m span prestressed ultra-high-performance concrete (UHPC) box girder until failure with four-point bending [38]. Based on the test and parametric analyses, a verified strain-stress diagram for cross-sectional analysis and a simplified calculation formula for the prestressed UHPC box girder were proposed. These studies reviewed above were conducted to research the flexural behavior, such as material properties, failure mode, and ultimate capacity, of PC box girders from decommissioned bridges [39][40][41]. However, investigation of the flexural behavior of a new precast box girder at a construction site has been rarely reported [42,43]. Therefore, the flexural behavior of a 30 m full-scale simply supported PC box girder is studied in the present work.
The nonlinear behavior in the ultimate limit state of a destructive full-scale model provides a valuable reference for the designing of new bridges [44]. At present, commercial finite element software [45,46] and some professional procedures [47] are used to conduct analysis of concrete structures. However, it is still difficult to calculate the descending section of the load-deflection curve. To achieve this goal, a nonlinear numerical model is developed using the finite strip method (FSM) in this paper. FSM was originally introduced by Cheung [48,49] and has been proven to be efficient and widely used in the analysis of structural members [50][51][52]. This article presents some tentative work to apply FSM to full-scale PC box girders. Based on FSM, the load-deflection curve of the structure can be obtained based on the bending-curvature relationship, so that the bearing capacity of the section can be checked directly. Parametric analyses are conducted with the proposed numerical model, and the design is optimized.
The rest of this paper is organized as follows. Section 2 introduces the engineering background and materials. Section 3 describes and discusses the flexural behavior of the 30 m full-scale simply supported PC box girder. Section 4 illustrates the nonlinear numerical model and presents parametric analyses of the ratio of reinforcement. Finally, Section 5 concludes the article and gives some recommendations for future work.

Details of the Engineering Background
The 30 m box girder was randomly selected from the prefabrication plant and was prepared for the North Approach Bridge of the Jingyue Yangtze River Bridge, located in Hubei province, China. The North Approach Bridge has four links which each consist of four continuous spans of 30 m precast PC box girders. The elevation and cross section of the mid-span of the bridge are shown in Figure 1a,b, respectively.

106
The assembly method was applied to the North Approach Bridge. The 30 m box girders were The assembly method was applied to the North Approach Bridge. The 30 m box girders were prefabricated at the plant and assembled using a bridge erecting machine. Firstly, the girders were simply supported with temporary supports on the pier; then, the longitudinal wet joints were poured, and the prestressing tendons in the negative moment zone were stretched; finally, the continuous girder structure was formed after the temporary supports were replaced.

Details of the Tested Girder
The elevation and cross section of the tested box girder are illustrated in Figure 2

126
The mix proportions of C50 concrete are shown in Table 1. The mechanical behavior of the concrete and 127 steel material was measured and is illustrated in Tables 2 and 3, respectively.

Material Properties
A 30 m box girder is a bonded, post-tensioned PC structure. The materials applied in the prefabricated girder include C50 concrete, Ø10 mm HPB235 (hot rolled plain bar, yield tensile strength = 235 MPa) and Ø16 mm HRB335 (hot rolled ribbed bar, yield tensile strength = 335 MPa) reinforcement, and seven-wire prestressing strands (nominal diameter is 15.24 mm). There are 32 high-strength, low-relaxation prestressing tendons, divided into eight bunches with four strands each. The standard tensile strength and controlled prestressing stress are 1860 MPa and 1395 MPa, respectively. The mix proportions of C50 concrete are shown in Table 1. The mechanical behavior of the concrete and steel material was measured and is illustrated in Tables 2 and 3, respectively.

Loading Instrumentation and Procedure
After 90 days of curing, the box girder was transported to the precast concrete pedestals and simply supported at both ends. Then, the reaction frame was built and connected to the pile foundation of the bridge. All the preparations were completed within 5 days; then the full-scale testing was conducted. The concrete samples were tested on the same day.
As illustrated in Figure 3, the load was applied at the mid-span section of the girder using a jack. A steel distributive girder divided the concentrated load into two equal halves, which were respectively applied on the top flange located above the web-top flange junction. The load was measured by load cells.

137
As illustrated in Figure 3, the load was applied at the mid-span section of the girder using a jack.

138
A steel distributive girder divided the concentrated load into two equal halves, which were respectively 139 applied on the top flange located above the web-top flange junction. The load was measured by load

Loading Procedure
We note that the tested PC box girder was just simply supported at both ends, while the North Approach Bridge has four links which consist of four continuous spans of box girders each. In this test, the bending moments in the continuous PC girder were calculated and were equivalent to the moments at the mid-span of the tested girder. Therefore, the corresponding applied load was obtained. Based on this principle, the applied loads corresponding to the design serviceability limit state (long term), serviceability limit state (short term), and design ultimate bending capacity were 133 kN, 186 kN, and 380 kN, respectively.
A concentrated load was applied repeatedly by the loading device. As shown in Table 4, the load was applied in multiple steps until the tested girder failed. After each load step was completed, the loading process was stopped for 10 minutes to record the load, strain, displacement, and cracking of the girder.

Arrangement of Test Instrumentation
The load, strain of the concrete, displacement, and cracking of the girder were observed after every load step. Two JMZX type load cells were used to measure the load to keep the structure under uniform stress. As illustrated in Figure 4a, resistance strain gauges T1 through T5 for concrete were arranged on the top flange to measure the strain of the compression zone, located at 1/4, 1/2, and 3/4 of the span along the length. Resistance strain gauges W1 through W14 were arranged on the web to measure the strain along the depth of the mid-span section of the girder. DH3816 static strain test system was used for strain data acquisition. As shown in Figure 4b, five JMDL type displacement sensors D1 through D5 were installed at the support point and the quarter points of the girder to observe the deflection. JMCD type crack width meter was used for measuring the crack widths of girder.
Appl. Sci. 2020, 10, x 6 of 20 We note that the tested PC box girder was just simply supported at both ends, while the North

144
Approach Bridge has four links which consist of four continuous spans of box girders each. In this 145 test, the bending moments in the continuous PC girder were calculated and were equivalent to the 146 moments at the mid-span of the tested girder. Therefore, the corresponding applied load was 147 obtained. Based on this principle, the applied loads corresponding to the design serviceability limit 148 state (long term), serviceability limit state (short term), and design ultimate bending capacity were 149 133 kN, 186 kN, and 380 kN, respectively.

150
A concentrated load was applied repeatedly by the loading device. As shown in Table 4, the load 151 was applied in multiple steps until the tested girder failed. After each load step was completed, the 152 loading process was stopped for 10 minutes to record the load, strain, displacement, and cracking of 153 the girder. Loading until the structure is about to fail, then unloading.

156
The load, strain of the concrete, displacement, and cracking of the girder were observed after 157 every load step. Two JMZX type load cells were used to measure the load to keep the structure under

Load-Deflection Curve
The load-deflection curve of the mid-span section is shown in Figure 5. It can be seen from the figure that the envelope line of the load-deflection curve can be approximated as five lines, representing five stages. These are the elastic stage (OA), concrete crack developing stage (AB), reinforced steel tendon yielding stage (BC), prestressing tendon inelastic stage (CD), and failure stage (DE).

188
The strain distribution in the top flange of the box girder at the mid-span is shown in Figure 6b.

189
It can be seen that the strain was nonuniform due to the shear lag effect [53−54]. The web-flange 190 junction was the maximum point, decreasing towards the midpoint and the cantilever flanges. When 191 the load was 1872 kN, the corresponding maximum compressive strain was only 1456 με , which is 192 far less than the ultimate compressive strain (3300 με ) [55].  It is observed that at the failure stage, the load began to decrease from 1872 kN (Point D) to 1858 kN (Point E), while the deflection increased rapidly from 267.85 mm to 294.05 mm. It could be inferred that the box girder structure would fail. Therefore, the test was terminated due to safety considerations. The maximum deflection at the middle span was 294.05 mm, which is 1/102 of the total length of the span. The residual deformation of the middle span was only 22.6 mm before the yielding of the prestressing tendon, while the value increased abruptly to 125.40 mm after the prestressing tendon yielded and broke. Figure 6a shows the measured strain along the depth at the mid-span cross section. It is clear that the average strain distributed along the depth of the girder agreed well with the plane section assumption. Moreover, with the load increase after cracking, the neutral axis moved toward the top of the girder.

Strain
The strain distribution in the top flange of the box girder at the mid-span is shown in Figure 6b. It can be seen that the strain was nonuniform due to the shear lag effect [53,54]. The web-flange junction was the maximum point, decreasing towards the midpoint and the cantilever flanges. When the load was 1872 kN, the corresponding maximum compressive strain was only 1456µε, which is far less than the ultimate compressive strain (3300µε) [55].

196
The crack distribution on the web and the maximum crack widths are shown in Figure 7 and   208

Cracks
The crack distribution on the web and the maximum crack widths are shown in Figure 7 and Table 5, respectively. It can be seen that when the load was 750 kN, the first crack appeared in the web, 9.2 cm in length and 47.0 cm away from the mid-span. As the applied load increased, the original crack continued to develop in the length and width directions; on the other hand, new cracks occurred at the mid-span. From 750 kN to 1100 kN, the crack was almost completely closed after unloading at each stage. As the load increased to 1600 kN, the maximum width of the unclosed crack was 0.04 mm. When the applied load was more than 1700 kN, the width of the original crack and unclosed crack increased rapidly. At the end of the test, the maximum crack was 176.2 cm in length and 6 mm in width, for which the unclosed width was 0.40 mm. All cracks were distributed within 16 m of the mid-span, and the average crack spacing was about 150 mm.     208     The measured cracking load was 750 kN, which is 1.98 times the applied load corresponding to the designed ultimate state of bearing capacity. Moreover, the measured maximum load was 1872 kN, which is 2.50 times the cracking load. It can be seen that the tested girder has a sufficient safety margin.
The failure mode of the tested girder was fracture of the prestressing tendon. It was observed that at the failure stage in the load-deflection curve, the load began to decrease, while the deflection increased rapidly. It could be inferred that the box girder structure would fail. When the applied load was 1872 kN, the measured maximum compressive strain of concrete in the compression zone was only 1456µε, which is far less than the ultimate compressive strain (3300µε). Therefore, the design may be further optimized for the concrete in the top flange that was not fully utilized.

Ductility
The large deformation that occurred before failure does not mean that the structure possesses good ductility [56]. While the ductility of a structure depends only on its inelastic deformation or energy dissipation capability, in consideration of the elastic and inelastic energy, Naaman and Jeong [57] defined the ductility index as where µ denotes the ductility index, E tol is the total energy, E tol = E el + E pl , and E el and E pl are the elastic energy and the plastic energy, respectively. As illustrated in Figure 8, E el and E pl can be calculated from the area of the corresponding part in the load-deflection curve. Based on Equation (1), the ductility index of the tested girder was 1.99. Therefore, the tested girder possessed good ductility.
Appl. Sci. 2020, 10, x 9 of 20 The failure mode of the tested girder was fracture of the prestressing tendon. It was observed 216 that at the failure stage in the load-deflection curve, the load began to decrease, while the deflection 217 increased rapidly. It could be inferred that the box girder structure would fail. When the applied load 218 was 1872 kN, the measured maximum compressive strain of concrete in the compression zone was 219 only 1456 με , which is far less than the ultimate compressive strain (3300 με ). Therefore, the design 220 may be further optimized for the concrete in the top flange that was not fully utilized.

222
The large deformation that occurred before failure does not mean that the structure possesses 223 good ductility [56]. While the ductility of a structure depends only on its inelastic deformation or 224 energy dissipation capability, in consideration of the elastic and inelastic energy, Naaman and Jeong 225 [57]

237
(1) The plane section assumption is applied, and normal strains along the depth are distributed 238 linearly.

239
(2) The reinforcement and concrete are well bonded without relative sliding.

Assumptions
Full-scale testing of a large structural member involves high cost; therefore, it is necessary to establish a reasonable numerical model on the basis of test results. A nonlinear numerical model was developed using the FSM. The basic assumptions are as follows: (1) The plane section assumption is applied, and normal strains along the depth are distributed linearly.
(2) The reinforcement and concrete are well bonded without relative sliding.
(3) The shear deformation is negligible. (4) The failure characteristics of the girder are the crushing of concrete in the compression zone or fracture of the prestressing tendon. (5) The section of concrete is divided into finite strips in which the strain is assumed to be uniformly distributed.

Method of Analysis
The load application was simulated by changing of the curvature, that is, increasing curvature for loading and reducing curvature for unloading. A flow chart of the analysis procedure is shown in Figure 9, and the detailed steps are as follows: (1) The beam is divided into n-many elements with the same length along the length direction, and each element is divided into finite strips in the height direction.

Material Stress-Strain (σ-ε) Relationship
(1) Concrete Stress-Strain Relationship The compression and tension constitutive model developed in references [55,58] was adopted herein. The compression constitutive model is as follows: where σ c and ε c are, respectively, the concrete compressive stress and strain, ε cp is the compressive strain when the stress is f c (ε cp = 2000µε), and ε cu is the ultimate compressive strain of concrete (ε cu = 3300µε). The constitutive model of the uniaxial tension stress-strain is given as [55,58] where σ t and ε t are, respectively, the concrete tensile stress and strain, and f t and E c are the tensile strength and elastic modulus of concrete, respectively. (

2) Reinforcement Stress-Strain Relationship
The following elastic hardening model was adopted for the tension and compression stress-strain relationship of the reinforcement [59,60]: where σ s and ε are the stress and strain of the reinforcement, and f y and ε y are the yield stress and strain of the reinforcement, respectively. E S and E S2 (E S2 = 0.01E S ) are the elastic modulus of the reinforcement before and after yielding, respectively. The tension stress-strain relationship of the prestressed reinforcement is shown as [59,60] 13.5 (6) where ε p and σ p are, respectively, the strain and stress of the prestressed reinforcement, E p is the elastic modulus of the prestressed reinforcement, and f 0.2 is the nominal yield stress of the prestressed reinforcement. (

3) Unloading Stress-Strain Relationship
The initial stiffness of the material is E 0 , as shown in Equation (7).
When the strain increases to its maximum value, the unloading elastic modulus is E 1 , and E 1 = 0.6E 0 [59,60]. In other cases, the elastic modulus is calculated by linear interpolation with E 0 and E 1 .

Verification of the Nonlinear Numerical Model
The load-deflection curve was computed using the nonlinear numerical model. In Figure 10, the calculated load-deflection curve is compared with the measured one. It can be seen that the calculated result agreed well with the measured values. Moreover, the ductility index obtained by the calculated load-deflection curve was 1.83, which was in good agreement with the measured one as well.
Appl. Sci. 2020, 10, x 13 of 20 the calculated load-deflection curve was 1.83, which was in good agreement with the measured one 298 as well.

312
It is known from experiments that the box girder failure is via fracture of the prestressing tendon.

313
The corresponding maximum compressive strain of concrete in the compression zone is only 1456 314 με , which is far less than the ultimate compressive strain (3300 με ). Therefore, it is necessary to 315 optimize the reinforcement design and improve the bearing capacity of the structure. For this 316 purpose, the design of the reinforcement and prestressing tendon is discussed in the following. To further verify the effectiveness of the program, the load-deflection curve of another concrete composite beam was checked. Related experimental overviews and test results were reported by Deng et al. [61]. A 1/3 scaled PC I-beam with a length of 9.98 m was constructed to act compositely with a 1100 × 80 mm concrete slab. Three grouted seven-wire prestressing strands (nominal diameter of 15.24 mm) were used for post-tensioning of the beam. Five-point loads were applied using actuators, and the displacement was measured by transducers. As illustrated in Figure 11, the calculated value obtained by the proposed nonlinear numerical model was in good agreement with the measured one.

312
It is known from experiments that the box girder failure is via fracture of the prestressing tendon.

313
The corresponding maximum compressive strain of concrete in the compression zone is only 1456 314 με , which is far less than the ultimate compressive strain (3300 με ). Therefore, it is necessary to 315 optimize the reinforcement design and improve the bearing capacity of the structure. For this 316 purpose, the design of the reinforcement and prestressing tendon is discussed in the following.

Discussion
It is known from experiments that the box girder failure is via fracture of the prestressing tendon. The corresponding maximum compressive strain of concrete in the compression zone is only 1456µε, which is far less than the ultimate compressive strain (3300µε). Therefore, it is necessary to optimize the reinforcement design and improve the bearing capacity of the structure. For this purpose, the design of the reinforcement and prestressing tendon is discussed in the following.

Reinforcement in the Compression Zone of the Top Flange
The tested box girder is equivalent to an I-beam, for which the reinforcement ratio in the compression zone of the top flange is defined as follows: where A y and ρ y are the reinforcement area and reinforcement ratio in the compression zone, and b w and h 0 represent the thickness of the web and effective height of the section, respectively. The reinforcement ratio in the compression zone of the tested box girder is 0.655%. Girders with reinforcement ratios of 0.355%, 0.655%, 1.230%, 1.830%, and 2.830% are discussed. The load-deflection curve of the mid-span for each reinforcement ratio is shown in Figure 12.
where ' y A and ' y ρ are the reinforcement area and reinforcement ratio in the compression zone, and w b 321 and 0 h represent the thickness of the web and effective height of the section, respectively.

322
The reinforcement ratio in the compression zone of the tested box girder is 0.655%. Girders with 323 reinforcement ratios of 0.355%, 0.655%, 1.230%, 1.830%, and 2.830% are discussed. The load-324 deflection curve of the mid-span for each reinforcement ratio is shown in Figure 12.

325
As can be seen from the figure, the load-deflection curves of the different reinforcement ratios 326 almost overlap each other. This is because the tested girder failed due to fracture of the prestressing 327 tendon. Therefore, the reinforcement ratio in the compression zone has no obvious influence on the 328 failure mode of the tested girder and can be ignored.  As can be seen from the figure, the load-deflection curves of the different reinforcement ratios almost overlap each other. This is because the tested girder failed due to fracture of the prestressing tendon. Therefore, the reinforcement ratio in the compression zone has no obvious influence on the failure mode of the tested girder and can be ignored.

Reinforcement in the Tension Zone of the Bottom Flange
We define the degree of prestress (PPR) as where      It can be seen from Figures 13 and 14 that as the PPR increases, the bearing capacity decreases, the maximum deformation at the mid-span increases, and the residual deformation and ductility index decrease. For instance, as the PPR increases from 0.795 to 0.972, the ultimate load decreases from 1995.5 kN to 1684.0 kN, the maximum deformation at the mid-span increases from 317.0 mm to 348.2 mm, the residual deformation decreases from 150.7 mm to 107.1 mm, and the ductility index of the component decreases from 1.98 to 1.64. Therefore, the reinforcement in the tensile zone has a small effect on the bearing capacity and deformation, but has a large effect on the ductility index of the tested girder. This is because when the PPR increases, the reinforcement area in the tension zone of the bottom flange decreases.

Prestressing Tendons
The equilibrium destructive state of PC structures is that, when the prestressing tendon breaks, the concrete in the compression zone is crushed and damaged. In this failure mode, the ratio of prestressing tendons is called the equilibrium reinforcement ratio (ρ b ), which is defined as [55] where α and β are the coefficients of the equivalent rectangular stress diagram, and t is the flange thickness. The tested box girder is equivalent to an I-beam, and b w and h 0 represent the thickness of the web and effective height of the section, respectively. ρ y is the ratio of reinforcement in the tensile zone of the bottom flange. The ratio of prestressing tendons (ρ p ) is defined as For the tested girder, the ratio of prestressing tendons is 0.934%, and the equilibrium reinforcement ratio is 1.446%. Girders with different ratios of prestressing tendon of 0.934%, 1.168%, 1.401%, 1.446%, 1.635%, and 1.868% are discussed. The load-deflection curve at the mid-span and the ductility index for each parameter are shown in Figures 15 and 16, respectively.

368
It can be seen from Figures 15 and 16  The suggested reinforcement ratio The tested girder

Ductility index
The ratio of prestressing tendon (%) The equilibrium reinforcement ratio

368
It can be seen from Figures 15 and 16  The suggested reinforcement ratio The tested girder

Ductility index
The ratio of prestressing tendon (%) The equilibrium reinforcement ratio It can be seen from Figures 15 and 16 that the ratio of prestressing tendons has an obvious influence on all of the control indices. The bearing capacity of the girder was observed to increase with increasing ratio of prestressing tendons, while the maximum deformation at the mid-span, the residual deformation, and ductility index decrease. For instance, as the ratio of prestressing tendons increases from 0.934% to 1.868%, the ultimate load increases from 1876.8 kN to 3706.2 kN, the maximum deformation at the mid-span decreases from 329.8 mm to 221.3 mm, the residual deformation decreases from 138.2 mm to 21.8 mm, and the ductility index of the component decreases from 1.83 to 1.32. With comprehensive consideration of the influence of various parameters, such as the bearing capacity, deformation, and ductility index of the structure, it is suggested that the ratio of prestressing tendons be increased to 1.401%. That is, the prestressing tendons should be increased from four strands to six strands in each duct of the tested girder. After the optimization of prestressing reinforcement, the ultimate load increases from 1876.8 kN to 2708.1 kN, the maximum deformation at the mid-span decreases from 329.8 mm to 269.2 mm, the residual deformation decreases from 136.2 mm to 65.4 mm, and the ductility index of the component decreases from 1.83 to 1.47.

Conclusions
This paper reports destructive experiments on a 30-meter-long simply supported prestressed concrete box girder. A nonlinear numerical model was developed using the finite strip method (FSM) on the basis of the experiment. Parametric analyses were conducted, and the design was optimized. The following conclusions may be drawn: (1) The failure mode of the tested girder was fracture of the prestressing tendon. The maximum compressive strain of concrete in the compression zone was only 1456µε, which is far less than the ultimate compressive strain (3300µε). Therefore, the concrete in the top flange was not fully utilized. (2) The maximum deflection was 1/102 of the span, and the ductility index of the tested girder was 1.99. Therefore, the tested girder possessed good ductility. (3) The measured cracking load was 750 kN, which is 1.98 times the applied load corresponding to the designed ultimate state of bearing capacity. Moreover, the measured maximum load was 1872 kN, which is 2.50 times the cracking load. It can be seen that the tested girder had a sufficient safety margin. (4) A nonlinear analysis procedure was performed using the FSM. The analysis procedure was demonstrated to be effective by comparing the analytical results with those of the tested girder and a laboratory-scale model. (5) The ratio of reinforcement in the compression zone has no obvious influence on the failure mode of the tested girder and can be ignored. The reinforcement in the tensile zone has a small effect on the bearing capacity and deformation of the tested girder, but has a large effect on the ductility index. (6) The ratio of prestressing tendons has an obvious influence on the bearing capacity, deformation, and ductility index. Considering the influence on the bearing capacity and ductility index of the structure, it is suggested that the ratio of prestressing tendons be increased to 1.041%. The prestressing tendons should thus be increased from four strands to six strands in each duct of the tested girder. After optimization of the prestressed reinforcement, the girder is ductile and the bearing capacity can be increased by 44.3%.