Experimental Study on the Flexural Properties of FRP-Reinforced Super-Span Concrete T-Beam after Service

Abstract

Super-span (20 m) non-prestressed T-section reinforced concrete beams have been in service for more than 30 years and are common in Chinese highway bridges. However, the actual performance of these super-span T-section reinforced concrete (RC) beams that have been reinforced with FRP, including their process of failure from a service state to a failure state, has not been determined. In this study, original RC T-beams, with a 20 m span and retrofitted with FRP, were taken from a highway bridge. Their flexural performance was detected via experiments in a laboratory. The experiments revealed that the sectional strain distribution is more non-uniform. The mid-span ribs clearly play a role in strengthening the section and the bearing reservation was studied based on a subsequent sectional analysis. It became clear that the load-bearing reservation of an old super-span T-beam changes during the entire life of the specimen; not only because of the depression of the resistant capacity and the reinforced measure, but also due to the updates to load codes.

1. Introduction

The era of 1980s to 1990s saw massive infrastructure development peak in China. As a result of China’s inferior technological development at the time, many RC bridges that were built during this golden period were built according to the standards of the former Soviet Union, developed in the 1970s. The components of the bridges are often of a long span and bulky. Nevertheless, these super-long span concrete members played a key role in bridge engineering.

The T-section beam (T-beam) is one of the most commonly used components because it is relatively light in weight and flexible for bridge engineering. Past and recent research has focused mainly on the performance of retrofitted T-beams [1,2,3,4,5,6,7,8,9,10,11] and has found that the morphology, number, propagation forms, and space of the flexural cracks are all related to the compressive strength of concrete, while the initial stiffness is related to its tensile strength [12]. The height-to-span ratio has a major influence on the flexural performance of T-beams, especially for beams with a span longer than 10 m. Prestressing technology is usually used to improve the flexural performance of T-beams [13], as achieving super spans without prestressing techniques is difficult. The ductility index is usually used to evaluate the deformation capacity of curved beams. The stiffness of beams is another important feature and is closely related to the strength of the web core concrete [14]. Externally bonding prestressed or non-prestressed FRP can effectively improve the bending and bearing capacity of beams [15]. T-section specimens are susceptible to FRP fracture and concrete crushing under a bending moment [16]. Increasing the width and elastic modulus of FRP can enhance its function under bending resistance. Anchoring both ends of FRP can ensure that it fully participates in resistance [17]. Almahmood et al. [18] tested the flexural performance of large-span T-beams and showed that GFRP bars and steel bars can improve the flexural stiffness and ductility of beams and that they are more conducive to the control of crack and deflection in large-span T-beams. The effective thickness of FRP has been shown to be suitable for bending reinforcement with only two layers, while there is no observed difference in reinforcement between the former and the two-to-four-layer reinforcement [19,20,21] used in NSM FRP bars that strengthen large-span T-section beams. Additionally, the authors found a relation between the failure mode and NSM reinforcement, with the specimen retrofitted with GFRP bars being seen to offer the best ductility. The state of old T-section beams in service has only been investigated via a finite element analysis because of large research costs and conditions that cannot be replicated in a laboratory [22]_. The fact that FRP material can be applied in bridges and beams so extensively is also attributed to its excellent durability in different types of environments. Much research has been dedicated to the study of the durability of FRP [23,24,25,26]. These former studies generally show that FRP—whether HFRP, GFRP, or BFRP—is suitable for many different types of complex and harsh environments. FRP can play an important role in retarding the performance decay of a structure.

At present, the strength, stiffness, deformation, and other properties of bridges retrofitted with FRP T-beams have been gradually clarified. Most of the relevant theories derive their findings from the experimental analysis of the ideal specimens in laboratories and from the classic mechanical models based on various assumptions. However, the ideal specimens reflect neither the realistic mechanical properties nor the influence of damage on the performance of the in-service components. In addition, compared with full scale original beam tests, equal scale specimen tests have been more widely used, while the effect of the size difference on the performance of T-beams cannot be evaluated accurately.

Various studies expanding the span of T-beams aim to attain results closer to the actual bridge beams, whereas the ultimate state loading tests of full-scale large-span beams have not been observed, owing to space and fund limitations. The absence of experiments with retrofitted full-scale large-span specimens has led to the lack of its understanding in practice. For example, the factors related to durability, the heterogeneity of material performance, and the bond slipping effects between different materials cannot be exactly described using a mechanical model. Therefore, it is necessary to conduct a flexural experiment with an original specimen, one which aims to determine the basic performance of FRP-retrofitted super-span T-beams after a long-term service.

Here, we removed a GFRP-retrofitted original T-shaped beam with a 20 m span from a 31-year-old RC bridge. The T-beams were transported to the laboratory for bending tests. Our experiments showed many important and interesting phenomena during loading. The findings also allow us to discuss the feasibility of using section analysis to predict the flexural performance of the reinforced super-span RC beam.

2. Test Specimen

A 1500 m span highway RC bridge in the Liaoning Province of China was built in 1991 and was reinforced in 2005. The main girder of the superstructure is the form of a T-shaped section, precast by ordinary reinforced concrete of a 20 m span and with non-prestressed, simply supported beams. In this study, one T-beam was taken down from the original bridge as a specimen, intended to be used for flexural performance experiments in the laboratory (Figure 1).

Compared to the newly cast-in-place specimens described in the literature, the original T-beam has many unique features. Firstly, five concrete ribs were designed at both sides of the web of the original T-beam (Figure 2a), and this measure was used to ensure the stability of the T-beam during loading. Additionally, it was obvious that widespread stains, local defects, and macro-cracks were distributed on the surface of the specimen. Meanwhile, a 28 mm initial deflection resulting from a creep at the middle span section was discovered, as shown in Figure 2b. These seem inevitable for a concrete specimen exposed to the natural environment for more than 30 years. However, as shown in Figure 2c, after 17 years of service, the GFRP strips were intact, and no debonding or cracking occurred.

The bridge was built according to the atlas published by the Ministry of Communications of the People’s Republic of China in 1973. According to the design document, the body of the T-beam was made of 250# concrete (f_ck ≈ 23 MPa), and grade II steel bars were adopted as mainly longitudinal bars. The longitudinal bars of the mid-span section of the T-beam were arranged as vertical strings. The ends of the longitudinal bars were bent at a 45° angle, as shearing reinforcement according to the moment envelope diagram. The pavement, also made of 250# concrete and with a 120 mm designed thickness, was laid at the top surface of the T-beam. In 2005, to enhance the bearing capacity of the bridge, the 20 m T-beam span was retrofitted by recasting the pavement on the top surface with C40 concrete, and a single layer inclined U-wrapped GFRP strips was bonded on the web surface with 300 mm spacing and a single layer on the bottom surface. The designed tension strength of the GFRP was greater than 500 MPa, and the average thickness and width were 1 mm and 300 mm, respectively. The main data of the specimen are shown in Figure 3. However, there were local discrepancies between the actual and standard size of the specimen, influenced by the initial defect of the specimen and cutting errors. In Figure 3, the dimensions given outside the brackets indicate the standard size of the specimen, and the numbers in the brackets indicate the actual size.

The standard values of the main parameters of materials according to the original design document are shown in

Table 1. Test results of concrete.

Sample Number	Average Diameter /mm	Average Height /mm	Compression Force /kN	Compressive Strength /MPa	Average Compressive Strength /MPa	Standard Deviation
cb-1	75.3	75.6	165.02	37	33.9	2.37
cb-2	75.1	75.3	177.52	40.1
cb-3	75.5	75.7	152.12	33.9
cb-4	75.3	75.8	147.05	33.0
cb-5	75.1	75.3	150.37	33.8
cb-6	75.3	75.4	150.23	33.8
cb-7	75.6	76.0	144.76	32.2
cb-8	75.6	75.7	136.53	30.4
cb-9	75.3	75.7	149.43	33.6
cb-10	75.8	75.3	147.56	32.7
cb-11	75.6	75.6	163.86	36.3
cb-12	75.4	75.7	143.35	32.1
cb-13	75.2	75.4	151.38	33.7
cb-14	75.4	75.5	156.18	35.0
cb-15	75.6	75.3	144.99	32.2
cp-1	75.4	75.4	213.90	47.8	50.4	3.95
cp-2	75.1	75.2	206.29	46.6
cp-3	75.6	75.3	255.21	56.8
cp-4	75.4	75.4	225.87	50.6
cp-5	75.1	75.0	222.74	50.3

. The original results of the material test are unknown because the original documents are missing.

The current concrete compressive strength of the T-beam specimens and the upper pavement can be determined via drill core sampling. In total, 15 concrete samples were taken from the beam body, and five samples were taken from the concrete pavement. The mechanical properties of the longitudinal reinforcement can be measured from the samples cut from the adjacent beams with identical conditions. The current GFRP tensile strength is immeasurable for the special property of the material. The main material parameters are presented in Table 1,

Table 2. Test results of reinforcement bars.

	Average Diameter /mm	Yield Strength/MPa	Average Value /MPa	Tensile Strength /MPa	Elongation /%
st-1	32	318.0	320.7	530.9	16.5
st-2	32	317.8		515.1	12.3
st-3	32	313		519.4	10.3
st-4	32	329.1		527.3	18.0
st-5	32	325.6		513.7	8.3

and

Table 3. Main parameters of materials.

	fcb /MPa	fcp /MPa	fy /MPa	fu /MPa	Es /GPa	fGFRP /MPa	EGFRP/GPa
Nominal value in original design	22.4	42.0	360	580	210	800	80
Actual measured value of current period	31.2	45.9	320.7	521.3	215.2	_	_

f_cb—Compressive strength of concrete in T-beam. f_cp—Compressive strength of concrete in pavement. f_y—Yield strength of longitudinal reinforcement. f_u—Ultimate strength of longitudinal reinforcement. f_GFRP—Ultimate strength of GFRP E_s—Elasticity modulus of main reinforcement. E_GFRP—Elasticity modulus of GFRP.

. In Table 1, “cb” is the concrete sample obtained from the body of the T-beam, and “cp” is the concrete sample obtained from the pavement.

3. Experimental Program

3.1. Test Preparation

It is difficult to carry out flexural performance tests in the laboratory. The stability and safety of specimens during loading is critical.

To simulate the practical state, the supports of the specimen were designed as the entire system, consisting of an upper rubber pad and lower rigid piers. The rigid pier connects to the horizontal ground anchor at the bottom of the pier, which not only ensures the stiffness of the bearing, but also meets the stability requirements of the specimen (Figure 4).

After the specimen was lifted, laser equipment was used for accurate alignment. For super-large span specimens, out-of-plane instability due to eccentric positioning or initial component defects must be considered. To ensure safety during the experiment, a pair of protective angle frames was placed on both sides of the 1/4 and 3/4 span partitions of the specimen and anchored to the ground with high-strength anchor bolts (Figure 5). There was 50 mm of space between the specimen and the protective angle frame.

3.2. Test Setup

The test device is shown in Figure 6. The loading reaction frame, placed perpendicular to the length direction of the specimen, was in the same plane as the mid-span section of the specimen. A 2000 kN vertical hydraulic jack was fixed at the center of the counter beam; the bottom of the jack was connected to the 100 T load sensor; and the end of the sensor was connected to the loading plate pair and placed on the rigid distribution steel beam.

The distribution beam was 3 m long, and the total length of the predesigned bending zone was 2500 mm. The center of the load distribution beam was strictly aligned with the center of the loading point, and two standard rubber pads at each end of the distribution beam were used as support for the distribution beam.

As shown in Figure 7, the strain gauges on the flexural specimen can be divided into three groups. In group I, three concrete strain gauges were arranged in each row of the pavement along the length direction of the specimen. The center point of the strain gauge in the middle corresponded to the mid-span section of the specimen, and the center distance of the strain gauge was 800 mm. Group II strain gauges were arranged on the surface of the two sides of the web in the mid-span area of the specimen. Four rows of strain gauges were arranged on each side, and two rows of strain gauges were arranged on each side of the middle line of the mid-span partition with a spacing of 400 mm. Each row contained three rows of strain gauges with a spacing of 150 mm. Group III comprised 1 × 2 mm reinforcement strain gauges with standard spacing. Three rows of reinforcement strain gauges were arranged on each web side, spanning 800 mm. The center of the middle row was within the mid-span section of the specimen. Five dial indicators were set up at both ends of the bending specimen bearing, quartile points, and the middle of the span.

3.3. Experimental Procedure

The force control mode was adopted in the bending test. Before the 75% estimated ultimate load, 15% of the estimated ultimate load was loaded at each stage. In the 75–85% estimated ultimate load range, each stage was loaded by about 10%. After 85% of the estimated load, each stage was loaded with about 3.5% of the estimated load until failure, and each stage was held for no less than 10 min.

From the initial loading to 200 kN, old dense micro-cracks appeared at the bottom edge of the web. When the load reached 300 kN, many micro-cracks extended upward, and the width of the web bottom simultaneously widened. The cracks extended to a height of 500 mm from the bottom of the web. At 400 kN, new cracks appeared at both ends of the specimen. Most of the new cracks were near the two sides of the mid-span partition in the bending section, and some of them extended upward along the old cracks. At 500–600 kN, the number of cracks in the specimen increased significantly; new cracks mainly occurred on the web surface at both ends of the specimen, while the cracks on the web surface close to the loading distribution beam widened rather than extending. The bonded GFRP rattled constantly in this load range, and part of the longitudinal reinforcement bars began to yield. After 600 kN, the deformation of the specimen increased sharply, with visible deformation on the web surface, and there was brittle fracture noise from the GFRP. After 700 kN, the obvious cracks on both sides of the mid-span diaphragm continued to extend upward, through the height of the web (Figure 8 and Figure 9).

The cracks at the bottom of the web were close to the network connection. During the last stage, with an applied load of 730 kN, the deformation of the mid-span section progressed rapidly, and multiple extended connected cracks appeared, with the widest crack being wider than 2 mm. When the load increased to 752 kN, the specimens produced multiple sounds, and the web’s longitudinal steel bars in the dense crack network region at the bottom of the loading beam (900 mm from the middle baffle plate) underwent a pull cut. The GFRP reinforcement at the bottom of the T-beam snapped. The specimens completely lost their bearing capacity, and the components were deflected toward the mid-span (Figure 10).

The ultimate state of the specimen showed that the failure was characterized by the rupture of longitudinal reinforcement. The position of the rupture point was 900 mm from the mid-span section. The longitudinal steel bars had a vertical layout, with 432 + 216 upright bars. Figure 11 shows the loss of bearing capacity resulting from the snap of the 32 mm diameter steel bars in the third line, and the adjacent steel bars (upper 16 and lower 32) all showed the phenomenon of pinching at the neck. The stress of the reinforcement group was rapidly redistributed after the tensile fracture of the lower 32 steel bars, and the adjacent steel bars immediately pulled off.

4. Analysis and Discussion

4.1. Analysis of Experimental Results

4.1.1. Load-Deflection Curve

The load-deflection curve of the mid-span section of the specimen is shown in Figure 12. The # is the number of specimen. The ultimate load of the specimen was 752 kN, the maximum mid-span deflection was 309.2 mm, and the ultimate bending capacity of the specimen was 3684 kN m. The mid-span deflection increased with increasing load, and the slope of the deflection changed significantly at 600 kN. Before 600 kN, the deflection of the mid-span varied linearly with the load, but after 600 kN, the deflection increased rapidly, indicating that the main reinforcement began to yield. The displacement of the mid-span point, span end, and quadrangle point was measured under the action of loads at all levels (Figure 13). As shown in Figure 13, before the yield load, the displacement distribution in the quadrants was basically symmetric. When the load was 100 kN, the ratio of the average quad-point and mid-span displacement was 82%. Notably, the displacement of measured points at 100 kN was not strictly symmetric: the displacement of point 4 was marginally larger than that of point 2, which could be attributed to the in-homogeneity of initial loading. When the load reached 600 kN, the average displacement of the quad-point was only 68% of the mid-span displacement. Therefore, the ratio of the quad-point displacement to the mid-span displacement gradually decreased with increasing load.

4.1.2. Analysis of Strain

The initial cracks on the original beam caused nonuniform crack propagation and strain distribution on the concrete under load. The distribution regularities of strain in groups Ⅰ, Ⅱ, and Ⅲ were measured by strain gauges, as shown in Figure 14 (C refers to concrete strain gauge, S refers to reinforcement strain gauge).

As shown in the figure, the strain distribution of the mid-span section conformed to the assumed rule of the plane section, within the elastic range along the height of the section. The location of the neutralization axis moved up with increased load. The strain distribution regularity of sections 2-1 and 2-3 (the sections 800 mm from the mid-span section) is shown in Figure 14b,c. It can be seen that the sectional strain distribution of sections 2-1 and 2-3 conformed poorly to the assumed rule of the plane section. According to the strain distribution, the neutral axis height of the T-beam was always within the height of the flange.

The yield moment of the longitudinal steel bars appeared at a load larger than 500 kN, which can be calculated from the strain and elastic modulus of steel bars. The yield displacement of the longitudinal bars was 62 mm, and the ultimate displacement was 309.2 mm. The ductility index of the beam was 4.98, which fulfilled the basic demand of the design code. Figure 14 indicates that the yield of steel bars happened in the sections on both sides before the mid-span section under the same load grade.

Additionally, the strain of abreast steel bars was not linearly distributed. Under the action of loads at all levels in the three test sections, from top to bottom, the strain at the bottom of the second and fifth rows was greater than that of other rows. The curves of sections 2-1 and 2-3 are expected to be the same because of symmetry, but the actual strain distribution did not strictly fit the pattern. This phenomenon could be attributed mainly to the heterogeneity of concrete and steel bars resulting from long-term service or the low construction quality at that time. As shown in Figure 14a–c, the strain distribution of steel bars was also asymmetrical. However, it must be noted that the strain distribution of steel bars of each section (section 2-1 or 2-3 or mid-span section) had a similar pattern. The strain of the second steel bar was always obviously larger than the other steel bars. The average tensile strain of each steel bar at every loading stage is shown in Figure 14d, where S2i means the average strain of the steel bar of the ith line. It is obvious that the distribution of average strain of steel bars also fit the pattern mentioned above. It is concluded that the strain distribution of the section has larger differences from the ideal condition of the plane section assumption, especially for an old large-span T-beam with longitudinal steel bars arranged vertically. It is obvious that the second steel bar had larger strain, which is consistent with the rupture point shown in Figure 11. It follows that the quality of the steel bars was not uniform, and the abnormal performance of individual steel bars could influence the sectional strain distribution and even the performance of the whole specimen.

However, it was found that the strain increment of the second steel bar changed with improved loading, according to Equation (1). As shown in Figure 15.

$$K_{2nd}=0.0474(P/P_u)+0.1651$$

(1)

In Equation (1), K_2nd is the strain increment index of the 2nd line steel bar, P and P_u is the vertical load and the estimated bearing capacity of the specimen, respectively. P_u, related to the ultimate moment M_u, which can be determined by the method of the Chinese design code of concrete structures GB50010-2010 [27] as follow:

if

$${\alpha }_1{f}_c{b}_f^{\prime }{h}_f^{\prime }+f_y^{\prime }{A}_s^{\prime }-f_y{A}_s\ge 0$$

(2)

$$M_u={\alpha }_1{f}_{c}bx(h_0-\frac{x}{2})+{\alpha }_1{f}_c(b_f^{\prime }-b)h_f^{\prime }(h_0-\frac{h_f^{\prime }}{2})+f_y^{\prime }{A}_s^{\prime }(h_0-a_s^{\prime })$$

(3)

else

$$M_u={\alpha }_1{f}_c{b}_f^{\prime }x(h_0-\frac{x}{2})+f_y^{\prime }{A}_s^{\prime }(h_0-a_s^{\prime })$$

(4)

In which f_c is the designed value of concrete strength; A_s and A_s’ is the area of steel bars in the compressive and the tensile zone. b is the thickness of the web, h₀ is the effective height of the section. h_f’ and b_f’ is the height and the width of the web suffering compressive load. x is the important index, calculated by Equation (5).

$${\alpha }_1{f}_c[bx+(b_f^{\prime }-b)h_f^{\prime }]=f_y{A}_s-f_y^{\prime }{A}_s^{\prime }$$

(5)

The strain distribution of the concrete web in each row is shown in Figure 16a–d. The middle strain in row 1 (strain gauges at the top of the flange) was smaller than the strain of both sides, but the difference decreased with increasing load. Comparing Figure 16 and Figure 17, we can see that when the beam surface was bending, the mid-span section deformed less than the other sections. In addition, the concrete strain was significantly greater in R5 than in other columns under various loads, which is also related to the detection of steel bars in this section. Figure 17a,b shows the strain of steel bars under different load grades. The regular is similar to the rule above. For the three test sections in the same section, the strain of the mid-span section is smaller than that of the cross-sections on both sides, and the reinforcement strain is symmetrical on both sides based on the mid-span section. Further, the mid-span section has strong carrying capacity.

Whether in concrete or steel bars, the strain and deformation of the mid-span section are smaller than those of adjacent sections on both sides, which must be attributed to the stiffening function of concrete ribs in the mid-span section. As shown in Figure 18, A-A and B-B are the sections with and without ribs. A big difference between the cross-sectional moment of inertia and cross-section resistance moment of the two sections can be observed. Thus, the normal stress and strain on the two sections was also different. According to the mechanics of the materials, the difference of stress in the two sections depends on the bending moment and the size of the rib. Notably, if the stiffening ribs are arranged on the section with the largest bending moments, the adjacent sections suffering approximate bending moments are also in danger, and the sectional strength also should be checked, especially with large spans and old T-beams.

4.2. Theoretical Analysis

According to the test results, during the loading process, the strain distribution conformed to the plane section assumption, and the strip method could be used to calculate the moment curvature curve.

The section was characterized by an upper concrete pavement layer and lower steel bars arranged vertically. The strain distribution of the section is shown in Figure 19, where b and b_f are the width of the flange and web; A_si, ε_si, and σ_si represent the area, strain, and stress of the longitudinal stress reinforcement in the mid-span section; A_frp, σ_frp, and ε_frp represent the cross-sectional area, stress, and strain of the FRP strengthened mid-span; f_c1, f_c2 and ε_c1, ε_c2 are the stress and strain of the concrete of T-beam and pavement; X and H are the height of compression zone and total height of the section; dh is the height of each strip; φ is the curvature of the section; and M is the bending moment of the section.

In addition to the flat section assumption, the following assumptions were also made when using the strip method for calculation: (i) the slip between steel bar, concrete, and FRP is ignored during loading; (ii) the tension stress of concrete is ignored; and (iii) there is no splitting failure in the limit state. Neglecting the tensile stress of concrete in the theoretical analysis could lead to slightly lower theoretical results.

For the T-beam, the cross-sections at each corner met the requirements of the force equilibrium equation (Equation (6)).

$${\displaystyle \int f_{c1}}({\epsilon }_c)b\cdot dh+{\displaystyle \int f_{c2}}({\epsilon }_c)b\cdot dh={\displaystyle \int A_{sit}}{\sigma }_{sit}(k_{2nd}{\epsilon }_{sit})\cdot dh+{\displaystyle \int A_{frp}}{\sigma }_{frp}({\epsilon }_{frp})\cdot dh-{\displaystyle \int A_{sic}}{\sigma }_{sic}({\epsilon }_{sic})\cdot dh$$

(6)

In Equation (6), A_sit and A_sic are the area of longitudinal steel bar under tensile and compressive stress, respectively; σ_sit and σ_sic are the related stress; A_frp and σ_frp are the area and stress of FRP; and φ of each loading stage corresponds to the neutralization axis X of the section. The value of φ is assumed during the calculation, the height X of the neutralization axis satisfying Equation (6) will be obtained, and the section M-φ curve can be obtained through strip iteration. The procedure terminates when the tensile strain of FRP reaches the ultimate value.

The compressive stress on the T-beam and pavement concrete f_ci(ε_ci) could be determined based on the constitutive law for concrete in the GB50010 standard (Code for design of concrete structures in China) [27], using Equations (7)–(12). E_c is the elastic modulus of concrete, related to its ultimate strength f_c^’, which can be calculated by Equation (4). ε is the strain of concrete. d_c, the compressive damage coefficient of concrete, is determined by Equation (3). In Equation (3), α_c is the descending coefficient, and f_c,r and ε_c,r are the compressive strength and corresponding strain of the peak point, respectively, on the constitutive curve of concrete. The ultimate compressive strain of concrete can be obtained from the table in GB50010 [27]. The specific definitions of parameters in Equations (7)–(12) refer to GB50010 (Figure 20a) [27]. The constitutive relation of rebar is selected according to the elastic-plastic bi-linear model, as shown in Figure 20b. Yield strength f_y and elastic modulus E_s, obtained from the test, are necessary. The constitutive law of the steel bar is expressed by Equation (8). The tensile stress and strain of the FRP are calculated according to the linear elastic law. The ultimate strain is determined by ultimate strength σ_frp and elastic modulus E_frp (Figure 20c).

$$f_c=(1-d_c)E_c\epsilon$$

(7)

$$d_c=\left\{\begin{array}{ll}1-\frac{{\rho }_{c}n}{n-1+x^n}\hspace{1em}& x\le 1\\ 1-\frac{{\rho }_c}{{\alpha }_c{(x-1)}^2+x}\hspace{1em}& x>1\end{array}\right.$$

(8)

$$E_c=4750\sqrt{f_c^{\prime }}$$

(9)

$${\rho }_c=\frac{f_{c,r}}{E_c{\epsilon }_{c,r}}$$

(10)

$$n=\frac{E_c{\epsilon }_{c,r}}{E_c{\epsilon }_{c,r}-f_{c,r}}$$

(11)

$$x=\frac{\epsilon }{{\epsilon }_{c,r}}$$

(12)

$${\sigma }_s=\left\{\begin{array}{ll}{E}_s{\epsilon }_s\hspace{1em}& {\epsilon }_s\le {\epsilon }_y\\ f_y\hspace{1em}& {\epsilon }_s>{\epsilon }_y\end{array}\right.$$

(13)

According to the above method, the M-φ curve of the ideal mid-span section of the specimen can be determined through iterative programming, as shown in Figure 21. It shows that the theoretical curve has a similar trend to the experimental results, even though the former has larger stiffness, which can be attributed to the loss of bonding stress between longitudinal steel bars and concrete or another related factor of concrete durability. However, it is seen that the theoretical bearing capacity is close to the experimental value, as shown in

Table 4. Comparison of theoretical and experimental value.

	My/kN.m	Pu/kN
Experimental result	2260.5	752.0
Theoretical result	2968.3	799.9
Err.	23.8%	5.9%

M_y—Moment in yield state; P_u–Bearing capacity.

. It is worth noting that the last point in the tested curve is not the ultimate point. The deficiency of the tested curve can be explained by the broken strain gauge at the ultimate moment.

4.3. Bearing State Analysis of the Whole Life of Super-Span T-Beam

During the whole life of the specimen, the concrete strength and the section form were different, while the service load in the design standard was continuously changed. The bearing state of the specimen was also different.

The concrete strength changed continuously during service. The pattern of strength variation of aged concrete can be calculated using an equation from the research of Gao et al. [28] as follows:

$${\mu }_f(t)=-2.861\times {10}^{-4}{t}^2+1.384\times {10}^{-2}t+0.8769$$

(14)

where t represents the time measured in years and μ_f is the average coefficient of variation. The concrete strength in

Table 5. The variation of design standard during service. # means the number of specimen.

Year	Concrete Strength/MPa		Section Form	Service Load Ms /kN m	Resistant Force MR /kN m	SR = Ms/MR
	Beam Body	Pavement
1991 (Design)	250# (18 MPa)	250# (18 MPa)		1509.0	2966.3	1.966
1991	30.26	30.26		1296.0	3011.3	2.324
2005 (Before reinforcing)	30.71	30.71		1725.0	3011.9	1.746
2005 (After reinforcing)	30.71	44.58		1725.0	3406.1	1.975
2022	31.2	45.9		2430.0	3290.0	1.354

was calculated by Equation (14).

The cross-section also changed continuously during service, as shown in Table 5. In 1991, the concrete strength of the body and pavement was 30.26 MPa. After 2005, the concrete strength of the pavement changed to 44.58 MPa, and a single-layer GFRP strip was attached to the bottom of the T-beam.

With the development of society, the bearing demand of bridges is increasing day by day. The corresponding design load is also continuously changing, as shown in Table 5. In China, the design code of bridge load was totally upgraded twice, in 2004 and 2018.

Based on Table 5, the relation between the safety reservation (SR) of the T-beam and the service year is drawn in Figure 22. The figure shows that in 1991, the initial value of the SR index was 2.324, higher than the designed value of 1.966. With the extended service term, the SR index dropped to 1.746, resulting from the upgrade of loading in the loading code in 2004, although the concrete strength improved slightly. Under reinforcement in 2005, the SR index return to 1.975, which was higher than the designed value. In the 17 years since, the current value of the SR index has dropped to 1.354, which can be attributed mainly to the upgrading of the service load.

5. Conclusions

The following conclusions can be drawn from the experiment and analyses:

(1)

The failure process of the retrofitted old super-span FRP reinforced concrete T-beam was recognized. The failure of the specimen initially occurred with the original cracks in the middle span of the specimen extending upward. The strain distribution of concrete is asymmetrical during bending. The bearing capacity of specimen losses is absolutely marked by the sudden fracture of GFRP and longitudinal steel bars.

(2)

The presence of the stiffened rib plate changed the stress state and strain distribution of the maximum bending moment section. The weakening effect of the stiffened rib plate on the adjacent section should be considered when the rib plate is installed on the maximum bending moment section.

(3)

It is difficult to perfectly meet the plane cross-section of the strain distribution of specially designed longitudinal steel bars arranged vertically. The sectional analysis carried out in this study should be revised by the experimental data.

(4)

The reliability of the super-span T-beam can be expressed by the SR index, which is mostly affected by the upgrading of the service load rather than the influence of service life and atmospheric environment.