Experimental Study on Shear Failure of 30 m Pre-Tensioned Concrete T-Beams Under Small Shear Span Ratio

Abstract

Pre-tensioned concrete T-beams with draped strands have been gradually promoted and used in bridge construction in recent years due to their advantages such as simple structure, efficient force distribution, and few defects. However, the current design codes exhibit conservative provisions for the calculation of the shear capacity of such beams under a small shear span ratio, which may lead to a large design value of beam web thickness. This is primarily due to insufficient experimental data. This paper details a full-scale experimental investigation on the shear failure mechanisms of two 30 m pre-tensioned concrete T-beams with draped strands, under a shear span ratio of 1, at which the shear capacity of the beams represents their upper limit. The specimens were tested to analyze their mechanical behavior, including load-deflection response, crack distribution, stirrup strain, and strand slip. The ultimate shear capacities of the test beams were 7107 kN and 6742 kN. To evaluate the applicability of current design codes, the experimental results were compared with theoretical predictions from five international design codes. The analysis revealed that the AASHTO code provided the highest upper limit of shear capacity for pre-tensioned concrete T-beams with draped strands, whereas the Chinese code (JTG 3362-2018) exhibited a significantly high safety factor of 4.09. These findings provide a basis for the optimized design of pre-tensioned concrete T-beams with draped strands and the determination of the upper limit of shear capacity.

1. Introduction

Precast prestressed concrete beams with small to medium spans are widely used in bridge engineering due to their simple structural forms and clear load-bearing mechanisms [1,2]. The main structural types include concrete hollow slabs, T-beams, and small box girders. However, concrete hollow slabs have gradually been phased out in recent years due to issues such as vulnerable hinge joints and bearing disengagement [3,4]. Small box girders, with their narrow internal cavities, face challenges in ensuring construction accuracy and efficiency due to the complexity of their reinforcement and formwork arrangement [5]. Post-tensioned precast prestressed beams are widely used for their fast construction speed, but for small to medium spans, issues such as duct blockage and high friction often arise, leading to insufficient prestressing at mid-span and potential durability concerns [6].

Pre-tensioned concrete T-beams with draped strands, where internal bent prestressing tendons are used, improve the shear resistance at the beam ends by applying prestressing force before concrete casting [7]. This enhances the stress state at the beam ends [8,9] and avoids the problems associated with post-tensioning, such as inadequate grouting and duct blockage [10,11]. For specific small-scale specimens, tests have demonstrated that the shear bearing capacities of pre-tensioned and post-tensioned beams are comparable [12]. As a result, such beams have been increasingly adopted in bridge construction in recent years [13,14,15,16,17].

With advancements in bridge construction technology and concrete materials, a trend toward thinner and lighter concrete beams has emerged. However, the shear behavior of beams is complex, and there is no unified theory for shear capacity calculation [18,19,20]. To prevent diagonal compression failure and excessive crack widths under shear loading, various codes specify upper limits for the shear capacity of concrete beams [21], which restrict the minimum web thickness. Nevertheless, current codes often exhibit significant discrepancies between calculated upper limits and actual shear capacities, leading to overly conservative designs [22].

Kang [23] and Shahawy [24] conducted experiments on the upper limit of the shear capacity of prestressed I-beams, investigating the influence of multiple factors on shear capacity. Qi et al. [25] performed shear tests on prestressed T-beams with draped strands. Duanmu et al. [26] conducted experiments on the upper limit of the shear capacity of four full-scale post-tensioned prestressed concrete T-beams. The study revealed that the upper limit of shear capacity in prestressed concrete deep beams is influenced by reinforcement ratios and shear span-to-depth ratios, while longitudinal prestressing enhances both cracking and ultimate loads. Tests have demonstrated that the flanges of T-beams significantly enhance the shear capacity of the beams [27]. However, many design codes do not account for the contribution of T-beam flanges. Hui Chen et al. [28] conducted a quantitative analysis of the randomness in the shear capacity of beams from a probabilistic perspective, utilizing three shear strength models from design codes and a reliable experimental database. Some studies have already predicted the shear strength of concrete beams based on physical models and machine learning [29,30]. Kim et al. [31] evaluated the shear performance of factory-produced precast prestressed concrete hollow core slabs through four-point loading tests, analyzing their mechanical characteristics. Deng et al. [32] conducted static load tests and finite element simulations, finding that prestress, concrete strength, and stirrup ratio can significantly improve the ultimate shear capacity of beams. Zheng [33] proposed a shear degradation model considering shear deformation to assess the stiffness degradation of concrete beams with diagonal cracks. Jiang [34] performed destructive shear capacity tests on retired concrete T-beams, providing references for the assessment of in-service bridges. Zhang [35] investigated the impact of surface reinforcement on the shear performance of concrete T-beams, discovering that this technique can enhance the overall stiffness and shear strength of beams while delaying the development of diagonal cracks. Jin [36] summarized the calculation formulas for the shear capacity of Ultra-High-Performance Concrete beams and analyzed the influencing factors, providing recommendations for optimizing the shear performance of Ultra-High-Performance Concrete beams. Li Wan et al. [37] conducted shear tests on scaled pre-tensioned concrete T-beams with draped strands and found that the upper limit of the beams’ shear capacity significantly exceeded the calculated values specified by various international codes. In summary, the current design codes tend to be overly conservative in calculating the upper limit of the shear capacity of concrete beams, significantly restricting the minimum sectional thickness in design. To reveal the actual shear capacity of concrete members under small shear span ratios and provide a basis for calculating the upper limit of shear capacity, extensive experimental studies have been conducted on various types of beams. However, research on prestressed structures remains limited, particularly regarding the upper limit of shear capacity for pre-tensioned concrete T-beams with draped strands.

This study is based on the second phase of the Nanchang-Zhangshu Expressway expansion and reconstruction project in China, focusing on pre-tensioned concrete T-beams with draped strands. This type of beam has a relatively new structural form that remains under-studied and rarely applied in engineering practice. Full-scale shear tests were conducted on two 30 m pre-tensioned concrete T-beams with draped strands to analyze their mechanical performance. The shear tests were conducted under a shear span ratio of 1, under which the shear capacity represents the upper limit value. The applicability of various codes to this type of beam was investigated through the tests, and the test results provide data supporting the parametric optimization design of the beams.

2. Overview of Specimens

2.1. Specimen Parameters

In this experiment, a total of two test beams were fabricated and labeled as Beam 1 and Beam 2. The dimensions of the test beams are shown in Figure 1. The T-beams both had a height of 180 cm, a web width of 28 cm, and a top flange width of 175 cm. The beams were made of C55 concrete. The longitudinal reinforcement in the top flange and the bottom of the beams used HRB400 steel reinforcement with diameters of 14 mm and 28 mm, while the stirrups used HRB400 steel reinforcement with a diameter of 12 mm. The longitudinal reinforcement in the lower part of the flange and the web used HPB300 steel reinforcement with a diameter of 10 mm.

The prestressed reinforcement consisted of low-relaxation steel strands with a diameter of 15.2 mm and a tensile strength of 1860 MPa. The T-beams were prefabricated on a long-line bed in the precast beam yard of Jiangxi Communications Engineering Group Co., Ltd., Nanchang, China. After the reinforcement cage was tied, the steel strands were threaded through. The draped strands were bent at a position 5 m from the mid-span, with an average bending angle of 6.4°. Among them, there were 16 straight strands with a controlled tensile stress of 1395 MPa and 21 draped strands with a controlled tensile stress of 1339 MPa. After the concrete was poured, it was left to stand for 6 h and then covered with a tarpaulin. Steam curing was carried out with a staged temperature rise process. After 7 days, the actual strength and elastic modulus of the concrete were confirmed to be no less than 90% of the theoretical values specified in the design code, and prestress was applied to the T-beams.

2.2. Material Properties

The concrete was prepared using P.O 52.5 ordinary Portland cement, which was manufactured by Nanchang Haibo Cement Products Co., Ltd., (Nanchang, China). To ensure the validity of the test, the test beams used the same C55 concrete as the engineering beams. During the casting of each beam, three standard concrete cube specimens were reserved. The average compressive strength of the specimens corresponding to Beam 1 was 64.8 MPa with a coefficient of variation of 3.4%, while that of the specimens corresponding to Beam 2 was 64.6 MPa with a coefficient of variation of 8.0%. The relevant tests were carried out in accordance with the Test Methods for Physical and Mechanical Properties of Concrete (GB/T 50081-2019) [38]. Tensile tests were performed on the steel reinforcement samples from the test beam, following the standard (GB/T 228.1-2021) [39]. Prior to the test, mechanical property tests were performed on the various types of steel reinforcement and strands used in the beam, and the obtained mechanical property parameters are listed in

Table 1. Mechanical properties of steel reinforcement.

Steel Type	Yield Strength (MPa)	Ultimate Strength (MPa)	Ultimate Elongation (%)
A10	332.0	461.2	13.5
C12	418.0	595.4	18.3
C14	446.0	580.4	20.2
C28	432.0	614.1	23.0
Strands	1383.3	1834.6	4.6

.

3. Test Scheme

3.1. Loading Device and Loading Scheme

The test setup is shown in Figure 2. The test beams have a shear span-to-depth ratio of 1, and the loading point is located 1.76 m from the center of the support. The supports placed at the beam ends are rotating hinge supports. A loading beam is installed below the hydraulic jack, and a force sensor is placed on top of it. To ensure the safety and controllability of the high-tonnage failure test, a restraining steel frame is installed at the beam ends as an anti-overturning device. The bolts at the bottom of the restraining steel frame are loosened to ensure that the beam ends remain simply supported during the test. Graded loading of the test beam is achieved by controlling the hydraulic pressure of the jack.

Before the formal loading begins, a preliminary test loading is conducted to test the sensitivity of the on-site sensors. After ensuring that the instruments are properly calibrated, the formal loading process is initiated.

The formal loading is carried out in accordance with the graded loading regulations specified in the Standard for Test Methods of Concrete Structures (GB/T 50152-2009) [40]. Before the test beam cracks, loading is applied in increments of 500 kN, with a holding time of 5 min for each level. After cracks appear in the web of the test beam, the loading is increased in increments of 300 kN per level. The test is stopped and unloading is performed when the concrete is crushed or the force sensor reading drops sharply, indicating that the component has reached its ultimate shear capacity.

The load is defined as the magnitude of the force applied by the jack. The shear force refers to the shear value acting on the beam from the beam end to the loading point, and its magnitude is equal to the vertical reaction force of the support adjacent to the loading point. Self-weight and other loads are not included in the loading levels. The loading levels and corresponding load magnitudes are shown in

Table 2. Loading levels.

Loading Stage	Loading Level	Load (kN)	Shear Force (kN)	Failure Process
Phase 1	Pre-loading	1000	940
	Unloading	0	0
	D1	500	470
	D2	1000	940
	D3	1500	1410
	D4	2000	1880
	D5	2500	2350
	D6	3000	2820
	D7	3500	3290
	D8	4000	3760
	D9	4500	4230
	D10	5000	4700	Cracking observed
Phase 2	D11	5300	4982
	D12	5600	5264
	D13	5900	5546
	D14	6200	5828
	D15	6500	6110
	D16	6800	6392
	D17	7100	6674
	D18	7400	6956
	D19	7600	7144	Failure
	Unloading	0	0

.

3.2. Measurement Scheme

During the loading process, data on crack development, reinforcement and concrete strain, beam deflection, force, and displacement were recorded. The main measurement contents and the sensors used are as follows:

The load magnitude and beam deflection were measured. The force sensor, which was from Bengbu Dayang Sensor Co., Ltd., (Bengbu, China), was placed between the hydraulic jack and the reaction beam to measure the load applied by the jack. Displacement sensors were installed at the supports and the bottom of the beam at the loading point to measure the displacement and deformation of the beam.

The strain in the reinforcement was measured. Resistance strain gauges produced by Xi’an Zhonghang Electronic Measuring Instruments Co., Ltd., (Xi’an, China) were used to measure the strain in the reinforcement. To ensure measurement accuracy, the surface where the strain gauges were attached was ground and cleaned before installation. After attachment, the strain gauges were waterproofed for protection.

The crack development and failure modes were observed. The crack patterns under different load levels and the failure mode of the beam at the ultimate shear capacity were recorded on the A-side during the test.

The strand slip was measured. Steel plate bases were attached at the beam ends to fix magnetic mounts, and digital dial indicators were used to measure the slip of the strands during the test.

The surface strain variation of the beam was measured using the VIC-3D system manufactured by Correlated Solutions Inc. (Irmo, SC, USA). The VIC-3D system is a non-contact, full-field measurement device based on digital image correlation technology. By analyzing the speckle pattern painted on the beam surface, the system uses high-precision algorithms to calculate image data before and after deformation, thereby obtaining the strain distribution on the beam surface. The VIC-3D device was placed on the B-side of the beam to capture the strain variation on the B-side surface.

4. Analysis of Test Results

4.1. Load–Deflection Curve Analysis

The relationships between the vertical displacement at the loading point and the shear force at the beam ends for Beam 1 and Beam 2 are shown in Figure 3. The results indicate that the mechanical characteristics of the two beams are extremely similar, with slight differences in their ultimate shear capacities.

During loading stages D1–D10, the displacement and load of the two beams exhibited linear relationships. The initial stiffness of the beams $k_0$ = 394.0 kN/mm, suggesting that the beams remained in an elastic state. At D10, diagonal cracks appeared in the web of the beams, leading to a reduction in stiffness and accelerated deflection growth at the loading points. The stiffness of the beams $k_1$ = 125.9 kN/mm, resulting in a stiffness degradation of 268.1 kN/mm. In engineering applications, prestressed structures are not permitted to continue operating after significant cracking occurs. Cracks in the beam can lead to issues such as steel corrosion and prestress loss, thereby affecting the beam’s durability and serviceability. Therefore, it is recommended that the load corresponding to the beam’s stiffness degradation be taken as the limit for design loads, while the load range from the cracking load to the failure load can serve as a safety margin, enabling a more rational utilization of the beam’s mechanical properties.

Beam 1 failed at stage D19. At this time, the ultimate shear load at the beam ends was 7107 kN, and the deflection at the loading point was 31.6 mm. Subsequently, the shear capacity of the beam dropped abruptly, and the final residual deformation was 47.7 mm. Compared with Beam 1, the shear capacity of Beam 2 was slightly lower. It failed at stage D17. The ultimate shear load at the beam ends was 6742 kN, and the final residual deformation was 35.1 mm.

Although there is a 5.4% difference in the ultimate shear capacities between Beam 1 and Beam 2, during the loading process, the data regarding the crack development characteristics and strain changes of the two beams were extremely similar. Therefore, in the subsequent chapters, the data of Beam 1 will be used to explain the mechanical behavior of the beams.

4.2. Crack Development and Failure Mode

The crack development process on the A-side during loading is shown in Figure 4. During the initial loading phase, the test beam remained in the elastic stage, with a linear load–displacement curve at the loading point. At stage D6, fine diagonal cracks appeared at the junction between the flange plate and the web near the beam ends. As the load increased, these cracks extended toward the transverse diaphragm at the beam ends and eventually penetrated into the diaphragm. At stage D10, diagonal cracks first emerged in the web when the applied load reached approximately 66.1% of the ultimate load. These cracks originated near the support region and propagated upward along the web at an angle of approximately 45°. In the practical application of prestressed beams, crack development must be strictly controlled. When such cracks are detected, the safety of the beam needs to be evaluated. These cracks can be used as early warning signs before the beam fails.

With further loading, the crack widths increased, and additional diagonal cracks formed. By stage D13, vertical cracks appeared at the bottom of the loading point and propagated upward. As the load continued to increase, the diagonal cracks in the web extended further and eventually reached the flange plate. At stage D19, when the shear force at the beam ends reached 7107 kN, the test beam underwent sudden brittle failure without obvious warning. Multiple diagonal cracks widened abruptly, accompanied by the spalling of surface concrete, exposure of stirrups in the web, significant shear slip at the loading cross-section, and audible crushing of concrete. The location and shape of the concrete spalling are indicated by the black areas in Figure 4d. The failure mode was identified as diagonal compression failure.

4.3. Principal Tensile Strain on the B-Side Surface

The variation of principal tensile stress in the web during the loading process and the failure mode of the beam are shown in Figure 5. As shown in Figure 5a, when the load reached 3000 kN (D6), a diagonal High Principal Tensile Strain (HPTS) region first appeared between the upper flange and the web of the beam, with a maximum principal tensile strain of 2270 × 10⁻⁶. This HPTS region corresponded to the location of diagonal cracks observed on the A-side during the D6 loading stage.

When the load increased to 5000 kN (D10), as illustrated in Figure 5b, the HPTS region in the flange extended toward the end diaphragm, while an additional HPTS zone developed diagonally from the support area. This high-strain zone indicated the propagation path of the main diagonal crack.

With further loading (D13), the width of this diagonal HPTS region expanded continuously. The maximum principal tensile strain in the web’s diagonal region reached 5600 × 10⁻⁶. Simultaneously, multiple diagonal HPTS zones emerged in the web, corresponding to the formation of several diagonal cracks.

Prior to beam failure, the original HPTS region bifurcated into two distinct zones. Subsequently, the beam experienced sudden diagonal compression failure without obvious warning signs. Cracks propagated along these HPTS zones, accompanied by concrete spalling in both the web and flange regions.

4.4. Stirrup Strain

The measured strain of the stirrups is shown in Figure 6. In the early stages of loading, the strain at measurement point G1 was positive, indicating tensile stress in these regions. The strain curves exhibited linear growth during this phase. Measurement points G2–G4 initially exhibited compressive strain due to their location within the concrete compression zone. When the load reached 5000 kN (D10), cracks formed in the compressed concrete of the web, causing a sharp increase in strain at the stirrup measurement points. The load–strain curves of these stirrups showed a distinct inflection point, reflecting the transition of the stirrups from compression to tension as the cracked concrete redistributed stress.

4.5. Strand Slippage

Pre-tensioned beams have no anchorage devices and need to apply prestress to the beam body through the bonding force between strands and concrete. When loaded to a certain level, the bonding force between the strands at the beam end and the concrete will exceed the limit value, causing slip and retraction of prestressed steel strands.

This test measured the slippage of three strands. The arrangement of measurement points and the variation of slippage with shear force at the beam ends are shown in Figure 7. As illustrated in the figure, almost no slippage occurred in the strands before the beam cracked. When the load reached 5600 kN (D12), the bond slippage at Measurement Point 1 was 0.57 mm, while slippage at the other points remained below 0.05 mm. As the load increased to 7100 kN (D17), the slippage at Measurement Points 1 and 2 increased sharply with minimal additional load, reaching a maximum slippage of 3.815 mm. This indicates a significant degradation in bond capacity between the concrete and the strands at these locations. In contrast, slippage at Measurement Point 3 remained below 0.6 mm, suggesting that the draped strands near the upper bent regions were more prone to bond slippage compared to the straight prestressing strands at the bottom during shear loading.

5. Comparison of Shear Capacity Upper Limits in Codes

To prevent excessive diagonal crack widths and diagonal compression failure in concrete beams, various codes specify upper limits for shear capacity. The Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts (JTG 3362-2018) [41] collected test data on the shear capacity of un-reinforced ordinary concrete beams. Based on the relationship between shear capacity and shear span-to-depth ratio, it established an upper limit formula using the lower envelope of experimental data. The Specifications for Design of Concrete Structures (GB 50010-2010) [42] incorporates a minimum size limitation formula that considers the influence of the height-to-width ratio on the upper limit of shear capacity. The Specifications for Design of Prefabricated Concrete Highway Bridges (JTG/T 3365-05-2022) [43] refitted formulas based on multiple codes and experimental data, accounting for the effects of prestressing. The AASHTO LRFD Bridge Design Specifications [44] provide an upper limit formula for shear capacity based on the modified compression field theory, which considers the enhancement of beam shear capacity due to the vertical component of prestressing $V_p$. Eurocode 2 [45] calculates the upper limit using a variable-angle truss model by defining the inclination of the compressive strut $\theta$. The calculation formulas of each code are shown in

Table 3. Calculation parameters and formulas of codes.

Codes	Calculation Formulas
JTG 3362	${\gamma }_0{V}_d\le 0.51\times {10}^{-3}\sqrt{f_{cu,k}}b{h}_0$
JTG/T 3365-05	${\gamma }_0{V}_d\le 0.23{\alpha }_s{\varphi }_s{f}_{cd}{b}_e{h}_e+V_{pe}$ $a_s={\left({\displaystyle \frac{b_e}{h_w}}\right)}^{0.14}$ $V_{pe}=0.95\left({\sigma }_{pe,i}{A}_{pb,i}\sin {\theta }_i+{\sigma }_{pe,e}{A}_{pb,e}\sin {\theta }_e\right)$
GB 50010	$h_w/b\le 4$, $V\le 0.25{\beta }_c{f}_{c}b{h}_0$ $h_w/b\ge 6$, $V\le 0.2{\beta }_c{f}_{c}b{h}_0$ When  $4<h_w/b<6$, calculate by linear interpolation.
AASHTO	$V\le 0.25f_c’b_v{h}_v+V_p$
Eurocode2	$V\le {\alpha }_{cw}bz{v}_1{f_{cd}}^{\prime }/\left(\cot \theta +\tan \theta \right)$

, and the definitions of specific parameters in the formulas can be found in the references.

For the test beams, the shear capacity upper limits were calculated using these codes and compared with the average values of the test results of the two beams, as shown in

Table 4. Shear capacity upper limits calculated by five codes.

Codes	JTG 3362	JTG/T 3365-05	GB 50010	AASHTO	Eurocode2
$V_{code}$	1695	2034	2884	4244	3335
$V_{test}/V_{code}$	4.09	3.40	2.40	1.63	2.08

. It can be seen that the upper limits specified by different codes vary but are all lower than the experimental value. Among them, the AASHTO code yields the highest upper limit (4244 kN, 61.2% of the experimental value), while China’s JTG 3362-2018 produces the most conservative result (1695 kN, 24.48% of the experimental value), with a safety factor of 4.09. The upper limit calculated by JTG/T 3365-05-2022 is slightly higher than that of JTG 3362-2018, at 2034 kN (29.37% of the experimental value). The results from GB 50010-2010 and Eurocode 2 are similar, with upper limits of 2884 kN and 3335 kN (41.65% and 48.16% of the experimental value), respectively.

6. Conclusions

This paper details an experimental study on the shear capacity of two 30 m pre-tensioned concrete T-beams with draped strands under a shear span ratio of 1. Data including the load–deflection curves of the two beams, as well as the crack development, the failure mode, the surface strain of the beam, and the strains of the steel bars and steel strands from Beam 1, were analyzed. The main conclusions are as follows:

• The mechanical characteristics of the two beams are similar. Before cracking, the load–deflection curves of the test beams were essentially linear. After diagonal cracks appeared in the webs, the slopes of the curves decreased, indicating a significant reduction in the stiffness of the beams. The development of high-strain regions observed by the VIC-3D system on the B-side matched with the crack propagation process recorded on the A-side. When the ultimate shear capacities of the beams were reached, the crack widths of the beams increased rapidly, and concrete blocks fell off the webs. Both beams exhibited typical diagonal compression failure characteristics. Based on the experimental results, it is recommended that the load corresponding to beam stiffness degradation be adopted as the design load limit, with a safety factor of approximately 1.5. The interval from the cracking load to the failure load can be defined as a safety margin, allowing for a more rational utilization of the beams’ mechanical properties.
• In the early loading stage, the concrete and reinforcement worked together through their bond, and strain increased slowly. After cracking occurred in the web, some stirrups and strands began to carry tensile forces, leading to rapid strain growth. When the load was below 5100 kN, the slippage of strands was generally small. At 7100 kN, the slippage of draped strands increased significantly. The upper draped strands were more prone to slippage compared to the straight strands at the bottom.
• The ultimate shear capacities of the two beams obtained from the test were 7107 kN and 6742 kN. Meanwhile, the upper limit of shear capacity for the pre-tensioned concrete T-beams with draped strands was calculated according to five domestic and international codes, and the results were compared with the average value of the experimental values. The findings indicate that the American AASHTO code yields the highest upper limit of shear capacity at 4244 kN. The Chinese GB-50010 and European Eurocode 2 codes provide similar calculations for the upper limit of shear capacity. The JTG-3362 code specifies an upper limit of shear capacity of 1695 kN, which is relatively low compared to the other codes, with a safety factor reaching 4.09. The test results demonstrate that the design codes are conservative in specifying the upper limit of the shear capacity of pre-tensioned concrete T-beams, which leads to increased bridge construction costs and material waste. The test results provide data supporting the lightweight design of subsequent beams, promoting more economical and efficient bridge construction.