Shear Behavior of Ultrahigh-Performance Concrete Pretensioned Bridge Girders

The widespread, growing interest in using ultrahigh-performance concrete (UHPC) in bridge superstructures in the US is being hindered by a lack of structural design models that are verified with large-scale experimental tests relevant to this class of fiber-reinforced cementitious composites. Offering compressive strengths of about 125–250 MPa (18–36 ksi), cracking tensile strengths up to 12 MPa (1.74 ksi) sustained well into the postcracking regime (El-Helou et al. 2022; Haber et al. 2018; Wille et al. 2011), and exceptional durability (Li et al. 2020; Alkaysi et al. 2016; Magureanu et al. 2012; Graybeal and Tanesi 2007), UHPC allows for higher levels of prestressing and slender and more efficient bridge girders than conventional concrete. These benefits translate into financial savings related to reductions in size of bridge elements, reduced load demands on the superstructure and substructure, elimination of potential girder lines and/or piers, and new opportunities in construction methodologies.

One of the key considerations in bridge design that affects the geometry of the structural components, and consequently the potential advantages of using UHPC in place of conventional concrete in parts (or all) of the superstructure, is an appropriate determination of the shear response of UHPC girders. A few researchers attempted to determine this response through experimental testing focused on evaluating the behavior of UHPC beams tested in shear (Graybeal 2006, 2009; Voo et al. 2006, 2010; Hegger and Bertram 2008; Hegger et al. 2009; Crane 2010; Xia et al. 2011; Yang et al. 2012; Baby et al. 2014; Pansuk et al. 2017). These efforts demonstrated that the tensile behavior of UHPC govern the shear capacity of UHPC girders, that UHPC can develop multiple and closely spaced cracks due to its fiber reinforcement even without transverse shear reinforcement, and that shear failure occurs when a dominant crack propagates over the depth of the girder’s web. A detailed summary of the main findings of a few of the shear tests found in the literature is presented in this paper.

Earlier work by Graybeal (2006) on three prestressed bulb-tee girders with height $h=914\mathrm{mm}$ (36 in.) and three Pi-shaped girder cross sections (Graybeal 2009) with $h=838\mathrm{mm}$ (33 in.) demonstrated that full-scale bridge girders made with UHPC can have a web thickness as small as 81 mm (3.2 in.) and withstand vertical shear stresses ($V/b_w{d}_v$, where $V$ is the ultimate shear capacity, $b_w$ is the width of the web, and $d_v$ is the effective shear depth) of more than 17.2 MPa (2.5 ksi) without needing transverse shear reinforcement. The testing of these prototype bridge girders confirmed the ability of the discrete fiber reinforcement in the UHPC matrix to facilitate development of multiple closely spaced diagonal cracks in the web as the shear demand increased before eventual formation of a dominant shear crack prompting girder failure. Given the high compressive strength of UHPC, Graybeal (2006) observed that the limiting parameter for shear failure was the postcracking tensile resistance of UHPC (i.e., postcracking strength and strain capacity) instead of the crushing of the concrete along the compression strut, as would be expected in conventional concrete girders.

Voo et al. (2010) conducted shear tests on eight prestressed I-section girders made with UHPC and reinforced with discrete steel fibers having different lengths (15, 20, and 25 mm or 0.59, 0.79, and 0.98 in.) and quantities (1.0% and 1.5% by volume). The girders had a height of 650 mm (25.6 in.) and a web width of 50 mm (2.0 in.) with no transverse shear reinforcement. Tight spacings of shear cracks were observed in the webs of all beams, and the girder failure was governed by the opening of a single shear crack at peak load. The study concluded that the tensile failure–based shear response occurs when (1) sufficient amounts of fibers are provided in the UHPC mix to result in a tensile strain-hardening behavior after first cracking, and (2) the contribution of the friction at crack interfaces due to aggregate interlock is greatly reduced because of the elimination of coarse particles from the mix.

Baby et al. (2014) evaluated the influence of the UHPC mix, the type of fiber reinforcement (steel or organic), the use of prestressing strands or conventional bars in the longitudinal direction (flexure), and the presence of vertical shear reinforcement in the web on the shear capacities of 11 beams with I-shaped cross sections. In addition to the conclusions reached by Graybeal (2006) and Voo et al. (2010), these tests revealed that the shear strength depends on (1) the localization strain of UHPC (strain at which softening begins), (2) the shape of the beam’s cross-section, and (3) the fiber orientation in the web. Baby et al. (2014) highlighted that the full yield strength of the transverse steel reinforcement will be engaged only if the localization strain of the UHPC is large enough to allow the reinforcement to yield before the principal tensile strain in the web reaches the UHPC localization strain.

Although the testing programs in the literature revealed key aspects of the behavior of UHPC girders, they did not provide sufficient information to correlate the shear response of these girders with respect to the tensile behavior of UHPC, particularly its strain-hardening behavior in tension. This investigation is crucial because it will allow for the development of predictive models that rely on the design and mechanical properties typically available in the design phase (through the execution of material testing and the selection of bridge girder geometry and steel reinforcement ratios). In this paper, the shear behavior of six prestressed, pretensioned bulb-tee UHPC bridge girders is experimentally investigated and discussed with respect to the tensile performance characteristics of UHPC obtained from material tests. The analysis of the test results focused on verifying the ability of UHPC to sustain its strain-hardening characteristics at the structural level and exploring numerous design parameters that can affect the shear capacity, including the UHPC material properties, the girder height, the web thickness, the number of prestressing strands, and the presence of discrete transverse steel reinforcement in the web. In a subsequent phase of the research program, the results of this experimental work are used to validate a predictive shear design methodology for UHPC girders developed by the authors, which is based on stress equilibrium and strain compatibility of the average stresses and strains in the web of beams.

The girder specimens were tested at the Federal Highway Administration (FHWA) Turner-Fairbank Highway Research Center structural testing laboratory. An overview of the test setup used for all girders is shown in Fig. 2. During each test, each girder was supported with a roller support at the end subjected to high shear (west side) and by a partial pin support assembly bearing on a load cell and a hydraulic jack at the other end (east side). Each girder was loaded in a four-point bending configuration with the east and west reaction points within the span located 305 mm (12 in.) and 610 mm (24 in.) from the centerline of the reaction frame, respectively, as shown in Fig. 3. The roller and partial pin supports each consisted of a 152-mm (6-in.) diameter steel cylinder inserted between two steel bearing plates having a thickness of 38.1 mm (1.5 in.), a width of 305 mm (12 in.), and a length equal to the width of the bottom flange. The bearing plates of the pin support were grooved to prevent rolling, whereas the plates at the roller support were flat. To relieve potential frictional forces on the pin support generated by the loading jack line of action relative to the inclination of the bearing location, an additional steel plate resting on a polytetrafluoroethylene (PTFE) sheet was included within the partial pin support assembly, as shown in Fig. 3. The additional steel plate had similar dimensions as the supports’ bearing plates. When the hydraulic jack applied load and deformation onto the east end of the girder, two reaction points near the reaction frame resisted the loading. These reaction points consisted of a pair of steel transfer plates reacting against the reaction frame through a set of three load cells with spherical bearing plates (two load cells on the west side of the midspan and one load cell on the east side of the midspan), a spreader beam, and a greased spherical bearing, as shown in Figs. 2 and 3. The greased spherical bearings at the reaction points and above the spreader beam allow the spreader beam to rotate. Each of the center transfer plates had a thickness of 102 mm (4 in.) and a width of 0.30 m (12 in.). All transfer and bearing plates were grouted to the girder’s top or bottom flanges and were long enough to fully support the full width of the flanges.

All girders had a 914-mm (36-in.) overhang on the end with the roller support and a 610-mm (24-in.) overhang on the end with the loading jack to ensure that the support reactions were located at a distance greater than the transfer length of the strands (which was estimated to be 15 in.). The total span, L, was 8.2 m (27 ft), and the shear span, a, was 2.74 m (9 ft) for girders H-P1, J-P1, J-P1S, and H-P2, respectively; L and a were 10.1 m (33 ft) and 3.35 m (11 ft) for girders H-P3 and H-P3R, respectively, giving a shear span-to-depth ratio of approximately 3.5 for all specimens. In all tests, the load was applied by the hydraulic jack in 44.5-kN (10-kip) increments until a load was achieved that was 20% greater than the load at which the first crack was detected. The loading process was then switched to displacement control at a jack displacement rate between $1.27\mathrm{mm}/\min$ ($0.05\mathrm{in.}/\min$) and $7.62\mathrm{mm}/\min$ ($0.30\mathrm{in.}/\min$). The loading was paused approximately five times to record measurements, mark cracks, and capture photographs. For all specimens, the instrumentation included 13 displacement transducers and four load cells as well as noncontact strain and displacement measurements via a digital image correlation (DIC) system. The displacement transducers included (1) six wire potentiometers (WPs) measuring the vertical displacement of the girder at the marked locations shown in Fig. 3, (2) three linear variable displacement transducers (LVDTs) mounted on three strands on the high shear end with the roller support (east end), and (3) two pairs of LVDTs mounted to the two sides of each of the top and bottom flanges. These last LVDTs measured displacements over a gauge length of 610 mm (24 in.), which is equal to the clear distance between the transfer plates at the reaction points under the spreader beam. The pair of top LVDTs were mounted at a vertical distance of 25.4 mm (1 in.) from the extreme top fiber, and the pair of bottom LVDTs were mounted on the bottom surface of the girder, located at a vertical distance of 50.8 mm (2 in.) below the girder, as shown in Fig. 3. For girder H-P3R with transverse steel reinforcement, 25 strain gages were mounted on the vertical bars to measure the bar strains during the test. One to three strain gauges were attached onto every second bar at the bottom, center, and top of the web for the vertical bars within the shear span and under the point loads, as shown in Fig. 4. The noncontact measurements were determined after completion of the test by analyzing the video recorded by a pair of DIC cameras covering the full shear span on one side of the girder (Fig. 2). These measurements included (1) a set of strain gauges extending over the full diagonal length of the web forming a 45° angle with the longitudinal axis of the girder (Fig. 3), used to detect the onset of diagonal cracking; and (2) a set of six strain rosettes (RSs), each consisting of three strain gauges forming angles of 0°, 60°, and 120° with the longitudinal axis of the girder, as shown in Fig. 3. The gauge lengths of the diagonal strain gauges were 287 mm (11.3 in.) for girders of shape P1 and P2, and 431 mm (17.0 in.) for girders of shape P3. The strain rosettes were used to measure the average concrete strains over several diagonal cracks at multiple locations over the height of the web. The data from the RSs were used to calculate the principal tensile and compressive strains in the web and the inclination angle of the diagonal compressive strains. To ensure continuous strain readings not skewed by the opening of the critical crack, the centers of five rosettes (RS1 through RS5) with a gauge length of 152.4 mm (6 in.) were placed in a line parallel and below the critical crack, as shown in Fig. 3, with a clear distance of at least 25.4 mm (1 in.) between the critical crack opening and gauge length. The rosettes were mounted to cover the full height of the web with the centers of RS2 and RS3 at midheight of the girder and the web, respectively. The locations of RS1, RS2, and RS4 varied slightly between each girder. RS1 was approximately 356 mm (14 in.) from the top of each girder, whereas RS3 and RS5 were 373 mm (14.7 in.) and 401 mm (15.8 in.) from the bottom of each girder, respectively. To obtain average strain measurements over the full depth of the web (including the critical shear crack), RS6 was mounted at the midheight of the web for all girders and had a gauge length of 355.6 mm (14 in.) for girders of shape P1 and P2, and 406.4 mm (16 in.) for girders of shape P3, as shown in Fig. 3.

One of the main objectives of this study was to investigate the shear capacity of UHPC girders with respect to mechanical property parameters identified from independent material tests. For this reason, companion specimens were cast from each of the six batches used to make the girders, which allowed for assessment of the UHPC’s compression and tension properties at the time of the structural tests. The compression test specimens were cast into cylindrical plastic molds having a diameter of 76.2 mm (3 in.) and a height of 152.4 mm (6 in.). They were cast vertically in a single lift of fresh UHPC and were subjected to brief external vibration (using a vibrating table) to release entrapped air. The compression cylinders were demolded at the time of detensioning of strands and stored in ambient environment, generally alongside the girder, until the time of the test. Three cylinders per batch were tested according to ASTM C1856 (ASTM 2017) to capture modulus of elasticity, $E$, compressive strength, $f_c^{\prime }$, and strain at compressive strength, ${\epsilon }_{cu}$. The average results of the compression parameters for each girder specimen are presented in Table 2.

The tension test specimens were molded into prismatic steel molds having a length of 432 mm (17 in.) and cross-sectional dimensions of $50.8\times 50.8\mathrm{mm}$ ($2\times 2\mathrm{in.}$). They were cast horizontally from a stationary placement point on one end of the mold and subjected to brief external vibration using a vibrating table. Similar to the cylinders, the tensile specimens were demolded at the time of detensioning of strands and generally stored alongside the girder until the time of the test. They were tested in direct tension according to AASHTO T 397 (AASHTO 2022), which is based on the test method developed by Graybeal and Baby (2013); this test method involves capturing the tensile load and associated strain over a 101.6-mm (4-in.) gauge length during a fixed-end uniaxial displacement-controlled test. Three prisms were tested for girders H-P1 and J-P1, four prisms were tested for girders J-P1S and H-P3R, and six prisms were tested for girders H-P2 and H-P3. The average tensile parameters, namely the average effective cracking stress, ${\overline{f}}_{t,cr}$, the average localization stress, ${\overline{f}}_{t,\mathrm{l}\mathrm{o}\mathrm{c}}$, and the average localization strain, ${\overline{\epsilon }}_{t,\mathrm{l}\mathrm{o}\mathrm{c}}$, were obtained from the individual stress–strain response of each of the tested prisms. The effective cracking stress, $f_{t,cr}$, of each specimen was taken as the stress at the intercept of a line with a slope equal to the elastic modulus and a strain offset of 0.02% [AASHTO T 397 (AASHTO 2022); Haber et al. 2018; El-Helou et al. 2022]. The localization stress, $f_{t,\mathrm{l}\mathrm{o}\mathrm{c}}$, and strain, ${\epsilon }_{t,\mathrm{l}\mathrm{o}\mathrm{c}}$, of each specimen were visually determined as the first point in the stress–strain plot where the stress decreases continuously with increasing strain. The average results of the tensile parameters of UHPC for each girder specimen at the time of the test are reported in Table 2. The average uniaxial stress–strain relationships for each girder specimen are shown in Fig. 5(a).

The stress–strain relationships for the transverse steel bars reinforcing the web of girder H-P3R were experimentally determined from five tensile coupon tests performed according to ASTM A370 (ASTM 2020) and are plotted in Fig. 5(b). The bars had an average yield strength of 483.3 MPa (70.1 ksi), an average ultimate tensile strength of 768.8 MPa (111.5 ksi), and average elongation of 12.5% at fracture. The bars’ modulus of elasticity was assumed to be 200 GPa (29,000 ksi).

The tensile parameters for the prestressing strands were experimentally determined from nine strand pullout tests performed according to ASTM A370 (ASTM 2020). The strands had an average yield strength, ${\overline{f}}_{py}$, of 1,692 MPa (246 ksi), an average ultimate tensile strength, ${\overline{f}}_{pu}$, of 1,934 MPa (281 ksi), and an average rupture strain, ${\overline{\epsilon }}_{pu}$, of 0.0682. The strand modulus of elasticity, $E_p$, was assumed to be 196.5 GPa (28,500 ksi). Based on these test results, the strands conform to the mechanical property thresholds of ASTM A416 (ASTM 2018a) for Grade 1,860 MPa (270 ksi) strands.

The shear force versus the maximum shear span deflection relationships for all tested girders are shown in Fig. 6, and the crack patterns at failure are shown in Fig. 7. A 5.0-mm (0.20-in.) displacement offset was introduced between each of the curves plotted in Fig. 6 for clarity. The shear force presented is equal to the shear at the critical crack and was obtained by adding the reaction at the roller support (calculated from equilibrium of the forces measured by the jack and the east and west load cells) to the shear force generated by the dead loads at the location of the critical crack. The measured maximum deflection of the shear span was taken as the vertical displacement under the west load cells with respect to a reference line connecting the supports.

The responses shown in the shear force–displacement plots in Fig. 6 are linearly elastic until the first diagonal crack occurred. As the load continued to increase, more diagonal cracks appeared and propagated toward the top flange of each girder causing a gradual loss of stiffness (slope), with the exception of girder H-P3R where the slope did not appreciably change until the yielding of the transverse steel bars. After a significant number of closely spaced cracks formed, the principal tensile deformation in the web began to localize into a dominant crack that gradually increased in width as the fibers bridging the crack pulled out of the cementitious matrix. Thereafter, the girder failed in shear (Fig. 7). No crushing of the UHPC in between cracks (compression field) was observed in any of the tested girders. For girder H-P3R, the presence of transverse steel bars in the web supplemented the fibers in resisting the tensile loads, resulting in a decrease in the crack spacing and a significant increase in the shear capacity (Figs. 6 and 7). A second critical point in the force–displacement behavior of specimen H-P3R can be identified at the change in the load-displacement slope, as shown in Fig. 6. This point likely corresponds to the local yielding of one or more of the steel bars in the web. However, the first local yielding of the bars (strain ${\epsilon }_{st}\ge \mathrm{2,400}\times {10}^{-6}$) was detected by the lower strain gauges installed on bars 10, 12, and 14 at a force 7.4% greater than the estimated first yielding highlighted in Fig. 6; this observation indicates that local yielding appears to have initiated at a location not monitored by the strain gauges. As the load continued to increase, the strain in the bars reached a strain greater than the yielding strain for most instrumented bars within the shear span. Table 3 shows the bar strain gauge readings right before crack localization and shear failure.

The behavior of the specimens after shear failure was different depending on the UHPC product and the presence of transverse reinforcement. The girders made with UHPC H with no transverse reinforcement appeared to carry larger post-peak loads than the specimens made with UHPC J, as shown in Fig. 6. However, because the critical crack widened immediately after the peak load (caused by the complete pullout of the bridging fibers), the observed postpeak strength of the girders is attributed to the redistribution of the internal stresses in which the wide and heavily reinforced flanges carried a substantial portion of the loads without a significant contribution from the web. Girder H-P3R did not show any post-peak behavior because the crack localization at failure was swift, prompting an abrupt halt to the loading protocol.

The experimental results for all girders are summarized in Table 4. The stress in the strands at the beginning of the test, $f_{pe}$, including all losses that occurred between strand release and the time of the test, was estimated by using the concrete strains measured by four vibrating wire gauges cast into the girder cross section at midspan. Two gauges were embedded between the top strands and two were embedded at the centroid of the bottom strands. The initial concrete strain profile was then constructed by comparing the concrete strains at the time of the test to the reference strains taken before detensioning of the strands. The difference in concrete strains at the centroid of strands was then determined, assuming a perfect bond between the strands and surrounding concrete. To estimate the difference in the stresses (prestress loss) in the strands between jacking and the time of the test, these strains were multiplied by the modulus of elasticity of the strands, $E_p=196.5\mathrm{GPa}$ (28,500 ksi). The prestress loss was 14% for girder H-P1, 22% for J-P1, 18% for J-P1S, 14% for H-P2, 18% for H-P3, and 16% for H-P3R.

The first diagonal crack was extremely narrow and could not be qualitatively detected for all girders. In fact, all the diagonal cracks before localization were undetectable to the naked eye. They were identified by spraying the surface of the girder’s web with an evaporative liquid that penetrated the cracks and evaporated from the web’s surface, making the cracks temporarily visible. No flexural cracks were detectable prior to diagonal cracking. Fig. 8 shows an example of the crack pattern of girder H-P3 with the detected prelocalization cracks highlighted with thin black lines. To quantitatively determine the shear force at first crack, $V_{cr}$, the noncontact strain gauges at 45° (Fig. 3) were used to determine the force at which a significant increase in readings occurred, as shown in Fig. 9. In Table 4, $a_c$ is the longitudinal distance between the roller support and the location of the critical crack at midheight of the web, ${\theta }_{\exp }$ is the average angle (over the web height) of the critical shear crack with the longitudinal axis measured with a protractor after completion of the test, $V_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ is the ultimate shear capacity, and ${\epsilon }_{T,\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ and ${\epsilon }_{B,\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ are the concrete flexural strains at the top and bottom of the section (tension positive) under the spreader beam at shear failure, respectively. The values of ${\epsilon }_{T,\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ and ${\epsilon }_{B,\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ were obtained by assuming a linear strain profile created by the measured change in strains in the UHPC during the test from the two pairs of top and bottom LVDTs that were installed under the spreader beam and then superposing the initial strains due to prestressing. The strains measured by the LVDTs were obtained by dividing the displacement readings by the LVDT gauge length. Based on these strain measurements, it is concluded that prior to shear failure, the UHPC in the bottom flange under the spreader beam has cracked and the strand stress-strain response likely remained elastic.

In all girders, no strand slip was detected by the LVDTs installed on the strands until after application of the peak applied load. The maximum slip after failure was also negligible for all girders, with a maximum value of 0.32 mm (0.0126 in.) for the middle top strand in the bottom bulb of girder H-P3R.

Many of the design and analysis approaches for the shear behavior of conventional concrete beams involve resolving the shear force into principal tensile and compressive components and then assessing the resistance offered by the concrete part and any discrete reinforcement in the web (AASHTO 2020; ACI 2019; CSA 2019). In these approaches, the principal stresses are typically informed from estimated biaxial relationships derived with respect to key uniaxial material parameters such as the compressive strength, $f_c^{\prime }$. For UHPC beams, the experimental tests performed by the authors and by other researchers (Voo et al. 2010; Baby et al. 2014) highlighted the effect of two other parameters on the shear behavior, specifically the localization stress, $f_{t,\mathrm{l}\mathrm{o}\mathrm{c}}$, and strain, ${\epsilon }_{t,\mathrm{l}\mathrm{o}\mathrm{c}}$. Given UHPC’s high compressive strength, in many girder cross-sectional configurations the shear failure is likely to originate from tensile behaviors rather than from concrete crushing. Moreover, the contribution of the UHPC tensile stress component is a substantial component of the shear resistance. For instance, more than 52% of the total shear capacity of girder H-P3R originated from the UHPC tensile behavior even though the girder was reinforced with discrete steel reinforcement at a ratio of 1.3% (${\rho }_v=A_v/b_{w}s$). In this section, the principal stresses and strains in the web of the tested girders are compared to the uniaxial parameters obtained from material characterization tests to assess the connection between the responses on the material and structural scale.

The experimental results from the beam shear testing of six bulb-tee pretensioned UHPC bridge girders are presented in this section. The girders were heavily prestressed with 17.8-mm (0.7-in.) diameter steel strands and had a web width of 76.2 mm (3 in.) and 101.6 (4 in.) and a height of 889 mm (35 in.) and 1,092 mm (43 in.). All girders except one had no transverse shear reinforcement in the web. The test variables include the type of UHPC product, the height of the beam and thickness of the web, the number of prestressing strands, and the presence of shear reinforcement in the beams. The principal stresses and strains in the web of each tested girder were obtained and compared to those obtained from uniaxial tests to determine whether the fundamental behavior of UHPC can be attained at the structural level. Based on these investigations, the following conclusions can be drawn:

Most data and models generated and used during the study appear in the published article. However, some information is proprietary or confidential in nature and may only be provided with restrictions (e.g., anonymized data of vendor and product names). The experimental and analytical data presented in this study are available from the authors upon reasonable request. All images and tables in this manuscript were developed by and are sourced to FHWA.

The research presented in this paper was funded by FHWA. The publication of this paper does not necessarily indicate approval or endorsement of the findings, opinions, conclusions, or recommendations either inferred or specifically expressed herein by FHWA or the US Government. This research could not have been completed were it not for the dedicated support of the technical professionals associated with the FHWA Structural Concrete Research Program.