CIVIL ENGINEERING 365 ALL ABOUT CIVIL ENGINEERING



AbstractBecause of their tensile strain-hardening characteristics, ultrahigh-performance concrete (UHPC) materials offer significant advantages in terms of beam shear capacity and postcracking behavior compared to conventional reinforced-concrete beams. These advantages rely on UHPC’s ability to sustain its strain-hardening characteristics at the structural level. This paper reports the results of an experimental investigation on the parameters influencing the structural shear behavior of prestressed UHPC bridge girders. Six pretensioned bulb-tee UHPC bridge girders were tested in shear with the following test variables: 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. The average relationship between the principal stress and strains in the web was monitored during the tests and compared to behavior obtained from uniaxial tests. The shear behavior and capacities of the tested girders were observed to be largely dependent on the tensile characteristics of UHPC. The results demonstrate UHPC’s capability to sustain its strain-hardening characteristics at the structural scale and highlight the importance of the crack localization strain, corresponding to the end of the tensile hardening behavior, to the global shear performance of UHPC girders.IntroductionThe 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  mm (36 in.) and three Pi-shaped girder cross sections (Graybeal 2009) with h=838  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/bwdv, where V is the ultimate shear capacity, bw is the width of the web, and dv 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.Experimental ProgramSpecimens and Test MatrixThe experimental program described in this paper comprises a total of six bulb-tee pretensioned bridge girder specimens made with UHPC and subjected to external loading proportioned to generate beam shear elastic and inelastic behaviors. The cross-sectional shape of the specimens was based on the Precast Concrete Economical Fabrication (PCEF) sections with geometrical modifications to obtain a narrower web and top flange width and a shallower bottom flange. The geometrical modifications were made by moving the side forms inward, inserting wooden blocks on both sides of the top flange, and adjusting the soffit width and elevation. The standard drawings for the original PCEF sections can be found in the New Jersey Department of Transportation Design Manual for Bridges and Structures (NJDOT 2016). Fig. 1 shows the cross-sectional dimensions and reinforcement details of the tested girders. Four girders (H-P1, J-P1, J-P1S, and H-P2) had a total length of 9.75 m (32 ft) and two girders (H-P3 and H-P3R) had a total length of 11.58 m (38 ft). The test matrix covered parameters that may control the shear design of UHPC bridge girders and included the following variables: (1) the UHPC product: two commercially available UHPC products, denoted “H” and “J,” were used to make the girders; (2) the girder height: four girders (of shape P1 and P2) had a height of 889 mm (35 in.) and two girders (of shape P3) had a height of 1,092 mm (43 in.); (3) the web width: five girders had a web thickness of 76.2 mm (3 in.) and girder H-P2 had a web thickness of 101.6 mm (4 in.), with the web thickness being accompanied by a change in top and bottom flange dimensions as shown in Fig. 1; (4) the number of prestressing strands: all girders were prestressed with a total of 26 straight 17.8-mm (0.7-in.) diameter steel strands, with 24 strands located in the bottom bulb and 2 strands in the top bulb (except for girder J-P1S, which had 18 strands in the bottom bulb and 2 in the top bulb, for a total of 20 strands); and (5) the presence of vertical (transverse) steel reinforcement in the web: only girder H-P3R contained transverse steel reinforcement, which consisted of one vertical Grade 414 MPa (60 ksi) No. 16 bar (No. 5 US bar size) spaced each 203.2 mm (8 in.) for the full length of the girder. The 17.8-mm (0.7-in.) diameter prestressing strands were seven-wire low-relaxation steel strands with a cross-sectional area of 189.7  mm2 (0.294  in2) and a specified minimum ultimate strength of 1,860 MPa (270 ksi); they were each pretensioned to 75% of their specified minimum ultimate strength and placed at a spacing of 50.8 mm (2 in.) center-to-center. The initial prestress force over cross-sectional area ratio was 25.0 MPa (3.63 ksi) for girders H-P1 and J-P1, 19.3 MPa (2.80 ksi) for girder J-P1S, 22.9 MPa (3.33 ksi) for girder H-P2, and 23.5 MPa (3.40 ksi) for girders H-P3 and H-P3R. The first (bottom) and second layers of strands were located 50.8 mm (2 in.) and 101.6 mm (4 in.) from the bottom of the section, respectively. The third (top) layer of strands was located 50.8 mm (2 in.) from the top of the section, as shown in Fig. 1. All girders had small amounts of vertical end-zone steel splitting reinforcement that extended a longitudinal distance equal to approximately one-quarter of the girder’s height from each end. The end-zone reinforcement consisted of vertical No. 16 single bars (No. 5 US bar size) in the web and closed loop bent No. 10 bars (No. 3 US bar size) around the strands.Mix Design and Girder FabricationTable 1 provides the details of the UHPC mix designs used in this study. Because these UHPC products are proprietary, they were supplied in three primary constituents: the preblended powder containing the granular constituents (e.g., cement, silica fume, and fine sand), liquid admixtures, and fibers. Both UHPC products used brass-coated steel fibers at a 2% dosage by volume, which were supplied from the same manufacturer. The fibers were straight and had a length of 13 mm (0.51 in.), a diameter of 0.2 mm (0.0079 in.), and a supplier-reported minimum tensile strength of 2,600 MPa (377 ksi).Table 1. UHPC mix design proportionsTable 1. UHPC mix design proportionsProperty, kg/m3 (lb/yd3)HJPreblended powder2,179a (3,672)2,182 (3,678)Water174 (294)166 (280)Liquid admixtures6.1 (10.3)73.6 (124)Steel straight fibers155 (262)157 (265)The specimens made with UHPC H (H-P1, H-P2, H-P3, and H-P3R) were fabricated at a precast plant in New Jersey, and the specimens made of UHPC J (J-P1 and J-P1B) were fabricated at a precast plant in Florida. UHPC H was mixed in concrete ready-mix trucks, whereas UHPC J was mixed in the precast plant’s central mixer. The batching process of both UHPC products started by blending all the dry granular constituents to ensure uniform particle dispersion and then gradually adding the water and superplasticizers until the mix reached the consistency of a viscous fluid. Afterwards, the fibers were uniformly dispersed in the mix and the mixing continued until a flow table spread equal to or greater than 203.2 mm (8 in.) was achieved. The flow table test was performed according to ASTM C1856 (ASTM 2017).The fresh UHPC was placed into rigid steel forms from one stationary discharge point located at approximately midlength of the girder form. The material flowed to each end of the form as it filled up the bottom bulb and then it rose upward through the web height before starting to flow again laterally as it filled the top bulb. The discharge point was then sequentially moved to top off the filling of the form. Minor external vibration was applied to the sides of the form to release entrapped air. The top surfaces of the specimens made of UHPC H were treated with a curing agent, covered with a heavy tarp, and subjected to elevated temperatures for approximately 48 h through the application of steam. The specimens made of UHPC J were covered with a plastic sheet and cured at outdoor ambient temperatures. The UHPC J specimens were fabricated in June 2019, during which the average daily temperature ranged between 22°C (72°F) and 32°C (89°F), whereas the UHPC H specimens were fabricated in Spring 2019 in colder ambient conditions, thus necessitating the elevated temperature curing. The forms were removed and the girders detensioned by consecutively flame cutting the strands once the UHPC reached a compressive strength of at least 96.5 MPa (14 ksi). The compression strength at time of detensioning of the strands was determined by testing two cylindrical specimens taken from each UHPC batch. The cylinders had a diameter of 76.2 mm (3 in.) and height of 152.4 mm (6 in.) and were tested according to ASTM C39 (ASTM 2018b) with modifications listed in ASTM C1856 (ASTM 2017).Test Setup and InstrumentationThe 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  mm/min (0.05  in./min) and 7.62  mm/min (0.30  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.Material CharacterizationOne 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, fc′, and strain at compressive strength, εcu. The average results of the compression parameters for each girder specimen are presented in Table 2.Table 2. Average uniaxial compressive and tensile parameters for each UHPC batch at the time of the shear testsTable 2. Average uniaxial compressive and tensile parameters for each UHPC batch at the time of the shear testsGirder IDUHPC IDE¯ GPa (ksi)fc′¯ MPa (ksi)ε¯cuf¯t,cr MPa (ksi)f¯t,loc MPa (ksi)ε¯t,locH-P1U-H48.5 (7,030)137 (19.9)0.0032110.5 (1.52)11.3 (1.64)0.00369J-P1U-J43.8 (6,350)158 (22.9)0.003997.9 (1.15)8.6 (1.25)0.00524J-P1SU-J43.6 (6,330)152 (22.1)0.003798.9 (1.29)9.3 (1.34)0.00439H-P2U-H47.7 (6,910)140 (20.3)0.0033810.8 (1.57)10.7 (1.56)0.00324H-P3U-H48.7 (7,070)160 (23.2)0.0037611.6 (1.68)11.5 (1.66)0.00275H-P3RU-H48.9 (7,090)158 (22.9)0.0036711.4 (1.65)10.9 (1.58)0.00332The tension test specimens were molded into prismatic steel molds having a length of 432 mm (17 in.) and cross-sectional dimensions of 50.8×50.8  mm (2×2  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, f¯t,cr, the average localization stress, f¯t,loc, and the average localization strain, ε¯t,loc, were obtained from the individual stress–strain response of each of the tested prisms. The effective cracking stress, ft,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, ft,loc, and strain, εt,loc, 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, f¯py, of 1,692 MPa (246 ksi), an average ultimate tensile strength, f¯pu, of 1,934 MPa (281 ksi), and an average rupture strain, ε¯pu, of 0.0682. The strand modulus of elasticity, Ep, 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.Test Results and ObservationsThe 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 εst≥2,400×10−6) 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.Table 3. Measured strains in the steel bars of girder H-P3R right before shear failure (values in microstrain)Table 3. Measured strains in the steel bars of girder H-P3R right before shear failure (values in microstrain)Strain gaugeBar 8Bar 10Bar 12Bar 14Bar 16Bar 18Bar 20Bar 22Bar 24Bar 26Bar 28Top——2,2262,747a2,724a3,141a2,886a452−426−131−345Middle—2,2472,732a3,078a3,136a3,273a2,242450−256−78−53Lower2,508a5,808a,b4,703a,b4,291a,b3,156a2,787a1,867443———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, fpe, 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, Ep=196.5  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.Table 4. Summary of key experimental resultsTable 4. Summary of key experimental resultsGirder IDUHPC IDfpe MPa (ksi)Vcr kN (kip)ac mm (in.)θexp (degrees)Vpeak kN (kip)VpeakVcrVpeakbwh MPa (ksi)εT,peakεB,peakH-P1U-H1,203 (174.5)820 (184)2,302 (80.0)271,242 (279)1.5118.3 (2.66)−0.000890.00088J-P1U-J1,090 (158.2)680 (153)1,175 (46.3)251,265 (284)1.8618.5 (2.68)−0.001160.00110J-P1SU-J1,148 (166.5)676 (152)946 (37.3)271,236 (278)1.8318.2 (2.64)−0.001020.00115H-P2U-H1,209 (175.3)841 (189)2,337 (92.0)281,491 (335)1.7716.4 (2.38)−0.001110.00097H-P3U-H1,151 (166.9)977 (220)1,588 (62.5)271,410 (317)1.4416.8 (2.44)—a—aH-P3RbU-H1,180 (171.2)942 (212)1,791 (70.5)27c/35d2,567 (577)2.7230.6 (4.44)—a—aThe 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, Vcr, 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, ac is the longitudinal distance between the roller support and the location of the critical crack at midheight of the web, θexp 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, Vpeak is the ultimate shear capacity, and εT,peak and εB,peak 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 εT,peak and εB,peak 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.Parameters Influencing Shear CapacityEffect of Tensile Behavior of UHPCThe girders tested in this study showed extensive postcracking ductility, with a peak shear strength over cracking shear capacity ratio, Vpeak/Vcr, greater than 1.44. This postcracking performance is attributed to the presence of fibers that compensate for the lost tensile resistance of the UHPC matrix at cracks, demonstrated by the occurrence of multiple parallel diagonal cracks. Given UHPC’s high compressive strength, the shear failure was governed by the tensile failure at a localized crack without crushing of the compression strut between cracks. The effect of the tensile parameters can be shown by comparing the experimental results of girders H-P1, made of UHPC H, and J-P1, made of UHPC J. Even though the ultimate tensile capacity, f¯t,loc, of UHPC H is approximately 31% greater than that of UHPC J (Table 2), the shear capacities of both girders were similar (Table 4). This behavior reveals the importance of the crack localization strain parameter, εt,loc, which governs the limit of postcracking hardening behavior and initiation of the localization crack. With an average localization strain value approximately 42% greater than that of UHPC H, UHPC J can develop tighter cracks and carry the girder to higher strain values, increasing the Vpeak/Vcr ratio (compare Vpeak/Vcr of 1.51 and 1.86 for girders H-P1 and J-P1, respectively).Note that the Vpeak/Vcr ratio discussion is presented herein to highlight the ductility of the shear response of UHPC girders after the initiation of the first diagonal crack; this ratio should not be solely relied on to assess the structural condition of UHPC bridge girders. As previously mentioned, the diagonal cracks in UHPC girders are extremely small and may not be visible to the naked eye; their identification might be possible by spraying an evaporative liquid that can penetrate the cracks making them temporarily visible. More research is needed to determine the appropriate crack width that can be used as warning of excessive distress.Effect of Girder’s Web Width and HeightThe webs of the tested girders were constrained by wide top and bottom flanges, which can restrict web deformation and improve crack control characteristics. Although such behavior is important for conventional concrete, UHPC inherently provides internal resistance through the fiber reinforcement, providing significant crack control characteristics at the material level, thereby reducing the web’s dependence on the constraint provided by the flanges for postcracking ductility. The effect of the web width and girder height in these tests can be examined by comparing the experimental results of girders H-P2 and H-P3 with those of girder H-P1. The vertical shear stresses, Vpeak/bwh, for girders H-P2 and H-P3 were about 8 and 10% lower, respectively, than the shear stress of girder H-P1, as shown in Table 4, indicating a minor or insignificant effect of these parameters on the structural shear performance of the tested girders.Effect of Prestressing ForceWhen designers decrease the prestressing force in concrete girders by reducing the number of prestressing strands, the precompression strains in the longitudinal reinforcement decrease, prompting an earlier initiation of flexural-shear cracks and a decrease in the shear capacity of the girder. In this study, although girder J-P1S was reinforced with 18 strands in the bottom flange and girder J-P1 was reinforced with 24 strands in the bottom flange, the shear capacities for both girders were similar, as shown in Table 4. This difference in prestressing level in these heavily reinforced girders was not sufficient to demonstrate a pronounced change in the shear behavior.Effect of Transverse Shear ReinforcementWhen vertical steel bars (one No. 16 bar, or No. 5 US bar size, at 20 203.2 mm or 8 in.) were added to the web of girder H-P3R, the shear capacity increased by 82 percent compared to girder H-P3, which did not have any transverse steel reinforcement. The strains in the steel bars were captured at multiple locations within the shear span throughout the test, as shown in Fig. 4. The strain gauge results of Table 3 and the force-displacement trend of girder H-P3R shown in Fig. 6 reveal that the yielding of the bars took place first and the localization of the UHPC in the web occurred substantially later. Therefore, the superposition of the UHPC resistance with the yielding force in the steel bars crossing the crack appears to be applicable when the localization strain of UHPC in the principal tensile direction is high enough to allow a transverse strain greater than the yielding strain to be attained. If the UHPC localization strain occurs before the yielding of the transverse steel bars, failure of the beam can occur before the yielding of the bars. This observation is also supported by the experimental work of Baby et al. (2014).The localization of the critical crack for girder H-P3R occurred right before failure. The critical crack closest to the west load cells occurred first, at a global inclination angle of 35°, and it appeared to form from a coalescence of the diagonal cracks existing before localization, which had an inclination angle of 27° (Fig. 7). Given that the bars crossing the crack at an inclination angle of 27° are engaged at failure, the total contribution of the transverse bars to the shear force, Vs, was 835.6 kN (187.7 kip), calculated according to Vs=Avfydvcotθ/s, in which Av=200  mm2 (0.31  in2) is the transverse steel area [i.e., one No. 5 bar within a spacing, s, of 203.2 mm (8 in.)], fy=483.3  MPa (70.1 ksi) for strains lower than 5,000 microstrain [Table 3; Fig. 5(b)], dv=895  mm (35.2 in.), calculated according to AASHTO LRFD BDS (AASHTO 2020), and θ=θexp=27°. This result indicates that the steel contribution to the capacity of girder H-P3R is about 33% of the total shear capacity and that approximately 55% of the capacity can be attributed to the resistance of the UHPC as determined from the testing of girder H-P3. It can also be concluded that the AASHTO LRFD BDS (AASHTO 2020) equation for transverse steel contribution is consistent with the shear results of H-P3 and H-P3R. It is proposed that the remaining 12% of capacity likely originated either from the differences in the mechanical properties of the in-place UHPC between the reinforced and unreinforced girders or from a complementary action between the steel bars and surrounding UHPC. The reinforcing steel bars can supplement the UHPC in resisting the initiation and propagation of cracks, leading to higher UHPC localization strain values than those observed in girder H-P3 without transverse steel. This topic is further discussed in the following section.Analysis of Principal Stresses and Strains in the WebMany 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, fc′. 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, ft,loc, and strain, εt,loc. 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% (ρv=Av/bws). 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.Principal Tensile StressIf most of the girder shear resistance is assumed to originate from a uniform stress state within the web of the girder, the total vertical shear resistance of each of the tested girders can be calculated from equilibrium of forces across a crack, as illustrated in Fig. 10 and described in Eqs. (1)–(3). Note that the UHPC offers uniaxial tensile resistance along the principal tensile plane (perpendicular to the crack), f1, but does not offer shearing resistance along the crack, which is commonly associated with conventional concrete subjected to beam shear: (1) in which (2) and (3) Table 5 presents a comparison between the principal tensile stress in the web of all tested girders at shear failure and the localization stress of UHPC obtained from direct tension tests. In Table 5, the effective shear depth, dv, is taken as the distance between the resultant of the compression and tension forces at ultimate flexural capacity as estimated by a strain compatibility analysis but not less than 0.9de or 0.72h, where de is the depth of the centroid of tensile steel reinforcement (AASHTO 2020). The vertical shear stress in the web at shear failure is defined as vpeak=Vpeak/bwdv, and the average principal tensile stress in the web at shear failure, f1,peak, is calculated by combining Eqs. (1)–(3) with V=Vpeak, f1=f1,peak, θ=θexp, and fs=fy.Table 5. Comparison between the principal tensile stress in the web at ultimate shear and the localization stress of UHPCTable 5. Comparison between the principal tensile stress in the web at ultimate shear and the localization stress of UHPCGirder IDdv mm (in.)vpeak MPa (ksi)f1,peak MPa (ksi)f1,peakft,locH-P1700 (27.6)23.3 (3.38)11.9 (1.72)1.05J-P1711 (28.0)23.4 (3.39)10.9 (1.58)1.26J-P1S702 (27.6)23.1 (3.35)11.8 (1.71)1.27H-P2698 (27.5)21.0 (3.05)11.2 (1.62)1.04H-P3889 (35.0)20.8 (3.02)10.6 (1.54)0.92H-P3R895 (35.2)37.6 (5.46)12.9 (1.88)1.19The ratio of f1,peak/ft,loc for all girders ranged between 0.92 and 1.27, indicating that the UHPC localization stress obtained from a direct tension test can give a reasonable representation of the average principal stress field generated in the web. The value for f1,peak appears to have increased from the value of ft,loc (Table 2) when the girder was reinforced with transverse steel (compare a ratio of 0.92 for H-P3 and 1.19 for H-P3R) or when the UHPC material had a higher localization strain (compare a ratio of 1.26 for J-P1 with ε¯t,loc=0.00369 and a ratio of 1.05 for H-P1 with ε¯t,loc=0.00524).Principal Tensile StrainThe principal tensile strain at ultimate shear and the localization strain of UHPC can be compared by analyzing the strain data recorded by the noncontact rosettes within the web of the girders. By capturing the strain field in three directions forming angles of 0°, 60°, and 120° with the longitudinal axis, the axial strains, εx and εy, the shear strain, γxy, the principal strains, ε1 and ε2, and the principal inclination angle, θ, can be calculated from Mohr’s circle of strains. Note that the value of εx utilized in the calculation of principal strains was determined by adding the measured strain the value from the longitudinal strain gauge (x-direction) of the rosette to the initial longitudinal strains generated by the prestressing force and self-weight of the girder. The initial vertical and shear strains due to initial prestress are assumed to be negligeable.Due to the longitudinal strain gradient caused by the initial prestressing force, applied flexural moment, and shear stresses, and the number of cracks captured within each of the strain gauges, the RS results varied throughout the depth of the web. Fig. 11 shows the variation of the principal strain, ε1, for girder H-P3 with respect to the location of rosettes RS1 through RS5 (located relative to the bottom of the section) and at different loading levels before failure of the beam. The smallest principal tensile strain near failure for each of the tested girders was captured by RS2 located at mid-height of the web, likely because the favorable crack control effects provided by the top and bottom flanges had the least impact at mid-height of the web.The minimum value of ε1 within the web, i.e., the strain recorded by rosette RS2 at the penultimate data point before failure (Vpenult=0.98 to 1.00Vpeak), and εt,loc are compared in Table 6. The results show that for each girder, the localization of the critical crack within the web occurred at a principal strain, ε1, higher than the localization strain measured from the uniaxial tensile test, with the highest strain measured on girder H-P3R containing transverse steel reinforcement (ε1,penult/εt,loc=1.38). Based on these results, it can be concluded that the constraints provided either by the top and bottom flanges or by discrete transverse steel reinforcement supplement the UHPC in controlling crack widths, resulting in higher values of principal tensile strains than those obtained from direct tension testing. However, it should be noted that extrapolating these results to deeper girders is a subject of investigation by the authors because deeper girders offer less flange-based restraint and unfavorable fiber orientations in the deep webs, which might decrease the localization strain, particularly when designed with little or no discrete reinforcement.Table 6. Comparison between the principal tensile strain at mid-height of the web and the localization strain of UHPC just before shear failure (RS2)Table 6. Comparison between the principal tensile strain at mid-height of the web and the localization strain of UHPC just before shear failure (RS2)Girder IDVpenultVpeakεx,penultεy,penultγxy,penultε1,penultε2,penultθpenult (degrees)ε1,penultεt,locε1,penult|ε2,penult|H-P10.980.000330.002890.004660.00427−0.0010530.61.164.07J-P11.00−0.000440.004040.005710.00543−0.0018325.91.042.97J-P1S0.98−0.000430.004410.005510.00565−0.0016824.41.293.37H-P20.990.000030.002930.003540.00377−0.0008125.31.164.67H-P30.95−0.000120.002510.002880.00315−0.0007623.71.154.17H-P3R0.980.000480.002910.005260.00459−0.0012032.61.383.81Principal Compressive Stress and StrainThe compressive strain experienced by the compression struts between the diagonal cracks of the web is obtained by examining the recorded value of the principal compressive strain, ε2,penult, measured by rosettes RS1 through RS5 at the penultimate data point before failure. The corresponding principal compressive stress, f2,penult, is obtained by first calculating f1,penult from Eqs. (1)–(3) (with V=Vpeak, θ=θpenult and fs=fy) and then adopting the principal compressive stress relationship of the Modified Compression-Field Theory (Vecchio and Collins 1986) shown in Eq. (4), which is derived from equilibrium of stresses acting on a cracked membrane element within the web and by assuming that the clamping stresses on the element are negligible (Bentz et al. 2006) (4) f2=−f1cot2θ−ρvfs(1+cot2θ)The maximum compressive stress, f2,penult, and strain, ε2,penult, recorded for the web of all tested girders and the secant compressive stiffness, E2,penult=f2,penult/ε2,penult, are shown in Table 7. With a maximum compressive stress demand of 78.6 MPa (11.4 ksi) (girder H-P3R), the utilized compressive capacity in the compression field was less than 50% of the uniaxial compressive strength, fc′, for all girders. However, the compressive stiffness appeared to decrease because of biaxial effects given that the compressive field was subjected to perpendicular (principal) tensile strains, ε1,penult, at least 2.57 times larger than the compressive strains, ε2,penult (ε1,penult/|ε2,penult|>2.57 in Tables 6 and 7, with the threshold value calculated from the strain measurements of rosette RS3 of girder H-P3R). Table 7 also compares the secant modulus of the compressed UHPC right before shear failure, E2,penult, to the average uniaxial modulus of elasticity, E¯, obtained from compression cylinders, with E2,penult/E¯ between 0.53 and 0.86 for all girders.Table 7. Principal compressive stress and strain observed in the web of each tested girder just before shear failureTable 7. Principal compressive stress and strain observed in the web of each tested girder just before shear failureGirder IDVpenultVpeakStrain rosetteε1,penultε2,penultθpenult (degrees)f1,penult MPa (ksi)f2,penult MPa (ksi)f2,penultf¯c′E2,penult MPa (ksi)E2,penultE¯H-P10.98RS30.00465−0.0015530.413.7 (1.98)−39.7 (−5.76)0.3025,665 (3,722)0.53J-P11.00RS20.00543−0.0018325.913.7 (1.99)−39.8 (−5.77)0.2525,738 (3,733)0.59J-P1S0.98RS20.00565−0.0016824.410.5 (1.52)−51.0 (−7.40)0.3330,389 (4,408)0.70H-P20.99RS30.00446−0.0012628.411.4 (1.65)−38.8 (−5.63)0.2830,840 (4,473)0.65H-P30.95RS30.00399−0.0009527.510.8 (1.57)−40.1 (−5.81)0.2541,953 (6,085)0.86H-P3R0.98RS30.00499−0.0019428.714.3 (2.08)−78.6 (−11.4)0.5040,543 (5,880)0.83Global Stress–Strain Behavior of the WebThe average shear stress–strain and principal tensile stress–strain trends for the tested girders are shown in Fig. 12 using the strain readings of rosette RS6. These trends were obtained by calculating the stresses [using Eqs. (1)–(3)] and strains (using Mohr’s circle of strains) at each recorded strain data point during the test. The results correspond to a smeared stress–strain response of the web’s membrane during the shear tests because rosette RS6 covers the central area of the web of each girder, including the critical crack. The principal tensile stress–strain curves of Fig. 12(b) highlight the overall strain-hardening behavior of UHPC within the web of the beams, with trends similar in shape to the average uniaxial stress–strain curves obtained from a direct tension test [Fig. 5(a)]. The results provide yet another verification that the strain-hardening characteristics of UHPC, observed at the material level, are also observed at the structural scale, delivering significant improvements to the shear capacity and ductility of the tested girders compared to what would traditionally be expected from a reinforced concrete member with little or no transverse reinforcement.Summary and ConclusionsThe 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: •The shear behavior of the tested UHPC girders with and without transverse steel reinforcement was characterized by the development of multiple closely spaced diagonal cracks with failure prompted by a localized and dominant crack forming from an existing crack or a coalescence of closely spaced cracks. The localization of the critical crack occurs when the bridging fibers start to pull out and the crack propagates through the depth of the web, which can occur without crushing of the compression strut between cracks because of the high compressive strength of UHPC;•Shear capacity was observed to be largely dependent on the tensile characteristics of UHPC. Changing the web thickness from 76.2 mm (3 in.) to 101.2 mm (4 in.), the height from 889 mm (35 in.) to 43 in. (1,092 mm), and the number of 17.8-mm (0.7-in.) diameter prestressing strands from 26 to 20 (23% decrease in prestress) did not appear to significantly affect the shear capacity of the tested girders;•In the shear test with transverse steel bars in the web, the yielding of the bars took place first and the localization of the UHPC at the critical crack occurred substantially later. Therefore, the superposition of the UHPC resistance with the yielding force in the steel bars crossing the crack appears to be applicable when the localization strain of UHPC in the principal tensile direction is high enough to allow a transverse strain greater than the yielding strain to be attained;•When an average constant shear stress is assumed within the effective shear depth of the girder, the value of the principal tensile stress in the UHPC at failure is similar to or larger than the stress at localization obtained from a direct tension test;•At localization, the principal tensile strain in the web of UHPC girders was greater than the localization strain obtained from uniaxial tests in the tested girders. This appears to be caused by the increase in crack opening resistance which may be provided by the top and bottom flanges, by discrete transverse steel reinforcement, or both;•The observed compressive stiffness of the web is smaller than the UHPC modulus of elasticity obtained from a uniaxial test because of biaxial effects. At failure, the ratio of the secant stiffness to the uniaxial stiffness was between 0.53 and 0.86 for all girders; and•The principal tensile stress–strain trends of the UHPC in the web are similar to those obtained from a uniaxial test, thus delivering significant improvements to the shear capacities and ductility of UHPC girders compared to what would traditionally be expected from a reinforced concrete member with little or no transverse reinforcement.Data Availability StatementMost 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.AcknowledgmentsThe 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.NotationThe following symbols are used in this paper:Av=area of transverse reinforcement within a distance s;a=shear span length;ac=longitudinal distance between the roller support and the location of the critical crack at mid-height of the web;bw=minimum thickness of the girder’s web;de=depth of the centroid of tensile steel reinforcement;dv=effective shear depth of the member;E=modulus of elasticity of UHPC;E¯=average modulus of elasticity of UHPC;Ep=modulus of elasticity of prestressing steel strands;E2,penult=secant compressive stiffness of UHPC at the penultimate data point before failure;fc′=compressive strength of UHPC;f¯c′=average compressive strength of UHPC;fpe=stress in the strands after all losses between strand release and the start of the shear tests;f¯pu=average ultimate tensile strength of prestressing strands;f¯py=average yield strength of prestressing strands;fs=stress in vertical steel reinforcement;ft,cr=effective cracking stress of UHPC;f¯t,cr=average effective cracking stress of UHPC;ft,loc=localization stress of UHPC;f¯t,loc=average localization stress of UHPC;fy=yield stress of vertical steel bars;f1=principal tensile stress;f1,peak=principal tensile stress in the web at shear failure;f1,penult=principal tensile stress at the penultimate data point before failure;f2=principal compressive stress;f2,penult=principal compressive stress at the penultimate data point before failure;h=overall depth of girder;L=total test span length;s=longitudinal spacing of transverse reinforcement;V=shear capacity of member;Vcr=shear capacity at the occurrence of first diagonal crack at the location of the critical crack;Vpeak=shear capacity of member at shear failure;Vpenult=shear force at location of critical crack at the penultimate data point before failure;Vs=shear resistance provided by the transverse reinforcement at failure;VUHPC=shear resistance provided by UHPC at failure;vpeak=vertical shear stress in the web at shear failure;γxy=shear strain in xy-plane;εB,peak=concrete flexural strain at bottom of the section under the spreader beam at shear failure;εcu=strain at ultimate compressive strength of UHPC;ε¯cu=average strain at ultimate compressive strength of UHPC;ε¯pu=average tensile rupture strain of prestressing strands;εst=strain in reinforcing vertical steel bars;εT,peak=concrete flexural strain at top of the section under the spreader beam at shear failure;εt,loc=localization strain of UHPC;ε¯t,loc=average localization strain of UHPC;εx=strain in the x-direction;εy=strain in the y-direction;ε1=principal tensile strain;ε1,penult=principal tensile strain at the penultimate data point before failure;ε2=principal compressive strain;ε2,penult=principal compressive strain at the penultimate data point before failure;θ=angle of inclination of diagonal compressive stress;θexp=average angle of the critical shear crack with the longitudinal axis measured with a protractor after the completion of the test;θpenult=angle of inclination of diagonal compressive stress at the penultimate data point before failure; andρv=reinforcement ratio of the transverse steel reinforcement taken as Av/bvs.References AASHTO. 2020. 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