Analysis of the Shear Capacity of Ultrahigh Performance Concrete Beams Based on the Modified Compression Field Theory

An analysis model of the shear capacity of prestressed ultrahigh performance concrete (UHPC) beams under the combined action of bending and shearing was established in this paper based on the modified compression field theory and by considering the unique material constitutive relation of UHPC. Shear tests were performed using three prestressed UHPC-T beams with different shear-span ratios to verify the correctness of the model. *e results showed that the shear-span ratio greatly influenced the shear capacity and failure modes of UHPC-T beams. Upon increasing the shear-span ratio, the failure modes of the three beams were inclined compression failure, shear compression failure, and diagonal tension failure, successively. When the shear-span ratio changed from 1.04 to 2.12, the shear bearing capacity decreased greatly; however, when the shear-span ratio changed from 2.12 to 3.19, the decrease of the shear bearing capacity was very small. In addition, the MCFT analysis model was used to analyze the experimental data, and the predicted results were in good agreement, which proved the applicability of the model. Finally, according to the existing shear test results of UHPC beams and based on the main influencing factors, a simplified formula for predicting the shear capacity of UHPC beams was obtained by fitting. Comparing theMCFTmodel with the results of other pieces of literature, this formula accurately predicted the shear capacity of UHPC beams. *e MCFTmodel and the simplified formula presented in this paper provide a powerful tool for predicting the shear performance of UHPC-T beams, which will contribute to the design and analysis of UHPC-T beams.


Introduction
Ultrahigh performance concrete (UHPC) is a new type of steel fiber-reinforced cement-based composite material with many excellent properties [1][2][3], including superhigh strength, high ductility, good durability, and resistance to environmental degradation [4][5][6][7]. Because of these excellent properties, UHPC has been widely used in bridge engineering, structure repair, and other fields [8][9][10][11][12]. e application of UHPC in bridge engineering can greatly reduce the weight of bridge structures and maintenance times, which help extend the service life of bridges and reduce costs [13,14].
With increasing in-depth research and applications of UHPC in engineering, scholars have carried out a series of studies on the shear performance of UHPC structures. Voo et al. [15,16] conducted 16 prestressed UHPC I-beam tests successively and found that the number and type of fibers had no significant effect on the cracking load, but increasing the fiber volume increased the failure load. Based on the plastic theory, the PSM-VEM model was proposed, which assumed that the critical crack ran through the whole beam height and was unaffected by the shear compression zone. A comparison with the test results showed that the model was suitable for the shear calculation of UHPC beams. Ngo et al. [17] used a self-developed shear test system to study the shear performance of UHPFRC. e results showed that the shear performance of UHPC was affected by the shear-span ratio and fiber volume, as well as the tensile strength. Higher shear-span ratios promoted lower shear strengths, while higher fiber volumes promoted higher shear strengths. According to the results, a theoretical prediction model of shear strength of UHPC considering the tensile strength and shear-span ratio was proposed. Ji et al. [18,19] conducted shear tests on 12 RPC-T beams. e experimental results showed that the ultimate shear capacity of the beams increased upon increasing the stirrup ratio and longitudinal reinforcement ratio and decreased upon increasing the shear-span ratio. According to the results, the softening coefficient was corrected to establish the truss model, and the shear performance of RPC beams was predicted. e above calculation methods of UHPC shear capacity used different theories to explain the shear failure mechanism of the structure from different perspectives [20][21][22][23]; however, the shear-span ratio is not fully considered by the limit equilibrium theory. e analysis accuracy of specimens with a shear-span ratio of 2 that undergo shear-pressure failure is relatively high, while it is relatively low for specimens with a small shear span. e plasticity theory primarily considers the influence of compressive strength and horizontal projected length of the main diagonal crack, but it does not consider the influence of stirrups, longitudinal reinforcement, or prestress on the shear capacity. Although the truss model provides a simple calculation method and clear concept, the theory does not conform to the deformation compatibility condition and cannot describe the whole shear stress process.
Due to the deficiency of the above theoretical model, Vecchio and Collins proposed the modified compression field theory [24,25], which considers the influence of shear-span ratio, stirrup ratio, prestress, and steel fiber on shear bearing capacity, and it has been adopted by Canadian and American codes [26,27]. Its main feature is the decomposition of the shear problem of the combined bending-shearing force state into pure shear and pure bending states, which are analyzed separately and then calculated by superposition. On this basis, Crane [28] predicted the shear capacity of six composite beams (UHPC I-beam at the bottom and HPC panel at the top) by using the modified compression field theory after considering the contribution of steel fiber. Liang and Wang [29] proposed an improved MCFT calculation model based on the modified compression field theory by considering the pin bolt effect of longitudinal bars and calculated the shear performance of UHPC beams. Baby et al. [30] used a hyperbolic model to characterize the compression constitutive model of UHPC and discussed the feasibility of applying the MCFT theory to evaluate the shear performance of prestressed ultrahigh performance reinforced concrete beams; however, in that current study, the constitutive model used to analyze the pure bending state was generally obtained by scaling based on the ordinary concrete constitutive model, which cannot clearly reflect the force characteristics of the UHPC material, leading to errors in the results. is paper aims to establish an analysis model for the shear capacity of UHPC beams based on the modified compression field theory. Considering the unique constitutive relation of UHPC materials, an improved analysis model was established and verified by experiments. A comparison of the results from codes and experiments showed that the existing shear strength formula is not suitable for predicting the shear capacity of UHPC-T beams; therefore, according to the MCFT model and the existing test results, a simplified prediction formula for the shear capacity of UHPC beams was obtained by fitting. e research results provide a practical calculation method for the shear design of UHPC beams and also provide a deeper understanding of the shear performance of UHPC-T beams.

Calculation Model Based on MCFT
e modified compression field theory was used to establish the strain compatibility equation and stress balance equation based on material mechanics and then combined with the UHPC constitutive relations to obtain the calculation method of the shear bearing capacity according to three convergence conditions.

Basic Assumptions.
e basic assumptions of the MCFT are as follows: (a) e shear stress and normal stress of the concrete microelement body are uniformly distributed when it is under load (b) e stress-strain of concrete is the average stressstrain of the cracked area (c) e principal stress direction of concrete is the same as the principal strain direction (d) Reinforced concrete does not experience bond-slip between each other, and there is an ideal bond between them (e) e axial stress of reinforcement is the only considered factor, and the reinforcement shear stress is not considered

Strain Coordination Equation.
According to the basic assumption, assuming that the UHPC and the reinforcing bar are in an ideal bonding state, and without considering the shear stress of the reinforcing bar, equations (1) and (2) can be obtained: where ε cx and ε cy represent the strain of UHPC in the x and y-directions, respectively, ε sx and ε sy represent the strain of the reinforcement in the x and y-directions, respectively, and ε x and ε y represent the average strain of the reinforced concrete microelements in the x and y-directions, respectively. e average strain of the reinforced concrete microelements conforms to Mohr's circle for strain. According to the geometric conditions in Figure 1, equations (3)-(5) can be obtained: 2 Advances in Materials Science and Engineering Combining equations (4) and (5), the average strain in the x-direction (ε x ) and y-direction (ε y ) can be obtained, as shown in equations (6) and (7): where ε 1 and ε 2 represent the principal tension strain and principal compressive strain of reinforced concrete, respectively, and θ represents the principal compressive strain angle of the concrete.

Stress Balance Equation.
According to the basic assumption, the average stress and average strain of concrete after cracking conform to Mohr's circle for stresses. Equation (8) can be obtained from Figure 2.
where f 1 and f 2 represent the main tensile stress and the main compressive stress, respectively, and v is the average shear stress of the section. Figure 3 shows the analysis model of a UHPC beam based on MCFT. As shown in Figure 3(a), equation (9) can be obtained: where V is the shear force of the beam, b w represents the width of the web, and h 0 represents the effective height of the section.
Considering the balance of forces in the vertical direction, equation (10) can be obtained from Figure 3(b): where A sv and f v represent the stirrup area and stirrup stress, respectively, and s is the stirrup spacing. From equations (8)-(10), the following equation can be obtained: Considering the balance of forces in the horizontal direction and combining with equations (8) and (12) can be obtained from Figure 3 where C F represents the axial resultant force of the longitudinal reinforcement in the horizontal direction of the section.

Material Constitutive
Relationship. Based on the strain coordination equation and stress balance equation, the constitutive models of ordinary steel bars, prestressed steel bars, and UHPC are introduced to establish the equation group.

Ordinary Steel Bars Constitutive Model.
It is assumed that the stress-strain relationship of the ordinary steel bars constitutive model is an ideal elastoplastic relationship as follows: where f y and ε n represent the yield stress and the strain of the steel bar, respectively, and E s represents the elastic modulus.

Prestressed Steel Bars Constitutive
Model. e constitutive relationship of prestressed steel bars is expressed in two stages, as follows: , ε x ≤ ε n ,  where E p , ε p , ε p0 , and f pu represent the elastic modulus, strain, proportional limit strain, and ultimate strength, respectively. e initial strain of the prestressed steel bars after tensioning is ε pi � f pi /E p ; therefore, the initial strain of the prestressed reinforcement component should be considered during calculation.

UHPC Constitutive Model.
Concrete is in the biaxial stress state and the uniaxial stress state, respectively, when considering the pure shear and pure bending stress states; therefore, the constitutive relationship for these two different stress states should be selected separately.
(1) Biaxial Stress State. e compression constitutive model of UHPC under biaxial stress state refers to the softening constitutive model of ordinary concrete and is scaled in equal proportion, as shown in Figure 4. e constitutive relationship of UHPC compression under biaxial stress is described by where ε 0 , ε 1 , ε 2 , f c ′ , and f c2 max , respectively, represent the peak uniaxial compressive strain, the main tensile strain, the main compressive strain, the uniaxial compressive strength, and the ultimate compressive strength of UHPC. e tensile constitutive model of UHPC under the biaxial stress state is shown in Figure 5, and the tensile constitutive relationship of UHPC is described by equation (17):where f cr represents the tensile strength and f tu represents the residual tensile stress after UHPC cracking. In this paper, f tu � 0.75f cr .
(2) Uniaxial Stress State. e constitutive relationship of UHPC under uniaxial compression adopts the stressstrain relationship proposed by Yang and Fang [31], and the compression constitutive relationship of UHPC under the uniaxial stress state is shown in the following equation:

Softened concrete
Nonsoftening concrete

Advances in Materials Science and Engineering
, E c is the initial modulus of elasticity, and E g is the secant modulus at the peak point of stress-strain curve. e uniaxial tensile constitutive model of UHPC is based on the uniaxial tensile test results of UHPC provided by Zhang et al. [32] and a two-stage tensile constitutive relationship. Considering the contribution of UHPC tensile performance after cracking to shear resistance, the following improvements are made. e stress-strain relationship is adopted in the tensile strain hardening section, and the stress crack width relationship in the stress softening section is proposed by Li et al. [33], as shown in Figure 6. e tensile constitutive relationship of UHPC under uniaxial stress state is shown in the following equation: where p represents the test fitting parameter, w p represents the crack width when the stress decreases, and 2 − p f t and l c denote the section characteristic length. For rectangular sections and T-sections, take l c � 2/3h, where h is the height of the section.

Section Analysis of Bending-Shearing Composite Action.
In the section analysis of bending-shearing composite action, the test beam is analyzed separately according to pure bending and pure shear stress forms, and the corresponding UHPC constitutive models are used in the calculation.

Shear Analysis of Beams.
In the shear analysis and calculations of the test beam, it is assumed that the shear force is uniformly distributed at the section height. Since the shear capacity of a T-shaped beam is affected by the flange width, the contribution of the flange plate to the shear bearing capacity is considered. In the calculation, the effective width of a T-shaped beam is taken as b + 2h i , and the UHPC constitutive model used equations (15)- (18). e calculation section is shown in Figure 7. e longitudinal and transverse strains are calculated by (6) and (7), respectively. e vertical shear V is calculated by equation (11), and the horizontal componentF c ′ is calculated by equation (12).

Flexural Analysis of Beams.
In the flexural analysis of beams, since ordinary concrete does not consider the strength of cracked concrete, the contribution of this part is not considered in the modified compression field theory; however, the residual tensile strength of UHPC beams after cracking cannot be ignored. erefore, this paper introduces the improved UHPC tensile component, which is calculated by equations (19) and (20). Figure 8 shows the stress-strain relationship under a pure bending moment. To perform an accurate calculation, this paper assumes that the shear stress is uniformly distributed. According to the strain simplified method proposed by Collins, the longitudinal strain at the half-height of the section is taken as the horizontal strain of the shear part during the calculation; therefore, the calculation of flexural resistance conforms to the assumption of a flat section, and the value of ε x calculated by equation (6) in the shear analysis is regarded as the longitudinal strain at half the height of the section. According to the force balance conditions, equation (21) can be obtained: Stress so ening section where σ c and σ t are the compressive and tensile stresses of the concrete, respectively, and A p and A s are the areas of the prestressed reinforcement and ordinary reinforcement, respectively. e flexural capacity M 1 can be expressed by equation (22) as follows: (22) where y p and y s are the positions of the prestressed reinforcement and ordinary reinforcement relative to the upper edge of the section, respectively. f where F C ′ and F C are the horizontal axial forces in the shearresistance and bending-resistance calculations, respectively, V and a are the shear force in the shear-resistance calculation and the distance of the actual position from the support, respectively, and M 1 is the bending moment in the bending-resistance calculation.
Combining the above deformation compatibility equation, stress balance equation, material constitutive relation, and three convergence discriminants, the MCFTbased calculation procedure of the shear bearing capacity of UHPC beam was compiled by MATLAB, as shown in Figure 9.      Table 2.

Test Specimens.
e calculated spans of the three constructed prestressed UHPC-T beams were 1.4 m, 2.8 m, and 4.2 m, respectively, and the shear-span radios were λ � 1.6, λ � 2.12, and λ � 3.19 respectively. e three test beams had the same cross section, the beam height was 0.6 m, the top plate width was 0.6 m, the lower edge width was 0.3 m, the web thickness was 70 mm, and the horseshoe edge height was 80 mm. e section and reinforcement arrangement of the test beam is illustrated in Figure 10. Two Φ15.2-4 prestressed steel strands were arranged in a horseshoe at the lower edge of the test beam, and the tensile stress was 1010 MPa. Five longitudinal bars and eight longitudinal bars with diameters of 12 mm were, respectively, arranged on the upper and lower edges of the section. Single-limb shearresistance stirrups were arranged at distances of 100 mm in the longitudinal direction of the test beam, and the diameters of the other structural reinforcements were 8 mm. e mechanical properties of the reinforcement are shown in Table 3.
After pouring UHPC, the test beams were covered with plastic film for 2 days and then demolded, followed by steam curing for 3 days (temperature ≥ 90°C; relative humidity > 90%). After steam curing, the beams were stored in a room for 28 days, then tensioned and grouted, and finally naturally cured until the test began.

Test Procedures and Instruments.
e device and instruments used in this test are shown in Figure 11. A hydraulic Jack was used for grading single-point loading. At the initial stage, the loading was carried out at 50 kN per stage. After obvious cracks appeared, the loading was controlled by displacement until the specimens were destroyed. e test involved the following main stages: (a) Load test: this was read by the pressure sensor arranged between the Jack and the reaction frame.  Table 4, where V cr and V max are the cracking load and ultimate load of the test beam, respectively. When the shear-span ratio increased from 1.06 to 2.12, the bearing capacity of the beam decreased by 39.64%, and when the shear-span ratio increased from 2.12 to 3.19, the bearing capacity decreased by 4.58%, indicating that the shear-span ratio greatly influences the shear performance of UHPC beams, and its influence degree decreases upon increasing the shear-span ratio. e reason is that vertical compressive stress is generated at the support reaction and concentrated load, which reduces the main tensile stress of concrete, which then improves the shear capacity of the beam. When the shear-span ratio is small, the vertical compressive stress affects the whole shearspan area; however, the influence of the vertical compressive stress is gradually limited to the support reaction and    Advances in Materials Science and Engineering 7 concentrated load upon increasing the shear-span ratio, which weakens its effect. In addition, upon increasing the shear-span ratio, when the failure mode of the beam changed from inclined compression failure to diagonal tensile failure, that is, the bearing capacity changed from compressive strength control to tensile strength control, there was a significant decrease, but the specific impact degree requires further study. Figure 13, three failure modes were observed in the three test beams, namely, inclined compression failure, shear compression failure, and diagonal tension failure. e failure mode of beam L1 was inclined compression failure. When the load reached 945 kN, the first inclined crack appeared in the web of the right shear span. As the load increased, the crack increased continuously. At this time, the cracks on the left side of the beam appeared more densely, a series of approximately parallel oblique cracks formed at the connection line between the loading point and the support, and the inclination angles of these cracks were in the range of 37-57°. e concrete between the load point and the support was compressed into pieces when the load reached 2700 kN, some of the concrete peeled outward, and the beam was destroyed.

Failure Modes and Crack Distributions. As depicted in
e failure mode of beam L2 was shear compression failure. e first diagonal crack appeared on the left side when loading to 302 kN. As the load increased, cracks appeared continuously on both sides of the webs. When the load reached 1000 kN, many dense diagonal cracks appeared on both sides, and the inclination angles of these cracks were in the range of 32-43°. When the load was increased to 1690 kN, a critical oblique crack between the support and the loading point appeared, and the inclination angle was about 41°. e sound of steel fiber tearing could be clearly heard, and the outer skin of the concrete was peeled off. e stirrup and the longitudinal bars successively yielded, and the concrete was crushed until the beam failed. e failure mode of beam L3 was diagonal tension failure. When the load was increased to 805 kN, the first diagonal crack appeared on the right web, and the crack developed continuously upon increasing the load. When the load reached 1045 kN, the crack width reached 0.21 mm. As the load continued to increase, many diagonal cracks appeared on both sides of the webs. e inclination angles of these cracks were within the range of 26-35°, and bending cracks began to appear in the bottom slab. When the beam approached failure, critical diagonal cracks appeared on the right side of the beam. e inclination angle was about 28°, the bending cracks of the bottom plate extended and widened, and horizontal tearing occurred at the junction of the top plate and the web until the beam broke.
Upon increasing the shear-span ratio, the inclination angle of the inclined crack of the beam decreased, and the failure mode also changed. When the beam underwent inclined compression failure, the shear bearing capacity was controlled by the compressive strength of concrete, so there was no steel fiber tearing phenomenon. When the beam underwent shear compression failure, the shear bearing capacity was controlled by the bite force between the compressive zone at the top of the detached body and the steel fiber at the inclined crack. e sound of steel fiber tearing could be clearly heard during the failure process. When the beam underwent diagonal tension failure, the shear bearing capacity was controlled by the tensile strength of concrete; however, due to the bridge effect of steel fiber, the tensile strength of the beam was improved, so the ultimate bearing capacity of beams L2 and L3 was similar. e compressive strength of UHPC concrete is much larger than the tensile strength, so the ultimate bearing capacity of beam L1 was much larger than that of beams L2 and L3. Figure 14 shows the loaddisplacement curves of the three beams. It can be seen that the stiffness of beam L1 was significantly greater than that of the other two beams. In the initial stage of loading, the curve slope changed slightly and approximately linearly, which indicates that the beam was in an elastic state. en, the curve slope decreased significantly, showing a nonlinear change, which indicates that the structure underwent inelastic damage, and the beam was in an inelastic state. e overall changes of the three curves are relatively gentle, without obvious inflection points because the UHPC beams contain steel fiber, which can still bear tensile stress after cracking. e maximum displacements for beams L1, L2, and L3 were 6.7 mm, 13.1 mm, and 25.6 mm, respectively. e slope of the curve of beam L3 decreased the fastest, which indicates that, upon increasing the shear-span ratio, the principal stress of the UHPC element changed from compressive to tensile, and the stiffness of the components decreased the fastest. is is because the shear-span ratio reflects the ratio of the bending moment and shear force of   Figure 13: Continued. 10 Advances in Materials Science and Engineering the beam failure section under a concentrated load. When the shear force is the same, the larger the shear-span ratio, the smaller the effective inertia moment of the cross section after the formation of oblique cracks, resulting in a significant decrease in beam stiffness. Figure 15 shows the load-web tensile strain relationship of three beams. e growth trends of the web tensile strain of the three beams were basically the same before the appearance of cracks. e web of beam L1 cracked when the strain reached 410 με, and the load was 945 kN. e web of beam L2 cracked when the strain reached 812 με, and the load was 1408 kN. e web of beam L3 cracked when the strain reached 390 με, and the load was 805 kN. After cracking, the web tensile strain increased rapidly, among which the L2 beam grew the fastest. Figure 16 shows the loadbottom plate tensile strain relationship of the three beams. e bottom plate tensile strain increased linearly before cracking. e bottom plate of beam L1 cracked when the strain reached 631 με, and the load was 1544 kN. e bottom plate of beam L2 cracked when the strain reached 230 με, and the load was 302 kN. e bottom plate of beam L3 cracked when the strain reached 383 με, and the load was 914 kN. After cracking, the bottom plate tensile strain increased rapidly. When the bottom plate tensile strain of beam L3 was about 2500 με, there were no data from the strain gauge due to the failure of the strain gauge at the bottom of the bending crack.

Bottom Plate Tensile Strain.
For the load-strain response, the data measured by strain gauges before cracking are reliable; however, after cracking, the distribution of cracks greatly influenced the strain test results. For example, the strain gauge across the cracks will record a larger strain, and the strain gauge not located across the cracks may even record a strain reduction due to cracking of the surrounding area; therefore, only the typical load-strain response is given here.

Calculation of Shear Capacity Based on Existing
Specifications. At present, there are few design specifications for UHPC. e French specification [34], the Swiss specification [35], the "Highway Bridge specification" [36], and the "Technical Specification for High-Strength Concrete Structures" [37] were used to calculate the shear capacities of the test beams. e ratios of the test values to the calculated values are presented in Table 5, where V exp indicates the test value and V cal is the calculated value. Table 5 shows that the measured values of the shear capacities of the three test beams were higher than the

Calculation Formula of the Shear Capacity of UHPC
Beam. e MCFT models contain many calculation parameters and complex convergence conditions, and the shear capacity calculations in existing specifications are too conservative. To facilitate the engineering applications of UHPC beams, the test data from previous studies were collected for fitting [15,18,32,38]. e influence of the concrete part, stirrup part, and prestressed reinforcement part on the shear bearing capacity of UHPC beams is considered, and the calculation formula of the shear bearing capacity is proposed. Each part of the formula takes into account the influence of the shear-span ratio and introduces its own calculation parameters. e specific formula is as follows: where V c , V s , and V p are the shear forces of the UHPC concrete, stirrups, and prestressed reinforcement, respectively; λ is the shear-span ratio, which has a value of 1.5 when the value is less than 1.5 and a value of 3 when the value is greater than 3; α 1 is the flange coefficient; f yv and ρ sv are the stirrup yield strength and stirrup ratio, respectively; N p0 is the resultant force of prestressed reinforcement and nonpre-stressed reinforcements when the normal stress of the calculated section of concrete is 0.

Comparison of Results Verification.
To verify the correctness and applicability of the MCFT model and formula,  the calculated results were compared and analyzed with previously published experimental data, as presented in Table 6. Table 6 shows that the values calculated using the MCFT model and fitting formula agree well with the experimental values. e concept of the formula is clear, and the calculation process is simple.
ese results indicate that the MCFT model and fitting formula can be used to analyze and calculate the shear capacity of UHPC beams.

Discussion on the Feasibility and Design Proposal.
In the MCFT analysis model proposed in this paper, to simplify the calculation, ε x in the shear calculation was taken as the longitudinal strain at half the height of the section in the bending calculation. e applicability of this method to the actual structure needs further discussion. In the shear design of a UHPC beam structure, when the shear-span ratio is small, the influence of the UHPC tensile strength can be ignored or used as a safety reserve in shear design. When the shear-span ratio is large, the contribution of the UHPC tensile strength to beam shear should be considered; therefore, to establish a complete UHPC shear calculation theory, more shear tests are still needed to lay the foundation for a theoretical analysis.

Conclusions
e following conclusions can be drawn according to the above research: (1) In this paper, the shear analysis model of UHPC-T beams based on the modified compression field theory fully considered changes in the shear performance of UHPC structures under the combined action of bending and shearing. e comparison between the calculated and experimental results proved the rationality of the assumptions in the theory, indicating that the established model was suitable for predicting the shear bearing capacity of UHPC beams. (2) e shear capacity of the UHPC beam decreased upon increasing the hear-span ratio, but the extent of the decrease gradually slowed. In this paper, when the shear-span ratio changed from 1.04 to 2.12, the shear bearing capacity decreased greatly, whereas the decrease was very small when the shear-span ratio changed from 2.12 to 3.19.  (3) e shear-span ratio affects the failure mode of beams. When the shear-span ratio is 1.06, the failure mode is inclined compression failure. When the shear-span ratio is 2.12, the failure mode is shear compression failure. When the shear-span ratio is 3.19, the failure mode is diagonal tension failure. (4) e shear capacity of the UHPC beam calculated by existing specifications led to conservative results; the smaller the shear-span ratio, the more obvious the difference. e simplified prediction formula proposed in this paper based on the MCFT model and existing test data fully considered the influence of the shear-span ratio. e calculation process was simple and was verified by previously published experimental results, which can provide a reference for the shear design of UHPC beams in practical engineering applications.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.