Experimental tests and numerical analyses on the shear performance of UHPC encased steel beams: Evaluation of shear strength formula

Abstract

To develop a design method for the shear capacity of ultra-high-performance concrete (UHPC) encased steel beams, shear tests were conducted on nine beam specimens. The key parameters investigated were the shear span ratio, stirrup ratio, and the thickness of the steel web. Based on the experimental results, a finite element (FE) model of the beam was established to further analyze failure modes and shear mechanisms. Using both experimental data and extensive FE simulations, two predictive formulae for the shear capacity of UHPC encased steel beams was proposed. The tests showed that the shear-compressive failure occurred in all the beam specimens. The vertical peak load dropped by 15.5% when the shear span ratio increased from 1.04 to 2.46. Conversely, the vertical peak load of the beam specimens increased with the increase of the stirrup ratio and the steel web thickness. The average ratios of the two prediction formulas to the experimental values are 0.89 and 0.92 respectively, and the average ratios of the two prediction formulas to the finite element calculation values are also 0.96 and 0.95 respectively, indicating that the proposed prediction formulae for the shear capacity of the UHPC encased steel beam are reasonable and slightly conservative. The findings of this investigation provide experimental and theoretical support for the shear design of the UHPC encased steel beams.

Keywords

ultra-high-performance concrete steel section shear failure finite element analysis shear capacity

Introduction

Concrete encased steel (CES) structures have been extensively employed in large-span and heavy-load structures owing to their high bearing capacity and outstanding seismic performance [1–3]. Nevertheless, ordinary concrete surrounding the steel shape is liable to durability damage in freezing-thawing or corrosive environments, which impacts the service life of CES structures. Consequently, the utilization of ultra-high performance concrete (UHPC) in CES structures has drawn widespread attention.

Ultra-high performance concrete (UHPC), formerly referred to as reactive powder concrete (RPC), is a fiber-reinforced cement-based composite material composed of raw materials including cement, mineral admixtures, reactive fine powders, fine aggregates, chemical admixtures, high-strength micro-steel fibers or organic synthetic fibers, and water. It exhibits exceptional impermeability and superior mechanical performance.

Currently, UHPC has been widely utilized in infrastructure rehabilitation and construction. Nadir et al. (2024a) investigated composite beams in which UHPC replaced normal concrete (NC) at the mid-span region and proposed analytical methods for various failure modes. Furthermore, Nadir et al. (2024b) conducted experimental studies on corner joints incorporating UHPC in the core zone, examining their hysteretic behavior under biaxial bending, and found that the composite joints exhibited ductile failure characteristics. Haidar et al. (2023) performed numerical analyses on the axial compressive behavior of slender steel tubes filled with UHPC and provided corresponding design recommendations.

Since the shear properties of UHPC differ significantly from those of normal concrete (NC), numerous researchers have conducted shear tests on reinforced UHPC beams. Abadel et al. (2022) experimentally investigated the shear behavior of deep beams made with NC and UHPC. The results showed that the shear strength of UHPC deep beams was significantly higher than that of NC deep beams, though with reduced deformation capacity. Extensive tests have been carried out on the shear performance of UHPC beams to examine the effects of parameters such as shear span ratio, stirrup ratio, steel fiber fraction, reinforcement ratio and longitudinal reinforcement strength on the shear performance of UHPC beams, and several methods for predicting the shear bearing capacity have been put forward (Ahmad et al., 2019; Chen et al., 2022, 2023; Wang et al., 2020). Ji et al. (2018) evaluated the shear behavior of T-section RPC beams and introduced a truss model incorporating four softening coefficients to develop a simplified shear capacity prediction formula. In addition, Lim and Hong, 2016 suggested that the allowable stirrup spacing in UHPFRC beams be limited to 0.75 times the beam height, based on the experimental findings.

Due to its superior shear capacity, UHPC can simplify construction by reducing or even eliminating the need for stirrups. Consequently, the shear behavior of flexural members without stirrups has been widely studied. Voo et al. (2006) conducted shear tests on large-scale RPC I-beams without stirrups and developed a shear capacity calculation model based on crack slip and plasticity theories. Ye et al. (2023) experimentally investigated the shear performance of externally prestressed UHPC T-beams without stirrups and proposed predictive formulas for shear cracking strength and ultimate shear capacity. Ridha et al. (2018) examined the shear behavior of RPC beams without transverse stirrups and found that while steel fiber content had little effect on the cracking load, it significantly improved the ultimate load capacity, ductility, and energy absorption.

Several experimental studies have investigated the application of UHPC in CES components, as reported in (Zhang et al., 2022, Zhang et al., 2023a; Zhu et al., 2025). However, to date, limited research has specifically focused on the shear behavior of UHPC-encased steel components (Hao et al., 2025). In current research indicates that the shear resistance of CES members is primarily governed by components such as steel sections, concrete, and stirrups (Taheri and Epackachi, 2024). Xue et al. (2023a, 2023b) developed multiple shear models to predict the shear capacity of steel-concrete composite beams, which were shown to achieve high accuracy. Considering the interfacial interaction, Xue et al. (2022) proposed an analytical method for predicting the shear strength of short steel-concrete columns. Some studies have suggested that the type of concrete material can significantly influence the shear performance of steel-reinforced concrete (SRC) beams. Yao et al. (2014) tested the shear performance of prestressed steel reinforced ultra-high strength concrete beams, and the results showed that such beams had high residual shear bearing capacity and post-cracking stiffness. Deng et al. (2020) conducted tests and pointed out that steel reinforced high ductile concrete beams have higher shear bearing capacity and ductility compared with ordinary concrete. Similarly, Pan et al. (2022) studied the shear resistance of steel reinforced recycled aggregate concrete after exposure to elevated temperatures, pointing out that its failure pattern was similar to that of ordinary CES beams at the same temperature, but with the increase of the replacement rate of recycled aggregate, the initial stiffness of the test beams decreased. These findings suggest that when UHPC is used in place of ordinary concrete in CES beams, the resulting shear behavior may exhibit distinct characteristics.

Therefore, to investigate the shear performance and develop a design method for UHPC-encased steel beams, experiments were conducted on nine beam specimens subjected to four-point vertical loading. The primary parameters considered in the study include the shear span ratio, stirrup ratio, and the thickness of the steel section web. Subsequently, finite element (FE) analyses were performed to further examine the failure modes and the primary factors affecting the shear strength of UHPC-encased steel beams. Based on both experimental and numerical results, two predictive formulas for shear capacity were developed through parametric analyses.

Test procedure

Specimen design and fabrication

The raw materials of the UHPC mainly include the ordinary Portland cement, 40∼70 mesh and 70∼140 mesh quartz sand (1:1), high-quality silica fume, S95 grade slag, high-efficiency polycarboxylate water reducer, retarder, and the steel fiber (diameter 0.23 mm, length 13 mm), etc. The mix proportions of UHPC are shown in Table 1.

Table 1.

Mix proportion of the UHPC.

Water-binder ratio	Cement	Silica fume	Slag	Quartz sand	Water reducer	Steel fiber^a
0.18	1	0.14	0.28	1.2	1.5%	2.5%

^aVolume fraction.

To investigate the shear failure mechanism and calculation methods for the shear capacity of UHPC encsed steel beams, specimens were designed in accordance with the principle of “strong bending and weak shear”. This design principle ensured that the beams would experience shear failure rather than bending failure. The design of the specimens mainly referred to the standard JGJ 138-2016 (Ministry of Urban and Rural Development of People’s Republic of China, 2016). The detailed design process is presented as follows: Initially, the shear capacity was estimated by taking into account the thickness of the steel web, the properties of UHPC, and the arrangement of stirrups. This estimation led to the determination of the support reaction forces. Subsequently, the support reaction forces were multiplied by an amplification factor of 1.5 to find the mid-span bending moment. Finally, based on the calculated mid-span bending moment, the appropriate quantity of longitudinal reinforcement bars and the dimensions of the steel flanges were determined. During this process, the strengthening effect of the steel web on bending was temporarily not considered.

A total of nine beam specimens, labeled B-1 through B-9, were fabricated. Their dimensions and reinforcement details are illustrated in Figures 1 and 2. Each beam measured 2000 mm in length, with a span of 1650 mm and a cross-sectional size of 150 mm × 300 mm. All H-shaped steel sections were fabricated by welding Q235 steel plates and positioned at the center of the beams. The longitudinal reinforcement and stirrups were made of HRB400-grade steel.

Figure 1.

Dimensions and structure of UHPC encased steel beams.

Figure 2.

Cross-sections in the shear span.

It should be noted that no special measures were implemented in this study to enhance the bond capacity between the steel section and the UHPC. This decision was based on findings from preliminary experiments (Zhang et al., 2023b), which demonstrated that the bond capacity between the steel section and UHPC is greater than that between steel sections and conventional concrete. As a result, construction procedures can be simplified, and the use of shear connectors, such as stud bolts, may be omitted without compromising structural performance.

The specimen preparation procedure was as follows: First, a reinforcement cage was assembled around the H-shaped steel. Next, the reinforcement cage was placed into the formwork. Subsequently, UHPC was poured into the formwork and cured under room temperature conditions for 28 days. Figure 3 illustrates the fabrication process of the steel cage and the completed UHPC pouring stage of the specimens.

Figure 3.

The fabrication of beam specimens.

Table 2 presents the design parameters, where H, B, t_t, and t_f denote the section height, section width, web thickness, and flange thickness of the H-shaped steel, respectively. The shear span ratio is denoted by λ, the shear span length by a, the effective depth by h₀, and the stirrup ratio by ρ_sᵥ. The main variables investigated were the shear span ratio, the stirrup ratio, and the web thickness of the steel section. Specifically, specimens B-1 to B-5 were considered to study the effect of shear span ratio; B-3, B-6, and B-7 examined the influence of stirrup ratio; and B-3, B-8, and B-9 evaluated the effect of steel web thickness.

Table 2.

Design of experimental beam parameters.

Specimen	H-shaped steel section(H × B × t_w × t_f)/mm	Shear span a/mm	Shear span ratio λ = a/h₀	Stirrups in the shear span	Stirrup ratio in the shear span ρ_sv/%
B-1	160 × 50 × 4 × 15	250	1.04	6@150	0.251
B-2	160 × 50 × 4 × 15	350	1.44	6@150	0.251
B-3	160 × 50 × 4 × 15	450	1.85	6@150	0.251
B-4	160 × 50 × 4 × 15	500	2.05	6@150	0.251
B-5	160 × 50 × 4 × 15	600	2.46	6@150	0.251
B-6	160 × 50 × 4 × 15	450	1.85	6@110	0.343
B-7	160 × 50 × 4 × 15	450	1.85	6@75	0.502
B-8	160 × 50 × 5 × 15	450	1.85	6@150	0.251
B-9	160 × 50 × 6 × 15	450	1.85	6@150	0.251

Material mechanical properties

During the concrete pouring process, three UHPC cubic specimens (100 mm × 100 mm × 100 mm) and three prismatic specimens (100 mm × 100 mm × 300 mm) for compressive strength testing, together with three dog-bone-shaped specimens (featuring a central cross-sectional dimension of 40 mm × 15 mm) for axial tensile testing, were cast simultaneously. All tests were conducted in accordance with the Standard GB/T 50081-2019 (Ministry of Urban and Rural Development of People’s Republic of China, 2019b). The loading rate was set at 0.3 MPa/s for compressive tests and 0.08 MPa/s for tensile tests. All specimens were cured in room temperature for 28 days. The average measured compressive strength f_cu is 112.9 N/mm², the average axial compressive strength f_c was 104 N/mm², and the average axial tensile strength f_t was 7.6 N/mm². In terms of DBJ43/T 325-2017 (Hunan Provincial Department of Housing and Urban-Rural Development, 2017), the modulus of elasticity E_c of UHPC was computed to be 3.9 × 10⁴ N/mm².

It should be noted that, due to the use of normal-temperature curing for the UHPC in this study, the measured cube strength is slightly below the minimum strength specified for UHPC in the design code, yet it satisfies the minimum strength requirement for RPC. For subsequent numerical analysis, the strength was extrapolated to 180 MPa.

The dimensions of the steel plate and steel bar specimens, as well as the loading procedure, were determined in accordance with the standard GB/T 228.1-2021 (State Administration for Market Regulation of the People’s Republic of China, 2021). The steel plate specimens were designed in a dog-bone configuration, while the length of the steel bar specimens was set to 15 times their nominal diameter. Three specimens of each size were prepared to ensure test reliability. The tensile loading rate was maintained at 10 MPa/s throughout the testing process. The measured yield strengths of the steel bars with diameters of 6 mm, 16 mm, and 25 mm were 441.5 N/mm², 426.5 N/mm², and 453.7 N/mm², respectively. The measured average yield strength f_a of steel plates with thicknesses of 4 mm, 5 mm, 6 mm and 15 mm were 229.3 N/mm², 235.1 N/mm², 248.7 N/mm² and 260.7 N/mm², respectively. The modulus of elasticity of steel bars E_s and that of steel plates E_a was taken as 2.0 × 10⁵ N/mm² and 2.06 × 10⁵ N/mm², respectively, according to China’s standard JGJ 138-2016.

Loading apparatus and measuring point layout

The test setup is illustrated in Figure 4(a), where a four-point loading method was adopted. Prior to formal loading, a pre-load—less than 5% of the estimated ultimate bearing capacity—was applied to verify the proper functioning of the loading equipment. The primary measurements collected during the tests included: (1) the vertical load-midspan deflection (P-Δ) curves, where P is the concentrate force at the loading point, (2) the strains of the longitudinal steel bars, stirrups, steel webs and flanges in the shear span, (3) the cracking and ultimate loads, and (4) the crack distribution.

Figure 4.

Test setup and strain gauge arrangement.

To measure the midspan deflection, five displacement meters were arranged at the midspan, the two loading points and two supports. The vertical load was monitored using a force sensor placed above the hydraulic jack. Taking specimen B-3 as an example, Figure 4(b) shows a typical layout of the strain gauges on the longitudinal steel bars, the stirrups, the steel flanges and the steel webs. Two sets of strain gauges were affixed to the steel webs within the shear spans. Strain gauges were also installed on the upper and lower longitudinal steel bars and the steel flanges at the same section as the strain rosettes. Additionally, strain gauges were mounted on the stirrups, particularly in the region between the loading points and adjacent supports.

Test results and analysis

Observations during loading

Crack propagation was monitored during the loading process of the specimens. It is worth noting that, in general, all nine beam specimens exhibited similar failure patterns. Therefore, the behavior during loading is illustrated using specimen B-3 as a representative example. At the initial stage, under a low load, the beam maintained its stiffness with no visible cracks. When the load was increased to 168.1 kN, the first vertical bending crack appeared in the pure bending zone at mid span. As the load increased, the vertical cracks in the pure bending zone gradually increased and extended upward to the lower flange of the shaped steel. The crack distribution was roughly symmetric with a maximum crack length of about 6 mm. When the load reached 255.2 kN, a diagonal crack developed in both bending-shear regions. The ends of the diagonal cracks pointed toward the supports and the loading points. As the loading continued, new diagonal cracks appeared in the shear span region, which were generally parallel to the initial oblique cracks. When the load was increased to 637.5 kN, no new cracks formed in the pure bending region, while multiple nearly full-length diagonal cracks developed in both shear span regions. At the peak load of 858.3 kN, the UHPC at the loading point was crushed and the midspan deflection was 4.2 mm. Due to the presence of the steel fibers, the UHPC at the crushing position did not spall significantly.

Figure 5 presents the failure pattern and crack distribution for the nine specimens. Due to the presence of steel web, the shear-compression failure was produced in all beam specimens. Unlike ordinary concrete encased steel beams, which typically develop a single major diagonal crack, the UHPC encased steel beams developed several diagonal cracks, each pointing to the loading point and the support. These cracks are roughly parallel to each other within the shear span ratio. This phenomenon is attributed to the “bridging” effect of the steel fibers and the presence of the shaped steel, which suppressed the propagation of the main diagonal crack, allowing multiple diagonal cracks to develop simultaneously.

Figure 5.

Failure pattern and crack distribution.

P-Δ curves

The vertical load-midspan deflection (P-Δ) curves of the nine beam specimens under different shear-span ratio, steel web thickness, and stirrup ratio are shown in Figure 6. As can be seen, there is no evident yield point on the curve before reaching the peak load, and the descent segment of the curve is steep after the peak point. The measured cracking load and deflection in the pure bending region (P_crb and Δ_crb), the cracking load and deflection in the shear span (P_crv and Δ_crv), peak load and deflection (P_m and Δ_m) is shown in Table 3.

Figure 6.

P-Δ curves under different factors.

Table 3.

Load and deflection at cracking and peak points.

No.	P_crb/kN	Δ_crb/mm	P_crv/kN	Δ_crv/mm	P_m/kN	Δ_m/mm
B-1	180.67	0.44	270.11	0.83	908.13	3.38
B-2	177.32	0.46	265.52	0.91	885.41	3.67
B-3	168.10	0.48	255.19	0.93	858.31	4.19
B-4	158.86	0.51	238.24	0.96	816.35	4.52
B-5	153.46	0.55	230.16	0.97	767.33	4.91
B-6	170.05	0.48	268.53	1.02	900.32	3.44
B-7	194.38	0.46	269.42	0.98	919.12	3.01
B-8	184.59	0.41	257.97	0.84	900.58	3.55
B-9	198.88	0.43	262.18	0.91	914.41	3.12

The effect of shear span ratio on the P-Δ curves of the beam specimens is presented in Figure 6(a), where the shear span ratios of specimens B-1 to B-5 are 1.03, 1.44, 1.85, 2.05 and 2.46, respectively. As the shear span ratio increased, both the vertical load and the stiffness of the beam specimen gradually decreased. Compared to the beam specimen B-1, when the shear span ratio was increased from 1.03 to 1.44, 1.85, 2.05, and 2.46, the vertical peak load decreased by 2.5%, 5.5%, 10.1%, and 15.5%, respectively.

Figure 6(b) illustrates the influence of steel web thickness t_w on P-Δ curves of the beam specimens. The results indicate that increasing the thickness of the steel web enhances both the vertical peak load and stiffness. When the thickness of the steel web increased from 4 mm to 5 mm and 6 mm, the vertical peak load increased by 4.9% and 6.5%, respectively. Similarly, Figure 6(c) presents the influence of the stirrup ratio ρ_sv on the P–Δ curve. The effect of increasing the stirrup ratio on the vertical peak load follows a trend similar to that observed with increasing web thickness. As the stirrup ratio increased from 0.251% to 0.343% and 0.502%, the peak vertical load increased by 4.9% and 7.1%, respectively.

It should be noted that beams are typically subjected to either flexural or shear failure. In seismic design for practical engineering applications, beams should be designed according to the principle of “strong shear and weak flexure” to ensure that flexural failure occurs prior to shear failure, thereby enhancing structural ductility and collapse resistance. Existing research has primarily focused on analytical methods for evaluating the flexural ductility and load-bearing capacity of beams. However, to fully realize the “strong shear and weak flexure” design criterion, a thorough understanding of beam shear resistance is essential. Therefore, this study centers on the determination of shear strength in beams. To achieve this objective, test specimens were intentionally designed with “weak shear and strong flexure” characteristics to induce shear-critical failure, enabling a direct assessment of their shear capacity. Typically, beams undergoing shear failure exhibit brittle behavior, characterized by limited displacement capacity and negligible ductility.

Load-strain curves

The primary strain is used to reflect the strain variation at the mid-height of the steel web in the shear span. The primary strain ε₁ can be computed according to equation (1) (Zhang et al., 2000), where ε₀, ε₄₅ and ε₉₀ is the strain in the horizontal, 45°, and vertical direction at the measuring points, respectively.

Figure 7 presents the typical load–primary strain (P–ε₁) curves for the steel webs. It can be observed that before reaching the peak load, the primary strain ε₁ in the steel web exceeded the yield strain. Beyond the peak load, ε₁ increased rapidly, indicating significant plastic deformation in the web.

ε_{1} = \frac{ε_{0} + ε_{90}}{2} + \frac{\sqrt{2}}{2} \sqrt{{(ε_{0} ‐ ε_{45})}^{2} + {(ε_{45} ‐ ε_{90})}^{2}}

(1)

Figure 7.

Load - primary strain curve of the webs.

The strain variation of the stirrups during the entire loading process was obtained from the strain gauges attached to the stirrups. The load-strain (P-ε_s) curves of the stirrups for the typical specimens are presented in Figure 8. It can be seen that, before reaching the peak load, the stirrups in the bending and shear regions had already yielded.

Figure 8.

Load-strain curve of the stirrups.

FE verification

To further investigate the shear performance of UHPC encased steel beams, nine beam specimens were simulated by the FE software ABAQUS, and the failure modes and bearing capacities of FE models were investigated.

FE model

The ideal elastic-plastic model was used for the longitudinal steel bars, stirrups, steel webs and the flanges (Segui, 2013). For the UHPC material, the concrete plastic damage (CPD) model available in the standard package of ABAQUS was adopted. The uniaxial stress-strain relations in tension and compression adopted the constitutive model proposed by Zheng (Zheng et al., 2011), which are shown in Figure 9. In this model, σ_t and ε_t represents the uniaxial stress and strain in tension, respectively. σ_c and ε_c denotes the stress and strain in compression, respectively. ε_t0 and ε_c0 is the strain at peak point of UHPC in tension and compression, respectively.

Figure 9.

FE model of the UHPC encased steel beam.

The damage variable d for UHPC in the CDP model can be calculated according to equation (2) (Yu et al., 2010), where σ and σ₀ represent the stress and peak stress on the uniaxial stress-strain curve of UHPC in compression or tension, respectively. If the stress does not exceed its peak strength, the damage variable d is equal to zero, indicating no damage.

Fakeh et al. (2025) proposed relevant parameters for the application of UHPC in ABAQUS and derived meaningful conclusions. Building upon this foundation, the present study conducts a corresponding sensitivity analysis. Considering the inherent variability of UHPC material properties and the influence of steel sections, the following parameters are adopted in this work: (1) the expansion angle φ = 30°; (2) the viscosity parameter μ = 0.001; (3) the flow potential eccentricity e = 0.1; (4) the ratio between initial biaxial and uniaxial compressive yield strength σ_b0/σ_c0 = 1.16; (5) the ratio of constant stress between the tension meridian and the compression meridian K_c = 2/3.

d = 1 ‐ σ / σ_{0}

(2)

The FE model of the UHPC-encased steel beam is depicted in Figure 9. The UHPC and rigid blocks were modeled using eight-node reduced integration solid elements (C3D8R), while the shaped steel sections were represented using four-node reduced integration shell elements (S4R). The longitudinal steel bars and stirrups were modeled using two-node linear reduced integration truss elements (T3D2). A uniform mesh size of 25 mm was adopted for the element discretization.

Boundary conditions included a fixed-pin support at one end of the beam and a roller support at the other. To prevent local failure at the contact areas, four rigid blocks were introduced at the support and loading points. As no significant bond-slip behavior was observed between the steel beams, reinforcing bars, and UHPC during the experimental tests, and to simplify the modeling process, interfacial slip between the steel beams and UHPC was not accounted for in the numerical model. Perfect bonding was assumed at these interfaces. Displacement-controlled loading was applied to capture the complete load–displacement response, including the descending branch of the load–deflection curve.

Calculated results

The comparison of the P-Δ curves obtained from the FE analysis and experimental test is presented in Figure 10. Despite the inherent variability in UHPC strength, the simulated curves closely match the experimental results, indicating that the FE model provides an acceptable level of accuracy. Figure 11 presents a comparison of the computed and measured vertical peak load $P_{m}^{FE}$ and $P_{m}^{T}$ . It can be observed that the ratio ${P_{m}^{FE} / P}_{m}^{T}$ ranges from 0.84 to 1.01, with a mean value of 0.92 and a variance of 0.056.

Figure 10.

Tested and FE calculated P- Δ curves.

Figure 11.

Comparison of FE calculated and tested peak loads.

In the FE simulation results, the tensile damage of the damage plastic model can be used to reflect the distribution of cracks. Figure 12 shows the comparison of the tested crack distribution and the calculated tensile damage for beam specimens B-2 and B-6. It can be found that vertical bending cracks were mainly developed in the pure bending region of the FE model, while several diagonal cracks parallel to the line between the loading point and the support occurred in the shear span, which is close to the tested crack distribution.

Figure 12.

The cracking morphological diagram of the test beam and the cloud diagram of concrete tensile damage.

Figure 13 illustrates the equivalent plastic strain of the shaped steel and the steel bar reinforcements for the beam specimens B-2 and B-6. It can be observed that the steel web and stirrups in the shear span have already yielded, which is consistent with the test results. In addition, the FE results indicate that the stress of the shaped steel flanges and longitudinal bars in the shear span is relatively low, suggesting that the steel flanges and longitudinal reinforcement have a limited contribution to the shear capacity. Overall, the FE model developed for the UHPC encased steel beam in this study demonstrates good agreement with the test results and is considered reliable for further analysis of shear capacity.

Figure 13.

Equivalent plastic strain diagram of the test beam.

Shear capacity of UHPC encased steel beam

Shear mechanism

From the above experimental tests and FE simulations, it can be observed that all UHPC encased steel beams experienced shear-compression failure, mainly due to the presence of shaped steel, and that the steel web and stirrups in the shear span have yielded. Therefore, referring to JGJ138-2016 (Ministry of Urban and Rural Development of People’s Republic of China, 2016), it is considered that the shear capacity of UHPC encased steel beam is primarily provided by the UHPC, the stirrups intersecting with the diagonal cracks, and the steel web. Here, the shear capacity sustained by the UHPC arises from the composite stress in the shear-compression zone, the tension present in the diagonal cracks, and the pinning action of the steel flanges and longitudinal bars. Figure 14 illustrates the shear mechanism of the diagonal section of the UHPC encased steel beam. The shear capacity V_u can be calculated by equation (3), where V_c, V_s and V_aw are the shear capacity provided by the UHPC, the stirrups and steel web respectively.

V_{u} = V_{c} + V_{s} + V_{aw}

(3)

Figure 14.

Shear mechanism of oblique section.

Shear capacities of hoops and steel web

The experimental tests and FE results indicate that the stirrups in the shear span reached or were close to the yield point. According to JGJ 138-2016 (Ministry of Urban and Rural Development of People’s Republic of China, 2016), the contribution of the stirrups to the shear capacity of the beam can be calculated using equation (4). Here, f_yv denotes the yield strength of the stirrups (equivalent to f_y in this case), and A_sv signifies the cross-sectional area of a single stirrup, h₀ is the effective depth, which is defined as the distance from the centroid of the tensile flange of the steel section and the tensile reinforcement to the extreme fiber of the compressed UHPC.

V_{sv} = f_{yv} h_{0} A_{sv} / s

(4)

The test and FE results demonstrate that the steel web in the shear span also reached its yield point. According to JGJ138-2016 (Ministry of Urban and Rural Development of People’s Republic of China, 2016), the contribution of the steel web to the shear capacity of the diagonal section can be determined by equation (5), where h_w denotes the height of the steel web.

V_{aw} = 0.58 f_{a} t_{w} h_{w} / λ

(5)

The bearing capacity of UHPC

The contributions of the stirrups and steel web to the shear capacity can be calculated using equations (4) and (5), respectively. Consequently, the shear force V_c carried by the UHPC exhibiting shear failure can be determined by subtracting the shear contributions of the stirrups and the steel web from the total shear force V, as shown in equation (6).

V_{c} = V ‐ (V_{sv} + V_{w})

(6)

To develop the predicting equation for the shear capacity V_c of the UHPC in the beam, the parameter analysis using the FE method were conducted, which include the cubic compression strength of UHPC f_cu, the shear span ratio λ, stirrup ratio ρ_sv, and the steel web thickness t_w. The section size of the FE beam model is 150 mm × 300 mm, the shaped steel grade is Q235, the longitudinal bar and stirrup grade are HRB400, and the calculated span is 1700 mm. Table 4 lists the variation range of analysis parameters as well as the corresponding UHPC strength in tension, shear span length, stirrup configuration, and section size of H-shaped steel, where the axial tensile strength f_t can be expressed as

f_{t} = 2.14 \sqrt{0.88 f_{cu}} ‐ 12.8

N/mm² (Zheng et al., 2011). Here, 60 FE models were established for analysis.

Table 4.

The range of the analysis parameters.

Parameters	Variation range	Notes
Concrete strength f_cu (N/mm²)	120; 150; 180	The cube size: 100 mm × 100 mm × 100 mm
Shear span ratio λ	1.04; 1.85; 2.46; 3.20; 4.02	Shear span a (mm): 250; 450; 600; 780; 980
Stirrup ratio ρ_sv	0.251%; 0.502%	6@150; 6@75
Steel web thickness t_w (mm)	4; 6	H-shaped steel: 160 × 50 × 4 × 15; 160 × 50 × 6 × 15

The codes JGJ138-2016 (Ministry of Urban and Rural Development of People’s Republic of China, 2016) and GB50010-2010 (Ministry of Urban and Rural Development of People’s Republic of China, 2014) determine the shear capacity of UHPC based on its tensile strength f_t, where V_c = α_cvf_tbh₀. Figure 15(a) shows the relationship between α_cv and the shear span ratio λ for beam specimens and the FE model that underwent shear failure. Through fitting, this relationship is expressed as α_cv = 10.8/(λ+2.2). Therefore, the shear capacity of the UHPC in the UHPC encased steel can be calculated using equation (7).

V_{c} = \frac{10.8}{λ + 2.2} f_{t} b h_{0}

(7)

Figure 15.

Relations between α_cv and λ.

Additionally, the codes JGJ/T465-2019 (Ministry of Urban and Rural Development of People’s Republic of China, 2019a) and GB/T31387-2015 (General Administration of Quality Supervision, 2015) determine the shear strength of fiber-reinforced concrete components based on the initial cracking strength f_t0 and the fiber characteristic value λ_f, expressed as V_c = α_cvf_t0bh₀ (1+β_vλ_f). Here, β_v is the influence coefficient of steel fiber on the shear strength. According to GB/T31387-2015 (General Administration of Quality Supervision, 2015), f_t0 = 0.053f_cu and β_v = 0.6, and the influence of β_v on UHPC is minimal. The fiber characteristic value λ_f is calculated using λ_f = ρ_fl_f/d_f. Figure 15(b) shows the relationship between α_cv and the shear span ratio λ for the beam specimens and the FE model. By fitting the data, the relationship is expressed as α_cv = 9.4/(λ+3.1). Therefore, when the initial cracking strength and fiber characteristic value are considered, the shear capacity V_c of UHPC can be calculated using equation (8).

V_{c} = \frac{9.4}{λ + 3.1} f_{t 0} (1 + β_{v} λ_{f}) b h_{0}

(8)

Shear bearing capacity

In summary, the shear capacity V_u of UHPC encased steel beams can be predicted by means of equations (9) or (10), where λ is a value ranging from 1.0 to 4.0.

V_{u} = \frac{10.8}{λ + 2.2} f_{t} b h_{0} + f_{yv} h_{0} A_{sv} / s + 0.58 f_{a} t_{w} h_{w} / λ

(9)

V_{u} = \frac{9.4}{λ + 3.1} f_{t 0} (1 + β_{v} λ_{f}) b h_{0} + f_{yv} h_{0} A_{sv} / s + 0.58 f_{a} t_{w} h_{w} / λ

(10)

Result comparison

Table 5 presents the experimentally measured shear capacity values V_u^T, the FE calculated values V_u^FE, and the predicted shear capacities V_u^P1 and V_u^P2 using equations (9) and (10) for the nine specimens. The mean value of the ratio V_u^P1/V_u^T is 0.89, with a standard deviation of 0.048. Similarly, the mean value of the ratio V_u^P1/V_u^FE is 0.96, with a standard deviation of 0.055. The mean value of the ratio V_u^P2/V_u^T is 0.92, with a standard deviation of 0.047, while the mean value of the ratio V_u^P2/V_u^FE is 0.95, with a standard deviation of 0.051. These ratios indicate that the results predicted by the two shear capacity formulas, based on the UHPC tensile strength and the UHPC initial cracking strength, are slightly lower than the test values and the FE results, within the range of 0.89 and 0.96. Considering the need to prevent shear failure in bending members in engineering applications, it can be concluded that both prediction formulas are conservative and therefore suitable for calculating the shear capacity of such composite beams.

Table 5.

Shear capacity comparison between tests, simulation and prediction.

No.	V_u^T/kN	V_u^FE/kN	V_u^P1/kN	V_u^P1/V_u^T	V_u^P1/V_u^FE	V_u^P2/kN	V_u^P2/V_u^T	V_u^P2/V_u^FE
B-1	908.13	910.18	805.65	0.88	0.88	829.98	0.91	0.95
B-2	885.41	847.57	755.27	0.85	0.89	781.11	0.86	0.91
B-3	858.31	773.68	705.78	0.82	0.91	733.10	0.92	0.94
B-4	816.34	683.54	676.11	0.82	0.98	704.32	0.85	0.92
B-5	767.33	659.26	659.54	0.92	0.99	688.25	0.89	0.92
B-6	900.32	833.46	859.58	0.95	1.03	930.79	1.02	1.06
B-7	919.12	918.57	874.45	0.95	0.95	945.21	1.01	1.03
B-8	900.58	785.34	804.74	0.89	1.02	802.91	0.90	0.92
B-9	914.41	830.95	843.17	0.92	1.02	817.87	0.91	0.93

Discussion

The nine UHPC encased steel beams designed for this test have shear span ratios ranging from 1.04 to 2.46, with all failure modes exhibiting shear-compression failure. Potential diagonal compression and diagonal tension failure modes have not been thoroughly investigated. Additionally, the steel used in this experiment has a strength grade of Q235, and the compressive strength of the UHPC cubes is 112.9 N/mm². Therefore, future experiments should focus on components using higher-strength steel and UHPC.

Conclusions

A series of experimental tests and finite element (FE) analyses were conducted on nine UHPC-encased steel beam specimens. These models were used to investigate the effects of the shear span ratio, stirrup ratio, and shaped steel web thickness. Based on the results obtained, the following conclusions can be drawn:

(1) Test results indicate that at the peak load, the steel web in the shear span of all specimens yielded. Additionally, the stirrups along the shear span also reached or approached yield, and the UHPC at the loading point was crushed. This indicates that the specimens exhibited shear-compression failure.

(2) The peak load of the beam specimens decreased as the shear span ratio increased. When the shear span ratio increased from 1.04 to 2.46, the vertical peak load decreased by 15.5%. Increasing the steel web thickness and stirrup ratio can improve the vertical load capacity of the beam specimens to some extent.

(3) The FE model for the UHPC encased steel beams was established. The FE calculations of crack distribution, failure modes, and peak loads were consistent with the experimental results. Therefore, the developed FE model can be used for subsequent shear capacity analysis.

(4) Two calculation formulae for the shear capacity of the diagonal section of the UHPC encased steel beam were proposed. The average ratio of the two predicted formulae to the test shear capacity was 0.89 and 0.92 respectively, and the average ratio of the two predicted formulae to the FE shear capacity was 0.96 and 0.95 respectively. This indicates that the prediction formulae are slightly conservative and can be used for shear design for safety.

Footnotes

Acknowledgements

The authors gratefully acknowledge the support provided by the support of the National Natural Science Foundation of China (51878589, 52078165), Natural Science Research Project of Guangling College of Yangzhou University (ZKZD23002), and the Open Fund of Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education by Harbin Institute of Technology (HITCE202105).

ORCID iD

Zhiyu Zhu

Author contributions

Huihui Luo: Writing – original draft, Methodology, Funding acquisition. Tianyu Shi: Formal analysis, Language editing. Ahmad Basshofi Habieb: Language editing. Kai Guo: Software, Validation. Ahmed Ahmad Omar: Validation. Kun Wang: Conceptualization, Supervision, Project administration. Zhiyu Zhu: Visualization, Methodology, Language editing. Dongdong Yang: Software. Zhaixian Chen: Data curation, Writing – review & editing, Validation.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (51878589, 52078165), Natural Science Research Project of Guangling College of Yangzhou University (ZKZD23002), and the Open Fund of Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education by Harbin Institute of Technology (HITCE202105)

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

Data will be made available on request.*

References

Abadel

Abbas

Almusallam

, et al. (2022) Experimental study of shear behavior of CFRP strengthened ultra-high-performance fiber-reinforced concrete deep beams. Case Studies in Construction Materials 16: e01103. https://doi.org/10.1016/j.cscm.2022.e01103

Ahmad

Bahij

Al-Osta

, et al. (2019) Shear behavior of ultra-high-performance concrete beams reinforced with high-strength steel bars. ACI Structural Journal 116(4): 3–14.

Chen

Zhou

Zhang

, et al. (2022) Experimental study on shear performances of ultra-high performance concrete deep beams. Structures 39: 310–322. https://doi.org/10.1016/j.istruc.2022.03.019

Chen

Zhou

Zhang

, et al. (2023) Shear performances of reinforced ultra-high performance concrete short beams. Engineering Structures 277: 115407. https://doi.org/10.1016/j.engstruct.2022.115407

Deng

Wang

, et al. (2020) Investigation on the shear behavior of steel reinforced NC/HDC continuous deep beam. Structures 23: 20–25. https://doi.org/10.1016/j.istruc.2019.10.002

Fakeh

Jawdhari

Fam

(2025) Recommended concrete damage plasticity parameters and constitutive models for UHPC in ABAQUS. Engineering Structures 333: 120154. https://doi.org/10.1016/j.engstruct.2025.120154

General Administration of Quality Supervision (2015) Inspection and Quarantine of the People's Republic of China Reactive Powder Concrete (GB/T 31387–2015). Beijing: China Standard Press.

Haidar

Jawdhari

Fam

(2023) Axial compressive strength of slender UHPFRC-Filled steel tubes. Engineering Structures 285: 116073. https://doi.org/10.1016/j.engstruct.2023.116073

Hao

Yang

Xue

, et al. (2025) Shear performance of deep partially precast high-strength steel reinforced UHPC T-beam: experimental study and a novel shear model. Engineering Structures 323: 119256. https://doi.org/10.1016/j.engstruct.2024.119256

10.

Hunan Provincial Department of Housing and Urban-Rural Development (2017) Technical Specification for Reactive Powder Concrete Structures (DBJ43/T 325-2017). Beijing: China Architecture and Building Press.

11.

, et al. (2018) Shear capacity of T-Section girders made of reactive powder concrete. Journal of Bridge Engineering 23(7): 04018041. https://doi.org/10.1061/(asce)be.1943-5592.0001253

12.

Lim

Hong

(2016) Shear tests for ultra-high performance fiber reinforced concrete (UHPFRC) beams with shear reinforcement. International Journal of Concrete Structures and Materials 10(2): 177–188. https://doi.org/10.1007/s40069-016-0145-8

13.

Ministry of Urban and Rural Development of People's Republic of China (2014) Concrete Structure Design Code (GB50010-2010). Beijing: China Building Industry Press.

14.

Ministry of Urban and Rural Development of People's Republic of China (2016) Composite Structure Technical Specification (JGJ 138-2016). Beijing: China Building Industry Press.

15.

Ministry of Urban and Rural Development of People's Republic of China (2019a) Standard for Design of Steel Fiber Reinforced Concrete Structures (JGJ/T465-2019). Beijing: China building industry press.

16.

Ministry of Urban and Rural Development of People's Republic of China (2019b) Standard for Test Methods of Concrete Physical and Mechanical Properties (GB/T50081-2019). Beijing: China building industry press.

17.

Nadir

Kadhim

MMA

Jawdhari

, et al. (2024a) Experimental investigation on UHPC-NSC composite beams. Structures 60: 105885. https://doi.org/10.1016/j.istruc.2024.105885

18.

Nadir

Ali

Jawdhari

, et al. (2024b) Cyclic behavior of UHPC corner beam-column joints under bi-directional bending. Structures 60: 105857. https://doi.org/10.1016/j.istruc.2024.105857

19.

Pan

Zheng

Xiao

, et al. (2022) Shear behavior of steel reinforced recycled aggregate concrete beams after exposure to elevated temperatures. Journal of Building Engineering 48: 103953. https://doi.org/10.1016/j.jobe.2021.103953

20.

Ridha

MMS

Sarsam

Al-Shaarbaf

IAS

(2018) Experimental study and shear strength prediction for reactive powder concrete beams. Case Studies in Construction Materials 8: 434–446. https://doi.org/10.1016/j.cscm.2018.03.002

21.

Segui

(2013) Steel Design. 5th edition. Stamford: Cengage Learning.

22.

State Administration for Market Regulation of the People's Republic of China (2021) Metallic Materials -Tensile Testing - Part 1: Method of Test at Room Temperature (GB/T 228.1-2021) Beijing: China building industry press, 2019. Beijing: China Standards Press.

23.

Taheri

Epackachi

(2024) Shear strength of encased composite columns. Journal of Constructional Steel Research 219: 108753. https://doi.org/10.1016/j.jcsr.2024.108753

24.

Voo

Foster

Gilbert

(2006) Shear strength of fiber reinforced reactive powder concrete prestressed girders without stirrups. Journal of Advanced Concrete Technology 4(1): 123–132. https://doi.org/10.3151/jact.4.123

25.

Wang

Song

, et al. (2020) Shear performance of reinforced ultra-high performance concrete rectangular section beams. Structures 27: 1184–1194. https://doi.org/10.1016/j.istruc.2020.07.036

26.

Xue

Shang

Yang

, et al. (2022) Shear strength prediction for concrete encased steel short columns: calibration based on current design codes. Journal of Building Engineering 45: 103626. https://doi.org/10.1016/j.jobe.2021.103626

27.

Xue

Chen

Shang

, et al. (2023a) Maximum shear strength of concrete-encased steel composite beams: a novel strength model and FE verification. Engineering Structures 291: 116490. https://doi.org/10.1016/j.engstruct.2023.116490

28.

Xue

Zhang

Shang

, et al. (2023b) Shear strength model for steel shape-reinforced concrete girders considering compatible steel–concrete interaction. Structures 56: 104976. https://doi.org/10.1016/j.istruc.2023.104976

29.

Yao

Jia

, et al. (2014) Shear performance of prestressed ultra high strength concrete encased steel beams. Construction and Building Materials 52: 194–201. https://doi.org/10.1016/j.conbuildmat.2013.11.006

30.

Pei

, et al. (2023) Shear behavior of externally prestressed ultra-high-performance concrete (UHPC) T-beams without stirrups. Engineering Structures 288: 116217. https://doi.org/10.1016/j.engstruct.2023.116217

31.

Teng

Wong

, et al. (2010) Finite element modeling of confined concrete-II: plastic-Damage model. Engineering Structures 32(3): 680–691. https://doi.org/10.1016/j.engstruct.2009.11.013

32.

Zhang

Wang

Chen

(2000) Mechanics of Materials. Beijing: China Architecture and Building Press.

33.

Zhang

Wang

, et al. (2022) Axial compressive behavior of steel-reinforced reactive powder concrete short columns. Structures 46: 433–444. https://doi.org/10.1016/j.istruc.2022.10.073

34.

Zhang

Wang

Zhang

, et al. (2023a) Seismic performance of steel-reinforced reactive powder concrete columns. Structures 54: 1788–1802. https://doi.org/10.1016/j.istruc.2023.05.100

35.

Zhang

Wang

Ling

, et al. (2023b) Bond-slip behavior between reactive powder concrete and H-shaped steel. Journal of Constructional Steel Research 210: 108058. https://doi.org/10.1016/j.jcsr.2023.108058

36.

Zheng

(2011) Experimental research on mechanical performance of normal section of reinforced reactive powder concrete beam. Journal of Building Structures 32(6): 125–134, (in Chinese).

37.

Zhu

Wei

Wang

, et al. (2025) Experimental and numerical investigation of the seismic performance of steel-reinforced ultra-high performance concrete beams. Structures 76: 108883. https://doi.org/10.1016/j.istruc.2025.108883