# Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Model

#### 2.1. Model Description

_{u}is the sum of the shear capacities of these two mechanisms: the composite truss V

_{c}and the vertical web V

_{ss}. As mentioned before, the crack and failure patterns of SRC beams are similar to those of R.C. beams, indicating that the composite truss can reach the corresponding shear strength at the maximum load. In contrast, the shear contribution of the vertical steel web can be determined following deformation compatibility to show the steel-concrete interaction.

#### 2.2. Truss-Arch Modeling of Composite Truss

_{ct}and the arch action V

_{ca}. As indicated in Figure 2, V

_{ct}can be expressed as:

_{ct}is the truss action’s shear contribution; b is the cross-sectional width; d is the distance from the center of the compressive rebar to that of the tensile rebar; ρ

_{sv}is the ratio of the transverse reinforcements; f

_{ys}is the yield strength of the transverse reinforcements; θ

_{t}is the angle between the horizontal axis and the compressive strut; A

_{sv}is the cross-sectional area of the stirrup ribs; s is the stirrup spacing.

_{t}can be obtained following the constant angle truss model (CATM) proposed by Kim and Mander [18]. As a mechanics-based model, CATM is deduced based on the principle of minimum potential energy, as follows:

_{sl}is the ratio of the tensile reinforcement, including longitudinal rebar and steel flange at the tensile section; A

_{v}is the shear area, A

_{v}= bd; A

_{g}is the gross area of the entire cross-section.

_{t}and σ

_{a}, respectively. If the value σ

_{t}+ σ

_{a}exceeds the effective strength of the diagonal concrete, the composite truss fails. In fact, the σ

_{t}and σ

_{a}are not in the same direction, and the shear contributions of the truss and arch models should follow the corresponding stiffness. Nevertheless, most existing research assumed that σ

_{t}and σ

_{a}worked in the same direction and applied plastic analysis for simplification, which has been proven acceptable for engineering purposes [19]. In this case, the shear contribution of the arch action V

_{ca}can be expressed as follows:

_{t}is the compressive stress of the diagonal concrete in the truss action, which can be obtained by the free-body diagram of the applied truss; c

_{a}is the cross-sectional depth of the arch, which equals the cross-sectional depth of the neutral axis at the loading section; β is the softened factor of the cracked concrete; φ is the inclination of the arch, φ = (h − c

_{a})/L; L is the length of the shear span; h is the height of the cross-section.

_{ce}varies according to the transverse tensile strain ε

_{t}. In this case, the compressive strength of concrete will be “softened” with the increase in the loading process [15]. Theoretically, the concrete softened should be evaluated using softening equations; nevertheless, obtaining ε

_{t}at a certain load level is complex, and iterative analysis must be included to obtain ε

_{t}accurately. In the proposed model, the concrete softening is evaluated by the equations in ACI 318 [17], in which the effect on concrete strength can be expressed as 0.85βf

_{c}and the softened factor β can be determined as:

_{si}is the total area of distributed reinforcement at spacing s

_{i}in the i-th direction of reinforcements crossing a strut at an angle α

_{i}to the axis of a strut, whose detailed meaning can be found in provision R23.5.3 in ACI 318 [17].

_{a}can be obtained based on the elastic analysis [9]:

_{s}/E

_{c}; E

_{s}and E

_{c}are the moduli of elasticity of steel and concrete, respectively; ρ

_{sl}′ is the ratio of the compressive reinforcement, including the steel flange and longitudinal rebar at the compressive section.

#### 2.3. Stress Decomposition of Steel Shape

_{yw}is the steel web’s yield strength.

_{x}= E

_{s}ε

_{x}, and the corresponding shear stress τ

_{x}can be deduced by the yielding criterion (Equation (8)). The steel web’s shear contribution V

_{ss}can be obtained by integrating τ

_{x}along the cross-section, as follows:

_{sa}is the shear contribution above the neutral axis; V

_{sb}is the shear contribution below the neutral axis; c

_{a}is the sectional depth of the compression area at the loading section, which can be obtained following Equation (7); a

_{ss}′ and a

_{ss}are the thickness of the concrete cover of the steel flanges in compression and tension; t

_{w}is the steel web’s thickness; ε

_{cf}is the strain of the steel flange in compression; ε

_{tf}is the strain of the steel flange in compression; ε

_{c}is the strain at the extremely compressive fiber at the loading section, ε

_{c}= (1 − 0.44λ)ε

_{c0}[21,22]; ε

_{c0}is the peak compressive strain of concrete.

_{sa}and V

_{sb}; therefore, using a suitable numerical integration method is advisable. In this case, the two-point Gauss truss model is utilized, and Equations (10) and (11) can be rewritten as follows:

_{i}and t

_{i}are the numerical weight factor and the normalized coordinate of the ith numerical point. In the two-point Gauss truss model, t

_{1}= −0.55735 and t

_{2}= 0.55735; ω

_{1}= ω

_{2}= 1.0.

#### 2.4. Calculation Process

- (1)
- Input the geometric dimensions, reinforcement details, and the properties of concrete and steel;
- (2)
- Calculate the shear resistance of the truss and arch actions V
_{ct}+ V_{ca}by Equations (1)–(7); - (3)
- Calculate the shear resistance of the vertical steel web V
_{ss}by Equations (9)–(15); - (4)
- Calculate the overall shear strength of SRC beams by V
_{ct}+ V_{ca}+ V_{ss}.

## 3. Results and Discussions

#### 3.1. Test Database

- (1)
- The compressive strength of concrete varies from 23.3 MPa to 46.6 MPa;
- (2)
- The yield strength of steel web varies from 265 MPa to 332 MPa;
- (3)
- The steel shape ratio varies from 2.16% to 6.62%;
- (4)
- The shear span-to-depth ratio varies from 0.84 to 2.00;
- (5)
- The width of the cross-section varies from 150 mm to 450 mm;
- (6)
- The height of the cross-section varies from 240 mm to 650 mm;
- (7)
- The stirrup ratio varies from 0.00% to 0.52%.

#### 3.2. Comparison between Tested and Calculated Results

_{u}= V

_{ct}+ V

_{ca}+ V

_{ss,p}, in which V

_{ct}+ V

_{ca}can be determined by the proposed truss-arch analogy and V

_{ss,p}is the steel web’s shear resistance using plastic analysis (V

_{ss,p}= 0.6f

_{yw}t

_{w}h

_{w}, where h

_{w}is the steel web’s cross-sectional height). Based on strength superposition, the average ratio of predicted results to tested results was found to be 1.44 with a coefficient of variation of 0.12, indicating that the proposed model can achieve higher precision. This comparison highlights the questionable validity of the strength superposition assumption, specifically when considering the steel web as plastic under pure shear. Moreover, the overestimated shear strengths indicate that the resistance along the vertical direction of the steel web is reduced due to the normal stress induced by bending. Therefore, the proposed steel-concrete interaction model, which incorporates strain compatibility, accurately predicts V

_{ss}(the shear strength of the steel web).

## 4. Conclusions

- (1)
- Multiple shear mechanisms, which consist of a vertical steel web and a composite truss, exist to resist the applied shear load. In the proposed model, the shear strength of the composite truss is evaluated using the traditional truss-arch model, and a stress decomposition based on von Mises yielding criterion is conducted within the steel shape to decouple its shear contribution. Finally, the total shear strength can be determined by superimposing the shear contributions of these two mechanisms;
- (2)
- Through verification with 50 available test results for SRC beams, the proposed model demonstrated its superiority. The predictions generated by the proposed model (with an AVG of 0.98 and a CoV of 0.10) exhibited significantly better agreement with the test results when compared with existing shear equations. For instance, the JGJ 138 equation had an AVG of 0.81 and a CoV of 0.18, the ANSI/AISC 360 equation had values of 0.73 and 0.27, and the Eurocode 4 equation had values of 0.74 and 0.31, indicating that the established model can effectively and reliably predict the shear strength of SRC beams.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Lai, B.L.; Zhang, M.Y.; Zheng, X.F.; Chen, Z.P.; Zheng, Y.Y. Experimental Study on the Axial Compressive Behaviour of Steel Reinforced Concrete Composite Columns with Stay-in-Place ECC Jacket. J. Build. Eng.
**2023**, 68, 106174. [Google Scholar] [CrossRef] - Lai, B.L.; Yang, L.; Xiong, M.X. Numerical Simulation and Data-Driven Analysis on the Flexural Performance of Steel Reinforced Concrete Composite Members. Eng. Struct.
**2021**, 247, 113200. [Google Scholar] [CrossRef] - Lai, B.L.; Tan, W.K.; Feng, Q.T.; Venkateshwaran, A. Numerical Parametric study on the Uniaxial and Biaxial Compressive Behavior of H-shaped Steel Reinforced Concrete Composite Beam-Columns. Adv. Struct. Eng.
**2022**, 25, 2641–2661. [Google Scholar] [CrossRef] - JGJ 138-2016; Code for Design of Composite Structures. China Architecture & Building Press: Beijing, China, 2016.
- ANSI/AISC 360-16; Specification for Structural Steel Buildings. American Institute of Steel Construction: Chicago, IL, USA, 2016.
- BS EN 1994-1-1:2004; Eurocode 4: Design of Composite Steel and Concrete Structures—Part 1-1: General Rules and Rules for Buildings. European Committee for Standardization: Brussels, Belgium, 2004.
- Xue, Y.; Shang, C.; Yang, Y.; Yu, Y. Prediction of Lateral Load-Displacement Curve of Concrete-Encased Steel Short Columns Under Shear Failure. Eng. Struct.
**2022**, 262, 114375. [Google Scholar] [CrossRef] - Chen, C.C.; Lin, K.T.; Chen, Y.J. Behavior and Shear Strength of Steel Shape Reinforced Concrete Deep Beams. Eng. Struct.
**2018**, 175, 425–435. [Google Scholar] [CrossRef] - Hwang, S.J.; Lee, H.J. Strength Prediction for Discontinuity Regions by Softened Strut-and-Tie model. J. Struct. Eng.
**2002**, 128, 1519–1526. [Google Scholar] [CrossRef] - Lu, W.Y. Shear Strength Prediction for Steel Reinforced Concrete Deep Beams. J. Constr. Steel Res.
**2006**, 62, 933–942. [Google Scholar] [CrossRef] - Yu, Y.; Yang, Y.; Xue, Y.; Liu, Y. Shear Behavior and Shear Capacity Prediction of Precast Concrete-Encased Steel Beams. Steel Compos. Struct.
**2020**, 36, 261–272. [Google Scholar] - Deng, M.; Ma, F.; Li, B.; Liang, X. Analysis on Shear Capacity of SRC Deep Beams based on Modified Strut-and-Tie Model. Eng. Mech.
**2017**, 34, 95–103. [Google Scholar] - Ke, X.J.; Tang, Z.K.; Yang, C.H. Shear Bearing Capacity of Steel-Reinforced Recycled Aggregate Concrete Short Beams based on Modified Compression Field Theory. Structures
**2022**, 45, 645–658. [Google Scholar] [CrossRef] - Chen, B.Q.; Zeng, L.; Liu, C.J.; Mo, J. Study on Shear Behavior and Bearing Capacity of Steel Reinforced Concrete Deep Beams. Eng. Mech.
**2022**, 39, 215–224. [Google Scholar] - Bentz, E.C.; Vecchio, F.J.; Collins, M.P. Simplified Modified Compression Field Theory for Calculating Shear Strength of Reinforced Concrete Elements. ACI. Struct. J.
**2006**, 103, 614–624. [Google Scholar] - Ichinose, T. A Shear Design Equation for Ductile R/C Members. Earthq. Eng. Struct. D
**1992**, 21, 197–214. [Google Scholar] [CrossRef] - ACI 318-14; Building Code Requirements for Structural Concrete. American Concrete Institute: Farmington Hills, MI, USA, 2014.
- Kim, J.H.; Mander, J.B. Influence of Transverse Reinforcement on Elastic Shear Stiffness of Cracked Concrete Elements. Eng. Struct.
**2007**, 29, 1798–1807. [Google Scholar] [CrossRef] - Pan, Z.; Li, B. Truss-Arch Model for Shear Strength of Shear-Critical Reinforced Concrete Columns. J. Struct. Eng.
**2013**, 139, 548–560. [Google Scholar] - Horne, M.R. Plastic Theory of Structures; Pergamon Press: Surrey, UK, 1979. [Google Scholar]
- Choi, K.K.; Park, H.G.; Wight, J.K. Unified Shear Strength Model for Reinforced Concrete Beams-Part I: Development. ACI Struct. J.
**2007**, 104, 142–152. [Google Scholar] - Choi, K.K.; Park, H.G. Unified Shear Strength Model for Reinforced Concrete Beams-Part II: Verification and Simplified Method. ACI Struct. J.
**2007**, 104, 153–161. [Google Scholar] - Xue, J.; Wang, X.; Ma, H.; Lin, J.; Chen, Z. Experimental Study on Shear Performance of Steel Reinforced Recycled Aggregate Concrete Beams. Build. Struct.
**2013**, 43, 69–72. [Google Scholar] - Barkhordari, M.S.; Feng, D.C.; Tehranizadeh, M. Efficiency of Hybrid Algorithms for Estimating the Shear Strength of Deep Reinforced Concrete Beams. Period. Polytech. Civ. Eng.
**2022**, 66, 398–410. [Google Scholar] [CrossRef] - Xue, Y.; Yang, Y.; Yu, Y. Shear Strength Model for Steel Reinforced Concrete Composite Members: Short Columns and Deep Beams. Eng. Struct.
**2020**, 216, 110748. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Steel shape-reinforced concrete beams; (

**b**) Shear failure mode of R.C. beam; (

**c**) Shear failure mode of SRC beam.

**Figure 2.**Model configuration (V

_{ct}and V

_{ca}are the shear resistance of the truss arch and arch action).

Ref. | Specimen ID | Steel Shape | f_{yw}/MPa | ρ_{ss}/% | L/mm | b/mm | h/mm | ρ_{sv}/% | ρ_{sl}/% | f_{c}/MPa | f_{ys}/MPa | f_{yw}/MPa | V_{e}/kN | V_{u}/kN |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

[8] | BH1 | H450 × 200 × 9 × 14 | 312 | 3.80 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 312 | 2423 | 2364 |

BH2 | H390 × 200 × 10 × 16 | 330 | 4.03 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 330 | 2399 | 2353 | |

BH3 | H300 × 200 × 13 × 15 | 313 | 3.84 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 313 | 2109 | 2216 | |

BH4 | H200 × 200 × 20 × 12 | 280 | 3.36 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 280 | 1766 | 1999 | |

BWH2 | H390 × 200 × 10 × 16 | 330 | 4.03 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 330 | 2399 | 2353 | |

BWH2A | H390 × 200 × 15 × 16 | 312 | 4.76 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 312 | 2281 | 2578 | |

BWH2B | H390 × 200 × 20 × 16 | 303 | 5.48 | 460 | 450 | 550 | / | 1.32 | 40.10 | / | 303 | 2605 | 2802 | |

[10] | SRC1-00 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 772 | 686 |

SRC1-00-T | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 751 | 686 | |

SRC1-00-E | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 799 | 686 | |

SRC1-00-D | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | / | 1.45 | 28.90 | / | 332 | 695 | 686 | |

SRC1-50 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | 0.09 | 1.45 | 27.70 | 380 | 332 | 861 | 798 | |

SRC1-25 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | 0.18 | 1.45 | 32.20 | 380 | 332 | 877 | 885 | |

SRC1-17 | H300 × 150 × 6.5 × 9 | 332 | 2.16 | 975 | 350 | 600 | 0.26 | 1.45 | 28.90 | 380 | 332 | 923 | 835 | |

D1-N | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 24.50 | 407 | 325 | 408 | 373 | |

D2-FS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 415 | 366 | |

D3-WS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 395 | 366 | |

DB1-15-NS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.30 | 407 | 325 | 391 | 359 | |

DB2-15-NS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 24.50 | 407 | 325 | 409 | 373 | |

DB3-NTNS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | / | 0.36 | 23.70 | / | 325 | 396 | 316 | |

DB4-15-FS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 414 | 366 | |

DB5-15-WS | H198 × 99 × 4.5 × 7 | 325 | 3.16 | 338 | 200 | 350 | 0.52 | 0.36 | 23.90 | 407 | 325 | 398 | 366 | |

[11] | PPSRC1 | H500 × 200 × 9 × 14 | 317 | 3.37 | 650 | 450 | 650 | 0.16 | 0.84 | 24.30 | 393 | 317 | 2170 | 1898 |

PPSRC2 | H500 × 200 × 9 × 14 | 317 | 3.37 | 975 | 450 | 650 | 0.16 | 0.84 | 24.30 | 393 | 317 | 1600 | 1388 | |

[12] | B1-1.5 | I16 | 312 | 4.97 | 390 | 200 | 260 | 0.28 | 1.21 | 27.09 | 298 | 312 | 304 | 287 |

B1-1.5p | I16 | 312 | 4.97 | 390 | 200 | 260 | 0.28 | 1.21 | 39.47 | 298 | 312 | 367 | 341 | |

B2-1.0 | I16 | 312 | 4.97 | 260 | 200 | 260 | 0.28 | 1.21 | 34.23 | 298 | 312 | 495 | 437 | |

B2-1.5 | I16 | 312 | 4.97 | 390 | 200 | 260 | 0.28 | 1.21 | 34.23 | 298 | 312 | 342 | 315 | |

B2-2.0 | I16 | 312 | 4.97 | 520 | 200 | 260 | 0.28 | 1.21 | 34.23 | 298 | 312 | 255 | 261 | |

B3-1.0 | I16 | 312 | 5.13 | 260 | 200 | 260 | 0.28 | 1.21 | 44.98 | 298 | 312 | 467 | 533 | |

B3-1.5 | I16 | 312 | 5.13 | 390 | 200 | 260 | 0.28 | 1.21 | 44.98 | 298 | 312 | 373 | 383 | |

B3-2.0 | I16 | 312 | 5.13 | 520 | 200 | 260 | 0.28 | 1.21 | 44.98 | 298 | 312 | 322 | 300 | |

[13] | SRRAC-1 | I16 | 265 | 6.62 | 342 | 150 | 300 | 0.05 | 1.13 | 30.00 | 393 | 265 | 379 | 400 |

SRRAC-2 | I16 | 265 | 6.62 | 342 | 150 | 300 | 0.05 | 1.13 | 26.40 | 393 | 265 | 366 | 382 | |

SRRAC-3 | I16 | 265 | 6.62 | 228 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 265 | 499 | 510 | |

SRRAC-4 | I16 | 265 | 6.62 | 342 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 265 | 371 | 388 | |

SRRAC-5 | I14 | 265 | 6.62 | 456 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 265 | 280 | 338 | |

SRRAC-6 | I16 | 283 | 5.78 | 342 | 150 | 300 | 0.05 | 1.13 | 27.60 | 393 | 283 | 339 | 378 | |

[23] | SRRC1 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 34.31 | 339 | 327 | 319 | 305 |

SRRC2 | I14 | 327 | 4.92 | 336 | 180 | 240 | 0.31 | 1.18 | 34.31 | 339 | 327 | 239 | 239 | |

SRRC3 | I14 | 327 | 4.92 | 432 | 180 | 240 | 0.31 | 1.18 | 34.31 | 339 | 327 | 184 | 207 | |

SRRC4 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 35.26 | 339 | 327 | 343 | 309 | |

SRRC5 | I14 | 327 | 4.92 | 336 | 180 | 240 | 0.31 | 1.18 | 35.26 | 339 | 327 | 245 | 242 | |

SRRC6 | I14 | 327 | 4.92 | 432 | 180 | 240 | 0.31 | 1.18 | 35.26 | 339 | 327 | 172 | 207 | |

SRRC7 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 36.03 | 339 | 327 | 325 | 313 | |

SRRC8 | I14 | 327 | 4.92 | 336 | 180 | 240 | 0.31 | 1.18 | 36.03 | 339 | 327 | 245 | 245 | |

SRRC9 | I14 | 327 | 4.92 | 432 | 180 | 240 | 0.31 | 1.18 | 36.03 | 339 | 327 | 178 | 208 | |

SRRC10 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 44.20 | 339 | 327 | 368 | 359 | |

SRRC11 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 46.61 | 393 | 327 | 368 | 373 | |

SRRC12 | I14 | 327 | 4.92 | 240 | 180 | 240 | 0.31 | 1.18 | 33.20 | 393 | 327 | 343 | 299 |

_{c}is the concrete strength in compression; f

_{ys}is the yield strength of stirrups; f

_{yw}is the steel web’s yield strength; L is the shear span length; V

_{e}is the experimental shear strength; V

_{u}is the shear strength calculated using the proposed model; ρ

_{sl}is the rebar ratio; ρ

_{ss}is the steel shape ratio; ρ

_{sv}is the stirrup ratio.

Code | V_{u} = V_{c} + V_{ss} | |
---|---|---|

V_{c} | V_{ss} | |

JGJ 138 [4] | $\frac{1.05}{\lambda +1}{f}_{\mathrm{t}}b{h}_{0}+{f}_{\mathrm{ys}}\frac{{A}_{\mathrm{sv}}}{s}{h}_{0}$ | $\frac{0.58}{\lambda}{f}_{\mathrm{yw}}{t}_{\mathrm{w}}{h}_{\mathrm{w}}$ |

ANSI/AISC-360 [5] | $0.17\sqrt{{f}_{\mathrm{c}}}b{h}_{0}+{f}_{\mathrm{ys}}\frac{{A}_{\mathrm{sv}}}{s}{h}_{0}$ | $0.60{f}_{\mathrm{yw}}{t}_{\mathrm{w}}{h}_{\mathrm{w}}$ |

BS EN 1994-1-1 [6] | $\left[0.18\left(1+\sqrt{2000/9{h}_{0}}\right){\left(100{\rho}_{\mathrm{sl}}{f}_{\mathrm{c}}\right)}^{\frac{1}{3}}\right]b{h}_{0}+0.9{f}_{\mathrm{ys}}\frac{{A}_{\mathrm{sv}}}{s}{h}_{0}\mathrm{cot}\theta $ | $0.58{f}_{\mathrm{yw}}{t}_{\mathrm{w}}{h}_{\mathrm{w}}$ |

_{0}is the distance from the centroid of the tensile reinforcements to the extreme compression fiber of concrete; f

_{t}is the concrete tensile strength.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Xue, Y.; Liu, Y.; Yu, Y.
Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams. *Buildings* **2023**, *13*, 1391.
https://doi.org/10.3390/buildings13061391

**AMA Style**

Zhang X, Xue Y, Liu Y, Yu Y.
Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams. *Buildings*. 2023; 13(6):1391.
https://doi.org/10.3390/buildings13061391

**Chicago/Turabian Style**

Zhang, Xu, Yicong Xue, Yaping Liu, and Yunlong Yu.
2023. "Compatible Truss-Arch Model for Predicting the Shear Strength of Steel Shape-Reinforced Concrete (SRC) Beams" *Buildings* 13, no. 6: 1391.
https://doi.org/10.3390/buildings13061391