# Study of Bond–Slip Behavior and Constitutive Model of a New M-Section Steel-Skeleton Concrete

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Design

#### 2.1. Specimen Design

#### 2.2. Material Properties

#### 2.3. Loading and Measurement Schemes

#### 2.4. Strain Measurement

## 3. Experimental Results and Load–Slip Curve of MSSC Specimens

#### 3.1. Analysis of Experimental Results

#### 3.1.1. The Failure Pattern of MSSC Specimens

**①**crack in Figure 9. The type

**①**crack started to appear when the load decreased to approximately 20% of the ultimate load and continued to extend outwards. Certain specimens showed cracks extending to their surface. In addition to the type

**①**crack, the crack pattern of the specimen can be divided into three categories:

#### 3.1.2. Scattering Results of DIC-3D

#### 3.1.3. Strain Distribution of M-Section Steel

#### 3.2. Load–Slip Curves and Characteristics

**Pu**, that is, the initial load

**Ps**, which corresponded to the slip value of

**Ss**.

**Su**, the load reached point B, which was the ultimate load

**Pu**. In addition, vertical through-cracks were generated on the east and west sides of the concrete at this point.

**Sr**, there was a tendency for the load to level off, that is, the residual load

**Pr**, which corresponded to a load size of approximately 30–60% of the ultimate load

**Pu**.

**Ss**, ultimate slip value

**Su**, and residual slip value

**Sr**, respectively. This curve reflects the basic characteristics of the bond strength of M-section steel to concrete, as shown in Figure 13b. Table 4 lists the specific values for each characteristic point.

## 4. Study on the Bond–Slip Constitutive Model of MSSC

#### 4.1. Parametric Analysis of Characteristic Average Bond Strength

#### 4.1.1. Analysis of Influencing Factors on Characteristic Average Bond Strength

#### Effect of Concrete Cover on Characteristic Average Bond Strength

#### Effect of Concrete Strength on Characteristic Average Bond Strength

#### Effect of Anchorage Length on Characteristic Average Bond Strength

#### 4.1.2. Regression Analysis of Characteristic Average Bond Strength

#### 4.2. Definition of Characteristic Slip Values and Regression Analysis

**Ss**, ultimate slip value

**Su,**and residual slip value

**Sr**. The test results indicated that the initial slip value

**Ss**was primarily influenced by the concrete cover and strength of the concrete, in addition to the above two influencing factors, while the ultimate slip value

**Su**and residual slip value

**Sr**were also influenced by the anchorage length. Based on the analysis above, the regression equation for the characteristic slip values was established as follows:

#### 4.3. The Bond–Slip Constitutive Equation of the MSSC

## 5. Finite Element Verification of the Bond–Slip Constitutive Model of MSSC

#### 5.1. General

#### 5.2. Finite Element Type

#### 5.3. Interaction

#### 5.4. Boundary Conditions and Loading Methods

#### 5.5. Material Properties

**Ψ**is the dilation angle, $\mathit{\in}$ refers to the eccentricity, ${\mathit{f}}_{\mathit{b}\mathbf{0}}/{\mathit{f}}_{\mathit{c}\mathbf{0}}$ is the ratio of the initial equibiaxial compressive yield stress to the initial uniaxial compressive yield stress, and

**Kc**is the ratio of the second stress invariant to the tensile meridian [42]. The uniaxial tensile and compressive stress–strain curves for concrete were obtained using the data acquired from the tests, and the specific parameters of the material are detailed in Section 2.2. In addition, referring to the ABAQUS/Explicit 6.14 user manual, the mechanical behavior of the tensile cracking and compression breaking of concrete was described by introducing damage factors, as shown in Equations (12) and (13).

#### 5.6. Cohesive Properties

**cos I**and

**cos II**are directional cosines, as shown in Equations (19) and (20), ${\mathit{\delta}}_{\mathit{m}}$ indicates the effective separation displacement value in the mixed-mode during loading, and ${\mathit{\delta}}_{\mathit{I}}$ and ${\mathit{\delta}}_{\mathit{II}}$ indicate the relative displacement values corresponding to the effective separation displacement values in the pure normal mode and pure shear mode surfaces, respectively, during the mixed-mode. In addition, ${\mathit{K}}_{\mathit{I}}$ and ${\mathit{K}}_{\mathit{II}}$ denote the interfacial normal and shear stiffnesses, respectively, and are expressed as Equations (21) and (22).

**α**indicates the B-K parameter.

**D**, which is expressed as follows:

**α**. In this study, according to the obtained bond–slip curve and the parametric analysis of the finite element model, setting ${\mathit{\sigma}}_{\mathit{I}}^{\mathit{max}}$

**=**${\mathit{\sigma}}_{\mathit{II}}^{\mathit{max}}$

**=**${\overline{\mathit{\tau}}}_{\mathit{u}}$, ${\mathit{\delta}}_{\mathit{I}}^{\mathit{max}}$

**=**${\mathit{\delta}}_{\mathit{II}}^{\mathit{max}}$

**=**${\mathit{S}}_{\mathit{u}}$, ${\mathit{\delta}}_{\mathit{I}}^{\mathit{f}}$

**=**${\mathit{\delta}}_{\mathit{II}}^{\mathit{f}}$

**=**${\mathit{S}}_{\mathit{r}}$, and

**α**= 2 [44,45] can better simulate the test results.

#### 5.7. Results of Finite Element Constitutive Model Validation

#### 5.7.1. Failure Mode

#### 5.7.2. Bond–Slip Curve

#### 5.7.3. Stress Clouds of MSSC Specimens

#### 5.7.4. Interfacial Bond-Failure Process

## 6. Conclusions

- Depending on the final failure pattern of the MSSC specimen, the crack pattern could be divided into three main types: diagonal, parallel, and composite cracks. The diagonal crack occurred mainly in specimens with a thinner concrete cover and was the predominant crack pattern. Parallel cracks were mainly observed in the specimens with a greater concrete cover thickness and higher concrete strength. However, the composite crack development pattern was more complex and occurred only in a few specimens.
- The DIC-3D scattering results showed that the displacement variation of the MSSC specimen in the X-direction was symmetrically distributed, and the specimen was mainly deformed in the X-direction, whereas the Y-direction and Z-direction had an obvious restraining effect on deformation in the X-direction.
- The load–slip curve of the MSSC specimen was divided into four major stages: the linear ascending, non-linear ascending, non-linear descending, and residual stages. In the early stages of loading, the specimen initially slipped slightly near the loading end where the bond strength was mainly supplied by the chemical adhesive force, but no cracks were produced. With the increase in the amount of slip, cracks gradually emerged on the concrete surface, and the load reached the ultimate peak Pu when vertical through-cracks appeared on the concrete sides. With a further increase in slip, the chemical adhesive force was gradually lost, while the frictional resistance and mechanical bite forces gradually increased. However, the growth was much less than the loss of chemical adhesive force, which resulted in a non-linear decrease in the load and the amount of slip. Consequently, when the load decreased to a certain value, it ceased to grow, reaching the residual load Pr. Here, the bond strength was mainly provided by a combination of frictional resistance and mechanical bite forces.
- Through a linear regression analysis of the test results, it was observed that the initial average bond strength ${\overline{\mathit{\tau}}}_{\mathit{s}}$ was mainly influenced by the concrete strength and anchorage length, while the residual average bond strength ${\overline{\mathit{\tau}}}_{\mathit{r}}$ was mainly affected by the concrete cover and anchorage length. In contrast, the ultimate average bond strength ${\overline{\mathit{\tau}}}_{\mathit{u}}$ was influenced by the concrete strength, concrete cover, and anchorage length. Based on this, the characteristic average bond strength equation was established, and a statistical regression method was used to obtain the bond–slip constitutive equation for M-section steel to concrete. Furthermore, a comparison with the test curves was verified, and the results showed that the fitted curves were consistent with the test curves.
- To further validate the reasonableness of the proposed bond–slip constitutive equation of M-section steel to concrete, numerical simulations were performed on the MSSC specimens. The results showed that the numerical simulation can better predict the entire failure process of the specimen. Moreover, the bond–slip curves obtained through the numerical simulation were consistent with the test results, thereby indicating the reliability of the constitutive relationship.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Cao, W.-L.; Wang, R.-W.; Yin, F.; Dong, H.-Y. Seismic Performance of a Steel Frame Assembled with a CFST-Bordered Composite Wall Structure. Eng. Struct.
**2020**, 219, 110853. [Google Scholar] [CrossRef] - Mohan, M.; Ramachandran, A.; Amran, M.; Borovkov, A. Determination of Buckling Behavior of Web-Stiffened Cold-Formed Steel Built-Up Column under Axial Compression. Materials
**2022**, 15, 2968. [Google Scholar] [CrossRef] - Al Zand, A.W.; Alghaaeb, M.F.; Liejy, M.C.; Mutalib, A.A.; Al-Ameri, R. Stiffening Performance of Cold-Formed C-Section Beam Filled with Lightweight-Recycled Concrete Mixture. Materials
**2022**, 15, 2982. [Google Scholar] [CrossRef] - Xu, Z.; Chen, Z.; Yang, S. Effect of a New Type of High-Strength Lightweight Foamed Concrete on Seismic Performance of Cold-Formed Steel Shear Walls. Constr. Build. Mater.
**2018**, 181, 287–300. [Google Scholar] [CrossRef] - Chen, L.; Wang, S.; Yin, C.; Li, S. Experimental Study on Constitutive Relationship between Checkered Steel and Concrete. Constr. Build. Mater.
**2019**, 210, 483–498. [Google Scholar] [CrossRef] - Zhang, G.; Qiao, D.; Sun, Z.; Yang, C.; Wang, Q. Experimental research on M-section steel truss floor. Ind. Constr.
**2020**, 50, 118–124. [Google Scholar] - Zhang, G.; Qiao, D.; Ding, M.; Sun, Z.; Yang, C.; Wang, Q. Finite element analysis of M-section steel truss floor based on ABAQUS. Steel Constr.
**2019**, 34, 60–64. [Google Scholar] - Dehestani, M.; Mousavi, S.S. Modified Steel Bar Model Incorporating Bond-Slip Effects for Embedded Element Method. Constr. Build. Mater.
**2015**, 81, 284–290. [Google Scholar] [CrossRef] - Feng, Q. Experimental Investigation of Stirrup Confinement Effects on Bond-Slip Responses for Corner and Middle Bars. Constr. Build. Mater.
**2022**, 314, 125629. [Google Scholar] [CrossRef] - Croce, P.; Formichi, P.; Landi, F. Experimental Assessment and Numerical Modeling of the Bond–Slip Correlation for Steel Rebars in r.c. Members. Materials
**2022**, 15, 951. [Google Scholar] [CrossRef] - Dey, A.; Valiukas, D.; Jakubovskis, R.; Sokolov, A.; Kaklauskas, G. Experimental and Numerical Investigation of Bond-Slip Behavior of High-Strength Reinforced Concrete at Service Load. Materials
**2021**, 15, 293. [Google Scholar] [CrossRef] - Madan, C.S.; Munuswamy, S.; Joanna, P.S.; Gurupatham, B.G.A.; Roy, K. Comparison of the Flexural Behavior of High-Volume Fly AshBased Concrete Slab Reinforced with GFRP Bars and Steel Bars. J. Compos. Sci.
**2022**, 6, 157. [Google Scholar] [CrossRef] - Madan, C.S.; Panchapakesan, K.; Anil Reddy, P.V.; Joanna, P.S.; Rooby, J.; Gurupatham, B.G.A.; Roy, K. Influence on the Flexural Behaviour of High-Volume Fly-Ash-Based Concrete Slab Reinforced with Sustainable Glass-Fibre-Reinforced Polymer Sheets. J. Compos. Sci.
**2022**, 6, 169. [Google Scholar] [CrossRef] - Lee, Y.-H.; Joo, Y.T.; Lee, T.; Ha, D.-H. Mechanical Properties of Constitutive Parameters in Steel–Concrete Interface. Eng. Struct.
**2011**, 33, 1277–1290. [Google Scholar] [CrossRef] - Wang, X.; Liu, Y.; Yang, F.; Lu, Y.; Li, X. Effect of Concrete Cover on the Bond-Slip Behavior between Steel Section and Concrete in SRC Structures. Constr. Build. Mater.
**2019**, 229, 116855. [Google Scholar] [CrossRef] - Chen, L.; Dai, J.; Jin, Q.; Chen, L.; Liu, X. Refining Bond–Slip Constitutive Relationship between Checkered Steel Tube and Concrete. Constr. Build. Mater.
**2015**, 79, 153–164. [Google Scholar] [CrossRef] - Shahidan, S.; Azmi, M.A.M.; Kupusamy, K.; Zuki, S.S.M.; Ali, N. Utilizing Construction and Demolition (C&D) Waste as Recycled Aggregates (RA) in Concrete. Procedia Eng.
**2017**, 174, 1028–1035. [Google Scholar] - Thomas, C.; Setién, J.; Polanco, J.A.; Cimentada, A.I.; Medina, C. Influence of Curing Conditions on Recycled Aggregate Concrete. Constr. Build. Mater.
**2018**, 172, 618–625. [Google Scholar] [CrossRef] - Sereng, M.; Djerbi, A.; Metalssi, O.O.; Dangla, P.; Torrenti, J.-M. Improvement of Recycled Aggregates Properties by Means of CO
_{2}Uptake. Appl. Sci.**2021**, 11, 6571. [Google Scholar] [CrossRef] - Liu, C.; Lv, Z.; Bai, G.; Yin, Y. Experiment Study on Bond Slip Behavior between Section Steel and RAC in SRRC Structures. Constr. Build. Mater.
**2018**, 175, 104–114. [Google Scholar] [CrossRef] - Liu, C.; Xing, L.; Liu, H.; Quan, Z.; Fu, G.; Wu, J.; Lv, Z.; Zhu, C. Numerical Study of Bond Slip between Section Steel and Recycled Aggregate Concrete with Full Replacement Ratio. Appl. Sci.
**2020**, 10, 887. [Google Scholar] [CrossRef] - Liu, B.; Bai, G.-L.; Xu, Z.-H.; Ma, J.-F.; Han, Y.-Y. Experimental Study and Finite Element Modeling of Bond Behavior between Recycled Aggregate Concrete and the Shaped Steel. Eng. Struct.
**2019**, 201, 109840. [Google Scholar] [CrossRef] - Liu, B.; Bai, G.-L.; Wang, Z.-Z. The Bond Stress-Slip Full Curve Equation between the RAC and H-Shaped: Experimental, Theoretical and Numerical Simulation Investigation. Constr. Build. Mater.
**2021**, 311, 125311. [Google Scholar] [CrossRef] - Bai, G.; Liu, B. Nonlinear Finite Element Analysis of Bond-Slip Performance of Recycled Aggregate Concrete Filled Circular Steel Tube. J. Adhes. Sci. Technol.
**2019**, 33, 1294–1319. [Google Scholar] [CrossRef] - Bai, G.; Ma, J.; Liu, B.; Chen, X. Study on the Interfacial Bond Slip Constitutive Relation of I-Section Steel and Fully Recycled Aggregate Concrete. Constr. Build. Mater.
**2020**, 238, 117688. [Google Scholar] [CrossRef] - Ding, Y.; Yu, K.; Li, M. A Review on High-Strength Engineered Cementitious Composites (HS-ECC): Design, Mechanical Property and Structural Application. Structures
**2022**, 35, 903–921. [Google Scholar] [CrossRef] - Tian, L.; Kou, Y.; Lin, H.; Li, T. Interfacial Bond–Slip Behavior between H-Shaped Steel and Engineered Cementitious Composites (ECCs). Eng. Struct.
**2021**, 231, 111731. [Google Scholar] [CrossRef] - Bai, L.; Yu, J.; Zhang, M.; Zhou, T. Experimental Study on the Bond Behavior between H-Shaped Steel and Engineered Cementitious Composites. Constr. Build. Mater.
**2019**, 196, 214–232. [Google Scholar] [CrossRef] - Luo, Q. Seismic Performance Analysis of Corrugated-Steel-Plate Composite Shear Wall Based on Corner Failure. J. Constr. Steel Res.
**2021**, 180, 106606. [Google Scholar] [CrossRef] - Cheng, Z.; Zhang, Q.; Bao, Y.; Deng, P.; Wei, C.; Li, M. Flexural Behavior of Corrugated Steel-UHPC Composite Bridge Decks. Eng. Struct.
**2021**, 246, 113066. [Google Scholar] [CrossRef] - Kong, F.; Huang, P.; Han, B.; Wang, X.; Liu, C. Experimental Study on Behavior of Corrugated Steel-Concrete Composite Bridge Decks with MCL Shape Composite Dowels. Eng. Struct.
**2021**, 227, 111399. [Google Scholar] [CrossRef] - Song, J.; Wang, W.; Su, S.; Wang, B.; Li, Y.; Lu, Z. Experimental Investigation of the Bond-Slip Behaviour between Corrugated Steel Plates and Concrete in CSRC Structures. Constr. Build. Mater.
**2021**, 299, 124315. [Google Scholar] [CrossRef] - Song, J.; Wang, W.; Su, S.; Ding, X.; Luo, Q.; Quan, C. Experimental Study on the Bond-Slip Performance between Concrete and a Corrugated Steel Plate with Studs. Eng. Struct.
**2020**, 224, 111195. [Google Scholar] [CrossRef] - JGJ55-2011; Ordinary Concrete Ratio Design Regulations. China Architecture & Building Press: Beijing, China, 2011.
- GB/T 50152-2012; Standard for Test Method for Concrete Structure. China Architecture & Building Press: Beijing, China, 2012.
- GB/T1228.1-2010; Tensile Testing of Metallic Materials—Part 1: Test Methods for Temperature. China Quality Inspection Press: Beijing, China, 2010.
- Yang, Y.; Guo, Z.; Xue, J.; Zhao, H.; Nie, J. Experiment study on bond slip behavior between section steel and concrete in SRC structures. J. Build. Struct.
**2005**, 26, 1–9. [Google Scholar] - Simulia. ABAQUS Standard User’s Manual; Version 6.14; Dassault Systèmes Simulia Corp.: Johnston, RI, USA, 2013. [Google Scholar]
- Nguyen, H.T.; Kim, S.E. Finite Element Modeling of Push-out Tests for Large Stud Shear Connectors. J. Constr. Steel Res.
**2009**, 65, 1909–1920. [Google Scholar] [CrossRef] - Shamass, R.; Zhou, X.; Alfano, G. Finite-Element Analysis of Shear-Off Failure of Keyed Dry Joints in Precast Concrete Segmental Bridges. J. Bridge Eng.
**2015**, 20, 04014084. [Google Scholar] [CrossRef] - Nasiri, E.; Liu, Y. The Out-of-Plane Behaviour of Concrete Masonry Infills Bounded by Reinforced Concrete Frames. Eng. Struct.
**2019**, 184, 406–420. [Google Scholar] [CrossRef] - Liu, B.; Bai, G.-L. Finite Element Modeling of Bond-Slip Performance of Section Steel Reinforced Concrete. Comput. Concr.
**2019**, 24, 237–247. [Google Scholar] - Bypour, M.; Gholhaki, M.; Kioumarsi, M.; Kioumarsi, B. Nonlinear Analysis to Investigate Effect of Connection Type on Behavior of Steel Plate Shear Wall in RC Frame. Eng. Struct.
**2019**, 179, 611–624. [Google Scholar] [CrossRef] - Jiang, W.-G.; Hallett, S.R.; Green, B.G.; Wisnom, M.R. A Concise Interface Constitutive Law for Analysis of Delamination and Splitting in Composite Materials and Its Application to Scaled Notched Tensile Specimens. Int. J. Numer. Methods Eng.
**2007**, 69, 1982–1995. [Google Scholar] [CrossRef] - Bui, Q.V. A Modified Benzeggagh-Kenane Fracture Criterion for Mixed-Mode Delamination. J. Compos. Mater.
**2011**, 45, 389–413. [Google Scholar] [CrossRef]

**Figure 11.**Longitudinal strain distribution at each position of MSSC specimens in the rising section of the load.

Specimen | Concrete Cover, Css/mm | Design Strength ${\mathit{f}}_{\mathit{c}\mathit{u}}$/MPa | Anchorage Length, ${\mathit{L}}_{\mathit{e}}$/mm | Number |
---|---|---|---|---|

MSSC-01 | 40 | 20 | 100 | 3 |

MSSC-02 | 30 | 20 | 100 | 3 |

MSSC-03 | 20 | 20 | 100 | 3 |

MSSC-04 | 20 | 20 | 75 | 3 |

MSSC-05 | 20 | 20 | 50 | 3 |

MSSC-06 | 20 | 25 | 50 | 3 |

MSSC-07 | 20 | 30 | 50 | 3 |

Design Strength | Modulus of Elasticity, Ec/MPa | Average Compressive Strength, ${\mathit{f}}_{\mathit{c}\mathit{u}}$/MPa | Average Tensile Strength, ${\mathit{f}}_{\mathit{t}}$/MPa |
---|---|---|---|

C20 | 24,325 | 19.92 | 1.91 |

C25 | 27,624 | 25.63 | 2.26 |

C30 | 29,536 | 31.01 | 2.57 |

Steel Type | Young’s Modulus, E/MPa | Yield Stress, ${\mathit{f}}_{\mathit{y}}$/MPa | Ultimate Stress, ${\mathit{f}}_{\mathit{u}}$/MPa | Elongation, A/% |
---|---|---|---|---|

M-section steel | 202,000 | 298.29 | 375.33 | 27 |

Specimen | ${\mathit{P}}_{\mathit{s}}$/KN | ${\overline{\mathit{\tau}}}_{\mathit{s}}$/MPa | ${\mathit{P}}_{\mathit{u}}$/KN | ${\overline{\mathit{\tau}}}_{\mathit{u}}$/MPa | ${\mathit{P}}_{\mathit{r}}$/KN | ${\overline{\mathit{\tau}}}_{\mathit{r}}$/MPa | ${\mathit{S}}_{\mathit{s}}$/mm | ${\mathit{S}}_{\mathit{u}}$/mm | ${\mathit{S}}_{\mathit{r}}$/mm |
---|---|---|---|---|---|---|---|---|---|

MSSC-01 | 15.503 | 0.399 | 37.937 | 0.976 | 20.032 | 0.515 | 1.198 | 2.623 | 3.560 |

MSSC-02 | 15.328 | 0.394 | 33.575 | 0.845 | 13.751 | 0.345 | 0.901 | 2.084 | 2.953 |

MSSC-03 | 15.192 | 0.391 | 30.082 | 0.773 | 10.433 | 0.268 | 0.794 | 1.911 | 2.760 |

MSSC-04 | 10.336 | 0.401 | 22.593 | 0.833 | 7.678 | 0.292 | 0.796 | 1.792 | 2.514 |

MSSC-05 | 7.054 | 0.429 | 14.032 | 0.851 | 6.131 | 0.371 | 0.801 | 1.363 | 2.050 |

MSSC-06 | 8.312 | 0.509 | 15.038 | 0.924 | 6.204 | 0.382 | 0.833 | 1.471 | 2.251 |

MSSC-07 | 12.081 | 0.735 | 18.562 | 1.128 | 6.422 | 0.398 | 0.898 | 1.692 | 2.698 |

Specimen | Initial Bond Strength, ${\overline{\mathit{\tau}}}_{\mathit{s}}$/MPa | Calculated/Test | Ultimate Bond Strength, ${\overline{\mathit{\tau}}}_{\mathit{u}}$/MPa | Calculated/Test | Residual Bond Strength, ${\overline{\mathit{\tau}}}_{\mathit{r}}$/MPa | Calculated/Test | |||
---|---|---|---|---|---|---|---|---|---|

Test | Calculated | Test | Calculated | Test | Calculated | ||||

MSSC-01 | 0.399 | 0.395 | 0.989 | 0.976 | 0.964 | 0.987 | 0.515 | 0.501 | 0.973 |

MSSC-02 | 0.394 | 0.395 | 1.002 | 0.845 | 0.869 | 1.028 | 0.345 | 0.372 | 1.079 |

MSSC-03 | 0.391 | 0.395 | 1.009 | 0.773 | 0.774 | 1.001 | 0.268 | 0.244 | 0.910 |

MSSC-04 | 0.401 | 0.399 | 0.995 | 0.833 | 0.806 | 0.968 | 0.292 | 0.312 | 1.069 |

MSSC-05 | 0.429 | 0.404 | 0.941 | 0.851 | 0.839 | 0.986 | 0.371 | 0.380 | 1.025 |

MSSC-06 | 0.509 | 0.564 | 1.108 | 0.924 | 0.977 | 1.057 | 0.382 | 0.380 | 0.995 |

MSSC-07 | 0.735 | 0.706 | 0.960 | 1.128 | 1.099 | 0.975 | 0.398 | 0.380 | 0.955 |

Dilation Angle (Ψ) | Eccentricity $(\in )$ | ${\mathit{f}}_{\mathit{b}0}/{\mathit{f}}_{\mathit{c}0}$ | ${\mathit{K}}_{\mathit{c}}$ | Viscosity Parameter |
---|---|---|---|---|

30° | 0.1 | 1.16 | 0.6667 | 0.005 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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**

Wei, J.; Yang, Q.; Yu, Y.; Wang, Q.; Zhou, L.; Chen, F. Study of Bond–Slip Behavior and Constitutive Model of a New M-Section Steel-Skeleton Concrete. *Materials* **2022**, *15*, 6776.
https://doi.org/10.3390/ma15196776

**AMA Style**

Wei J, Yang Q, Yu Y, Wang Q, Zhou L, Chen F. Study of Bond–Slip Behavior and Constitutive Model of a New M-Section Steel-Skeleton Concrete. *Materials*. 2022; 15(19):6776.
https://doi.org/10.3390/ma15196776

**Chicago/Turabian Style**

Wei, Jun, Qingshun Yang, Yang Yu, Qing Wang, Lexiang Zhou, and Fei Chen. 2022. "Study of Bond–Slip Behavior and Constitutive Model of a New M-Section Steel-Skeleton Concrete" *Materials* 15, no. 19: 6776.
https://doi.org/10.3390/ma15196776