# Experimental and Numerical Study on the Shear Performance of Short Stud Shear Connectors in Steel–UHPC Composite Beams

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## Abstract

**:**

## 1. Introduction

## 2. Research Significance

## 3. Experimental Program

#### 3.1. Test Specimens

^{2}shear pocket in each precast slab was prepared to verify the validation of the short studs in full-depth precast UHPC slabs.

#### 3.2. Material Properties

_{c}′ and splitting tensile strength f

_{t}for each batch were higher than 150 MPa and 10 MPa, respectively. The elastic modulus E

_{c}and Poisson’s ratio v can also be found in Table 1.

_{s}, yield strength f

_{y}, and ultimate strength f

_{u}of about 205,000, 330, and 440 MPa, respectively. Furthermore, Q235B steel with an actual f

_{y}of 253.29 MPa and f

_{u}of 425.03 MPa was used for the steel beam.

#### 3.3. Test Setup and Loading Procedures

## 4. Experiment Results and Discussion

#### 4.1. Failure Modes

#### 4.2. Load–Slip Curves

#### 4.3. Shear Performance of Short Stud Shear Connectors

_{u}, initial shear stiffness k, and ductility were discussed in this section. In Table 2, the results for the individual stud shear connectors are summarized. The initial shear stiffness k was defined as the secant slope of the load–slip curve at a slip of 0.2 mm. For the ductility, both the slip capacity δ

_{u}at 0.9P

_{u}in the post-peak load stage and the characteristic slip capacity δ

_{uk}(δ

_{uk}= 0.9δ

_{u}) are presented. If the δ

_{uk}exceeds 6 mm, a shear connector can be regarded as ductile [9].

_{u}, k, and δ

_{uk}, respectively. Hence, sufficient thickness of the UHPC slab should be ensured to achieve superior structural performance.

_{u}and initial shear stiffness k for M-25-75 were 212.73 kN and 657.32 kN/mm, respectively, which were 1.29 and 1.23 times those for M-22-75. However, the characteristic slip capacity δ

_{uk}for M-25-75 (3.02 mm) was only 68.48% for M-22-75 (4.41 mm). Thus, the deformation ability of a large-diameter short stud shear connector should be well considered.

_{u}for P-25-75 was only 10.82 kN, while the enhancement in the slip capacity for P-25-75 was 8.94% of that of M-25-75. Therefore, steel–UHPC composite structures with precast slabs can be considered for the sake of shortening the construction period.

_{u}and the cross-section area A

_{s}, considering a partial factor γ

_{v}of 1.25 (P

_{code-s}= 0.8f

_{u}(πd

^{2}/4)/γ

_{v}). For concrete crushing, the shear prediction was a function of the stud height h, stud diameter d, concrete strength f

_{c}′, and elastic modulus E

_{c}(P

_{code-c}= 0.058(h/d+1)d

^{2}(f

_{c}′E

_{c})

^{1/2}/γ

_{v}). The comparisons between the shear prediction from Eurocode 4 and the experiments are presented in Table 2. For the tests in this study, the prediction for the P

_{code-s}was smaller than the P

_{code-c}, indicating that the predicting failure mode was stud fracture rather than concrete crushing. However, all the shear predictions for stud fracture presented conservative results, with the P

_{code-s}/P

_{u}ranging from 0.64 to 0.71. Except for M-22-50, the calculated results for concrete crushing overestimated the shear strength, with the error varying from 17% to 29%.

## 5. Finite Element Analysis

#### 5.1. FE Model

#### 5.1.1. Element Type and Meshing

#### 5.1.2. Interaction and Contact Conditions

#### 5.1.3. Boundary Conditions and Load Application

#### 5.1.4. Material Modelling

- 1.
- Concrete

_{c}′ = the compressive strength of UHPC, which can be found in Table 1; ξ = the strain ratio, which can be determined as ξ = ε/ε

_{0}; ε

_{0}= the strain at ultimate compressive strength, equal to 0.0035 in this study; n = the ratio of elastic modulus, which can be calculated as n = E

_{c}/E

_{cs}; E

_{c}= the tangent modulus at the initial stage, which can be obtained in Table 1; E

_{cs}= the secant modulus at the ultimate compressive strength.

_{ct}= the average tensile stress at the strain hardening stage, which can be found in Table 1; ε

_{ca}= the peak strain in the elastic stage corresponding to f

_{ct}; ε

_{pc}= the ultimate strain, equal to 0.0008; w

_{p}= the crack width corresponding to the stress of 2

^{−p}f

_{ct}; p = the experimental fitting parameter, equal to 0.95.

- 2.
- Stud shear connectors and steel beams

#### 5.2. Verification of FE Modes

#### 5.2.1. Failure Modes

#### 5.2.2. Load–Slip Curves

#### 5.3. Parametric Study

#### 5.3.1. Effect of Stud Diameter

#### 5.3.2. Effect of Stud Tensile Strength

#### 5.3.3. Effect of Steel Beam Tensile Strength

#### 5.3.4. Effect of Monolithic Slab Concrete Strength

#### 5.3.5. Effect of Precast Slab Concrete Strength

#### 5.3.6. Effect of Shear Pocket Concrete Strength

## 6. Conclusions

- A stud height-to-diameter ratio larger than 1.59 (35/22) was required for steel–UHPC composite structures with thin UHPC slabs (50 mm thick) to achieve a stud fracture failure.
- Adopting a thicker UHPC slab can improve the shear performance of short studs, in terms of strength, stiffness, and ductility. Specimens with larger studs can obtain more significant shear capacity and initial shear stiffness, but a smaller slip capacity. Specimens with precast UHPC slabs exhibited a comparative shear resistance and initial shear stiffness but a preferable slip capacity compared to the monolithic counterpart.
- The FE analysis results agree well with the experimental results of the failure modes, load–slip curves, ultimate shear capacity, and shear stiffness, demonstrating the applicability of the FE models presented in this paper.
- According to the parametric analysis results, it was indicated that the shear capacity of the short studs was enhanced when the stud diameter, stud tensile strength, and steel beam tensile strength increased. A higher shear stiffness can be obtained in specimens with a larger stud diameter and tensile strength. With an increase in the stud tensile strength, the slip capacity can be improved. The monolithic slab, precast slab, and shear pocket concrete strength had a negligible effect on the shear performance of the short stud shear connectors in steel–UHPC composite beams.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Fabrication procedure of test specimens: (

**a**) for monolithic casting specimen; (

**b**) for precast slab specimen.

**Figure 4.**Fabrication procedure of test specimens: (

**a**) specimen M-22-50; (

**b**) specimen M-22-75; (

**c**) specimen M-25-75; (

**d**) specimen P-25-75.

**Figure 5.**Load–slip curves for each specimen: (

**a**) specimen M-22-50; (

**b**) specimen M-22-75; (

**c**) specimen M-25-75; (

**d**) specimen P-25-75.

**Figure 6.**Load–slip relationships: (

**a**) comparison of load–slip relationships; (

**b**) general load–slip response.

**Figure 8.**Contact conditions of the FEM model: (

**a**) steel beam-to-concrete slab; (

**b**) head stud-to-concrete; (

**c**) precast slab-to-shear pocket.

**Figure 10.**Comparison of failure modes from experimental and FE analysis: (

**a**) concrete damage (taking M-22-50 as an example); (

**b**) stud Mises stress.

**Figure 11.**Comparison of load–slip curves from experimental and FE analysis: (

**a**) specimen M-22-50; (

**b**) specimen M-22-75; (

**c**) specimen M-25-75; (

**d**) specimen P-25-75.

**Figure 12.**Load–slip relationship from parameter study: (

**a**) effect of stud diameter; (

**b**) effect of stud tensile strength; (

**c**) effect of steel beam tensile strength; (

**d**) effect of monolithic slab concrete strength; (

**e**) effect of precast slab concrete strength; (

**f**) effect of shear pocket concrete strength.

Types | f_{c}′ (MPa) | f_{t} (MPa) | E_{c} (MPa) | v | |
---|---|---|---|---|---|

Concrete | Precast slab | 156.6 | 10.3 | 42890 | 0.205 |

Shear pocket (former) | 159.1 | 10.8 | 43568 | 0.206 | |

Shear pocket (latter) and monolithic slab | 150.5 | 10.2 | 42589 | 0.208 | |

Types | ϕ22 stud | ϕ25 stud | Steel beam | ||

Steel | E_{s} (MPa) | 205300 | 208500 | 207130 | |

f_{y} (MPa) | 331.28 | 332.36 | 253.29 | ||

f_{u} (MPa) | 431.25 | 451.82 | 425.03 |

Specimen | Aspect Ratio | P_{u}(kN) | k (kN/mm) | δ_{u}(mm) | δ_{uk}(mm) | P_{code-s}(kN) | P_{code-s}/P_{u} | P_{code-c}(kN) | P_{code-c}/P_{u} | Failure Mode |
---|---|---|---|---|---|---|---|---|---|---|

M-22-50 | 1.59 | 147.83 | 432.17 | 4.38 | 3.94 | 104.92 | 0.71 | 147.26 | 1.00 | Stud fracture/pulling-out and concrete spalling |

M-22-75 | 2.73 | 164.66 | 532.77 | 4.90 | 4.41 | 104.92 | 0.64 | 212.07 | 1.29 | Stud fracture |

M-25-75 | 2.40 | 212.73 | 657.21 | 3.36 | 3.02 | 141.94 | 0.67 | 249.63 | 1.17 | Stud fracture |

P-25-75 | 2.40 | 201.91 | 517.50 | 3.66 | 3.29 | 141.94 | 0.70 | 249.63 | 1.24 | Stud fracture |

_{u}= ultimate shear strength; k = initial shear stiffness; δ

_{u}= slip capacity; δ

_{uk}= characteristic slip capacity.

Group | Specimen | Stud Diameter (mm) | Stud Tensile Strength (MPa) | Steel Beam Tensile Strength (MPa) | Concrete Strength | Casting Method | |
---|---|---|---|---|---|---|---|

Slab (MPa) | Shear Pocket (MPa) | ||||||

I | GI-D13 | 13 | 452 | 425 | 150 | - | Monolithic |

GI-D19 | 19 | ||||||

GI-D25 | 25 | ||||||

GI-D30 | 30 | ||||||

II | GII-SC300 | 25 | 300 | 425 | 150 | - | Monolithic |

GII-SC400 | 400 | ||||||

GII-SC500 | 500 | ||||||

GII-SC600 | 600 | ||||||

III | GIII-SB235 | 25 | 452 | 235 | 150 | - | Monolithic |

GIII-SB345 | 345 | ||||||

GIII-SB390 | 390 | ||||||

GIII-SB420 | 420 | ||||||

IV | GIV-C100 | 25 | 452 | 425 | 100 | - | Monolithic |

GIV-C120 | 120 | ||||||

GIV-C150 | 150 | ||||||

GIV-C200 | 200 | ||||||

V | GV-S100P150 | 25 | 452 | 425 | 100 | 150 | Precast |

GV-S120P150 | 120 | ||||||

GV-S150P150 | 150 | ||||||

GV-S200P150 | 200 | ||||||

VI | GVI-S100P100 | 25 | 452 | 425 | 100 | 100 | Precast |

GVI-S100P120 | 120 | ||||||

GVI-S100P150 | 150 | ||||||

GVI-S100P200 | 200 |

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**MDPI and ACS Style**

Fang, Z.; Fang, S.; Liu, F.
Experimental and Numerical Study on the Shear Performance of Short Stud Shear Connectors in Steel–UHPC Composite Beams. *Buildings* **2022**, *12*, 418.
https://doi.org/10.3390/buildings12040418

**AMA Style**

Fang Z, Fang S, Liu F.
Experimental and Numerical Study on the Shear Performance of Short Stud Shear Connectors in Steel–UHPC Composite Beams. *Buildings*. 2022; 12(4):418.
https://doi.org/10.3390/buildings12040418

**Chicago/Turabian Style**

Fang, Zhen, Shu Fang, and Feng Liu.
2022. "Experimental and Numerical Study on the Shear Performance of Short Stud Shear Connectors in Steel–UHPC Composite Beams" *Buildings* 12, no. 4: 418.
https://doi.org/10.3390/buildings12040418