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To improve the shear behavior and design applicability of rubber ring perfobond connectors (RPBLs), a new rubber ring that aims to make the shear stiffness of RPBLs controllable was proposed. Firstly, the conceptual design and configuration of the new rubber rings were presented and discussed. Subsequently, finite element (FE) models for modified push-out tests of new RPBLs were established based on the validated modeling method. The initial shear stiffness is dominated by the horizontal projected contact area between hole walls and concrete dowels.

Perfobond connectors (PBL) are increasingly used in steel-concrete composite structures due to their excellent shear and fatigue capacity [

Applications of PBL groups.

Although many researchers investigated the shear behavior of PBLs [

Since the shear distribution of PBL groups is relevant to the shear stiffness of PBLs, a feasible solution for alleviating the shear concentration is to reduce the shear stiffness of partial connectors. Rubber is a kind of hyperelastic material that is much softer than steel and concrete. It is convenient to control the contact area between steel and concrete by using rubber. Based on this concept, Xu [

In this paper, a new rubber ring that aims to make the shear stiffness of RPBLs controllable was proposed. The conceptual design and configuration of the new rubber rings were presented and discussed. Subsequently, FE models for modified push-out tests of new RPBLs were established based on the validated modeling method [

According to the analyses performed in [

New rubber rings.

In terms of Type-A, two hollows with large central angles are set on the left and right sides of the circumference. At the early loading stage, the hole contacts the concrete dowel on the sides. The contact area between steel and concrete along the loading direction decreases by using Type-A rubber rings. In contrast, the contact area along the tensile direction, which is perpendicular to the loading direction, is the same as that of PBLs. In terms of Type-B, the hole contacts with the middle parts of the concrete dowel so that the initial stiffness of connectors is expected to be smaller than that of PBLs and larger than that of current RPBLs. Besides, the RPBLs with Type-B rubber rings could present very low stiffness on the direction perpendicular to the loading direction, which might be useful in some applications.

However, Type-A and Type-B present the anisotropy performance which is inconvenient and hard to install on site precisely. To improve the practicability of RPBLs, the isotropic Type-C rubber ring is proposed. The isotropy is formed by the proper array of hollows and rubber. There are more than 4 sectors with the same angle evenly distributing along the circumference. The stiffness of RPBLs by using Type-C rubber rings could be very close in different directions so that contractors do not need to care about the rotation of rubber rings during installations.

Figure

Configuration of new rubber rings. (a) Type-A. (b) Type-B. (c) Type-C.

To evaluate the shear behavior of perfobond connectors with the new rubber rings, numerical simulation was conducted in this study. Referring to the validated modeling method [

Finite element models.

The boundary condition of the models was consistent with that of the corresponding modified push-out tests. All the degrees of freedom of the reference point on the rigid ground were restrained. The bottom surface of concrete blocks contacted the top surface of the rigid ground. As regards the loading, the uniform displacement load was applied to the loading surface, as shown in Figure

As regards the material properties, concrete was simulated by Concrete Damage Plasticity Model (CDPM) provided by ABAQUS [

In this section, a parametric study with 28 FE models was conducted to evaluate the feasibility and design recommendation of new rubber rings. Comparisons of the geometric shapes and the shear-slip curves were presented among the models with varying parameters, including the types, wing sizes, central angles, offset angles, and rubber ring thickness. Table

Summary of parametric study results.

Model | Type | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

PBL | — | — | — | — | — | — | — | 547.3 | 60.0 | 1.00 | 443.9 |

RPBL | 2 | 2 | 10 | Cur. | — | — | — | 7.5 | 0.0 | 0.00 | 376.4 |

A_ | 2 | 4 | 10 | A | 2 | 151 | 90 | 446.6 | 45.0 | 0.75 | 327.5 |

A_ | 2 | 4 | 10 | A | 2 | 120 | 90 | 330.4 | 30.0 | 0.50 | 325.9 |

A_ | 2 | 4 | 10 | A | 2 | 83 | 90 | 193.0 | 15.0 | 0.25 | 323.6 |

B_ | 2 | 4 | 10 | B | 2 | 97 | 0 | 477.9 | 45.0 | 0.75 | 324.4 |

B_ | 2 | 4 | 10 | B | 2 | 60 | 0 | 356.9 | 30.0 | 0.50 | 314.5 |

B_ | 2 | 4 | 10 | B | 2 | 29 | 0 | 229.9 | 15.0 | 0.25 | 308.3 |

C_ns4_ | 2 | 4 | 10 | C | 4 | 45 | 0 | 361.3 | 27.5 | 0.46 | 338.5 |

C_ns4_ | 2 | 4 | 10 | C | 4 | 45 | 22.5 | 268.9 | 30.0 | 0.50 | 340.8 |

C_ns6_ | 2 | 4 | 10 | C | 6 | 30 | 0 | 316.3 | 31.1 | 0.52 | 339.3 |

C_ns6_ | 2 | 4 | 10 | C | 6 | 30 | 15 | 372.5 | 30.0 | 0.50 | 346.0 |

C_tw4_lw10 | 2 | 4 | 10 | C | 6 | 30 | 0 | 316.3 | 31.1 | 0.52 | 339.3 |

C_tw4_lw6 | 2 | 4 | 6 | C | 6 | 30 | 0 | 328.1 | 31.1 | 0.52 | 365.6 |

C_tw2_lw10 | 2 | 2 | 10 | C | 6 | 30 | 0 | 351.1 | 31.1 | 0.52 | 437.6 |

C_tw2_lw6 | 2 | 2 | 6 | C | 6 | 30 | 0 | 309.2 | 31.1 | 0.52 | 438.9 |

C_ns6_ | 2 | 2 | 10 | C | 6 | 45 | 0 | 528.4 | 45.9 | 0.77 | 428.5 |

C_ns6_ | 2 | 2 | 10 | C | 6 | 30 | 0 | 351.1 | 31.1 | 0.52 | 437.6 |

C_ns6_ | 2 | 2 | 10 | C | 6 | 15 | 0 | 120.1 | 15.7 | 0.26 | 439.1 |

C_ns6_o0 | 2 | 2 | 10 | C | 6 | 30 | 0 | 351.1 | 31.1 | 0.52 | 437.6 |

C_ns6_o8 | 2 | 2 | 10 | C | 6 | 30 | 7.5 | 344.3 | 30.8 | 0.51 | 439.6 |

C_ns6_o15 | 2 | 2 | 10 | C | 6 | 30 | 15 | 408.4 | 30.0 | 0.50 | 434.5 |

C_ns6_o23 | 2 | 2 | 10 | C | 6 | 30 | 22.5 | 355.7 | 29.2 | 0.49 | 438.0 |

C_ns6_o30 | 2 | 2 | 10 | C | 6 | 30 | 30 | 289.8 | 28.9 | 0.48 | 443.7 |

C_ns6_tr1.5 | 1.5 | 2 | 10 | C | 6 | 30 | 0 | 345.8 | 31.1 | 0.52 | 430.0 |

C_ns6_tr2 | 2 | 2 | 10 | C | 6 | 30 | 0 | 351.1 | 31.1 | 0.52 | 437.6 |

C_ns6_tr3 | 3 | 2 | 10 | C | 6 | 30 | 0 | 354.7 | 31.1 | 0.52 | 360.2 |

C_ns6_tr4 | 4 | 2 | 10 | C | 6 | 30 | 0 | 299.1 | 31.1 | 0.52 | 348.9 |

Firstly, the feasibility of the conceptual designs of Type-A, Type-B, and Type-C rubber rings was discussed. Figure

Type-A rubber rings with varying central angles: (a)

Figures

Shear behavior of Type-A rubber rings. (a) Global shear behavior. (b) Initial shear stiffness. (c) Effects of

From Figure

Compared with Type-A, the middle of the two hollows is positioned on the central line of rubber rings in Type-B. Figure

Type-B rubber rings with varying central angles: (a)

Shear behavior of Type-B rubber rings. (a) Global shear behavior. (b) Initial shear stiffness. (c) Effects of

Figures

Although Type-A and Type-B rubber rings could make the shear stiffness controllable, their anisotropy sometimes is unfavorable, especially on the condition of the requirement of precise installations. An alternative solution is the isotropic Type-C rubber ring, whose isotropy is formed by the uniform array of hollows and rubber. Figure

Type-C with varying numbers of sectors and offset angles: (a)

Figure _{s} = 4. The reason is that the range of the offset angle is relatively broad on the condition that _{s} is small, resulting in the significant variation of the horizontal projected area. Compared with Figure _{s} = 6. Therefore, the number of periodical sectors of Type-C rubber rings is recommended to be no less than 6.

Shear force-slip curves of Type-C rubber rings. (a) Global shear behavior, _{s} = 4. (b) Initial loading stage, _{s} = 4. (c) Global shear behavior, _{s} = 6. (d) Initial loading stage, _{s} = 6.

Based on the analyses above, the new rubber rings are feasible to decrease the initial shear stiffness of PBLs and even make them controllable. Among the 3 types of new rubber rings, Type-C is isotropic and not sensitive to the installation errors, such as the rotational offset, when the number of periodical sectors is no less than 6. Consequently, the Type-C rubber ring is selected as the proposed new rubber ring in this study. The proper side wing sizes, the effects of central angles and offset angles, and the impacts of rubber ring thickness are investigated in the following sections.

Figure

Type-C with varying wing sizes: (a)

Figures

Effects of side wing sizes. (a) Global shear behavior. (b) Initial shear stiffness. (c) Effects of wing sizes on shear stiffness. (d) Effects of wing sizes on yield loads.

Figure

Figure

Type-C with varying central angles: (a)

Figure

Effects of central angles. (a) Global shear behavior. (b) Initial shear stiffness. (c) Effects of

Figure

Type-C with varying offset angles: (a)

. Effects of offset angles. (a) Global shear behavior. (b) Initial shear stiffness. (c) Effects of

From Figures

Lastly, Figure

Type-C with varying rubber ring thickness: (a) _{r} = 3 mm, and (d)

Figure

Effects of rubber ring thickness. (a) Global shear behavior. (b) Initial shear stiffness. (c) Effects of

To sum up, employing the isotropic Type-C rubber ring on a conventional PBL is feasible to make the shear stiffness controllable. The proper thickness and length of side wings are 2 mm and 10 mm to improve the yield load and the convenience of installation. According to the required shear stiffness, the central angle ratio of hollows to sectors should be between 0.25 and 0.75. The effects of offset angles are negligible if the number of periodical sectors is no less than 6. Besides, the thickness of rubber rings is suggested as 2 mm on the concern of fabrication and obtaining moderate stiffness.

Finally, an analytical equation for the shear stiffness of new RPBLs is proposed by regression analyses based on the numerical results. The shear stiffness of new RPBLs increases with the increase of

Comparison of numerical and calculated results.

This paper proposed a new rubber ring that aims to make the shear stiffness of RPBLs controllable. Firstly, the conceptual design and configuration of the new rubber rings were presented and discussed. Subsequently, FE models for the modified push-out tests of new RPBLs were established based on the validated modeling method [

The initial shear stiffness is dominated by the horizontal projected contact area between hole walls and concrete dowels. The shear stiffness of new RPBLs is about 35%, 60%, and 82% of the shear stiffness of PBLs when

Based on the numerical results, the proper thickness of side wings is no larger than 2 mm. The thicker side wing could reduce the confinement effects provided by surrounding concrete on concrete dowels, resulting in a drop of the yield load of new RPBLs. The central angle ratio of hollows to sectors is the dominant factor in the shear stiffness of RPBLs, which should be in the range from 0.25 to 0.75.

The number of sectors is suggested to be no less than 6 so that the shear behavior of new RPBLs is irrelevant to the offset angle, which could effectively improve the convenience of installation on site. The shear stiffness is not related to the thickness of rubber rings. To improve the yield load of RPBLs and obtain the moderate recovered stiffness, the thickness of rubber rings is recommended as 2 mm.

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

The authors declare that they have no conflicts of interest.

The authors would like to acknowledge Zhejiang Department of Transport for the funding support of Project of Science and Technology Program of Department of Transport, Zhejiang Province (2019049).