# Some Considerations on the Behaviour of Bolted Stainless-Steel Beam-to-Column Connections: A Simplified Analytical Approach

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## Abstract

**:**

## 1. Introduction

## 2. Stainless- vs. Carbon-Steel

## 3. Beam-to-Column Connections

## 4. Analytical Evaluation of the Joint Resistance

## 5. Discussion of the Results from the Proposed Analytical Approach

## 6. Assessment of the Plastic Mechanism by FE Modelling of the Joints

- 1
- The ratio (ρ
_{j}) of the ultimate moment (M_{j,u}) to the pseudo-plastic resistance (M_{j,R}), usually called the plastic over-strength:$${\rho}_{i}=\frac{{M}_{j,u}}{{M}_{j,R}}$$ - 2
- The ratio (ρ
_{j}) of the rotation capacity of the joint (ϕ_{u}) to the rotation value corresponding to the pseudo-plastic resistance (${\varphi}_{{M}_{j,R}}$), usually defined as the joint ductility:$${\mu}_{j}=\frac{{\varphi}_{u}}{{\varphi}_{{M}_{j,R}}}$$

_{i}vary in a range from 1.63 to 2.83, while the ductility µ

_{j}varies in a range from 2.65 to 4.45. Therefore, as thought, all specimens show considerable inelastic deformations prior to failure.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**A typical experimental stress–strain curve for carbon-steel S235 (black line) vs. different types of stainless-steel stress–strain curves represented by means of a modified Ramberg–Osgood model [17].

**Figure 2.**Magnification of steel stress–strain curves shown in Figure 1 at small strains.

**Figure 3.**A visual sketch of typical (

**a**) unstiffened Extended End-Plate, (

**b**) stiffened Extended End-Plate, (

**c**) unstiffened Flush End-Plate, (

**d**) stiffened Flush End-Plate and (

**e**) Top-and-Seat Angle Cleat.

**Figure 4.**Stress–strain curve of stainless-steel type EN 1.4301. The points (282, 0.007) and (510, 0.24) on this curve correspond to the 0.2% proof strength (${f}_{0.2})$ and to the yield strength (${f}_{y})$, respectively.

**Figure 5.**Geometrical properties of investigated joints. (

**a**) Extended End-Plate (EEP); (

**b**) Flush End Plate (FEP); (

**c**) Top-and-Seat Angle Cleat (TSAC).

**Figure 6.**Derivation of pseudo-plastic moment resistance using Zanon and Zandonini method [42].

**Figure 8.**Comparison of moment-rotation curves obtained using Eurocode 3 (EC3) and proposed methods with the experimental ones [29] (solid lines) and estimation of the experimental pseudo-plastic moment resistance (${M}_{j,R,exp}$) (black dot) by means of Zanon and Zandonini method [42] (dashed lines): (

**a**) Extended End-Plate (EEP), (

**b**) Flush End-Plate (FEP), (

**c**) Top-and-Seat Angle Cleat connection (TSAC).

**Figure 10.**Comparison of numerical (left) and experimental (right, reprinted with permission from Ref. [29]) failure modes. (

**a**) Extended End-Plate (EEP), (

**b**) Flush End-Plate (FEP), (

**c**) Top-and-Seat Angle Cleat connection (TSAC).

**Figure 11.**Bolt forces vs. joint rotation curves. (

**a**) Extended End-Plate (EEP), (

**b**) Flush End-Plate (FEP), (

**c**) Top-and-Seat Angle Cleat (TSAC).

Part | ${E}_{0}$ [MPa] | ${\sigma}_{0.2}$ [MPa] | ${\sigma}_{u}$ [MPa] | n [-] | m [-] | ${\epsilon}_{f}$ [%] |

I240 × 120 × 12 × 10—Flange | 196,500 | 248 | 630 | 5.20 | 2.37 | 66 |

I240 × 120 × 12 × 10—Web | 205,700 | 263 | 651 | 6.70 | 2.41 | 65 |

Angle Cleat | 197,600 | 280 | 654 | 12.22 | 2.49 | 55 |

End Plate | 198,000 | 282 | 655 | 12.20 | 2.50 | 54 |

M16 (A80) Bolt | 191,500 | 617 | 805 | 17.24 | 3.68 | 12 |

**Table 2.**Comparison of the plastic moment evaluated with EC3, ${M}_{j,R,EC3}$, proposed method, ${M}_{j,R}^{*}$, and the method of Zanon and Zandonini [42] from the experimental curves, ${M}_{j,R,exp}$, (Units: kNm).

Model | ${\mathit{M}}_{\mathit{j},\mathit{R},\mathit{E}\mathit{C}3}\text{}$ | ${\mathit{M}}_{\mathit{j},\mathit{R}}^{*}$ | ${\mathit{M}}_{\mathit{j},\mathit{R},\mathit{e}\mathit{x}\mathit{p}}\text{}$ | ${\mathit{M}}_{\mathit{j},\mathit{R},\mathit{e}\mathit{x}\mathit{p}}$$\mathbf{/}{\mathit{M}}_{\mathit{j},\mathit{R},\mathit{E}\mathit{C}3}\text{}$ | ${\mathit{M}}_{\mathit{j},\mathit{R}}^{*}$$\mathbf{/}{\mathit{M}}_{\mathit{j},\mathit{R},\mathit{e}\mathit{x}\mathit{p}}\text{}$ |
---|---|---|---|---|---|

FEP | 23.80 | 41.72 | 40.20 | 1.69 | 1.04 |

EEP | 22.00 | 42.00 | 41.79 | 1.91 | 1.01 |

TSAC | 6.56 | 11.96 | 12.18 | 1.86 | 0.98 |

Average | - | - | - | 1.82 | 1.01 |

Model | ${\mathit{S}}_{\mathit{j},\mathit{i}\mathit{n}\mathit{i},\mathit{C}\mathit{M}}\text{}$ | ${\mathit{S}}_{\mathit{j},\mathit{i}\mathit{n}\mathit{i},\mathit{e}\mathit{x}\mathit{p}}\text{}$ | ${\mathit{S}}_{\mathit{j},\mathit{i}\mathit{n}\mathit{i},\mathit{C}\mathit{M}}$$\mathbf{/}{\mathit{S}}_{\mathit{j},\mathit{i}\mathit{n}\mathit{i},\mathit{e}\mathit{x}\mathit{p}}\text{}$ |
---|---|---|---|

FEP | 6042 | 2274 | 2.66 |

EEP | 7699 | 3928 | 1.96 |

TSAC | 1818 | 1001 | 1.82 |

Average | - | - | 2.15 |

Model | Plastic Mechanism (EC3) |
---|---|

FEP | End plate in bending |

EEP | End plate in bending |

TSAC | Bending of flange cleat |

Model | Plastic Mechanism (EC3) | Ultimate Failure Mode (FEM) | Maximum Rotation ϕu (FEM) (mrad) | ρ_{j} | µ_{j} |

FEP | End plate bending | Bolt failure in tension | 118 | 1.91 | 4.45 |

EEP | End plate bending | Fracture of the bolt in tension | 153 | 1.63 | 3.73 |

TSAC | Bending of flange cleat | Bolt failure in tension and shear | 159 | 2.83 | 2.65 |

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**MDPI and ACS Style**

Sarfarazi, S.; Shamass, R.; Mascolo, I.; Della Corte, G.; Guarracino, F.
Some Considerations on the Behaviour of Bolted Stainless-Steel Beam-to-Column Connections: A Simplified Analytical Approach. *Metals* **2023**, *13*, 753.
https://doi.org/10.3390/met13040753

**AMA Style**

Sarfarazi S, Shamass R, Mascolo I, Della Corte G, Guarracino F.
Some Considerations on the Behaviour of Bolted Stainless-Steel Beam-to-Column Connections: A Simplified Analytical Approach. *Metals*. 2023; 13(4):753.
https://doi.org/10.3390/met13040753

**Chicago/Turabian Style**

Sarfarazi, Sina, Rabee Shamass, Ida Mascolo, Gaetano Della Corte, and Federico Guarracino.
2023. "Some Considerations on the Behaviour of Bolted Stainless-Steel Beam-to-Column Connections: A Simplified Analytical Approach" *Metals* 13, no. 4: 753.
https://doi.org/10.3390/met13040753