# Sustainable Design for CFS Structures: Experimental Data and Numerical Models of Hinged Connections

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Steel Quality and Connectors

#### 2.2. Connection’s Geometry and Testing Methodology

## 3. Experimental Testing Results

#### 3.1. Experimental Results for Connections with Rivets—SSPR

#### 3.2. Experimental Results for Connections with Screws STS

- In Area I, the initial stiffness attained 2150 N/mm for SSPR-A and 2170 N/mm for SSPR-B. For the screw joints, the initial stiffness reached 2295 N/mm for STS-A and 2360 N/mm for STS-B, respectively. These initial values are about 40% higher than the stiffness in the elastic Area II due to the presence of embedded drawings.
- Area II, with elastic behavior, is wider compared to the initial one. The average stiffness value was 1520 N/mm for SSPR-A and 1598 N/mm for STS-B.
- Area III corresponds to the plastic range when the displacements increase more than the loads. The average stiffness was 628 N/mm for SSPR-A and 677 N/mm for STS-B.
- Area IV represents the failure area when the node can no longer take loads, and the displacements increase until the rivets break or the screws are torn-up due to the shearing of the material around holes.

#### 3.3. Failure Modes of the SSPR and STS Connections

## 4. Numerical Simulation of Joints with 1D Finite Elements

#### 4.1. Input Data

- Linear (conventional);
- Nonlinear, of bilinear type;
- Nonlinear, of parabolic type.

_{s}and F

_{i}represent the limit values of the considered interval, d

_{s}and d

_{i}the displacements corresponding to the forces, according to the curves in Figure 13.

_{x}= k

_{e}= k

_{1}= k, which is the first value of the axial rigidity in the elastic behavior presented in Figure 13a and Figure 14, respectively, and k

_{p}= k

_{2}mentioned also in Figure 13a and Figure 14, were adopted.

#### 4.2. Joints Modelling

#### 4.3. Numerical Analysis Results for the Joints

- Joint A/B lin—the basic model with a hinged joint;
- SSPR-A/B bil—model with bilinear behavior of the axial stiffness of bar 2;
- SSPR-A/B pol—model with polynomial behavior of the axial stiffness of bar 2;
- STS-A/B bil—model with bilinear behavior of the axial stiffness of bar 2;
- STS-A/B pol—model with polynomial behavior of the axial stiffness of bar 2.

^{2}. At a force of 10,000 N, the maximum stress was 33.61 N/mm

^{2}, except for the SSPR-A pol case, which no longer converged after reaching the failure point.

^{2}at a load of 6000 N, and at 10,000 N, the maximum stress was 25.21 N/mm

^{2}except for SPRB-pol, which no longer converged.

## 5. Case Study on a 2D Truss Beam

#### 5.1. Structural Analysis Assumptions

#### 5.2. Results

^{2}in the conventional model at joints 19 and 33, located on the top chord and belonging to the first and last panels of the truss. For the nonlinear model, the maximum stress of 343 N/mm

^{2}occurs at nodes 21 and 31, also located on the top chord but belonging to the second and the last panels of the truss. The total load applied to the truss for both models was 30 kN.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Laboratory experimental test on S355 steel sheets: (

**a**) samples with extensometer mounted in universal testing machine; (

**b**) samples tested.

**Figure 2.**Stress–strain curves for S355 steel sheet in tensile test: (

**a**) curves for the 5 specimens; (

**b**) average curve.

**Figure 5.**Force–displacement results for (

**a**) joint connection type SSPR-A; (

**b**) joint connection type SSPR-B.

**Figure 12.**Hinged joint with nonlinear behavior (

**a**) conceptual sketch for the degree of freedom for the T-joint of beam type elements; (

**b**) numerical model geometry.

**Figure 13.**Characteristic curves for the axial stiffness, k

_{x}: (

**a**) Idealized bilinear representation; (

**b**) Polynomial curve.

**Figure 18.**(

**a**) Comparison of experimental and numerical curves for type A joint; (

**b**) Comparison of experimental and numerical curves for type B joint.

Joint part | Material | Strength | |
---|---|---|---|

Flange | S355 [42] C150 × 45 × 10 t = 1.2/1.6 mm | 355 MPa—Yield strength experimental | 490 MPa—Maximum strength experimental |

Post | |||

Steel-Steel pop-rivets 4.8 × 10 mm [48] | Zinc coated steel | 2900 N—Shear strength [48] | 3100 N—Tensile strength [48] |

Self-tapping screw 5.5 × 22 mm [48] | Zinc coated steel | 500 MPa—Shear strength [48] | 1000 MPa—Tensile strength [48] |

Specimen | C-Profile Thickness (mm) | Connector | |
---|---|---|---|

S-1A SSPR | S-1A STS | A = 1.2 | (SSPR) Steel-Steel Pop-Rivet |

S-2A SSPR | S-2A STS | ||

S-3A SSPR | S-3A STS | ||

S-4A SSPR | S-4A STS | ||

S-5A SSPR | S-5A STS | ||

S-1B SSPR | S-1B STS | B = 1.6 | (STS) Self-Tapping Screw |

S-2B SSPR | S-2B STS | ||

S-3B SSPR | S-3B STS | ||

S-4B SSPR | S-4B STS | ||

S-5B SSPR | S-5B STS |

Joint Type | Stiffness [N/mm] | F_{max}[N] | d_{1}[mm] | d_{ult}[mm] | ||
---|---|---|---|---|---|---|

${\mathrm{k}}_{\mathrm{i}}$ | ${\mathrm{k}}_{\mathrm{x}}={\mathrm{k}}_{\mathrm{e}}={\mathrm{k}}_{1}=\mathrm{k}$ | ${\mathrm{k}}_{\mathrm{p}}={\mathrm{k}}_{2}$ | ||||

SSPR-A | 2150 | 1520 | 628 | 6150 | 2.65 | 5.50 |

SSPR-B | 2170 | 1560 | 644 | 7800 | 3.20 | 7.00 |

STS-A | 2295 | 1575 | 669 | 14,500 | 5.85 | 12.50 |

STS-B | 2360 | 1598 | 677 | 17,400 | 8.40 | 13.20 |

Degree of Freedom (DOF) | Conventional Joint Linear | Nonlinear SSPR-A | Nonlinear SSPR-B | Nonlinear STS-A | Nonlinear STS-B |
---|---|---|---|---|---|

U_{x} | blocked | Nonlinear SSPR-A bil/pol | Nonlinear SSPR-B bil/pol | Nonlinear STS-B bil/pol | Nonlinear STS-B bil/pol |

U_{y} | blocked | blocked | blocked | blocked | blocked |

U_{z} | blocked | blocked | blocked | blocked | blocked |

R_{x} | blocked | blocked | blocked | blocked | blocked |

R_{y} | blocked | blocked | blocked | blocked | blocked |

R_{z} | free | free | free | free | free |

Case | Nodes | Load F_{z} (N) |
---|---|---|

1 | 18, 20, 22, 24, 26, 28, 30, 32, 34 | −250 |

2 | −500 | |

3 | −700 | |

4 | −1000 | |

5 | −2000 | |

6 | −3000 | |

7 | −3250 | |

8 | −3350 | |

9 | −3400 | |

10 | −3500 |

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**MDPI and ACS Style**

Taranu, G.; Venghiac, V.-M.; Olteanu-Dontov, I.; Rotaru, A.; Toma, I.-O.
Sustainable Design for CFS Structures: Experimental Data and Numerical Models of Hinged Connections. *Sustainability* **2022**, *14*, 7813.
https://doi.org/10.3390/su14137813

**AMA Style**

Taranu G, Venghiac V-M, Olteanu-Dontov I, Rotaru A, Toma I-O.
Sustainable Design for CFS Structures: Experimental Data and Numerical Models of Hinged Connections. *Sustainability*. 2022; 14(13):7813.
https://doi.org/10.3390/su14137813

**Chicago/Turabian Style**

Taranu, George, Vasile-Mircea Venghiac, Ioana Olteanu-Dontov, Ancuta Rotaru, and Ionut-Ovidiu Toma.
2022. "Sustainable Design for CFS Structures: Experimental Data and Numerical Models of Hinged Connections" *Sustainability* 14, no. 13: 7813.
https://doi.org/10.3390/su14137813