# Numerical Study on Cyclic Response of End-Plate Biaxial Moment Connection in Box Columns

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## Abstract

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^{®}ConXL™ moment connection has been prequalified according to the (American Institute of Construction) AISC Seismic Provisions for use with tubular columns and the rest of connections do not consider biaxial resistance. The research reported herein investigated the cyclic response of box-columns joints, connected to I beams using the four-bolt extended endplate connection, subjected to bidirectional bending and axial load on the column. To conduct the study, complex nonlinear finite element models (FEMs) of several I beam to box column joint configurations were constructed and analyzed under cyclic loading using the ANSYS software. The results reveal that the failure is concentrated in the beams of all joint configurations except for the columns with axial load equal to 75% of the column capacity, where a combined failure mechanism is achieved. The energy dissipation capacity of joints with a greater number of beams is lower than joints with fewer beams. The bidirectional effect of the seismic action and the level of axial load must be considered to avoid the formation of a column-hinge fragile failure mechanism also the behavior exhibited by 3D joints is more realistic than 2D joints according to real structures.

## 1. Introduction

^{®}ConXL™, appears as prequalified in [7] for use with I-beam to tubular column joints. The ConXtech

^{®}ConXL™ moment connection was tested and patented by [8]. In this connection, the I-beams are connected to HSS or built-up box columns by means of a field-bolted proprietary collar assembly. The prequalification of the connection was performed with reduced flanges beam and concrete filled columns. The width of the column is limited to 400 mm. The goal of this connection was industrialization and elimination of any welding in worksite. Out of 17 cyclic tests performed, only five were tested under biaxial bending (all interior joints with four beams attached to the column). Exterior joints with beams in three sides and corner joints were not studied. Furthermore, the tests were conducted under constant axial load in the column.

## 2. Description of Moment Connection

## 3. Finite Element Model

^{®}ConXL™ connection. This factor considers a reduction in column capacity due to the bidirectional bending on the column. No further details are given in [7] or [8]. A preliminary model in FEM was calibrated including dimensions and other specifications of specimens and boundary and loading conditions according to [10]. In the model, one beam to column joint configuration was analyzed. To reduce the computational cost, a BEAM188 element with two nodes was employed in beam and column outside of connection region. The elements of connection such as bolts, nuts, end-plate, vertical and horizontal stiffeners were modeled with SOLID186 element and nonlinearities of material, geometric and contact were considered. Finally, the hysteresis and moment-rotation curve were compared with experimental data of specimen #2, obtaining an acceptable agreement was achieved between the finite element analysis results and experimental specimen #2, as shown in Figure 4.

#### 3.1. General Characteristics of the Numerical Model

#### 3.2. Element Type and Mesh

#### 3.3. Boundary Conditions, Contacts and Loading

#### 3.4. Material Modeling

## 4. Analysis Results

#### 4.1. Seismic Performance for Different Joints

_{c}) is the resultant force in horizontal direction and can be calculated using principles of structural mechanics. Equating the work performed by beam forces with work performed by equivalent force, an equivalent displacement (Δ) is obtained (Figure 8). The formulation of method in this research is shown as follows:

#### 4.2. Hysteretic Behavior

#### 4.3. Failure Mechanism

## 5. Conclusions

- (1)
- The moment connection studied complies with the design philosophy, failure mechanisms and behavior established by Seismic Provisions. For all joint configurations a drift angle in excess of 0.04 (rad) and a flexural resistance greater than 0.8 Mp for all axial load levels is achieved.
- (2)
- The failure is concentrated in the beams of all joint configurations except in joints 3D and 2D for an axial load of 75% the column capacity, where a combined failure mechanism (plastic deformations in beam and column) is achieved, showing a good correlation with the strong column/weak beam criteria developed for the Contech
^{®}ConXL™ connection. - (3)
- The elements outer diaphragm and vertical diaphragm, end-plate and bolts remain in elastic range while the beam reach the maximum inelastic incursion until 5% interstory drift. Additionally, the several components of connection around to panel zone avoid their distortion.
- (4)
- The equivalent damping and dissipated energy is similar for the five joint types, being greater in the 3D joints than the 2D joints. The global deformation in 3D joints is greater than 2D joints even with the same number of beams. Therefore, the response of joints may be underestimated if 3D effects are not considered.
- (5)
- The axial load level and bidirectional effect simultaneously affect the performance of joints as can be observed in the loss of energy dissipation. However, hysteretic loops without significant pinching are observed for all joint configurations.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

α | Angle from V_{c} |

Δ | Equivalent column top displacement |

F | Vertical load at the beam end |

H | Distance between zero moment points |

L | Distance between the loading points |

M_{p} | Plastic moment of beam |

V_{c} | Equivalent force in the top column |

V_{cx} | Equivalent force in the top column in X direction |

V_{cx} | Equivalent force in the top column in Y direction |

W_{1} | Work performed by loads at beam end |

W_{2} | Work performed by Vc force |

δi | (i = 1,2,3,4) vertical displacement at the beam for east, west, north and south |

ε_{u} | Ultimate deformation |

ε_{y} | Yielding deformation |

θ | Rotation angle due to moment of beam |

σ_{u} | Ultimate stress |

σ_{y} | Yielding stress |

## References

- Wang, Y.Y. Lessons learned from the “5.12” Wenchuan earthquake: Evaluation of earthquake performance objectives and the importance of seismic conceptual design principles. Earthq. Eng. Eng. Vib.
**2008**, 7, 255–262. [Google Scholar] [CrossRef] - Okazaki, T.; Lignos, D.; Midorikawa, M.; Ricles, J.; Love, J. Damage to Steel Buildings Observed After the 2011 Tohoku Earthquake. Earthq. Spectra
**2013**, 29, 219–243. [Google Scholar] [CrossRef] - Eslami, M.; Namba, H.; Kodur, V.; Mhamid, M.; Morovat, M. Seismic behavior of composite beam connected to HSS column with large width-to-thickness ratio. Eng. Struct.
**2019**, 183, 423–442. [Google Scholar] [CrossRef] - Sherman, D.R. Designing with structural tubing. Eng. J. Aisc
**1996**, 33, 101–109. [Google Scholar] - FEMA-355D. State of the Art Report on Connection Performance; Federal Emergency Management Agency: Washington, DC, USA, 2000. [Google Scholar]
- ANSI/AISC 341-16. Seismic Provisions for Structural Steel Buildings; American Institute of Steel Construction: Chicago, IL, USA, 2016. [Google Scholar]
- ANSI/AISC 358-16. Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications; American Institute of Steel Construction: Chicago, IL, USA, 2016. [Google Scholar]
- ConXtech Inc. Test Report on ConXL Connection Assembly of Stanford Law School; ConXtech Inc.: Pleasanton, CA, 2009. [Google Scholar]
- Yang, C.; Yang, J.F.; Su, M.S.; Liu, C.Z. Numerical study on seismic behaviors of ConXL biaxial moment connection. J. Constr. Steel Res.
**2016**, 121, 185–201. [Google Scholar] [CrossRef] - Nuñez, E.; Torres, R.; Herrera, R. Seismic performance of moment connections in steel moment frames with HSS columns. Steel Compos. Struct.
**2017**, 25, 271–286. [Google Scholar] - Herrera, R.; Salas, C.; Beltran, J.; Nuñez, E. Experimental performance of double built-up T moment connections under cyclic loading. J. Constr. Steel Res.
**2017**, 138, 742–749. [Google Scholar] [CrossRef] - Ataollahi, S.; Banan, M. Numerical cyclic behavior of T-RBS: A new steel moment connection. Steel Compos. Struct.
**2016**, 21, 1251–1264. [Google Scholar] [CrossRef] - Ricles, J.M.; Peng, S.W.; Lu, L.W. Seismic Behavior of Composite Concrete Filled Steel Tube Column-Wide Flange Beam Moment Connections. J. Struct. Eng.
**2004**, 130, 223–232. [Google Scholar] [CrossRef] - Herrera, R.; Ricles, J.; Sause, R. Seismic performance evaluation of a large-scale composite MRF using pseudodynamic testing. J. Struct. Eng.
**2008**, 134, 279–288. [Google Scholar] [CrossRef] - Saleh, A.; Zahrai, S.; Mirghaderi, S. Experimental study on innovative tubular web RBS connections in steel MRFs with typical shallow beams. Struct. Eng. Mech.
**2016**, 57, 785–808. [Google Scholar] [CrossRef] - Erfani, S.; Ali Asnafi, A.; Gourdazi, A. Connection of I-beam to box-column by a short stub beam. J. Constr. Steel Res.
**2016**, 127, 136–150. [Google Scholar] [CrossRef] - Čermelj, B.; Može, P.; Sinur, F. On the prediction of low-cycle fatigue in steel welded beam-to-column joints. J. Constr. Steel Res.
**2016**, 117, 49–63. [Google Scholar] [CrossRef] - Esfandyary, R.; Razzaghi, M.; Eslami, A. A parametric investigation on the hysteretic behavior of CFT column to steel beam connections. Struct. Eng. Mech.
**2015**, 55, 205–228. [Google Scholar] [CrossRef] - Faridmehr, I.; Osman, M.; Tahir, M.; Nejad, A.; Hodjati, R. Seismic and progressive collapse assessment of SidePlate moment connection system. Struct. Eng. Mech.
**2015**, 54, 35–54. [Google Scholar] [CrossRef] - Fadden, M.; McCormick, J. HSS-to-HSS seismic moment connection performance and design. J. Constr. Steel Res.
**2014**, 101, 373–384. [Google Scholar] [CrossRef] - Tahir, M.; Juki, I.; Ishak, M.; Plank, R. Performance of partial strength connection connected by thick plate between column flanges. Struct. Eng. Mech.
**2014**, 51, 215–228. [Google Scholar] [CrossRef] - Gholami, M.; Deylami, A.; Tehranizadeh, M. Seismic performance of flange plate connections between steel beams and box columns. J. Constr. Steel Res.
**2013**, 84, 36–48. [Google Scholar] [CrossRef] - Saneei, Z.; Ghassemieh, M.; Mazroi, A. WUF-W connection performance to box column subjected to uniaxial and biaxial loading. J. Constr. Steel Res.
**2013**, 88, 90–108. [Google Scholar] [CrossRef] - ANSYS Multiphysics 17.2, ANSYS Inc.: Canonsburg, PA, USA, 2017.
- Moura, P.; Carvalho, H.; Figueiredo, L.; Aires, P.; Bártolo, R. Unitary model for the analysis of bolted connections using the finite element method. Eng. Fail. Anal.
**2019**, 104, 308–320. [Google Scholar] - Díaz, C.; Victoria, M.; Martí, P.; Querin, O.M. FE model of beam-to-column extended end-plate joints. J. Constr. Steel Res.
**2011**, 67, 1578–1590. [Google Scholar] [CrossRef] - Kim, T.S.; Kuwamura, H. Finite element modeling of bolted connections in thin-walled stainless steel plates under static shear. Thin-Walled Struct.
**2007**, 45, 407–421. [Google Scholar] [CrossRef] - Chopra, A.K. Dynamics of Structures: Theory and Applications to Earthquake Engineering; Prentice-Hall: Englewood Cliffs, NJ, USA, 2007. [Google Scholar]

**Figure 4.**Model in FEM calibrated according to [10].

**Figure 5.**(

**a**) Boundary conditions in numerical model, (

**b**) contacts type in numerical model and (

**c**) elements in moment connection.

**Figure 9.**Summary of normalized moment-rotation at each east beam under different axial load levels in the column.

**Figure 12.**Summary of equivalent load vs according to rotation according to equivalent load-displacement method.

**Figure 13.**Summary of tangent stiffness vs. rotation according to equivalent load-displacement method.

**Figure 14.**Summary of secant stiffness vs. rotation according to equivalent load-displacement method.

**Figure 15.**Summary of dissipated energy vs. rotation according to equivalent load-displacement method.

**Figure 16.**Summary of equivalent damping vs. rotation according to equivalent load-displacement method.

No. | Group | Joint | Axial Load (P/Py) |
---|---|---|---|

1 | 1 beam (1B) | 1B - 00 | 0 |

2 | 1B - 25 | 25% | |

3 | 1B - 50 | 50% | |

4 | 1B - 75 | 75% | |

5 | 2 beams - corner (2BC) | 2BC - 00 | 0 |

6 | 2BC - 25 | 25% | |

7 | 2BC - 50 | 50% | |

8 | 2BC - 75 | 75% | |

9 | 2 beams - interior (2BI) | 2BI - 00 | 0 |

10 | 2BI - 25 | 25% | |

11 | 2BI - 50 | 50% | |

12 | 2BI - 75 | 75% | |

13 | 3 beams (3B) | 3B - 00 | 0 |

14 | 3B - 25 | 25% | |

15 | 3B - 50 | 50% | |

16 | 3B - 75 | 75% | |

17 | 4 beams (4B) | 4B - 00 | 0 |

18 | 4B - 25 | 25% | |

19 | 4B - 50 | 50% | |

20 | 4B - 75 | 75% |

No. | No. of cycles | Drift Angle (θ) (rad) |
---|---|---|

1 | 6 | 0.00375 |

2 | 6 | 0.005 |

3 | 6 | 0.0075 |

4 | 4 | 0.01 |

5 | 2 | 0.015 |

6 | 2 | 0.02 |

7 | 2 | 0.03 |

8 | 2 | 0.04 |

Elements Connection | Contact | Movement in Normal Direction | Movement in Tangential Direction |
---|---|---|---|

Column-Horizontal Stiffeners | Bonded | No separation | No slip |

Column-Vertical Stiffeners | Bonded | No separation | No slip |

Vertical Stiffeners-Horizontal Stiffeners | Bonded | No separation | No slip |

End Plate-Horizontal Stiffeners | Bonded | No separation | No slip |

End Plate-Vertical Stiffeners | Bonded | No separation | No slip |

End Plate-End plate | Frictional | Separation allowed | Slip allowed |

Beam-End plate, Bolt-Nut | Bonded | No separation | No slip |

Bolt- End plate, Nut-End plate | Frictionless | Separation allowed | Slip allowed |

Element | Designation | σ_{y}(MPa) | ε_{y} | σ_{u}(MPa) | ε_{u} |
---|---|---|---|---|---|

Bolts | ASTM-A-490 | 1156 | 0.00586 | 1433 | 0.14 |

Beam | ASTM-A-36 | 293 | 0.001465 | 445 | 0.24 |

Column | ASTM-A-36 | 293 | 0.001465 | 445 | 0.24 |

Horizontal diaphragms | ASTM-A-36 | 293 | 0.001465 | 445 | 0.24 |

Vertical diaphragms | ASTM-A-36 | 293 | 0.001465 | 445 | 0.24 |

End-plate | ASTM-A-36 | 293 | 0.001465 | 445 | 0.24 |

Joint | Maximum Load (kN) | Maximum Rotation (rad) | Initial Stiffness (kN/mm) | Dissipated Energy (kJ) | Maximum Equivalent Damping at 4% Drift Ratio (%) |
---|---|---|---|---|---|

1B - 00 | 155.75 | 0.050 | 2.90 | 328.71 | 34.5 |

1B - 25 | 155.75 | 0.050 | 2.89 | 318.53 | 32.8 |

1B - 50 | 155.75 | 0.050 | 2.91 | 322.87 | 33.4 |

1B - 75 | 149.63 | 0.050 | 2.91 | 314.04 | 33.5 |

2BC - 00 | 221.50 | 0.071 | 3.02 | 666.78 | 32.8 |

2BC - 25 | 221.50 | 0.071 | 3.01 | 671.03 | 33.5 |

2BC - 50 | 219.03 | 0.071 | 2.99 | 658.58 | 32.8 |

2BC - 75 | 209.13 | 0.071 | 2.99 | 653.18 | 34.5 |

2BI - 00 | 334.25 | 0.050 | 5.25 | 662.04 | 32.2 |

2BI - 25 | 336.00 | 0.050 | 5.18 | 613.86 | 31 |

2BI - 50 | 332.50 | 0.050 | 5.27 | 623.54 | 30.5 |

2BI - 75 | 337.75 | 0.050 | 5.21 | 609.25 | 30.5 |

3B - 00 | 373.70 | 0.067 | 4.54 | 976.54 | 31 |

3B - 25 | 373.70 | 0.067 | 4.57 | 982.28 | 31.3 |

3B - 50 | 373.70 | 0.067 | 4.50 | 957.35 | 31.5 |

3B - 75 | 371.75 | 0.067 | 4.52 | 900.20 | 31.3 |

4B - 00 | 475.18 | 0.071 | 5.30 | 1251.40 | 30 |

4B - 25 | 475.18 | 0.071 | 5.26 | 1250.20 | 29.8 |

4B - 50 | 475.18 | 0.071 | 5.32 | 1247.00 | 29.5 |

4B - 75 | 480.13 | 0.071 | 5.23 | 947.20 | 30.5 |

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**MDPI and ACS Style**

Gallegos, M.; Nuñez, E.; Herrera, R.
Numerical Study on Cyclic Response of End-Plate Biaxial Moment Connection in Box Columns. *Metals* **2020**, *10*, 523.
https://doi.org/10.3390/met10040523

**AMA Style**

Gallegos M, Nuñez E, Herrera R.
Numerical Study on Cyclic Response of End-Plate Biaxial Moment Connection in Box Columns. *Metals*. 2020; 10(4):523.
https://doi.org/10.3390/met10040523

**Chicago/Turabian Style**

Gallegos, Marco, Eduardo Nuñez, and Ricardo Herrera.
2020. "Numerical Study on Cyclic Response of End-Plate Biaxial Moment Connection in Box Columns" *Metals* 10, no. 4: 523.
https://doi.org/10.3390/met10040523