# A Component-Based Model for Novel Modular Connections with Inbuild Component

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## Abstract

**:**

## 1. Introduction

- (1)
- the component-based model for novel modular connections was developed based on parameter analysis results.
- (2)
- the force-deformation response of each component was determined with the help of the finite element method.
- (3)
- assembly of all components to overall rotational joint. At last, the results of the simplified model were compared with the results of the elaborate finite element model.

## 2. Parameter Analysis

#### 2.1. Establishment and Validation of FEM

#### 2.2. Parameter Setting

#### 2.3. Parameter Analysis Results

#### 2.3.1. Thickness of Side Plate and Bolts Preload

#### 2.3.2. Thickness of Beam End Plate

#### 2.3.3. The Height and Thickness of the Inbuild Component

#### 2.3.4. Allowable Construction Errors

#### 2.3.5. Dimension of Floor and Ceiling Beams

## 3. Component-Based Model

#### 3.1. Component Identification

- (1)
- The rigid body assumption was made to beam end plate.
- (2)
- The allowable construction errors and relative dislocation between the upper and lower column were considered as the mechanical properties of intramodule connections (will be discussed in Section 3.2.3).
- (3)
- Based on assumption (2), only rotational deformation will be considered in intermodule connections.
- (4)
- The enhancement stiffeners’ effect on connections was neglected.

#### 3.2. Characteristics of Components

#### 3.2.1. Joint Panel (Shear Behavior)

#### 3.2.2. Converged Section Component

#### 3.2.3. Interaction Mechanism

#### 3.3. Component Identification

## 4. Validation

#### 4.1. Intramodule Connections

#### 4.2. Global Connections

## 5. Conclusions

- (1)
- Bolt preload, side plate thickness and inbuild component height had little influence on mechanical properties of novel modular connections. The thickness of the inbuild component affected the initial stiffness and continuity of the connection but had no effect on the ultimate bending capacity of the joint. The allowable construction error mainly affected the initial stiffness of the joint but did not change the ultimate bending strength of the joint. The height of twin beams was proportional to the initial stiffness and ultimate bending capacity of the novel modular building connections. When the height of the floor beam was equal to that of the ceiling beam, the continuity index of the connections was better. When the height of floor beam was larger than the ceiling height, the rotational difference between upper and lower columns increased and the continuity of connections decreased.
- (2)
- A component-based model for novel modular connections was established. The advantage of the model was that it can describe the deformation of intramodule connections and intermodule connections, respectively. The key factor of the model was the converged section component, and its force–displacement relationship under various parameters was obtained by the fitting method. The interaction mechanism between inbuild component and columns was analyzed. It was found that the inbuild component improved the mechanical properties of the converged section component under compression but had little effect on the mechanical properties under tension. Taking the allowable construction errors into consideration, the deformation mode can be divided into three stages which would cause a “slip” in moment-rotation curves of a related model.
- (3)
- A simplified finite element model of intramodule connection was built and compared with the finite element model meshed by “shell element”. For connections without the inbuild component, the failure mode was the tension (compression) failure at the column open end (called “II” region in the paper). The inbuild component can improve the mechanical properties of the intramodule connection under negative bending moment by protecting the “II” from compression failure. When the connection was under positive bending moment, the initial stiffness was increased by improving the mechanical properties of “I” region, but the failure mode remained unchanged. The curves with construction error were between that without the inbuild component and without construction error. In general, the simplified finite element model could accurately predict the mechanical properties and behavior of intramodule connections.
- (4)
- The simplified finite element model of global novel modular connections was built and compared with the refined finite element model. Length and section characteristics of the “beam” element that represented the intermodule connection was clearly stated. The conservative estimation method was proposed to evaluate the weakening effect of allowance construction error on initial stiffness of global modular connections. The average error of the simplified finite element model about initial stiffness and ultimate bending moment was 3.9% and 9.3%, respectively. In general, the proposed model can predict the mechanical behavior of novel modular building connections within the acceptable margin of error.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Loading and support condition of novel modular connections: (

**a**) Finite element model; (

**b**) Test specimens.

**Figure 7.**Parameters setting of finite element model: (

**a**) Relative dislocation between units; (

**b**) Relative rotation between units.

**Figure 9.**Moment-relative dislocation curves of connections: (

**a**) Thickness of side plate; (

**b**) Bolts preload.

**Figure 10.**Continuity index-moment curves of connections: (

**a**) Thickness of side plate; (

**b**) Bolts preload.

**Figure 17.**Moment-rotation curves: (

**a**) The height of inbuild component; (

**b**) The thickness of inbuild component.

**Figure 18.**Moment-relative dislocation t curves of connections: (

**a**) The height of inbuild component; (

**b**) The thickness of inbuild component.

**Figure 19.**Continuity index-moment curves of connections: (

**a**) The height of inbuild component; (

**b**) The thickness of inbuild component.

**Figure 31.**The component deformation mode of novel modular connections: (

**a**) The skeleton; (

**b**) Converging section component; (

**c**) Diagonal springs; (

**d**) Beam connection; (

**e**) The beam element (intermodule connection).

**Figure 39.**Spring model for understanding interaction mechanism between inbuild component and converged section component.

**Figure 41.**Finite element model of intramodule connection for validation. (

**a**) Simplified finite element model; (

**b**) Refined finite element model.

**Figure 42.**Moment-rotation curves of intramodule connections: (

**a**) Under positive bending moment without inbuild component; (

**b**) Under positive bending moment with inbuild component; (

**c**) Under negative bending moment with inbuild component; (

**d**) Under negative bending moment with inbuild component and take construction errors into consideration.

Specimen No. | Floor Beam | Ceiling Beam | Column | Stiffener Thickness |
---|---|---|---|---|

T1 | [ 250 $\times $ 140 $\times $ 10 | [ 200 $\times $ 140 $\times $ 10 | □150 $\times $ 150 $\times $ 8 | None |

T2 | [ 250 $\times $ 140 $\times $ 10 | [ 250 $\times $ 140 $\times $ 10 | □150 $\times $ 150 $\times $ 8 | None |

T3 | [ 250 $\times $ 140 $\times $ 10 | [ 200 $\times $ 140 $\times $ 10 | □150 $\times $ 150 $\times $ 8 | 12 mm |

No. | a | b | c | d | e | f | z_{0} | R^{2} |
---|---|---|---|---|---|---|---|---|

${f}_{1}$ | 0.00835 | 7.75261 | 0.000219 | 3.24409 | 0.06114 | 0.996 | ||

${f}_{2}$ | 1.0174 | 0.990 | ||||||

${f}_{3}$ | 1.03139 | 0.43665 | 0.26507 | 0.11452 | 0.25916 | 0.991 | ||

${g}_{1}$ | 0.000385 | 0.00942 | −0.02198 | 0.990 | ||||

${g}_{2}$ | 0.31558 | 0.76463 | −0.07116 | 0.990 | ||||

${g}_{3}$ | −3.891 | 1.4221 | 3.40341 | 0.991 |

Joint No. | Initial Stiffness $(\mathbf{k}\mathbf{N}\mathbf{m}/\mathbf{r}\mathbf{a}\mathbf{d})$ | Ultimate Bending Moment $\left(\mathbf{k}\mathbf{N}\mathbf{m}\right)$ | ||||
---|---|---|---|---|---|---|

Simplified | FEM | Error | Simplified | FEM | Error | |

B250 | 13,180 | 12,438 | +5.9% | 111 | 115 | −3.5% |

B225 | 10,029 | 9860 | +1.71% | 105 | 99 | 6.1% |

B200 | 7896 | 7650 | +3.2% | 90 | 84 | 7.1% |

B250-P | 13,937 | 13,518 | +3.1% | 119 | 123 | −3.3% |

B225-P | 10,714 | 10,734 | −0.19% | 107 | 104 | 2.9% |

B200-P | 8362 | 8318 | +0.53% | 91 | 87 | 4.6% |

B250-P | 14,796 | 14,603 | −1.3% | 157 | 167 | −6.0% |

B225-P | 11,316 | 11,606 | −2.5% | 128 | 146 | −12.3% |

B200-P | 8849 | 9022 | −1.9% | 113 | 125 | 9.6% |

**Table 4.**Comparison between the simplified model and the finite element model of novel modular connections.

Joint No. | Initial Stiffness $(\mathbf{k}\mathbf{N}\mathbf{m}/\mathbf{r}\mathbf{a}\mathbf{d})$ | Ultimate Bending Moment $\left(\mathbf{k}\mathbf{N}\mathbf{m}\right)$ | ||||
---|---|---|---|---|---|---|

Simplified | FEM | Error | Simplified | FEM | Error | |

F250C250M | 20,268 | 21,194 | −4.37% | 250 | 275 | −9.10% |

F250C225M | 23,898 | 24,717 | −3.31% | 265 | 285 | −7.03% |

F250C200M | 25,319 | 25,410 | −0.36% | 275 | 310 | −11.29% |

F225C225M | 20,836 | 22,878 | −8.9% | 234 | 261 | −10.34% |

F225C200M | 18,582 | 20,682 | −10.15% | 220 | 245 | −10.20% |

F200C200M | 16,350 | 17,375 | −5.90% | 206 | 223 | −7.62% |

G1-M | 15,195 | 14,880 | 2.12% | 245 | 272 | −9.93% |

G2-M | 11,946 | 12,346 | −3.24% | 245 | 271 | −9.59% |

G3-M | 10,745 | 10,861 | −1.07% | 245 | 269 | −8.92% |

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**MDPI and ACS Style**

Ma, R.; Xia, J.; Chang, H.; Xu, B. A Component-Based Model for Novel Modular Connections with Inbuild Component. *Appl. Sci.* **2021**, *11*, 10503.
https://doi.org/10.3390/app112110503

**AMA Style**

Ma R, Xia J, Chang H, Xu B. A Component-Based Model for Novel Modular Connections with Inbuild Component. *Applied Sciences*. 2021; 11(21):10503.
https://doi.org/10.3390/app112110503

**Chicago/Turabian Style**

Ma, Renwei, Junwu Xia, Hongfei Chang, and Bo Xu. 2021. "A Component-Based Model for Novel Modular Connections with Inbuild Component" *Applied Sciences* 11, no. 21: 10503.
https://doi.org/10.3390/app112110503