# Dynamic Properties of Timber–Concrete Composite Beams with Crossed Inclined Coach Screw Connections: Experimental and Theoretical Investigations

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Timber

^{3}and a moisture content of 11.2%. Their moisture content was determined using tests according to GB/T 1931-2009 [25], and their density was measured following the GB/T 1933-2009 [26] guidelines. For the tests, a drying oven with machine model DHG-9140(A) (101-2), produced by Yiheng Scientific Instrument Co., LTD., Shanghai, China, was used. The basic mechanical properties of glulam were obtained using material tests according to EN 408 [27]. The dimensions of the samples used in the tensile, compressive, and shear tests were 30 mm × 10 mm × 300 mm (height × width × length), 50 mm × 50 mm × 300 mm, and 55 mm × 32 mm × 300 mm, respectively. A testing machine produced by MTS System (China) Co., Ltd. (Shanghai, China) with a maximum capacity of 300 kN, was used for the material tests. The corresponding test results are shown in Table 1.

#### 2.1.2. Concrete

#### 2.1.3. Steel

#### 2.2. Specimens

#### 2.2.1. Shear Connectors

#### 2.2.2. Timber–Concrete Composite (TCC) Beams

_{c}/l is the width-to-span ratio, which was 0.2, 0.3, and 0.4 in this study. Therefore, the TCC beams were named after b

_{c}/l, which are TCC0.2, TCC0.3, and TCC0.4, respectively. Also, this study tested two different concrete slab heights, 100 mm and 120 mm. The TCC beam with a 100 mm high concrete slab was designated as TCC0.4; while the TCC beam with a 120 mm thick concrete slab was specified as TCC0.4-hc120.

#### 2.3. Test Set-Up

#### 2.4. Equipment and Experimental Procedure

## 3. Experimental Results

#### 3.1. Push-Out Test of Connectors

#### 3.2. Dynamic and Bending Test of the TCC Beams

_{1(exp)}denotes the measured values of fundamental frequencies of the first flexural modal, and ζ

_{1}was used to indicate the first modal damping ratio of the TCC beams. The specific test results are listed in Table 5.

_{(exp)}. The beams were tested to the ultimate load; P

_{u}is the ultimate load and presents the failure mode, as shown in Figure 13.

## 4. Analytical Investigation

_{1}) should be greater than 8 Hz. If f

_{1}is lower than 8 Hz, it is easy to cause discomfort to the users, and even footfall will cause resonance of the floor, causing safety problems [6,7,32,33]. For example, Eurocode 5 [10] stipulates that the f

_{1}should be greater than 8 Hz. If the f

_{1}of the floor is estimated to be lower than 8 Hz, special analysis and design should be carried out. As one of the important indicators of the dynamic properties of the floor, the fundamental frequency is an important indicator to evaluate whether the vibration performance of the floor is good. Therefore, the analysis of the f

_{1}of the TCC beam is an important task of this study.

#### 4.1. Theoretical Calculation

_{1}) of the floor system, as shown in Formula (1):

_{eff}, which is based on the ‘γ-method’, as shown in Formula (2):

_{c}and A

_{t}are the section area of concrete slab and timber beam, respectively; a

_{c}and a

_{t}are the distance between the centroid of concrete slab or timber beam to the neutral axis of the composite section, respectively; s is the distance of shear connectors; K is the slip stiffness of shear connections; and L is the clear span of beams.

_{1}) of the simply supported beams, as shown in Formula (4):

_{s}and K

_{u}are the slip moduli of the connector at the serviceability limit and the ultimate state, respectively. When studying the vibration behavior of beams, the values of K

_{s}were used to calculate the (EI)

_{eff}of TCC beams in the serviceability limit state. Using the Eurocode 5 and Murray methods, the semi-theoretical predicted values f

_{1(EC5)}and f

_{1(M)}of the fundamental frequencies of the TCC beams can be obtained, respectively, as shown in Table 6. Additionally, Tao et al. [23] have provided a theoretical calculation method of connector stiffness. Based on the connection stiffness calculation method, the full-theoretical predicted values of the fundamental frequencies can be obtained, as the values of f′

_{1(EC5)}and f′

_{1(M)}shown in Table 6.

#### 4.2. Discussion

#### 4.2.1. Fundamental Frequency

_{1}> 8 Hz for the floor can be satisfied. From the comparison between the measured values and the calculated values, the value of the maximum difference between experimental frequency and full calculated frequency is 2.13 Hz, it can be seen that the calculation methods in the Eurocode 5 and Murray methods have good reliability.

#### 4.2.2. Effect of the Dimensions of Concrete Slabs

_{eff}and (EI)

_{(exp)}of TCC beams increases, while the fundamental frequency decreases both in the calculated value and in the measured value. According to Equation (1), although the stiffness of the concrete slab increases with the increase in the slab width, the increase in self-weight caused by the increase in slab width still reduces the fundamental frequency of the TCC beams. Similarly, when the slab heights of the concrete are increased from 100 mm to 120 mm, the flexural stiffness (EI)

_{eff}of the TCC beam also increases significantly, but its fundamental frequency still decreases. Therefore, it can be preliminarily identified that the self-weight of concrete slab changes, caused by the dimension change, has a greater effect on the fundamental frequency of the TCC beams than the flexural stiffness (EI)

_{eff}, and the values of fundamental frequency using the Murray method have a similar pattern. In addition, the damping ratio decreases significantly as the width and height size of the concrete slab increase.

#### 4.2.3. Effect of the Connection

_{eff}and (EI)

_{(exp)}of the TCC beam decreases when reducing the shear stiffness of the connectors. Meanwhile, when changing the screw diameter from 16 mm to 12 mm, the fundamental frequency of the TCC beams decreases smoothly, but the damping ratio increases notably, according to Table 6. This indicates that under the same conditions, the natural frequency of the specimen is inversely proportional to the damping ratio.

## 5. Conclusions

_{1}> 8 Hz for floor comfort.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 9.**Bending test set-up. Reprinted with permission from Ref. [30]. 2023, Elsevier.

**Figure 10.**The time domain signals of acceleration response: (

**a**) TCC0.2; (

**b**) TCC0.3; (

**c**) TCC0.4; (

**d**) TCC0.4-CO12; (

**e**) TCC0.4-hc120.

**Figure 11.**The frequency spectrum: (

**a**) TCC0.2; (

**b**) TCC0.3; (

**c**) TCC0.4; (

**d**) TCC0.4-CO12; (

**e**) and TCC0.4-hc120.

**Figure 12.**Load–deflection curves. (Exp.: experimental results). Reprinted with permission from Ref. [30]. 2023, Elsevier.

Properties | E_{t} (MPa) | f_{cl} (MPa) | f_{tl} (MPa) | f_{tp} (MPa) |
---|---|---|---|---|

Value | 13,500 | 38.2 | 39.4 | 9.4 |

_{t}is the modulus of elasticity, f

_{cl}is the compression strength in the longitudinal direction, f

_{tl}is the tension strength in the longitudinal direction, and f

_{tp}is the shear strength parallel to the grain.

Properties | E_{c} (MPa) | f_{c} (MPa) | f_{t} (MPa) |
---|---|---|---|

Value | 33,000 | 28.3 | 2.5 |

_{c}is the elastic modulus of concrete, f

_{c}is the compression strength, and f

_{t}is the tension strength.

Specimen Code | b_{c}/l | b_{c} (mm) | h_{c} (mm) | Connector |
---|---|---|---|---|

TCC0.2 | 0.2 | 930 | 100 | CBIS16-200 |

TCC0.3 | 0.3 | 1395 | 100 | CBIS16-200 |

TCC0.4 | 0.4 | 1860 | 100 | CBIS16-200 |

TCC0.4-CO12 | 0.4 | 1860 | 100 | CBIS12-200 |

TCC0.4-hc120 | 0.4 | 1860 | 120 | CBIS16-200 |

_{c}is the concrete slab width, h

_{c}is the concrete slab height, l is the span of the beam, and b

_{c}/l is the concrete slab width-to-span ratio.

Connector Code | Screw Diameter (mm) | Screw Length (mm) | Penetration Depth (mm) | K_{s}(kN/mm) | K_{u}(kN/mm) | F_{max}(kN) |
---|---|---|---|---|---|---|

CBIS16-200 | 16 | 200 | 135 | 42.92 | 39.31 | 73.50 |

CBIS12-200 | 12 | 200 | 135 | 40.54 | 34.30 | 58.40 |

_{s}is the slip modulus of the connection at the serviceability limit, K

_{u}is the slip modulus of the connection at the ultimate state, and F

_{max}is the shear capacity of the connection.

Specimen Code | (EI)_{(exp)}(×10 ^{12} N⋅mm) | P_{u} (kN) | d (mm) | f_{1(exp)} (Hz) | ζ_{1} (%) |
---|---|---|---|---|---|

TCC0.2 | 25.6 | 313.7 | 9.3 | 25.60 | 2.9 |

TCC0.3 | 27.4 | 310.6 | 8.5 | 21.85 | 2.7 |

TCC0.4 | 28.8 | 316.7 | 8.3 | 19.54 | 2.2 |

TCC0.4-CO12 | 28.2 | 273.2 | 7.1 | 19.04 | 2.8 |

TCC0.4-hc120 | 28.3 | 242.2 | 6.6 | 18.07 | 2.1 |

_{(exp)}is the bending stiffness, d is the mid-span deflection at 0.4 P

_{u,}P

_{u}is the ultimate load, f

_{1(exp)}is the measured values of fundamental frequencies of the first flexural modal, and ζ

_{1}is the first modal damping ratio of the TCC beams.

Specimen Code | (EI)_{eff} (×10^{12} N·mm) | (EI)_{(exp)} (×10^{12} N·mm) | f_{1(EC5)} (Hz) | f′_{1(EC5)}(Hz) | f_{1(M)} (Hz) | f′_{1(M)}(Hz) | f_{1(exp)} (Hz) | ζ_{1} (%) |
---|---|---|---|---|---|---|---|---|

TCC0.2 | 26.5 | 25.6 | 23.08 | 23.71 | 22.85 | 23.47 | 25.60 | 2.9 |

TCC0.3 | 28.1 | 27.4 | 19.78 | 20.23 | 19.58 | 20.11 | 21.85 | 2.7 |

TCC0.4 | 29.5 | 28.8 | 17.74 | 18.21 | 17.56 | 18.03 | 19.54 | 2.2 |

TCC0.4-CO12 | 29.0 | 28.2 | 17.58 | 17.25 | 17.40 | 17.08 | 19.04 | 2.8 |

TCC0.4-hc120 | 34.5 | 28.3 | 17.58 | 18.02 | 17.40 | 17.84 | 18.07 | 2.1 |

_{eff}is the bending stiffness of the TCC beams calculated based on the γ-method, (EI)

_{(exp)}is the experimental bending stiffness of the TCC beams, f

_{1(EC5)}is the fundamental frequency calculated according to Eurocode 5 with the experimental stiffness of the connector, f

_{1(M)}is the fundamental frequency calculated according to Murray [34] with the experimental stiffness of the connector, f′

_{1(EC5)}is the fundamental frequency calculated according to Eurocode 5 with the theoretical stiffness of the connector, and f′

_{1(M)}is the fundamental frequency calculated according to Murray [34] with the theoretical stiffness of the connector.

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**MDPI and ACS Style**

Wen, B.; Tao, H.; Shi, B.; Yang, H.
Dynamic Properties of Timber–Concrete Composite Beams with Crossed Inclined Coach Screw Connections: Experimental and Theoretical Investigations. *Buildings* **2023**, *13*, 2268.
https://doi.org/10.3390/buildings13092268

**AMA Style**

Wen B, Tao H, Shi B, Yang H.
Dynamic Properties of Timber–Concrete Composite Beams with Crossed Inclined Coach Screw Connections: Experimental and Theoretical Investigations. *Buildings*. 2023; 13(9):2268.
https://doi.org/10.3390/buildings13092268

**Chicago/Turabian Style**

Wen, Bo, Haotian Tao, Benkai Shi, and Huifeng Yang.
2023. "Dynamic Properties of Timber–Concrete Composite Beams with Crossed Inclined Coach Screw Connections: Experimental and Theoretical Investigations" *Buildings* 13, no. 9: 2268.
https://doi.org/10.3390/buildings13092268