# Experimental Investigations and Numerical Simulations of the Vibrational Performance of Wood Truss Joist Floors with Strongbacks

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## Abstract

**:**

## 1. Introduction

^{2}for the root-mean-square acceleration and suggested the fundamental frequency should exceed 8 Hz. Khokhar [5] investigated the impact of bridging (lateral element) between the joists on the vibration performance of solid lumber joists floors. The vibration performance of wood I-joist floors was investigated by Weckendorf [6] and Weckendorf et al. [7]. Meanwhile, traditional and recent design methods to minimize timber floor vibrations were summarized by the authors. Zhang [8] and Zhang et al. [9,10,11] studied the vibration performance related to serviceability of solid timber joists, I-joists, and open metal-web joist floors system and assessed the influence of the space of the adjacent joists, sheathing and strongbacks on vibration performance. Jarnero and Jarnero et al. [12,13] studied the effects of the addition of subflooring layers and boundary conditions on vibration performance of the wood floor in a laboratory. The effects of detailed structure construction including a gypsum ceiling, battens, blocking, furring channels, and post-tensioning on the vibration performance of lightweight engineered timber floors were revealed by Bernard [14]. Recently, some studies have been focused on mass timber floor systems for long-span floor structure, such as cross-laminated timber (CLT) floors [15,16], timber–concrete composite (TCC) floors [17,18,19,20], a combination of ribs and thick panels composing a composite section [21], and so on.

## 2. Configurations of Wood Truss Joist Floor

^{3}. The OSB sheathing has orthotropic material directions with 4080 MPa for average major elastic modulus and 2080 MPa for average minor elastic modulus. The major material direction of OSB panel in-plane is for normal to the joist. The rim boards of LVL plates with the thickness of 38 mm have the average density of 600 kg/m

^{3}. The average elastic moduli of LVL plate were 13,000 MPa for longitudinal direction, and 1000 MPa for other directions. In terms of the SPF wood made for the truss joists with the average density of 560 kg/m

^{3}, the longitudinal, radial, and tangential elastic moduli were 8700, 600, and 400 MPa, respectively. For SPF strongbacks with the average density of 540 kg/m

^{3}, the longitudinal, radial, and tangential elastic moduli were 9000, 870, and 710 MPa, respectively. Five floor configurations (floors A–E) with strongbacks from zero to four were tested and modeled in the study, listed in Table 1.

## 3. Experimental Floor Test Method

#### 3.1. Vibration Mode and Frequency Testing

#### 3.2. Point Load Deflection Testing

#### 3.3. Human Induced Vibration Tests under Single Person Loading

## 4. Numerical Simulation Method

## 5. Results and Discussion

#### 5.1. Vibration Frequencies and Modes

#### 5.2. Point Load Deflections

_{l}≤ 2 mm, for l < 3 m; and d

_{l}≤ 8/l

^{1.3}, for l ≥ 3 m

_{l}represents the deflection at the floor center under a 1 kN point load. The results show that Floor D and Floor E meet the requirement based on the modeled and measured maximum displacement. Floor C is close to the serviceability requirement; the numerical estimation results meet the requirement (0.75 mm), but the measured results still had a gap of 0.02 mm to meet the requirement. Floors A and B do not meet the serviceability requirement based on the experimental measurements or numerical calculations.

#### 5.3. Floor Vibration under Single Person Walking Loading

^{2}in the simulation by a decrease ratio of 22%. The use of two strongback rows at mid-span (Floor C) had further decreased the peak acceleration to 1.44 m/s

^{2}with the decrease ratio of 43% compared to Floor A. The case of walking along L path produced higher peak acceleration, about 1.5 times than that of walking along W path at the floor center. In the aspect of L path, addition of a strongback row at mid-span (Floor B) effectively decreased the peak acceleration at point A by a decrease of 6% in the simulation. The use of two strongback rows in Floor C still had the decrease effect on peak acceleration with the decrease ratio of 25% compared to Floor A. However, addition of three strongback rows of Floor D (one for the mid-span and one each at one-third of the span) had minimal influence on decreasing the vibration accelerations; and negligible influence on the acceleration reduction is observed for use of four strongback rows of floor E (two for the mid-span and one each at one-third of the span), see Figure 22. The closer the strongback was to the mid-span, the more significant the vibration acceleration reduction at point A was. Furthermore, the strongbacks mainly reduced the vibration on point A for the direction of perpendicular to the joists (W path) and the effect on the vibration reduction of point A for the direction of parallel to the joists (L path) was relatively weak.

^{2}than that of point A (Figure 20b and Figure 25b). Similar to the displacement response at point A during vibration, the displacement response at point B for W walking path, and the L walking path is illustrated in Figure 26. It was found that the addition of strongbacks had a negligible influence on reducing the peak accelerations at point B on the sheathing between the joists, and the values were around 6 m/s

^{2}, see Figure 27.

## 6. Conclusions

- (1)
- The use of strongbacks significantly can improve the floor stiffness and lower the peak deformation of the sheathing. The use of one strongback rows at mid-span and the use of two strongback rows at mid-span effectively decreased the maximum deformation of point loading at floor center by 11% and 24%, respectively. The effect of adding strongbacks at one-third of each span on decreasing the maximum deformation at the floor center was minimal. In addition, strongbacks does not improve greatly the integrity of the floor, and the deflection influence under point loading on other joists that are three joists spaces away is minimal.
- (2)
- The strongbacks do not significantly affect the fundamental natural frequency of wood truss joist floors. The increase in the stiffness of the floors due to addition of strongbacks compensated for the increased mass of the floors. All the tested wood truss joist floors have similar fundamental frequencies of about 15 Hz. However, strongbacks with the increase of the number from zero to four influenced the higher-order mode frequencies of the wood truss joist floors.
- (3)
- Each footstep on wood truss joist floors resulted in each clear transient vibration including a stiff initial peak and quickly decays. Walking along L path (parallel to the joist) produced higher vibration response at the floor center of wood truss joist floors than that of walking along W path (perpendicular to the joist).
- (4)
- The strongbacks substantially reduced the peak acceleration of the sheathing at the joists. The closer placements of strongbacks were to the mid-span, the more significant reduction of vibration was. The use of a strongback row at mid-span effectively decreased the peak acceleration of vibration at floor center on the joists by a decrease of 22% for W path and 6% for L path. The use of two strongback rows at mid-span has further decreased the peak acceleration at floor center on the joists by 43% for W path and 25% for L path. The addition of strongbacks at one-third of each span had negligible influence on reducing the peak accelerations at floor center. Two strongback rows at mid-span perform best effect on reduction of vibration response at floor center.
- (5)
- However, the strongbacks have limits of reduction peak acceleration of the sheathing between the joists. It was found that the addition of strongbacks had a negligible influence on reducing the peak accelerations at point B on the sheathing between the joists.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Connection details for the wood truss joist floor: (

**a**) edge joists connecting to the framing walls; (

**b**) the end of the joist connecting to the framing walls.

**Figure 6.**Walking direction and path: (

**a**) perpendicular to the joist direction (W path); (

**b**) parallel to the joist direction (L path).

**Figure 18.**Walking direction and path: (

**a**) perpendicular to the joist direction (W path); (

**b**) parallel to the joist direction (L path).

**Figure 22.**Tested and simulated peak acceleration at points A for the floors: (

**a**) W path and (

**b**) L path.

**Figure 26.**Displacement responses at points B for tested floors: (

**a**) W walking path and (

**b**) L walking path.

Floor | Joist Spacing | Sheathing Thickness | Strongback Configuration | Test | Modeling |
---|---|---|---|---|---|

A | 400 mm | 15 mm | None | √ | √ |

B | 400 mm | 15 mm | One strongback row at mid-span | √ | √ |

C | 400 mm | 15 mm | Two strongback rows at mid-span | √ | √ |

D | 400 mm | 15 mm | One strongback row at mid-span and one strongback row at one-third of the span | √ | √ |

E | 400 mm | 15 mm | Two strongback rows at mid-span and one strongback row at one-third of the span | √ | √ |

Type of Connections | Directions | Disp1 (m) | Load 1 (N) | Stiffness (kN/m) |
---|---|---|---|---|

Single-shear screwed OSB panel connections | OSB minor axis (shear) | 0.001 | 807 | 807 |

OSB major axis (shear) | 0.001 | 863 | 863 |

Type of Connections | Directions | Disp1 (m) | Load 1 (N) | Stiffness (kN/mm) |
---|---|---|---|---|

Metal plate connections | Major axis (shear) | 0.000158 | 5500 | 34.80 |

Minor axis (tension) | 0.000158 | 9000 | 56.96 |

Items | SPF Truss | SPF Strongback | OSB Sheathing | LVL Rim Board |
---|---|---|---|---|

EL [MPa] | 8700 | 9000 | 4280 | 13000 |

ER [MPa] | 660 | 870 | 2080 | 1000 |

ET [MPa] | 400 | 710 | 2080 | 1000 |

GLR [MPa] | 500 | 600 | 1000 | 700 |

GLT [MPa] | 500 | 600 | 50 | 700 |

GRT [MPa] | 53 | 30 | 57 | 60 |

μLR | 0.43 | 0.03 | 0.15 | 0.335 |

μLT | 0.47 | 0.2 | 0.3 | 0.03 |

μRT | 0.2 | 0.43 | 0.15 | 0.466 |

ρ [kg/m^{3}] | 560 | 540 | 650 | 600 |

Floor | F1 (Hz) | F2 (Hz) | F3 (Hz) |
---|---|---|---|

A | 15 | 17.8 | 21 |

B | 14.8 | 18.8 | 23.4 |

C | 15 | 18.8 | 25.3 |

D | 15 | 20.1 | 25.4 |

E | 15 | 20.6 | 27.4 |

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**MDPI and ACS Style**

Shen, Y.; Zhou, H.; Xue, S.; Yan, X.; Si, J.; Guan, C.
Experimental Investigations and Numerical Simulations of the Vibrational Performance of Wood Truss Joist Floors with Strongbacks. *Forests* **2021**, *12*, 1493.
https://doi.org/10.3390/f12111493

**AMA Style**

Shen Y, Zhou H, Xue S, Yan X, Si J, Guan C.
Experimental Investigations and Numerical Simulations of the Vibrational Performance of Wood Truss Joist Floors with Strongbacks. *Forests*. 2021; 12(11):1493.
https://doi.org/10.3390/f12111493

**Chicago/Turabian Style**

Shen, Yinlan, Haibin Zhou, Shuo Xue, Xingchen Yan, Jiahao Si, and Cheng Guan.
2021. "Experimental Investigations and Numerical Simulations of the Vibrational Performance of Wood Truss Joist Floors with Strongbacks" *Forests* 12, no. 11: 1493.
https://doi.org/10.3390/f12111493