# Modal Parameter Identification and Comfort Assessment of GFRP Lightweight Footbridges in Relation to Human–Structure Interaction

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction and Background

## 2. Summary of the Examined Lightweight Footbridges

## 3. Modal Testing, Vibration and Comfort Analysis Methods

#### 3.1. iDynamics Based Smartphone Accelerometer Data Collection

^{2}and 80 m/s

^{2}can be registered, widely covering the range of expected values.

_{Fmax}directly from the vibration velocity history, according to the simplified method described in DIN 4150-2 [75,76]. In the calculation of the KB

_{Fmax}according to [76], the c

_{F}constant is by default set to 0.8, and this value is adopted in the post-processing of the vibration data. Before exporting the vibration data, a band-pass filter around the estimated first natural flexural frequency (i.e., +0.5 Hz and −0.5 Hz) of the bridge is applied to the raw vibration data to eliminate any second-order effects (e.g., resulting from the vibration of local deck elements).

#### 3.2. First and Second Measurement Sets of Heel Tests

#### 3.3. Modal Analysis

#### 3.3.1. First Natural Flexural Frequency

#### 3.3.2. Structural Damping Ratio

_{TC}) and footbridge.

#### 3.4. Comfort Analysis of Lightweight GFRP and Steel Footbridges

^{2}) for a time period of 100 s.

## 4. Results of Parameter Identification of Lightweight GFRP and Steel Footbridges

#### 4.1. Heel Tests: First Measurement Set

#### 4.1.1. First Natural Flexural Frequency

#### 4.1.2. Structural Damping Ratio

#### 4.2. Heel Test: Second Measurement Set

#### 4.2.1. First Natural Flexural Frequency

#### 4.2.2. Structural Damping Ratio

#### 4.3. Dynamic Vibration Tests

#### 4.3.1. Comfort Assessment during Walking

^{2}, which according to the JRC document for the design of lightweight footbridges [60] can be classified as maximum comfort (comfort class 1—CC1: a

_{vert.}< 0.5 m/s

^{2}) [81].

#### 4.3.2. Comfort Assessment during Jogging

^{2}, corresponding from medium (0.5 m/s

^{2}> a

_{vert}. > 1.0 m/s

^{2}) over minimal comfort (1.0 m/s

^{2}> a

_{vert.}> 2.5 m/s

^{2}) to discomfort (a

_{vert.}> 2.5 m/s

^{2}) according to the JRC document [81]. The relative acceleration increase as a function of the pedestrian density is shown in Figure 22.

^{2}.

## 5. Discussion of the Modal Parameters and Comfort Assessment

#### 5.1. General Observations

^{2}with increasing pedestrian density. The decrease mainly depends on the structural mass and thus the dimensions of the bridge in question. These findings are in accordance with the formulas for the first natural flexural frequency of [86] as shown in Figure 25, where the addition of non-structural mass by the pedestrians on the bridge causes a reduction in the natural flexural frequency. The magnitude of the reduction in the first natural flexural frequency depends on the ratio between the total non-structural mass of the pedestrians to the mass of the bridge, where the total mass of the pedestrians is limited by the usable surface area of the bridge deck.

^{2}. The effect of the location of the pedestrians in the second set is detectable but limited [51]. This localized dynamic loading causes localized areas of higher structural damping as the bridge dissipates more energy via the pedestrians on the bridge, which in turn absorb this energy into the body ligaments to accommodate the increased dynamic response. The magnitude of the absorbed energy, and consequently the increase in the structural damping ratio of the bridge, is strongly dependent on the number and positioning (static or dynamic) of the pedestrians on the bridge deck.

#### 5.2. Relation between Modal Parameters and Vertical Accelerations

_{0}> 5 Hz [58]) does not necessarily lead to an acceptable comfort level, certainly for the load case of jogging. For example, the GFRP footbridge at Puurs (P_GFRP) and the steel footbridge at Sinaai (S_Steel) have an initial value of the first natural frequency (only the operator on the bridge deck) of, respectively, 3.81 Hz and 4.69 Hz, which are lower than 5 Hz, but they will not have the largest vertical accelerations under the load cases of walking and jogging. It can be concluded that the guidelines specified in Eurocode 0 do not apply to the comfort analysis of lightweight footbridges and that, in absence of better guidelines, additional in situ vibration analyses should be performed on this type of bridge.

## 6. Analytical Comparison

#### 6.1. First Natural Flexural Frequency

#### 6.2. Comfort Analysis

_{d,vert}) calculated according to [81] for different pedestrian densities and different structural damping ratios (i.e., 0.5% and 1.0% according to CUR96:2019 and the structural damping ratio according to the interpolation in Figure 26) are presented in Figure 27. In addition to the calculated values, the measured maximum, RMS and 95 percentile values of the vertical accelerations for four pedestrian densities for the load case of walking for the GFRP footbridge in Puurs (P_GFRP) are shown with the triangular, square and circular marker, respectively.

_{d,vert}< 0.5 m/s

^{2}) according to [81], can be obtained for very small pedestrian densities (i.e., d

_{TC}< 0.01 P/m

^{2}). Indeed, the vertical accelerations will rise quickly and soon reach comfort class 4 with discomfort at a pedestrian density of 0.11 P/m

^{2}(≈1P) and 0.24 P/m

^{2}(≈2P) for 0.5% and 1.0%, respectively.

^{2}until 0.21 P/m

^{2}, after which it will be limited to maximum comfort class 3 (i.e., 1.0 m/s

^{2}< a

_{d,vert}< 2.5 m/s

^{2}) with minimum comfort. These predictions are closer to the actual measured maximum vertical acceleration values. It can be argued that better agreement between analytically calculated and measured maximum vertical accelerations can be found for the walking load case if experimentally obtained values of the structural damping ratio that take into account the human–structure interaction are used, although the predictions still overestimate the actual vibration levels. For the jogging load case, there are currently no guidelines. In view of the observations made in Section 4.3.2, this is a lack in the regulations.

## 7. Conclusions

- The basic value of the first natural flexural frequencies for the GFRP footbridges is between 3.8 Hz and 12.5 Hz, and for the steel footbridges, it is between 4.5 Hz and 8.8 Hz. The first natural frequency will decrease by 2% to 20% with increasing pedestrian densities up to 0.5 P/m
^{2}. The initial values of the structural damping ratio with only the operator on the bridge deck are between 3.0% and 8.0% for the GFRP footbridges and between 1.0% and 6.5% for the steel footbridges. The structural damping ratio will increase by a factor between 1.5 and 5.5 with increasing pedestrian density at 0.5 P/m^{2}. In addition, the position of the pedestrians on the bridge deck has a small but noticeable influence on the increase in the structural damping ratio. The position of the pedestrians on the bridge deck influences the dynamic loading pattern and, consequently, the bridge’s response. For example, a large group of pedestrians walking in unison or concentrated in a specific area can cause localized dynamic loading and excite specific modes of vibration in the bridge. This can lead to localized areas of higher structural damping. Furthermore, pedestrians positioned near structural members or sensitive regions of the bridge may cause higher dynamic responses in those areas, affecting the overall damping behaviour of the structure. These observations point at significant human–structure interaction for small lightweight footbridges. - The vertical accelerations are acceptable for the walking load case (CC1) but quickly become unacceptable for the jogging load case (CC3 and CC4). In the international guidelines, only the accelerations for walking are considered. As a result of the increasing damping, the experimentally measured 95 percentile vertical acceleration values do not increase proportionally with increasing pedestrian density, contradicting international guidelines. Excluding human–structure interaction therefore leads to uneconomic designs of lightweight footbridges. Despite the high basic first natural flexural frequency (f
_{0}> 5 Hz) of some of the tested lightweight GFRP and steel footbridges, the comfort will be minimal (CK3) or even worse for the jogging load case. The statement of Eurocode 0, declaring that no check of the vibrations should be carried out if the first natural flexural frequency is larger than 5 Hz, is therefore not valid for these lightweight footbridges. It is recommended to always carry out an in situ check of the vibration behaviour and comfort. - Good agreement between calculated and measured first natural flexural frequency values for the GFRP bridge in Puurs can be obtained by the analytical formula from the Dutch guideline CUR96:2019. Following the current guidelines in combination with the recommended damping ratios (0.5% and 1.0%) for GFRP bridges stated in CUR96:2019 clearly overestimates the vertical accelerations for the walking load case. However, if experimentally obtained pedestrian density-dependent structural damping ratio values are used, better agreement can be obtained between the analytically predicted and the experimentally measured maximum acceleration values for the walking load case.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Test setup and distribution of pedestrians during load case LC1 (

**top**) and LC2 (

**bottom**) of set 2.

**Figure 4.**Filtered vibration data in the three main directions of a heel test with one pedestrian on the bridge deck for the GFRP footbridge in Puurs (GFRP_P).

**Figure 5.**Logarithmic decrement of the second vibration based on the heel test with one person on the bridge deck for the GFRP footbridge in Puurs (GFRP_P).

**Figure 7.**Absolute values of the vertical Z-accelerations and indication of the maximal, RMS and 95 percentile value for the GFRP footbridge in Puurs (GFRP_P) with 35 jogging pedestrians (0.50 P/m

^{2}).

**Figure 13.**Relative ratio of LC1/LC2 for the first natural flexural frequency for the footbridges of set 2.

**Figure 16.**Relative ratio of LC1/LC2 for the structural damping ratio of the footbridges of the second set.

**Figure 18.**Maximum, RMS and 95 percentile values of vertical acceleration during walking and jogging on the GFRP footbridge in Puurs (GFRP_P) for different pedestrian densities.

**Figure 20.**Relative vertical accelerations in function of the pedestrian density of the dynamic vibration test with the walking load case.

**Figure 22.**Relative vertical accelerations in function of the relative increase in pedestrian density of the dynamic vibration test with the jogging load case.

**Figure 25.**Evolution of the first natural flexural frequency for the GFRP footbridge in Puurs (GFRP_P): measured vs. calculated.

**Figure 26.**Evolution and linear interpolation of the structural damping ratio for the GFRP footbridge in Puurs (GFRP_P).

**Figure 27.**Comparison of measured and predicted accelerations for the GFRP footbridge in Puurs (GFRP_P).

No. | Set | Year | Location | Material | Abbreviation | Length L (m) | Width W (m) | Surface Area A (m ^{2}) |
---|---|---|---|---|---|---|---|---|

1 | 1 | 2020 | Waregem | GFRP | GFRP_W | 10.00 | 4.00 | 40.00 |

2 | 1 | 2019 | Puurs | GFRP | GFRP_P | 16.60 | 4.20 | 69.72 |

3 | 1 | 2017 | Oudenaarde | Steel | Steel_O | 14.00 | 2.15 | 30.10 |

4 | 1 | 2017 | Sinaai | Steel | Steel_S | 17.50 | 3.30 | 57.75 |

5 | 2 | 2018 | Tremelo | GFRP | GFRP_T | 10.80 | 3.00 | 32.40 |

6 | 2 | 2012 | Tremelo | Steel | Steel_T | 33.20 | 3.00 | 99.60 |

7 | 2 | 2018 | Beersel | GFRP | GFRP_B | 7.00 | 2.00 | 14.00 |

8 | 2 | 2020 | Beersel | Steel | Steel_B | 10.00 | 2.20 | 22.00 |

**Table 2.**Number of pedestrians and corresponding pedestrian densities during the dynamic vibration tests.

No. | MC | Bridge | # Pedestrians (-) (Pedestrian Density (P/m^{2})) | ||||
---|---|---|---|---|---|---|---|

DT1 | DT2 | DT3 | DT4 | DT5 | |||

1 | 1 | GFRP_W | 4 (0.10) | 8 (0.20) | 20 (0.50) | 36 (0.90) | - |

2 | 1 | GFRP_P | 4 (0.06) | 7 (0.10) | 16 (0.23) | 24 (0.34) | - |

3 | 1 | Steel_O | 7 (0.23) | 14 (0.47) | 35 (1.16) | 42 (1.40) | - |

4 | 1 | Steel_S | 6 (0.10) | 12 (0.21) | 29 (0.50) | 42 (0.73) | - |

5 | 2 | GFRP_T | 4 (0.12) | 7 (0.22) | 10 (0.31) | 17 (0.52) | 33 (1.02) |

6 | 2 | Steel_T | 10 (0.10) | 15 (0.15) | 20 (0.20) | 25 (0.25) | 30 (0.30) |

7 | 2 | GFRP_B | 2 (0.14) | 3 (0.21) | 4 (0.29) | 7 (0.50) | 14 (1.00) |

8 | 2 | Steel_B | 3 (0.14) | 5 (0.23) | 7 (0.32) | 11 (0.50) | 22 (1.00) |

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**MDPI and ACS Style**

Uyttersprot, J.; De Corte, W.; Van Paepegem, W.
Modal Parameter Identification and Comfort Assessment of GFRP Lightweight Footbridges in Relation to Human–Structure Interaction. *J. Compos. Sci.* **2023**, *7*, 348.
https://doi.org/10.3390/jcs7090348

**AMA Style**

Uyttersprot J, De Corte W, Van Paepegem W.
Modal Parameter Identification and Comfort Assessment of GFRP Lightweight Footbridges in Relation to Human–Structure Interaction. *Journal of Composites Science*. 2023; 7(9):348.
https://doi.org/10.3390/jcs7090348

**Chicago/Turabian Style**

Uyttersprot, Jordi, Wouter De Corte, and Wim Van Paepegem.
2023. "Modal Parameter Identification and Comfort Assessment of GFRP Lightweight Footbridges in Relation to Human–Structure Interaction" *Journal of Composites Science* 7, no. 9: 348.
https://doi.org/10.3390/jcs7090348