Vibration serviceability assessment of the world's longest suspended footbridge in 2020

1 Vibration serviceability assessment of the world's longest suspended 1 footbridge in 2020 2 António Tadeua,b,*, António Romeroc, Sara Diasa, Filipe Pedroa, Michael Bretta,d, Miguel 3 Serraa, Pedro Galvínc, e, Filipe Bandeiraa 4 aItecons - Institute for Research and Technological Development in Construction, Energy, Environment and 5 Sustainability, Rua Pedro Hispano s/ n., 3030-289 Coimbra, Portugal 6 bUniversity of Coimbra, ADAI - LAETA, Department of Civil Engineering, University of Coimbra, Pólo II, Rua 7 Luís Reis Santos, 3030-788 Coimbra, Portugal 8 cEscuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, ES- 9 41092 Sevilla, Spain 10 dUniversity of Coimbra, ADAI - LAETA, Department of Mechanical Engineering, University of Coimbra, Pólo 11 II, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal 12 eENGREEN - Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, 13 Camino de los Descubrimientos s/n, ES-41092 Sevilla, Spain 14 15 * Corresponding author. e-mail: [email protected] 16 Abstract 17 This paper investigates the vibrations induced by humans through in situ behaviour tests of the 18 516 Arouca footbridge (Portugal), the world's longest span in 2020 (516 m). The study consists 19 of in situ experimental tests in which the structure was subjected to wind and pedestrian loads. 20 The bridge is first described, to provide design and construction details, after which its dynamic 21 behaviour is evaluated. The estimated natural frequencies were found to be similar to those 22 previously computed by the finite element method. In addition, modal damping ratios and 23 scaling factors are given. The dynamic responses due to pedestrian loads are then analysed. The 24 2 damping ratios were found to increase with higher structural response, which highlights the 1 dependence of the damping ratio on the amplitude of the structural response. 2 Pedestrian comfort was evaluated by analysing the amplitudes and accelerations of the 3 vibrations and complemented by applying a survey to the visitors. The results of the in situ tests 4 showed that the bridge can provide users with a challenging and rewarding experience as they 5 cross it, without suffering displacements and accelerations that they might find unnerving. 6 Keywords: suspended footbridge; FE model; in situ testing; experimental analysis; modal 7 identification; pedestrian traffic; human-induced vibrations; human perception; survey. 8 1- Introduction 9 With the development of technology, the challenges of construction have been improved, 10 encouraging us to design and construct exceptional structures. Bridges are undoubtedly one of 11 those structures. Slender footbridges have gained popularity over the years, and the structure 12 itself has become a tourist attraction. Constructed in 2020, the 516 Arouca Bridge was at the 13 time of its construction the longest span footbridge in the world. This bridge is in a stunning 14 location within the Arouca Geopark (Portugal), which is recognised as a geological heritage site 15 of international relevance and is classified as a UNESCO Global Geopark. The bridge crosses the 16 Paiva river at height of 175 m in relation to the river bed, linking Alvarenga to Canelas. 17 When the challenge of designing the bridge was presented to Itecons (bridge design/project 18 authorship), the request was to conceive a structure that would offer an exciting experience, as 19 the location is an attraction for leisure activities and extreme sports such as hiking, climbing, 20 rafting, etc. The level of excitement is related to the height of the bridge in relation to the river 21 bed, its slenderness, and its perceived stability. It is well known that vibration in structures 22 induces a sense of insecurity in people, even though it does not mean that the structure is 23 unsafe. Moreover, it is also well known that people induce vibration in structures [1]–[3]. 24 3 Large span and slender bridges are more prone to suffer vibration serviceability problems 1 [4], given their usual low stiffness, mass, damping, and natural frequencies. Bridges of this type 2 are often vulnerable to dynamic loads due to the movement of pedestrians. Significant lateral 3 and vertical vibrations are frequently associated with suspension bridges under the movement 4 of pedestrians [5], [6]. 5 There are many guidelines and recommendations relating to this issue [7]–[13]. Despite all the 6 available information, there is no international design code that sets out limits and admissible 7 values for the response of the structure under different actions [11], [14]. The problem of 8 pedestrian-induced vibration is mainly considered in these guidelines/standards in two ways: a) 9 by establishing the range of frequencies that characterise the pedestrian-structure interaction; 10 b) by treating the problem separately in terms of the direction (longitudinal, lateral or vertical) 11 in which the pedestrian action is applied. Most of these standards only establish the need to 12 assess the structure’s dynamic behaviour if some of its natural frequencies are within the 13 interaction range and do not define a methodology to check the required comfort level [15]. 14 It is recognised that vibration serviceability criteria are still a matter of ongoing research. Dong 15 et al. [16] used vision-based methods to collect displacement, and velocity to determine 16 serviceability assessment. Rezende et al. [17] developed a methodology to evaluate the dynamic 17 behaviour of long-span steel footbridges based on an equivalent beam model. Nimmen et al. 18 [18] reported a full-scale dataset collected specifically for the further development and 19 validation of models for crowd-induced loading. The pedestrian and bridge motions are 20 registered simultaneously using wireless triaxial accelerometers and video cameras. Venuti and 21 Tubino [19] presented a characterisation of pedestrian-induced loading on footbridges in 22 restricted traffic conditions, and compared the reliability of current guidelines and advanced 23 spectral models in the serviceability assessment of footbridges with respect to vertical 24 vibrations. 25 4 The comfort limit ranges according to HiVoSS [13] and SETRA [12] were taken into account in 1 the 516 Arouca design stage, meaning that it was ensured that the first natural frequencies occur 2 below the critical range frequencies and the dynamic behaviour under pedestrian excitation was 3 evaluated. The acceleration related indices combined with vibration frequencies were used to 4 define the serviceability limit. 5 In two previous studies [20], [21], the authors analysed the wind load effects on the 516 6 Arouca Bridge and presented a design approach to analyse the quasi-static and dynamic 7 behaviour of the bridge through theoretical, analytical, and numerical models. The 8 uncertainties, when it comes to defining the structural and loading parameters in the 9 serviceability assessment of footbridges, led to an in situ experimental work that validated the 10 assumptions made during the design phase [22], [23]. 11 In fact, it is crucial to ensure in the design phase that a structure will provide enough comfort to 12 the users, since vibration problems can be difficult and very expensive to solve after 13 construction. Very recently, and probably due to this new tendency for big span bridges, several 14 studies [16], [24]–[28] have focused on investigating the vibration serviceability of footbridges. 15 For instance, Cao and Chen [29] proposed an online big data approach to investigate the limits 16 of vibration serviceability in a real environment. A smartphone-based application was developed 17 to assess data on personal judgment of vibration level, vibration signals, environmental, and 18 biological factors. That kind of information is needed, gathering data on the human perception 19 of the structural dynamic response. With this in mind, a survey is being given to tourists on the 20 516 Arouca Bridge so that we can acquire this kind of data. The present study considered the 21 answers of 1030 visitors (data available so far) about the experience. 22 This paper pursues already ongoing experimental work by studying the vibrations and 23 displacements induced by the wind and by pedestrians through in situ behaviour tests on the 24 516 Arouca. Bridge responses caused by people walking at different speeds, running, jumping, 25 5 and swinging (simulating a deliberately harmful action) as they crossed it were recorded. All 1 tests were performed under similar very low wind conditions. 2 The next section presents relevant information about the design codes and guidelines on 3 this subject. The 516 Arouca bridge is described in Section 3. Section 4 briefly presents the finite 4 element (FE) model used in the bridge design and reports the HiVoSS and SETRA approach used 5 to determine the maximum acceleration through FE models. Details of the in situ tests are given 6 in Section 5. Then, the modal parameters, including the damping ratios, of the structure are 7 identified from an operational modal analysis (OMA) in Section 6. In addition, the dynamic 8 behaviour of the bridge is analysed from different pedestrian loads and deliberately harmful - 9 vandal - loading. The last section assesses the comfort classes of the bridge according to the 10 European guidelines HiVoSS and SETRA and by presenting the inquiry results. The results are 11 presented and discussed, and conclusions are drawn. 12 13 2- Design codes and guidelines 14 The first design code that involves vibration serviceability is BS 5400-2 [4]. It presents a 15 procedure to check for vertical vibrations caused by a single pedestrian and was defined for 16 footbridges whose natural frequency of the fundamental vertical mode of vibration was up to 17 5 Hz. The Ontario Highway Bridge Design Code [14] requires the determination of the dynamic 18 response of a bridge to a simulated footfall force, analogous to BS 5400-2[4]. Many years later, 19 in 2002, the code was updated to the version that is still in force, BS 5400: BD 37/01 [15]. The 20 main modification to the code was the requirement to also check vibration serviceability in the 21 lateral direction. This additional requirement derives in part from experience with lateral 22 vibrations of the London Millennium Bridge [13]. Pedestrians are more sensitive to horizontal 23 vibrations than to vertical ones, and vibrations are higher in crowded conditions. For this reason, 24 6 lower limit values for lateral vibrations were established. All footbridges with fundamental 1 lateral frequencies lower than 1.5 Hz now have to undergo a dynamic analysis. 2 SETRA and HiVoSS are currently the more complete and widely used guidelines to design this 3 type of bridge [16]. Even though these codes recommend vibration comfort limits, they also 4 state that it is up to the building promotor/builder to decide which comfort limits are to be met. 5 The methodology provided by these guidelines classifies the footbridge in terms of the required 6 comfort level and the expected level of traffic. However, this classification cannot be considered 7 an absolute criterion because the concept of comfort is highly subjective and the acceleration 8 feeling is experienced differently. To take this subjectivity into account, the guidelines establish 9 ranges rather than thresholds. In fact, both guidelines provide the same four ranges of 10 accelerations, distinguishing between vertical and lateral: maximum, mean minimum, and 11 uncomfortable/unacceptable. 12 However, the comfort limit ranges according to HiVoSS [13] and SETRA [12] were taken into 13 account in the design stage, thereby ensuring that the first natural frequencies occur below the 14 critical range frequencies and confirming the need for a dynamic evaluation of pedestrian 15 excitation. These guidelines are only used to assess vibration comfort limits when a group of 16 people walk on the bridge. Figures 1 and 2 illustrate the limits of both the critical ranges for 17 natural frequencies with pedestrian excitation, and the defined comfort classes with common 18 acceleration ranges, respectively. 19 Regarding the critical range of frequencies, SETRA defines four classes, while HiVoSS only 20 distinguishes acceptable from critical (two classes). In the HiVoSS guideline, it is considered that 21 the lateral vibrations are not affected by the second harmonic of pedestrian loads. However, it 22 considers that the bridge might be excited to resonance by the second harmonic of pedestrian 23 loads for vertical accelerations in bridge structures with natural frequencies between 2.5 Hz and 24 7 4.6 Hz. In that case, the critical frequency range for vertical and longitudinal vibrations expands 1 to a larger range [1.25 to 4.6] Hz. 2 The two guidelines define identical comfort classes regarding acceleration values (Figure 2). 3 Both also alert to the lock-in phenomenon, which can be triggered by lateral acceleration levels 4 exceeding 0.1 m/s2. 5 HiVoSS SETRA a) b ) 6 Figure 1: Frequency comfort limit ranges according to the European guidelines HiVoSS and SETRA: a) Vertical 7 direction; b) Lateral direction. 8 a) b) Figure 2: Acceleration comfort limit ranges according to the European guidelines HiVoSS and SETRA: a) Vertical 9 direction; b) Lateral direction. 10 3- The Arouca 516 footbridge 11 The structure under study is a suspension bridge for pedestrian use, with a span of 516.5 m. 12 The suspension system consists of two main cables (catenaries) and hangers (main and 13 secondary), which support a total of 127 metal deck modules. Each catenary is composed of 14 seven steel wire ropes (steel core, E=100GPa, m=51kg/m and A=5915 mm2), with a wire rope 15 nominal diameter of 40 mm. The ends of these cables were attached to the anchoring blocks, 16 and the cables were placed resting on a saddle at the top of the pillars, 36.3 m high. The main 17 cables are 530.305 m long with a sag of about 53.56 m. 18 8 The hangers are composed of a single wire rope with a nominal diameter of 12 mm. The 1 hangers vary in length between 2.361 m and 35.684 m. A single deck module is 4016 mm long 2 and 2100 mm wide. It is made mainly from UPN profiles and some angle profiles, all of S275 3 steel. The floor of the module is made of a lightweight steel grid panel. 4 The modules are connected through nodes fitted at the ends, where the hangers are also 5 connected. Each module (with a mass of 505.6 kg) is hung from the catenaries via a total of 8 6 secondary cables, which are shared with the adjoining modules. Of these eight cable hangers, 4 7 are designed to carry most of the gravity load (main hangers) and the other 4 are post-tensioned 8 secondary hangers designed to reduce the rotation of the deck and prevent some lateral 9 movement. 10 11 a) b) c) d) 9 e) f) Figure 3: Views of the Arouca 516 Bridge: a) View from the Alvarenga side; b) Bridge pillar design (dimensions in m); 1 c) Generic view; d) View from underneath; e) Structural design of the bridge; f) Structural design of the module with 2 the deck and lateral grids. 3 4 5 4- Finite Element simulation of the bridge 6 Simplified theoretical, analytical and numerical models were used in a preliminary design 7 stage to define the bridge configuration under static and dynamic loading to ensure [21]: 8 6) a relatively low tensile force on the main cables when struck by wind up to a velocity 9 of about 190 km/h and a live load of 2.2 kN/m2; 10 ii) low inclination of the deck modules in the longitudinal direction (less than 15%); 11 iii) low displacements on the bridge when a group of 34 people cross the bridge (less than 12 1.5 m); 13 iv) natural frequencies of the first eigenmodes below the critical ranges indicated by the 14 European guidelines HiVoSS and SETRA associated with pedestrian excitation (0.5 Hz 15 16 Figure 7: Wind velocity and direction (test 1). 1 2 6- Evaluation of the dynamic behaviour of the footbridge 3 6.1 Modal parameter identification 4 Natural frequencies and modal damping ratios were identified from the structural response 5 due to wind action (Test 10) acquired over 1800 s per channel. The data were sampled to 200 Hz. 6 The structural response was filtered by applying a 30 Hz Chebyschev low pass filter of the 8th 7 order to limit the analysis in the frequency range of interest 0-6 Hz. The modal parameters were 8 found from an operational modal analysis (OMA) using enhanced frequency domain 9 decomposition (EFDD) [34]. The EFDD technique is based on the decomposition of the power 10 spectral density matrix using the singular value decomposition (SVD). 11 Figure 9 represents the SVD of the acceleration caused by the wind action using four 12 projection channels and a frequency resolution of 0.0097 Hz. The range of frequencies analysed 13 (from 0 – 6.0Hz) has been defined to assess the risk of resonance entailed by pedestrian traffic 14 according to HiVoSS and SETRA guidelines. The peaks found in the curves correspond to the 15 natural frequencies of the structure. Some peaks related to in-plane mode shapes are found in 16 the comfort limit ranges given in Figures 1 and 2. The HiVoSS and SETRA guidelines state that 17 pedestrian bridges with natural frequencies in these ranges should be subjected to a dynamic 18 evaluation of pedestrian excitation, which is the aim of this section. 19 17 (a) (b) Figure 8: Singular Value Decomposition from ambient vibration (wind action, test 10) for (a) in-plane and (b) out- 1 plane mode shapes. 2 The experimental mode shapes are initially estimated as unit norm vectors from the OMA. 3 They are then scaled using the mass-normalised mode shapes of the finite element model 4 described in Section 4. The experimental mass normalised mode shapes are found by the least 5 squares solution of the following [35]–[37]: 6 {𝜓𝐸𝑥𝑝 }𝑗=[𝜙𝐹𝐸]{𝑅}𝑗 (2) 7 where, [𝜙𝐹𝐸] is a matrix that collects the FE mass normalised mode shapes and {𝑅}𝑗 is a 8 transformation vector. Then, the experimental modal mass is estimated as [35]–[37]: 9 𝑚𝐸𝑥𝑝,𝑗={𝑅}𝑗 𝑇{𝑅}𝑗 (3) 10 and the related j-the scaling factor is obtained as 𝛼𝑗= 1/√𝑚𝐸𝑥𝑝,𝑗 . Then, the identified 11 experimental mode shapes are mass normalised, and the modal kinetic energy is proportional 12 to 𝑚𝐸𝑥𝑝. 13 As mentioned before, The FE model was first used to obtain the natural frequencies and mode 14 shapes. Figures 9 and 10 illustrate the first out-of-plane (lateral displacement) and in-plane 15 modes (vertical displacements). 16 18 Perspective Top view Side view Frontal view Figure 9: First out-of-plane mode shapes obtained numerically be the FE model (frequency of 0.116 Hz). 1 2 3 4 5 Perspective Top view Side view Frontal view Figure 10: First in-plane mode shapes obtained numerically be the FE model (frequency of 0.157 Hz). 6 Tables 2 and 3 summarise the natural frequencies, the modal damping ratios, and the 7 natural frequencies provided by the FE model for in-plane and out-of-plane mode shapes. The 8 estimated standard deviations of both natural frequencies and damping ratios are also included. 9 Furthermore, the complexity of the mode shapes is low, which shows measurements and modal 10 19 parameter estimation are correct and the structure presents proportional damping. The 1 identification frequency range is limited by the number of sensors in the bridge. 2 The FE model reliably predicts the natural frequencies of the first-mode shapes. The Modal 3 Assurance Criterion (MAC) [38] between the experimental and numerical mode shapes is also 4 presented in Tables 3 and 4. A good agreement was obtained between the natural frequencies 5 obtained from the finite element model and the experimental results, with maximum errors 6 respectively below 22% and 10% for in-plane and out-of-plane mode shapes. The identified 7 mode shapes have a cumulative mass fraction of approximately 82% and 95% for in-plane and 8 out-of-plane mode shapes. The MAC diagonal value is greater than 0.8 in all cases, except for 9 the sixth in-plane, and the third out-of-plane modes, probably because they were not properly 10 excited by the wind action and also due to the uncertainties in the cable tension. As for the sixth 11 symmetric in-plane mode, the difference is more significant because the FE model cannot 12 accurately handle the additional tension induced in the cable when this mode is excited. 13 In addition, two torsional modes at 0.407 Hz and 0.476 Hz were identified with damping 14 ratios equal to 0.914% and 0.945%, respectively. These mode shapes could contribute to the 15 structural response in the case of vandalism, such as when a group of people provoke the 16 movement from the upstream to the downstream side, thus inducing a swinging motion. 17 The mode shapes are represented in Figures 11 and 12. However, the identified mode 18 shapes are limited by the number of measurement points. 19 20 Table 3: Summary of in-plane (vertical) mode shapes and the estimated natural frequencies fExp, modal damping 21 ratios ζ, complexity, and modal masses 𝑚𝐸𝑥𝑝. The natural frequencies fFE of the FE model and the MAC value are 22 also shown. 23 FExp [Hz] Standard deviation [Hz] Complexity [%] fFE [Hz] MAC [-] 𝜉 [%] Standard deviation [%] 𝑚𝐸𝑥𝑝 [kg] 0.147 0.53E-6 0.059 0.157 0.999 1.05 0.032 18228 0.214 1.39E-6 0.012 0.249 0.994 0.70 0.017 9815 0.302 0.58E-6 0.047 0.350 0.986 0.55 0.008 11217 20 0.364 2.13E-6 0.027 0.418 0.949 0.64 0.004 12132 0.443 2.59E-6 0.164 0.526 0.975 0.52 0.004 11513 0.504 1.18E-6 0.303 0.617 0.581 0.57 0.005 16743 0.591 0.72E-6 19.863 0.691 0.917 0.35 0.007 10166 0.672 0.83E-6 0.126 0.789 0.959 0.41 0.006 6485 0.737 0.33E-6 0.943 0.874 0.986 0.16 0.001 6804 0.810 8.30E-6 0.818 0.961 0.956 0.78 0.023 4792 0.959 1.25E-6 0.395 1.130 0.983 1.15 0.006 4882 1.031 1.60E-6 3.27 1.217 0.973 0.87 0.008 6521 1.103 2.74E-6 2.536 1.300 0.917 0.58 0.003 5939 1 2 Table 4: Summary of out-of-plane (lateral) mode shapes and estimated natural frequencies fExp , modal damping 3 ratios ζ, complexity, and modal masses 𝑚𝐸𝑥𝑝. The natural frequencies fFE of the FE model and the MAC value are 4 also shown. 5 FExp [Hz] Standard deviation [Hz] Complexity [%] fFE [Hz] MAC [-] 𝜉 [%] Standard deviation [%] 𝑚𝐸𝑥𝑝 [kg] 0.113 0.83E-6 0.006 0.116 0.951 1.45 0.035 60723 0.131 1.85E-6 42.127 0.135 0.853 1.65 0.080 51331 0.196 2.57E-6 0.145 0.205 0.585 1.48 0.050 20076 0.214 2.36E-6 0.832 0.221 0.979 0.84 0.029 38154 0.257 4.70E-6 1.326 0.267 0.966 1.65 0.037 44071 0.293 1.30E-6 0.569 0.311 0.973 0.91 0.022 37921 0.344 8.93E-6 0.214 0.356 0.945 0.95 0.010 26473 0.389 2.30E-6 0.45 0.402 0.953 0.90 0.006 31027 0.428 10.72E-6 0.085 0.451 0.967 0.63 0.007 31695 0.514 7.35E-6 17.173 0.544 0.869 0.87 0.025 16830 0.571 3.45E-6 4.602 0.633 0.969 0.63 0.011 26604 6 21 Figure 11: Experimental (circles) and numerical (solid line) in-plane mode shapes. 1 2 22 Figure 12: Experimental (circles) and numerical (solid line) out-of-plane mode shapes. 1 Additional computations have been performed to study the effect of the temperature 2 variation on the natural frequencies. An increase in temperature of 30 ˚C was considered, which 3 resulted in a length of the main cables of 532.214 m (additional 0.19 m) and a sag of 53.91 m. 4 The FE model simulations lead to a small decrease of about 0.3% in the natural frequencies. 5 6 6.2 Dynamic response due to pedestrian loads 7 The power spectral density (PSD) of the acceleration at all instrumented sections was 8 analysed to identify the natural frequencies excited by the pedestrian load. Obviously, the wind 9 action was also active during this test. The PSD is obtained from the average of 8 segments of 10 the original time series with 50% overlap applying a Hamming window [39]. The time responses 11 at an upstream position of 1/3 of the bridge span (Position 3) during Test 1 is shown in Section 12 7. The analysis of the PSD allows identification of the mode shape that contributes to the 13 structural response to pedestrian load. 14 Figures 13 and 14 show the PSD of the vertical and lateral accelerations recorded during the 15 walking tests at section corresponding to L/3 (position 3). The PSD due to the wind action, 16 recorded during a half-hour period, is also represented as a reference for the unloaded case. 17 These figures also represent the maximum acceleration obtained numerically, provided by 18 uniformly distributed loads computed for the 34 pedestrians and three different structural 19 damping ratios (ξ=0.2%, ξ=2.0% and ξ=4.0%) according to the HiVoSS and SETRA guidelines. 20 23 These damping ratio values represent the range estimated from the measurements for the 1 different tests and agree with those indicated by HiVoSS and SETRA (ξ=0.2% is, in any case, the 2 minimum value, ξ=2.0% corresponded to welded steel structures, and ξ=4.0% is associated with 3 bolted steel structures). The highlighted/shaded areas represent the critical ranges for natural 4 frequencies of footbridges with pedestrian excitation for vertical and lateral vibrations, 5 according to the HiVoSS and SETRA guidelines. Since the lateral vibrations are not affected by 6 the second harmonic of pedestrian loads, only the vertical case (Figure 13) shows two ranges, 7 (in the case of HiVoSS) corresponding to the first and second harmonics (see Figure 5). 8 The frequency contents show peaks at the natural frequencies identified in the SVD (Figure 9 8). The effect of the 34 pedestrians was found to reduce the lowest natural frequencies of the 10 structure by around 2%. The acceleration levels produced by the pedestrian load are higher than 11 those caused by the wind load, and a noticeable amplification is found in the critical ranges of 12 natural frequencies represented between vertical dashed lines. 13 14 15 24 Figure 13: PSD of the vertical acceleration at the at section corresponding to L/3 (position 3) for the walking tests. 1 The critical ranges of natural frequencies are represented between vertical dashed lines: SETRA guideline (left); 2 HiVoSS guideline (right). 3 25 32 7- Assessment of comfort classes 1 The assessment of pedestrian comfort is commonly represented as the limit acceleration for 2 the footbridge, and the perception of motion and vibration are subjective and therefore 3 different for each pedestrian [13]. The analyses of the comfort class for the walking tests are 4 discussed. Special attention was paid to the human perception of the vibration of the footbridge. 5 A questionnaire was prepared, designed to be answered by the first groups of people who 6 visited the bridge after the opening so as to learn their thoughts on the experience of crossing 7 the footbridge. A total of 1030 visitors completed the questionnaire. 8 The assessment of the comfort classes allows us to define the time percentage of the 9 response that exceeds the acceleration limits [13]. The vibration was continuously measured by 10 all seismometers. The maximum response at the measurement positions was recorded when 11 the group of pedestrians was near a seismometer. The vibration level gradually decreases over 12 time. Therefore, to evaluate the comfort classes, a representative interval of the response is 13 defined as the time period around the maximum level of acceleration that exceeds a noise level. 14 This level is obtained as the mean value of the acceleration in a time window of 4 seconds around 15 the maximum response. 16 Given the amount of recorded data, Test 1 is used to illustrate the performed analysis. All 17 other results are summarised in figures, most of which can be found in the supplementary 18 material. 19 Figure 22 (a-c) shows the acceleration responses at an upstream position of the bridge 20 midspan (Position 3) when the group of 34 people crossed the bridge from one side to the other 21 side at a slow pace of 0.5 m/s (1.8 km/h). Each plot includes the acceleration limits following the 22 European guideline HiVoSS [13]. 23 As expected, larger acceleration amplitudes are observed at each seismometer when the 24 group of volunteers was moving in its vicinity. In addition, the displacements recorded by the 25 33 GNSS antennas on the X (longitudinal direction), Y (vertical direction), and Z (lateral direction)- 1 axes are presented (Figure 23). As expected, the transversal displacement is very low given that 2 the wind speed was below 3.0 m/s, and the people moved slowly. As can be seen, the middle 3 platform module had a maximum Y-axis displacement of 0.48 m, a maximum X-axis 4 displacement of 0.12 m, and a Z-axis displacement of 0.06 m. 5 34 a) b) c) Figure 22: Test 1 – Walking on the bridge at 0.5 m/s (1.8 km/h) - position 3 upstream of the bridge span for: a) 1 Longitudinal acceleration (X-axis); b) Vertical acceleration (Y-axis); c) Lateral acceleration (Z-axis). 2 Figure 23: Test 1 – Walking on the bridge at 0.5 m/s (1.8 km/h) - at the at section corresponding to 2L/3 (position 7) 3 for X-, Y- and Z-axis displacement recorded by the GNSS antenna. 4 35 The analysis of these results allowed us to evaluate the total time for which each comfort 1 level was sensed for the three axes (see Figure 24:). These acceleration ranges and percentages 2 for all monitoring positions and for all walking tests (Tests 2 to 4), are presented in the 3 supplementary material. The comfort level can be classified as maximum or medium most of the 4 time, according to the ranges represented, especially in the vertical direction. The percentage 5 of time for which the acceleration was at uncomfortable levels was almost zero for Test 1. 6 a) b) c) Figure 24: Acceleration ranges and percentages, for all monitoring positions, obtained during Test 1: a) X axis 7 (longitudinal direction); b) Y axis (vertical direction); c) Z axis (lateral direction). 8 9 36 a) b) Figure 25: Analysis of the tests: a) Maximum displacement recorded by the GNSS antennas; b) Total time 1 percentage and the position at which the uncomfortable level limit was highest. 2 The maximum displacements, recorded by the GNSS antennas, (Figure 25: a) for the walking 3 tests (Tests 1- 4) are 0.74 m, 0.13 m, and 0.08 m for the vertical, transverse, and longitudinal 4 directions, respectively. These correspond to 1/697, 1/3969, and 1/6450 of the bridge span, 5 which are considered very small fractions. For the jumping tests, the maximum displacement 6 was below the values recorded for the walking tests, with the vertical and longitudinal directions 7 registering 0.35 m and 0.12 m, respectively. In the lateral direction, the maximum value was 8 0.03 m. 9 As can be seen, the results corroborate the previous analysis done for Test 1; the faster the 10 pace, the greater the acceleration provoked by the pedestrian excitation. Analysis of these 11 results also leads to the conclusion, as expected, that higher frequency spectra amplitudes are 12 associated with the frequencies excited by the movement of the group. Test 4 (random pace) 13 corresponds to the behaviour expected of the public on the bridge. The results show that the 14 acceleration values are very low and the discomfort level can be assumed to be nearly negligible 15 (Figure 25: b). 16 17 37 7 Human perception 1 Human perception of footbridge vibration in general is a combination of movement of the 2 system, physical perception, and psychological reaction to vibration. Occupants in various 3 settings will be more sensitive to exactly the same vibration than others, depending on the 4 frequency of occurrence, duration, and time of day. According to Grether [41], humans are more 5 sensitive to vertical vibrations in the frequency range of 4–8 Hz due to resonance phenomena 6 within the body itself. In addition, human perception depends on the activity of a person at the 7 time of the perceived event. 8 The classification of uncomfortable vibrations is very subjective. Determining acceptability 9 can be a challenge due to the large number of factors upon which vibration perception depends. 10 The bridge visitors anonymously responded to a questionnaire. Between the opening and the 11 submission of this paper, 1030 people responded to the inquiry about the experience, Figure 26. 12 The questionnaire was available in Portuguese, Spanish, English, and French and was provided 13 by the bridge guide, who invited people to answer it at the end of the bridge tour. The survey 14 questions are presented in the supplementary material. 15 The survey given to visitors starts by asking if the person feels fear during the crossing. 84.8% 16 answered no. The visitors are then asked about the comfort level perceived during the crossing, 17 with four options given for comfort class maximum, medium, minimum, and unacceptable, 18 associated respectively with practically imperceptible vibration, merely perceptible vibration 19 but not unpleasant, perceived vibration but not intolerable and intolerable. The results show 20 that 59% of the surveyed visitors chose the maximum comfort option, 38% chose medium 21 comfort, and 2.1% and 0.9% classified vibration comfort as minimum and unacceptable, 22 respectively, which is in accordance with the vibration assessment presented in the previous 23 section. People were also asked if they felt safe; 96.1% said yes. 24 25 38 1 2 Did you feel fear before crossing the bridge? Did you feel safe? Would you recommend the experience? Did you consider that too many people were on the bridge? What was your comfort level regarding vibration when crossing the bridge? Did the experience of crossing the bridge exceed your expectations? Figure 26: Volunteers’ answers. 3 4 8- Conclusions 5 This paper has investigated the vibrations and displacements induced by the wind and 6 humans through in situ behaviour tests on the 516 Arouca pedestrian bridge in Portugal. The 7 tests were carried out by a group of 34 people, which is 2778 kg of total mass on the footbridge. 8 Bridge responses caused by people crossing (walking at different speeds), running, jumping, and 9 swinging (simulating a deliberately harmful action) were recorded. All tests were performed 10 under similar very low wind conditions. 11 39 Some major conclusions can be drawn from the research work: 1 - The evaluated mode shapes and corresponding natural frequencies were found to be 2 similar to those previously computed by a finite element model at the design stage. 3 - The damping ratios were found to be appropriate for the present lighter, slender bridge. 4 These increase with the pace of walking, as the structural response increases, 5 highlighting the dependence of the damping ratio on the amplitude of the structural 6 response. 7 - European guidelines (HiVoSS and SETRA) were used to compute numerical acceleration 8 levels. The results, obtained for three different damping ratios (0.2%, 2%, and 4%) were 9 found to be much higher than the acceleration measurements. 10 - The effect of the 34 pedestrians was found to reduce the lowest natural frequencies of 11 the structure by around 2%. 12 - The use of GNNS antennas seems to be a suitable way to measure the static behaviour 13 of this type of bridge. The maximum displacements recorded by those for the walking 14 tests were 0.74 m, 0.13 m, and 0.08 m for the vertical, transverse, and longitudinal 15 directions, respectively. These correspond to 1/697, 1/3969, and 1/6450 of the bridge 16 span, which are considered very small fractions. 17 - The effect of the temperature variation on the natural frequencies of the bridge is 18 minimal and thus can be neglected. 19 - The acceleration levels produced by the pedestrians had a noticeable amplification, 20 found in the critical ranges of natural frequencies indicated in the guidelines (HiVoSS and 21 SETRA). Peaks outside the critical range of natural frequencies were also found and 22 correspond to the second harmonic of the pedestrian load. 23 - The lateral component of the acceleration shows predominant peaks corresponding to 24 the natural frequencies of the out-of-plane mode shapes. 25 40 - The amount of time for which the acceleration limits, imposed by the HIVOS and SETRA 1 guidelines, were exceeded was calculated. The results demonstrate that depending on 2 the test type, the acceleration levels may vary. Higher accelerations happen when 3 pedestrians jump simultaneously on the bridge or produce a swinging motion, which is 4 not allowed and therefore considered uncommon. 5 - The damping ratios were found to increase with the pace of walking as the response of 6 the structural response increased, highlighting the dependence of the damping ratio on 7 the amplitude of the structural response. A damping of 2% was reached when a group of 8 34 people walked on the bridge. 9 - The survey results contribute to assessing human sensitivity to the vibrations of this kind 10 of bridge. 97% of visitors considered that the vibration could be classified as practically 11 imperceptible vibration or slightly perceptible, showing that the visitors felt completely 12 safe while on the bridge. Overall, the results show that the comfort limits defined in the 13 European guidelines (HiVoSS and SETRA) are suitable for this type of bridge. 14 15 16 17 Acknowledgments 18 The authors would like to acknowledge the support provided by Arouca City Hall (Câmara 19 Municipal de Arouca), with special thanks to the mayor, Margarida Belém, and the Council 20 Engineer Conceição Oliveira; to the group of 34 volunteers for their time and patience; to José 21 Rego for the photos; to the Portuguese enterprises MEO - Serviços de Comunicações e 22 Multimédia, SA, and Geoide Geosystems SA, for the internet connection and GNS antennas data, 23 respectively; to LNEC (National Laboratory of Civil Engineering) for the anemometer data and 24 their help in the group and work coordination. Finally, the authors would also like to 25 41 acknowledge the financial support provided by the Spanish Ministry of Science, Innovation and 1 Universities (PID2019-109622RB-C21). 2 References 3 [1] S. R, “The influence of human occupants on the dynamic properties of slender 4 structures,” University of Sheffield, 2002. 5 [2] P. Kumar and A. Kumar, “Human induced vibrations in structures,” Int. J. Mech. Eng. 6 Robot. Res., vol. 1, no. 1, pp. 44–54, 2014. 7 [3] R. Sachse, A. Pavic, and P. Reynolds, Human-structure dynamic interaction in civil 8 engineering dynamics: A literature review, vol. 35, no. 1. 2003. 9 [4] M. Huang, “Dynamic Characteristics of Slender Suspension Footbridges,” no. May, p. 10 268, 2006. 11 [5] E. T. Ingólfsson, C. T. Georgakis, and J. Jönsson, “Pedestrian-induced lateral vibrations of 12 footbridges: A literature review,” Eng. Struct., vol. 45, pp. 21–52, 2012, doi: 13 10.1016/j.engstruct.2012.05.038. 14 [6] S. Ali, D. Thambiratnam, X. Liu, and S. Fawzia, “Numerical study of pedestrian 15 suspension bridge with innovative composite deck,” Heliyon, vol. 6, no. 7, p. e04473, 16 Jul. 2020, doi: 10.1016/j.heliyon.2020.e04473. 17 [7] “BS 5400 Steel, concrete and composite bridges - Part 2: Specifications for loads,” 1978. 18 [8] “EN 1995-2:1997 Eurocode 5: Design of timber structures. Bridges,” 1997. 19 [9] “CAN/CSA-S6-00 Canadian Highway Bridge Design Code,” 2000. 20 [10] “DIN-Fachbericht 102 Concrete bridges,” 2003. 21 [11] M. Schlaich, K. Brownlie, J. Cozett, J. Sobrino, J. Stráský, and K. Takenouchi, fib Bulletin 22 No. 32 - Guidelines for the design of footbridges, no. December. e International 23 48 1 a) b) c) Figure S.3: Acceleration ranges and percentages for all monitoring positions, obtained during Test 4: a) X axis 2 (longitudinal direction); b) Y axis (vertical direction); c) Z axis (lateral direction). 3 4 49 Survey questions 1 Personal data: 2 1- Age: 3 2- Height: 4 3- Weight: 5 4- Nationality: 6 5- Did you feel fear before crossing the bridge? 7 Options: Yes/No 8 6- What was your comfort level regarding vibration when crossing the bridge? 9 Options: Maximum (practically imperceptible vibration) / Medium (merely perceptible 10 vibration but not unpleasant) / Minimum (perceived vibration but not 11 intolerable) / Unacceptable (intolerable) 12 7- Did you feel safe? 13 Options: Yes/No 14 8- Did you consider that too many people were on the bridge? 15 Options: Yes/No 16 9- Would you recommend the experience? 17 Options: Yes/No 18 10- Did the experience of crossing the bridge exceed your expectations? 19 Options: Yes/No 20 21 22 23