Comparison against Structures Made of Conventional Construction Materials

The related paper reports new experimental data for dynamic properties (i.e. modal mass, natural frequency and damping ratio) of eight FRP composite footbridges in Europe, which helps to resolve the weakness in knowledge and understanding of dynamic properties of FRP footbridges. In addition, dynamic properties are reviewed with the results of six other FRP footbridges and 124 non-FRP footbridges built after 1991. A comprehensive comparison of these 138 sets of dynamic properties shows that FRP footbridges possess similar fundamental frequencies at the same span, but usually higher damping ratios (mean of 2.5% c.f. mean of <1.0% for steel, concrete and steel-concrete composite). Additionally, natural frequencies and damping ratios identified from free decays measured on FRP footbridges are response amplitude dependent. Comparing the accelerance peaks of FRP and conventional footbridges revealed that the FRP footbridges are, on average, around 3.5 times more responsive to resonant excitation than the conventional bridges having the same bridge length, deck width and mode shape due to their significantly lower modal mass.


Introduction 25
Fibre-reinforced polymer (FRP) composite shapes and systems are increasingly used in the 26 construction sector, motivated by their successful structural applications in aviation, chemical, 27 architectural and engineering merits in having FRP components/structures . 48 This paper provides new experimental data on the dynamic properties of eight as-built FRP 49 footbridges in Europe, created from tests conducted by the authors. In addition, it presents a 50 comprehensive comparison of dynamic properties between FRP and non-FRP footbridges built 51 after 1991 (for modern non-FRP footbridges), and provides a discussion on the similarities and 52 differences of expected vibration responses. The comparison is based on the new experimental 53 data presented herein, as well as for six other FRP footbridges and 124 modern non- FRP 54 footbridges reported in the literature. In addition, the amplitude dependency of natural 55 frequencies and damping ratios of two tested FRP footbridges is evaluated. Moreover, the 56 accelerance peaks in the vertical direction are compared between FRP and conventional 57 footbridges. The study reported in the paper offers crucial missing knowledge and the 58 understanding required for us to have reliable design of FRP footbridges, and it can support the 59 preparation of national or international consensus design guidance for dynamic design. 60 Following this introductory section, Section 2 describes the eight FRP footbridges tested by 61 the authors. Section 3 details the modal testing and modal parameter identification carried out. 62 Section 4 is used to demonstrate the amplitude-dependence of frequency and damping ratio. 63 The comparison of the fundamental frequencies and damping ratios of FRP and non- FRP 64 footbridges is made in Section 5, while the comparison of accelerance peaks of FRP footbridges 65 and conventional footbridges is made in Section 6. Concluding remarks from the research work 66 are given in Section 7. 67

Description of FRP footbridges 68
Introduced in this section are eight as-built FRP composite footbridges, five in the UK, two in 69 The Netherlands and one in Italy. In terms of structural form these footbridges consist of four 70 girder bridges, two truss bridges and two suspension bridges. Unless otherwise stated the FRP 71 material has glass fibre reinforcement embedded in a thermoset matrix, usually from the 72 polyester resin family. 73

St. Austell Bridge 83
St. Austell Bridge is the first all-FRP structure on the UK rail network [12] and was fabricated 84  10 93 m, located on the campus of TU Delft, the Netherlands [13]. The FRP deck is 2 m wide and 94 was moulded together with two longitudinal FRP beams underneath. The three components are 95 of vacuum infused FRPs with a foam inner core. To support the footbridge, the two girders sit 96 on neoprene pads at the span ends. The deck is surfaced with an epoxy layer with embedded 97 gravel. The two spans are linked only by a steel bolted moment-free connection.

Delft Bridge B 101
The Delft Bridge B shown in Fig. 4 is 14.9 m long and 4.5 m wide, and was designed to take 102 pedestrians, cyclists and a 12 tonnes service vehicle [13]. It crosses over a canal in the 103 municipality of Delft, the Netherlands. The load-bearing structure is slightly cambered and it 104 consists of four FRP longitudinal beams connected using an FRP cover to form the 105 superstructure. Each beam is made using vacuum infused FRP with a foam inner core, thereby 106 having a similar construction to Delft Bridge A, introduced in Section 2.3. The footbridge 107 supports rest on neoprene pads, which also provide longitudinal restraint. The FRP handrail 108 system is 1 m high and consists of individual vertical uprights as seen in Fig. 4. Using two steel 109 bolts they are connected to the deck at 100 mm spacing. The total mass is around 6600 kg. Folkstone Railway Line [14]. This bridge, installed in January 2017, replaces a steel bridge 117 6 after a section of railway line was damaged by flooding. The superstructure is made of 118 pultruded shapes (3.325 m high truss) and infused FRP sections with a foam inner core (2.4 m 119 wide deck and parapet panels), bolted and bonded together. The 1.5 m high parapet panels were 120 designed as a modular system and bolted to the truss members. The mass of each span is around 121 5500 kg. 122

Prato Bridge 123
The Prato Bridge is a 25 m simply supported truss footbridge for pedestrians and cyclists, 124 opened in 2008 [15,16]. As seen in Fig. 6(a) it crosses a dual carriageway in Prato, Italy. connections have gusset plates of stainless steel. The deck is 2.5 m wide at the middle and 3.6 127 m at the span ends, and is assembled of pultruded FRP planks, which are each 5 m long and 128 500 mm wide and 40 mm deep. These planks are bolted at the ends, as well as at their mid-129 span to transverse members of channel shapes below the deck. The FRP planks themselves 130 provide additional lateral bracing into the structure. Seen in Fig. 6(b) is the metal mesh that 131 provides a barrier (for a hand rail) along the sides of the Prato Bridge. The structure weighs 132 about 8000 kg [16], and rests on two concrete piers (Fig. 6a) Table 1 summarises the essential dynamic testing and analysis details in our FRP footbridge 159 test programmes. Five of these bridges were characterised for their dynamic properties using 160 the impact hammer (IH) testing method, while the other three bridges were characterised using 161 the ambient vibration (AV) testing method [20]. The IH testing method was chosen for the 162 footbridges with spans below 20 m, while AV was employed for the footbridges with longer 163 span. The key reason for employing IH is that the response of the shorter structures to ambient 164 excitation is too low to acquire good quality AV data [21]. 165 To identify the first few vibration modes of interest, a sufficiently dense grid of test points (TPs) 166 on the deck is essential. The test programme for each bridge was divided into several set-ups, 167 to cover the required test grid using the limited number of accelerometers available. The IH 168 impact point on the deck remained unchanged. The measured force signal served as the 169 reference signal. In AV testing, the signal from the accelerometer that remained in one location 170 throughout served as the reference signal. The reference point on each bridge was carefully 171 identified by preliminary tests so that the targeted vibration modes were observable. 172 In total three types of accelerometers were used for vibration response measurement, including 173 the: Honeywell QA750 with nominal sensitivity 1300 mV/g ( Fig. 9(a)); PCB 393C 174 accelerometer with nominal sensitivity of 1000 mV/g ( Fig. 9(b)); Dytran accelerometer 175 3166B1 with nominal sensitivity of 500 mV/g ( Fig. 9(c)). A signal conditioner is required only 176 when QA750 accelerometers are employed. Either a four-channel SignalCalc Quattro by Data 177 Physics (shown in Fig. 10(a)) or a sixteen-channel SignalCalc Mobilyser by Data Physics 178 (shown in Fig. 10(b)) was utilised for signal acquisition in real time. 179 In IH testing, the hammer operator, crouching on the deck, operated an instrumented hammer 180 to impact the reference TP. The force signals were measured using a load cell embedded in the 181 hammer and the resultant vibrations in the structure were measured using the accelerometers. 182 The two hammers used were a Dytran Model 5803A (sensitivity 0.231 mV/N and weight 5. 6.0 [23] to identify modal parameters. The artificial damping that was introduced by the applied 196 exponential window was eliminated during modal parameter identification [22]. 197 By contrast, in AV testing, only vibration responses were measured under the natural excitation 198 of wind and/or road traffic passing underneath. During data recording the footbridge had to be 199 closed to pedestrian traffic. A reference-based data-driven Stochastic Sub-space Identification 200 (SSI) algorithm, available in MACEC 3.2 [24][25][26][27], is applied for data pre-processing and modal 201 parameter identification. 202 For the five FRP footbridges with spans < 20 m, the modes up to 20 Hz were identified. The 203 modes below 10 Hz were identified for the Prato Bridge and the modes below 5 Hz for the two 204 suspension bridges. Identified vibration modes are summarised in Table 2 and the description  205 of mode shapes is related to the modal displacement of the deck, unless stated otherwise. Note 206 that test results from the IH testing are related to the hammer operator-structure system rather 207 than the structure itself [28][29][30][31]. The presence of hammer operator imposes an obvious 208 influence on the dynamic properties of Parson's Bridge and Delft Bridge A, but a negligible 209 influence for St Austell Bridge, Dover Bridge and Delft Bridge B. The hammer-operator 210 influence on damping is known to be stronger than on changing the fundamental frequency. In 211 Table 2 corrected values for the relevant modes for Parson's Bridge and Delft Bridge A are  212 given in brackets. The detailed correction procedure can be found in [31]. 213 For the five FRP footbridges with spans < 20 m, the fundamental frequency of the first vertical 214 or torsional mode is well beyond the frequency range of 1.

Amplitude-dependence of frequency and damping ratio 242
Damping and natural frequencies of low-frequency modes of actual engineering structures are 243 known to usually be response amplitude dependent [32][33][34][35], which is due to inherent 244 nonlinearities, including effects from frictional forces at connections and supports, geometrical 245 non-linearity, substructure-soil interaction or structural damages and so on. Fundamental 246 frequencies and damping ratios of a footbridge estimated using the data obtained from vibration 247 tests, in which induced vibration responses are usually at a relatively low level, might therefore 248 be quite different from those of the bridge under its actual operational condition. Indeed, the 249 estimation of fundamental frequency and damping ratio over an operating range of response 250 amplitude is more important for estimating actual vibration performance. 251 To determine amplitude-dependency of the natural frequency and damping ratio for a targeted 252 vibration mode, the free vibration response was measured under a human walking or jumping 253 on a bridge to excite a targeted mode, as much as is practical. Then the logarithmic decrement 254 method [36] is used to extract the required dynamic properties.  whilst the damping ratio first increases from 2.16% to 2.46% and then decreases to 1.77%. 268 In IH testing, the vibration response for the first vertical mode at the mid-span has an 269 acceleration up to 0.2 m/s 2 , and the identified frequency and damping ratio are 4.75 Hz and 270 2.3%, respectively (bracketed results in Table 2). These values agree well with the frequency 271 and damping ratio read from Fig. 13(a) and (b), respectively. 272

Wilcott Bridge 275
The vertical acceleration of Wilcott Bridge was measured, induced by a pedestrian walking 276 over the bridge at 2.2 Hz, exciting the third vertical bending mode (see Table 2). Fig. 14 shows 277 for the free decay at the quarter-span, filtered with a second order Butterworth filter having 278 cut-off frequencies 2.0 Hz and 2.4 Hz. The corresponding frequency-and damping ratio-279 acceleration peak changes are presented in Fig. 15(a) and (b), respectively. Two types of 280 nonlinearity can be observed from inspecting the results in the frequency-acceleration peak 281 curve. With acceleration response amplitudes up to 0.13 m/s 2 (vertical lines in Fig. 15), the 282 frequency increases with the peak value and the structure exhibits hardening non-linearity [37]. 283 In contrast, this FRP footbridge exhibits a softening non-linearity [37] when acceleration peak 284 is > 0.13 m/s 2 . There is a corresponding dramatic change in damping ratio either side of 0.13 285 m/s 2 , as shown in Fig. 15(b). The ambient vibration response, filtered with the same filter, has 286 a peak of about 0.05 m/s 2 , which suggests the fundamental frequency and damping ratio under 287 natural excitation are 2.18 Hz and 1.0%. These results correlate strongly with the fundamental 288 frequency of 2.21 Hz and damping ratio of 1.0% stated in Table 2. In addition, efforts were 289 made during the test programme to excite other modes by using human-induced excitation. The 290 outcome of these excitation exercises was that no useful free decay results could be achieved. concrete composite bridges [46,60,68,[71][72][73][74][75][76][77][78][79], five timber bridges [63,[80][81][82][83] and one 301 aluminium bridge [19]. Summarised in the Appendix table is the information for 51 of these 302 124 non-FRP footbridges to include: bridge description; test method; measured fundamental 303 frequency and damping ratio of the first vertical mode. The Appendix table also has the same 304 engineering information for 14 FRP footbridges. Bridge description and measured fundamental 305 frequency of the remaining 73 non-FRP footbridges used in the comparison evaluation can be 306 found in reference [63]. 307 The table in the Appendix has eleven column headers, which are for: footbridge number; name; 308 country of location; description for form of bridge; year of construction; the girder material; 309 span in metres; if known, the modal mass in tonnes; the fundamental frequency of vibration in 310 Hz; the damping ratio; the test method used to measure the dynamic properties. Note that 11 311 conventional material bridges [64, 65, 67, 69, 71-73, 82, 83] and three FRP bridges [40,41], 312 with the test method marked by OMA*, were tested by using the operational modal analysis 313 method with the presence of excitation from pedestrians performing walking, running, jumping 314 or bouncing. Therefore, the modal parameter results presented for these structures might have 315 been influenced by the presence of people that move on the structure. 316

Fundamental frequency evaluation 317
Vibration serviceability design guidelines for non-FRP footbridges imply that the vibration 318 issues will be avoided if a footbridge has fundamental vertical frequency above 5 Hz (Sétra 319

Damping ratio evaluation 352
Damping ratio is another important property for vibration analysis. The damping level of a 353 structure is not only affected by the construction material, but also by the types of structural 354 connections/joints and bridge bearings [32]. Damping ratios measured on full-scale footbridges 355 are the most representative reference values for structural design. Bachmann et al. [88] 356 summarised the damping ratios of 43 footbridges built before 1991, and they reported the 357 average damping ratios for reinforced concrete, pre-stressed concrete, steel-concrete composite 358 and steel footbridges to be 1.3%, 1.0%, 0.6% and 0.4%, respectively. In design guidelines for 359 these footbridges, a particular damping ratio is usually recommended for vibration response 360 analysis. In AASHTO Load Resistance Factor Design Bridge Design Specifications [89], 2%, 361 1% and 5% are suggested for the dynamic analyses of bridges of: concrete; welded and bolted 362 steel; timber. In Eurocode 5 for timber [90], 1% and 1.5% damping ratios are recommended 363 for footbridges without and with mechanical joints. Owing to limited experimental data from 364 FRP footbridges, the 2016 Prospect for New Guidance in the Design of Fibre Reinforced 365 Polymers [10] recommends an average damping ratio of 1.5% for a conservative lower limit 366 for vibration serviceability analysis. In the AASHTO Guide Specifications for Design of FRP 367 Pedestrian Bridges [86], a damping ratio in the range 2%-5% is considered as more 368 representative in structural analysis. 369 Presented in Fig. 18 [46,60,68,71,72,[74][75][76][77][78][79]91], three of timber 375 (hexagram symbol) [80][81][82] and one of aluminium (diagonal cross symbol) [19]. In addition, 376 the measured damping ratios of the 14 FRP footbridges described in Section 5.1 are introduced 377 using a cross symbol to enable a comparison to be made. The range of damping ratios is from 378 0.14 to 7.9% and the range of spans from 4.8 to 173 m. It is observed that there is no obvious 379 relationship between the damping ratio and main span length, which agrees with the finding of 380 Tilly et al. [32]. Plotted in Fig. 19 are the CDFs for the five different construction materials. It 381 can be seen that 75% of steel footbridges, 58% steel-concrete footbridges and 75% concrete 382 footbridges have damping ratios < 1%. In comparison, only 14 % of FRP footbridges have 383 damping ratios below 1% and 57% of FRP footbridges have a damping ratio > 2%. It is noted 384 that the damping ratio of the three timber footbridges range from 2.4% to 4.7%. 385 The mean, minimum and maximum damping ratios for footbridges of different construction 386 materials are summarised in Table 3. The tabulated results show that at 0.85% steel footbridges 387 have the lowest mean damping level, followed by 0.96% and 0.97% for concrete footbridges 388 and steel-concrete footbridges. At over three times higher, timber footbridges have the highest 389 mean damping level at 3.38%. For FRP footbridges the mean is 2.5%, with the widest range 390 from 0.4% to 7.9%. The average damping levels of steel footbridges and steel-concrete 391 composite footbridges reported herein are higher (by 113% and 62%, respectively) than those 392 for bridges built before 1991 reported in a review by Bachmann et al. [88]. However, the 393 average damping level of concrete footbridges at 0.86% is similar to the value for pre-stressed 394 concrete footbridges and is lower than value for reinforced concrete bridges reported by 395 Bachmann et al. [88]. Over the past three decades the mean damping ratios for steel, concrete 396 and composite concrete-steel bridges have become more similar. The recommendations of the 397 design guidelines that still propose use of different damping values for these three materials 398 might therefore need to be updated to reflect this new reality. 399

Comparison of accelerance peaks of FRP and conventional footbridges 402
In this section a comparison is made between the accelerance peaks of FRP and conventional 403 footbridges of the same bridge length, deck width and mode shape. 404 The accelerance peak at the fundamental frequency v f of a footbridge of given bridge length, 405 deck width and mode shape can be approximately calculated as 406 where m is the modal mass and  is the damping ratio [92]. The fundamental frequency v f 408 can be determined from Eq. (1) for a given span length. The modal mass is proportional to the 409 physical mass per square metre. 410 The representative values of physical mass per square metre for FRP and conventional 411 footbridges are estimated using the data from ten FRP footbridges and nine conventional 412 material footbridges. These 19 footbridges are in public use and they are chosen because of the 413 availability of data on physical mass. Summarised in Tables 4 and 5 are their descriptions, for  414 girder material, total length, main span length, width, total physical mass of girder structure 415 and mass per square metre. The last columns in the two tables show that the average physical 416 mass per square metre for the nine conventional footbridges is around 1200 kg/m 2 which is 417 around 8.6 times higher than that of the ten FRP footbridges (around 140 kg/m 2 ). This means 418 that the modal masses of conventional bridge will be 8.6 times larger than that for the FRP 419 bridge of the same bridge length, deck width and mode shape. 420  According to Eq.(2), the accelerance peak at the fundamental frequency v f of FRP bridge is 424 8.6 times larger than that for the non-FRP bridge of the same bridge length, deck width, 425 damping ratio and mode shape. However, owing to a positive feature that the average damping 426 value of FRP bridges is around 2.5 times larger (Table 3), the accelerance peak at the 427 fundamental frequency v f of FRP bridge is likely to be about 3.5 times larger. The same 428 conclusion can be drawn for accelerance peaks at higher frequencies. 429 Given that FRP footbridges are found to be, on average, more responsive to dynamic loading 430 by humans than conventional structures, there is strong possibility that their modes could be 431 responsive to excitation by 3 rd or even higher harmonics of the walking force. The minimum 432 frequency limit of 5 Hz that is often deemed appropriate for conventional structures might be 433 too low for FRP footbridges. 434

Concluding remarks 435
In this paper, we present new vibration testing and modal analysis results for eight FRP 436 footbridges. A literature review has also been made to extract dynamic properties of 124 post-437 1991 non-FRP footbridges that are made of steel, concrete, steel-concrete composite, timber or 438 aluminium, and six FRP footbridges. Comparing dynamic properties of 14 FRP footbridges 439 with the non-FRP footbridges shows that fundamental frequencies at the same spans are 440 independent of structural material. FRP footbridges are found to have, on average, a 2.5 times 441 higher damping ratio for the first vertical mode than that of steel, concrete, and steel-concrete 442 composite footbridges. However, they seem to have a lower damping ratio than timber 443 footbridges. The frequencies and damping ratios of FRP footbridges identified from the 444 measured free decay responses are found to be dependent on response amplitude. This 445 amplitude dependence for natural frequency is likely to improve vibration performance of these 446 bridges (compared with the alternative of amplitude-independent natural frequency) due to 447 difficulties to develop resonance response when structural frequency is varying with amplitude. 448 In addition, it is found that the accelerance peaks of FRP footbridges are, on average, about 3.5 449 times higher than those of conventional footbridges. We conclude that it may be inappropriate 450 to use the minimum frequency limits from serviceability guidelines for conventional bridges, 451 as is currently frequent practice, to ensure satisfying the vibration serviceability state in the 452 design of FRP bridges. This study provides crucial missing technical information that is 453 required for developing reliable design method for 'light-weight' FRP footbridges, and it will 454 support the preparation of national and international consensus design guidance for their 455 dynamic design.