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Suspension Bridges - an overview ScienceDirect Topics

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• 3.4.1 Suspension bridges 3.4.1 Suspension bridgesSuspension bridges (Figure 18.4) typically consist of two (and sometimes four) parallel cables separated by a distance approximately equal to the roadway deck width that they support. These cables act as tension elements and extend from anchors at each of their ends over the tops of the intermediate towers. The deck is suspended by strong ropes running from the deck level to the main cables. The main cables can consist of parallel strong wires that are aerially spun in place or prefabricated wire ropes. The deck can be stiffened by a truss or by girder elements. The purpose of the stiffening element is to ensure aerodynamic stability and to limit the local angel changes in the deck. Suspension bridges are used for spans of 300– 2300 m. The bridge can be erected without any ground-based towers. The resulting bridge is very elegant in appearance, and its form clearly expresses its function. As the existing inventory of suspension bridges have aged, inspections have revealed active corrosion and stress corrosion cracking in many of the wires comprising the main cables. This has led to the installation of dehumidification systems in many of the new and existing bridges.Figure 18.4. Forth Road Bridge, Queensferry, Scotlandcourtesy of Barry Colford.URL: https://www.sciencedirect.com/science/article/pii/B9780128000588000189Weiwei Lin, Teruhiko Yoda, in , 2017
• 1.3.8.6 Suspension Bridges 1.3.8.6 Suspension BridgesA typical suspension bridge is a continuous girder suspended by suspension cables, which pass through the main towers with the aid of a special structure known as a saddle, and end on big anchorages that hold them. Fig. 1.26 shows the essential structural members and elements of typical, including tower, hanger, main girder, and the anchorage. The main forces in a suspension bridge are tension in the cables and compression in the towers. The deck, which is usually a truss or a box girder, is connected to the suspension cables by vertical suspender cables or rods, called hangers, which are also in tension. The weight is transferred by the cables to the towers, which in turn transfer the weight to the anchorages on both ends of the bridge, then finally to the ground.Fig. 1.26. Image of the suspension bridge.The curve shape of the suspension cables is similar to that of arch. However, the suspension cable can only sustain the tensile forces, which is different from the compressive forces in the arch. Also because of this, the cable will never “buckle” and highly efficient use of high strength steel materials becomes possible. The use of suspension bridges makes longer main spans achievable than with any other types of bridges, and they are practical for spans up to around 2 km or even larger. The top 10 largest suspension bridges in the world are listed in Table 1.4. The Akashi Kaikyō Bridge (Fig. 1.27) crosses the busy Akashi Strait and links the city of Kobe on the mainland of Honshu to Iwaya on Awaji Island, in Japan. Since its completion in 1998, the bridge has had the longest central span of any suspension bridge in the world at 1991 m. The central spans of the top 10 largest suspension bridges are longer than 1300 m, indicating the incomparable spanning capability of this bridge type. The suspension bridge will be discussed in detail in Chapter 11.Table 1.4. List of Longest Suspension BridgesRankNameMain Span (m)Year OpenedLocationCountry1Akashi Kaikyō Bridge19911998Kobe-Awaji IslandJapan2Xihoumen Bridge16502009ZhoushanChina3Great Belt Bridge16241998Korsør-SprogøDenmark4Yi Sun-sin Bridge15452012Gwangyang-YeosuSouth Korea5Runyang Bridge14902005Yangzhou-ZhenjiangChina6Nanjing Fourth Yangtze Bridge14182012NanjingChina7Humber Bridge14101981Hessle-Barton-upon-HumberUnited Kingdom8Jiangyin Bridge13851999Jiangyin-JingjiangChina9Tsing Ma Bridge13771997Tsing Yi-Ma WanHong Kong10Hardanger Bridge13102013Vallavik-BuNorwayFig. 1.27. The Akashi Kaikyō Bridge (Japan, the longest bridge since 1998).URL: https://www.sciencedirect.com/science/article/pii/B9780128044322000013A. Pipinato, in , 2016
• 14.4 Case studies 14.4 Case studiesThis section demonstrates smartphone applications for measuring bridge response using a noncontact approach. The bridge and the monitoring system are introduced. Image processing techniques, which measure vertical deflections of the bridge while it was exposed to forced excitations, are discussed and explained. The bridge fundamental frequency computed from smartphone videos and calculated from GNSS data is in a good agreement.14.4.1 Pedestrian suspension bridgeThe Wilford Suspension Bridge (see Fig. 14.3), which has a status of Grade II listed heritage buildings, is located in Nottingham, the United Kingdom. It is a pedestrian bridge, which also serves as a water aqueduct. The suspended span is 69 m long, crosses the River Trent, and links Nottingham and West Bridgford. The bridge has two main cables, in which a steel structure covered with a timber deck is suspended. The bridge was rebuilt/renovated between 2008 and 2010. The bridge dynamic displacement and modal properties were studied using a multimode GNSS processing (Yu et al., 2014) and combination of GPS and robotic total station (Psimoulis et al., 2016). The natural vertical frequency of the bridge was found to be around 1.69 Hz.Figure 14.3. Smartphone monitoring setup for the Wilford Suspension Bridge.In this study, Samsung S9 plus (S1) and Samsung S8 (S2) are selected to capture dynamic properties of the bridge. Smartphones are positioned at slightly different locations approximately 45 m away from the bridge on the left bank of the river. Fig. 14.3 shows smartphone monitoring setup. Smartphones record 4k videos at 30 fps. The experiment is organized by the University of Nottingham as a part of student assignment. GNSS collects vertical displacements at the midspan and 1/3-span (or 23 m from the left end of the suspended superstructure) of the bridge. The bridge is excited by 10 students jumping near GNSS locations. In this example, the bridge dynamic response is analyzed for a period when the jumping took place at the 1/3-span of the bridge.An image frame as recorded with S1 is shown in Fig. 14.4. Four reference points on the structure are selected to derive a transformation matrix (see Fig. 14.4 (left)). The matrix converts any given coordinate point to the defined coordinate system requiring no additional scale factors. The bottom and top left points (bottom and top of the hanger) are set to [0, 0] and [0, 6] x and y coordinates (in meters), respectively. x coordinates for the bottom and top left points are 65 m, and y coordinates are kept the same as for the points on the left side. A region of interest (ROI) includes both GNSS antenna locations. Targets T-1 and T-2 are selected close to the antenna locations. Mini eigenvalue algorithm is chosen to detect features in the targets. Targets with their features and centers (calculated as an average value from feature coordinates) are shown in Fig. 14.4 (right).Figure 14.4. Image processing approach. Selection of (left) reference points and ROI, and (right) targets.Vertical displacement histories of T-1 for the duration of excitations, which lasted approximately 40 s, computed from the video recorded with S1 are plotted in Fig. 14.5(a) The signal is preprocessed with a low-pass filter, and camera movements are removed. The signal has either noise or human-induced vibrations before and after forced excitations (see displacements before 10 s and after 55 s). Maximum peak-to-peak displacements are around 14 mm, which are similar to GNSS measurements. Fig. 14.5(b) gives a closer look at the period between 22 and 35.5 s for T-1 displacements from S1 and S2. The plot shows that S1 provides a better quality video than S2, resulting in smoother displacements. Measurement plots are synchronized/merged manually. S2 T-1 oscillations between 27 and 32 s are lagging behind S1 T-2, resulting in a high root mean square deviation (i.e., 2.5 mm for the period between 22 and 35.5 s). PSD is computed to find the first vertical frequency of the bridge. For both smartphone signals, the fundamental frequency at T-1 location is 1.671 Hz (see Fig. 14.5(c)). GNSS measured 1.675 Hz.Figure 14.5. The bridge dynamic response: T-1 vertical displacements form (a) S1 for the duration of excitation and (b) both S1 and S2 for 13 s period; (c) PSD of T-1.S1 video allows the computation of vertical displacements of the deck at hanger connections along the length of the bridge. Fig. 14.6 depicts upward (positive) and downward (negative) displacements at the 24th second. The deck displacement curve for the first 48 m from the left side of the bridge (i.e., side that is closer to the camera) is a parabolic and realistic. The part of the deck further away from the camera view has large measurement discrepancies. The vertical distance between the selected reference points (as shown in Fig. 14.4) is equal to 682 and 309 px on the left and right sides, respectively, leading to larger measurement error.Figure 14.6. Bridge vertical displacements at hanger connections to the deck.The Wilford Suspension Bridge study demonstrates that accurate dynamic response can be obtained using smartphone cameras. The difference between the first frequency calculated from GNSS and smartphones measurements is only 0.2%. Small displacements can be measured. In Fig. 14.6, the maximum peak-to-peak vertical displacement of the first hanger from the right side is ± 0.85 mm, which is 682[px]6000[mm]×0.85[mm]≅110[px]. With more sophisticated image processing algorithms, accuracies smaller than 1/50 px can be achieved.URL: https://www.sciencedirect.com/science/article/pii/B978012819946600014XM. De Miranda, in , 2016
• 7.5.2 Application to the Vincent Thomas Bridge 7.5.2 Application to the Vincent Thomas BridgeThe Vincent Thomas Bridge is a suspension bridge located in Los Angeles Harbor, San Pedro, California. The bridge superstructure consists of a main span of approximately 457 m, two suspended side spans of 154 m each, and a 10-span approach of approximately 545 m length on either end. The total bridge length is approximately 1850 m. The bridge was completed in 1964, and in 1980 was instrumented with 26 accelerometers as part of a seismic upgrading project. The strong-motion instrumentation was installed and is maintained by the California Division of Mines and Geology. Figure 7.7 shows the elevation and plan view of the sensor locations. A summary of the sensor locations and numbering is presented in Table 7.4.7.7. (a) Overall schematic of the bridge with sensor locations; (b) elevation of the bridge and plan view of sensor locations.Table 7.4. Numbering and locations of sensorsSensor No.Location1, 14, 23West tower, base of south column2West tower, top of deck truss3Center of main span, bottom of deck truss4Center of main span, top of deck truss5Main span, 1/3rd Pt., top of deck truss6East tower, top of deck truss7Center of side span, top of deck truss8, 10East tower, top of south column9,13, 19East tower, base of south column11East tower, top of north column12East tower, top of deck truss15Center of main span, N. edge of deck16Center of main span, S. edge of deck17Main span, 1/3rd Pt., N. edge of deck18Main span, 1/3rd Pt., S. edge of deck20East tower, base of north column21Side span, center, N. edge of deck22Side span, center, S. edge of deck24, 25, 26East anchor, baseAs an example of the frequency domain NeXT method, two sets of acceleration data collected from the bridge on occasions two months apart due to ambient excitation were used. Ambient excitations to the bridge are mainly caused by wind load and traffic load. The total length of the time history was 380 seconds for Set 1 and 360 seconds for Set 2. The 26 accelerometers installed on the bridge to measure accelerations in three different directions, namely, vertical, lateral and longitudinal directions. For the purposes of the current discussion, it was surmised from previous inspection records that deck vertical vibration was of the primary concern as related to structural health. Six sensors measuring the deck vertical acceleration were thus chosen for analysis. The six sensors chosen are sensors 15, 16, 17, 18, 21, and 22 as shown in Fig. 7.7.The time histories pertaining to data from Set 1 are plotted in Fig. 7.8 as an example. It should be noted that the time histories shown in Fig. 7.8 exhibit some non-stationary features. Direct current (DC) shift is also observed on some of the channels. Similar features were also seen in Set 2. After detrending the data, the cross spectra between sensor 15 and sensors 16, 17, 18, 21, 22 together with 15 itself are calculated. The FNExT technique described in the earlier section was used to identify modal parameters from ambient vibration data. Previous studies have shown that the dominant modes of vibration of the bridge concentrate in the frequency range between 0.2 Hz and 1.1 Hz. Focus is thus placed on this frequency range during the FNExT technique identification process. The selection of model order in FNExT technique can be facilitated by directly observing the peaks in cross-spectrum plots or by using more sophisticated frequency domain indicators such as the modal indicator function and complex modal indicator function.7.8. Acceleration time history from Set 1.A comparison of results obtained through the use of the proposed technique with those from two previous studies is presented in Table 7.5. Niazy (1991) studied the dynamics of the Vincent Thomas Bridge using both FEM based and ambient vibration based experimentally identified modal parameter. Luş et al. (1999) used the Observer/Kalman filter Identification (OKID) technique to identify modal parameters of the Vincent Thomas Bridge using response data from the 1987 Whittier earthquake and 1994 Northridge earthquake. As can be seen from Table 7.5 the results from the proposed method show good agreement with previous results. In particular, all modes identified using ambient vibration reported by Niazy (1999) are identified using the proposed method with good accuracy with the exception of a single mode around 0.579 Hz. Figures 7.9 and 7.10 show the measured and synthesized (using identified modal parameters) cross spectrum function of sensors 15, 16, 17, 18, 21 and 22 pertaining to Sets 1 and 2, respectively. The agreement between the measured and synthesized cross spectrum function is excellent.Table 7.5. Modal frequencies of vertically dominant modes as reported by Niazy (1991) and Luş et al. (1999) and Identified by FNExT technique using only deck vertical response (Unit: Hz)FNExT Ambient1FNExT Ambient2Luş et al. – Whittier earthquakeLuş et al. – Northridge earthquakeNiazy – AmbientNiazy – FEM0.2260.2270.2340.2250.2160.2010.2420.242––0.2340.2230.3660.3690.3880.3040.3660.336–––––0.3440.464–0.4640.4590.4870.4220.5370.5400.5760.5330.5790.526––0.61700.600––0.6370.6370.61740.632––0.7730.7670.7690.791–0.7720.8040.8050.8040.8110.8350.8530.8590.857–––0.9740.9650.9470.9741.0880.068–1.110–1.0651Set 12Set 27.9. Measured and synthesized cross spectrum function pertaining to Set 1. The solid line represents the measured data whereas the dashed line represents the synthesized data.7.10. Measured and synthesized cross spectrum function pertaining to Set 2. the solid line represents the measured data whereas the dashed line represents the synthesized data.URL: https://www.sciencedirect.com/science/article/pii/B9781845693923500074J.W.S. Hearle, in , 2016
• 13.4.3 Bridges 13.4.3 BridgesIn former times, fibre ropes were commonly used in suspension bridges for foot traffic (Fig. 13.24 (a)), and examples can still be found (Fig. 13.24 (b)). Indeed DIY instructions for building a small rope suspension bridge can be found on Google. Not surprisingly, the first railway suspension bridge, which was built in 1855 over the Niagara Gorge, USA, used steel cables. Once again, a reluctance to change established technology means that the potential for fibre ropes has been neglected, even for the on-off plans for the longest single span suspension bridge, across the Strait of Messina, between mainland Italy and Sicily, where the saving in weight would be considerable.Fig. 13.24. (a) An old rope bridge in Japan. (b) Crossing a rope bridge in New Guinea.URL: https://www.sciencedirect.com/science/article/pii/B9781782424659000148E. Caetano, in , 2016

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