LJUNGAN BRIDGE, ANGE SWEDEN

LJUNGAN BRIDGE, ANGE SWEDEN Design of dampers for the hangers 3 to 6 Documentation of the installation procedure and the verification Measurements from 13.9.5-14.9.5 Report: W983/115 Contract: M-79-5

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 2 Ljungan Bridge, Ange Sweden Design of dampers for the hangers 3 to 6 Documentation of the installation procedure and the verification Measurements from 13.9.5-14.9.5 Client: MULTICON GMBH WESEL Prepared by: Prof. Sedlacek & Partner Technologien im Bauwesen GmbH TRAGWERKSPLANUNG BAUDYNAMIK WINDINGENIEURWESEN STAHLBAU KONSTRUKTIVER GLASBAU SOFTWAREENTWICKLUNG Pauwelsstraße 19 D 52 74 Aachen Authors: Dr.-Ing. Michael Hortmanns This report consists of 5 pages. Aachen, November 28 th 25

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 3 Content 1 Objectives...4 2 Design of the dampers...5 2.1 Maximum allowable amplitudes...5 2.2 Maximum amplitudes without dampers...5 2.3 Required structural damping of the hangers...6 2.4 Damper Design...7 3 Measurements...15 4 Results...17 5 Conclusion...2 6 References...21 Annex A Detailed Results of manual excitation

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 4 1 Objectives At a railway bridge crossing the river Ljungan close to Ange in Sweden full-scale tests were performed in order to measure the first eigen-frequencies and the structural damping of each hanger. These data have been used for the design of dampers, which were installed in September 25. This report describes the design of the dampers and the measurements at the bridge after the installation of the dampers. Figure 1.1 Sight view on the bridge from North (the bridge in the front is not connected to the arch bridge)

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 5 2 Design of the dampers 2.1 Maximum allowable amplitudes The maximum allowable amplitudes were given by the client Bankverket in Sweden. The following table shows the tolerable values, which will ensure, if they are not exceeded, that no additional fatigue-damage problems will occur. Table 2.1 Tolerable amplitudes Hanger maximum tolerable amplitudes given by Bankverket perpendicular =y parallel =x mm mm SW-6O 2, 2, SW-5OO 2, 2, SW-4OO 1,5 1,5 SW-3OO 1, 1, 2.2 Maximum amplitudes without dampers For the design of the dampers the maximum vibration amplitudes of the hangers, induced by trains crossing the bridge, have to be known. These amplitudes can be obtained from the report [3]. In this report long term measurements at the hangers SW-3OO, SW-4OO, SW- 5OO and SW-6OO are documented. In the figures 4.19-4.21 and 4.23-4.25 Time histories of the response for different kind of trains are reported. Based on these results the following maximum amplitudes for each hanger will be used.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 6 Table 2.2 Maximum measured vibration amplitudes of the hangers, obtained from [3], yellow fields estimated based on measured damping values and maximum amplitudes for hangers SW- 5OO SW-3OO Hanger measured maximum vibration amplitudes ID9 perpendicular =y ID9 parallel =x ID19 perpendicular =y ID19 parallel =x maximum tolerable amplitudes given by Bankverket perpendicular =y parallel =x measured structural damping mean value perpendicular =y measured structural damping mean value parallel =x mm mm mm mm mm mm - - SW-3WO 19,8 1,67 7,2 8, 1, 1,,1,6 SW-4WO 24,23 8,8 2,77 3,6 1,5 1,5,13,1 SW-5WO 16, 2,33 2,5 1,33 2, 2,,15,3 SW-6O 2,8 4,2 3,25 2,4 2, 2,,14,11 SW-5OO 16, 7, 2,5 4, 2, 2,,15,1 SW-4OO 35, 11, 4, 4,5 1,5 1,5,9,8 SW-3OO 11, 4, 4, 3, 1, 1,,18,16 SW-3WU 22, 6,4 8, 4,8 1, 1,,9,1 SW-4WU 26,25 4,4 3, 1,8 1,5 1,5,12,2 SW-5WU 8, 1,273 1,25,727 2, 2,,3,55 SW-6U 22,4 7,7 3,5 4,4 2, 2,,13,6 SW-5OU 2,4,778,375,444 2, 2,,1,9 SW-4OU 22,5 6,769 2,571 2,769 1,5 1,5,14,13 SW-3OU 6, 8, 2,182 6, 1, 1,,33,8 2.3 Required structural damping of the hangers For the design of the dampers it will be assumed, that the maximum amplitudes will occur for a quasi resonant vibrations. This allows to calculate the maximum required structural damping by using the following formulae: δ = required, i δ, i * y y max, i tolerable, i with: δ required required logarithmic decrement of damping for hanger i δ o,i y max,i y tolerable,i existing logarithmic decrement of damping without damper for hanger i maximum measured vibration amplitude for hanger I tolerable vibration amplitude for hanger i and the additional damping δ i for hanger i is then: δ = δ i required, i δ, i For the damper design both directions, parallel and perpendicular are considered. The following table shows the required damping for each hanger. The values, marked yellow are values which are calculated assuming, that the maximum amplitudes for these hangers are

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 7 the same than for the hangers which were analysed in the long term measurements of the university of Stockholm [3]. Table 2.3 Required damping values for each hanger for vibrations parallel and perpendicular Frequency (without dampers) Frequency (without dampers) gen. Mass (with d=8mm and m=39,46 kg/m) minimum log. Decrement of structural damping mimimum log. Decrement of structural damping total log. Decrement of damping required total log. Decrement of damping required additional Damping required additional Damping required Hanger perpendicular parallel Length d=8mm perpendicular parallel perpendicular parallel perpendicular parallel Hz Hz m kg - - - - - - SW-3WO 6,25 7,81 6,24 123,1,1,6,198,64,188,58 SW-4WO 5,67 6,45 7,36 145,1,13,1,21,59,197,49 SW-5WO 4,98 5,71 8, 157,8,15,3,12,35,15,5 SW-6O 4,35 4,98 8,23 162,4,1,1,146,23,136,13 SW-5OO 3,71 4,3 8, 157,8,13,6,12,35,17,29 SW-4OO 5,96 7,23 7,36 145,1,8,5,21,59,22,54 SW-3OO 6,6 7,72 6,24 123,1,8,12,198,64,19,52 SW-3WU 7,52 8,3 6,24 123,1,9,1,198,64,189,54 SW-4WU 4,69 5,57 7,36 145,1,12,2,21,59,198,39 SW-5WU 5,8 6,25 8, 157,8,3,55,12,35,9, SW-6U 5,3 5,96 8,23 162,4,13,6,146,23,133,17 SW-5OU 4,79 5,67 8, 157,8,1,9,12,35,2, SW-4OU 5,47 6,16 7,36 145,1,14,13,21,59,196,46 SW-3OU 6,84 8,5 6,24 123,1,33,8,198,64,165,56 2.4 Damper Design The dynamic properties of the damper shave been calculated based on the provisions given by den Hartog. The calculation is given exemplary for the damper 4WO in the following tables. The exciting force amplitude of F =2 N in the calculation was estimated based on the results of the long term full scale tests. Assuming a quasi resonant response of the hangers, the force amplitude can be calculated with: F = y δ ω m π i 2, i max, i i gen, i with: y max,i maximum amplitude measured at hanger i δ i ω i m gen,i For hanger 4WU this gives: existing logarithmic decrement of damping without damper for hanger i circular-frequency for hanger I generalized mass for hanger i F,4WU,13 = π = π 2 24, 23/1 (2 5, 67) 145 18,5 N In the calculations the exciting force has been taken constant for all hangers.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 8 The first table shows the calculation result for a damper which increases the damping up to the required damping value. Table 2.4 Calculation sheet for the damper properties of hanger 4WU, for the required damping value SW-4WO log. Decrement δvorh,13 gen. Mass M gen 145 kg Eigenfrequenc y f e 5,67 Hz Exciting Force F err 2 N gen. Stiffness c gen 184.195 N/m min. massratio required 1,9 µerf % min. mass m erf required 1,589 kg opt. Dampig ratio in % D opt,63 opt. Damping constant k opt 7 kg/s Frequency damper f D 5,61 Hz Stiffness damper c D 1.973 N/m Amplitude Hauptma. y 1,47 mm rel. Ampl. y Damper Dämpfer 1,82 mm It can be seen, that the relative amplitude of the damper is very large. Therefore the calculation has been optimised such, that the relative amplitude is in a range of only 3 mm. This ensures, that no fatigue problems will occur at the cantilever beams inside the damper boxes. The result for the second calculation is given in Table 2.5. These calculations were done for all hangers and all directions. The final dampers design consists of 4 boxes for each hanger, which means, that the damper mass calculated in Table 2.5 is divided into 4 parts. This procedure allows to minimize the size of the cantilever spring inside the boxes and to minimize the external dimensions of the entire damper for each hanger. Due to the mass, which is larger than the mass which is necessary to reach the required damping value, the maximum additional damping will become larger and the dampers will work in a broad range of frequencies. This gives additional safety and ensures, that the dampers will be effective also when trains with different weight, and therefore different influence on the eigen-frequencies of the hangers, will pass the bridge. The damping inside of the boxes is realized with silicon oil. Due to the low temperatures, which may occur at the site in Sweden a Silicon oil with properties, which are comparable over a wide range of temperatures has been used.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 9 Table 2.5 Calculation sheet for the damper properties of hanger 4WU, for rel. Amplitudes of ca. 3mm SW-4WO log. Decrement δvorh,13 gen. Mass M gen 145 kg Eigenfrequenc y f e 5,67 Hz Exciting Force F err 2 N gen. Stiffness c gen 184.195 N/m min. massratio required 4,9 µerf % min. mass m erf required 5,933 kg opt. Dampig ratio in % D opt,1166 opt. Damping constant k opt 49 kg/s Frequency damper f D 5,45 Hz Stiffness damper c D 6.95 N/m Amplitude Hauptma. y,77 mm rel. Ampl. y Damper Dämpfer 3,2 mm The dampers consist of 4 boxes filled with silicon oil, a cantilever beam with circular cross section and a mass, which is connected at the end of the beam. The length of the cantilever beams can be adjusted by screws at the top of the boxes. The amount of silicon oil can be changed by removing the cantilever beams and then to fill in or to remove silicon oil. This procedure is necessary to get the correct height of silicon oil inside of the boxes. The height of the silicon oil in the boxes has to be in a specific range, because the distance on which the damper masses are dipped into the silicon oil is the dominant parameter to get the correct damper constant. This process was done in the laboratory in Aachen. Therefore, the dampers could be delivered to the bridge with their final adjustment. During the installation process only two times the dampers have been readjusted (5WU and 3 WU). The following figure shows the sketches prepared by the company Multicon.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 1 Figure 2.1 Drawings of the dampers, prepared by Multicon GmbH The dampers have been installed in the middle of each hanger. The position of the dampers are illustrated in the following figure.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 11 Figure 2.2 Position of the dampers The damper have been installed with the help of a rail bus on the bridge. The following figures show some images of the installation procedure. Figure 2.3 Fixation of the bottom ring

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 12 Figure 2.4 Connecting the two halves of the damper with screws Figure 2.5 Control of the screws and fixation with Logtite

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 13 Figure 2.6 Installing the "cones" and sealing with Silicone Figure 2.7 Damper installed with measurement equipment

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 14 Figure 2.8 Almost all dampers installed Figure 2.9 Full scale bridge with all dampers installed

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 15 3 Measurements The hangers are excited by hand in resonance parallel and perpendicular to the bridge axis. The vibration amplitudes are measured with 2 sensors (accelerometers), which are fixed at a level close to the middle of each hanger. The definition of hanger numbering and the numbering of the sensors are shown in the following figure. Please note, only the accelerometers A and B have been used for the verification measurements. The numbering of the hangers is the same like in the first measurements. Figure 3.1 Definition of hanger numbering and of the positions of the accelerometers The hangers are numbered as follows: iwo iwu ioo iou Hanger number i, West upstream Hanger number i, West downstream Hanger number i, East upstream Hanger number i, East downstream During the installation and measurement process the bridge was occupied by a rail-bus, which was used to get access to the hangers. The following figure shows the rail-bus on the bridge.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 16 Bild 3.1 Rail bus in the middle of the bridge The weight of the rail bus is much larger that the weight of the tractor, which was used in the first measurements. Due to the weight of the rail bus the normal forces in the hangers were increased and the eigen-frequencies have been larger, than those expected in the calculations for the damper design. This effect was large for all measurements, where the railbus was standing completely on the bridge. In the comparisons of the results (see 4) it can be seen, that for the hangers on the West-side of the bridge the measured frequencies are much closer to the expected frequencies than the frequencies on the East Side of the bridge. Bild 3.2 Signboard at the rail bus with characteristic data, especially weight = 28,3 t

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 17 4 Results The following table shows a comparison of the damping values required and the measured damping values. Table 4.1 Comparison of measured damping values with damper with the damping values required total log. Decrement of damping required total log. Decrement of damping required total log. Decrement of damping measured with damper (mean value of evaluable range of amplitudes) safety factor: damping measured/ damping required Hanger perpendicular parallel perpendicular parallel perpendicular parallel - - - - - - SW-3WO,198,64,3,16 1,5 2,5 SW-4WO,21,59,31,4 1,5 6,8 SW-5WO,12,35,27,23 2,3 6,6 SW-6O,146,23,25,15 1,7 6,5 SW-5OO,12,35,33,17 2,8 4,9 SW-4OO,21,59,4,16 1,9 2,7 SW-3OO,198,64,33,12 1,7 1,9 SW-3WU,198,64,25,2 1,3 3,1 SW-4WU,21,59,3,32 1,4 5,5 SW-5WU,12,35,2,2 1,7 5,7 SW-6U,146,23,2,35 1,4 15,2 SW-5OU,12,35,27,4 2,3 11,4 SW-4OU,21,59,3,22 1,4 3,8 SW-3OU,198,64,2,11 1, 1,7 The measured damping values are always equal or larger than the required values. The maximum safety factors are 2,8 for vibrations perpendicular to the bridge axis and 15,2 for vibrations parallel to the bridge axis. Table 4.2 shows a comparison of the eigen-frequencies. As mentioned already the rail bus had a significant influence on the eigen-frequencies. Almost all eigen-frequencies on the East side of the bridge are larger than the expected ones. Anyway, even the frequencies were not always in the expected range, the effectiveness of the dampers is always sufficient. Another special effect can be seen at hanger 5WU. In the first measurements already, the eigen-frequencies for this hanger were lower with the tractor on the bridge. This result was

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 18 marked with stars in figure 3.2 and figure 3.3. of report W967/65). Obviously the dynamic behaviour of this hanger is influenced by the connection between the hanger and the arch. Figure 4.1 shows this in detail. The relatively small gap between the hanger and the borders of the lower flange of the arch lead to a direct contact between the hanger and the flange if the hanger starts vibrating. Therefore it is difficult to excite the hanger without the hanger touching the bottom flange. Even the frequencies are not in the expected range the damping values with damper are sufficient, also for this hanger. Very small gap Figure 4.1 Detail of the connection between hanger 5WU and the arch

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 19 Table 4.2 Comparison of the Eigen-frequencies for the first mode perpendicular and parallel to the bridge axis, results of the first measurements, expected frequencies with dampers and the measured values with the rail bus on the bridge Hanger Frequencies without Frequencies expected with Frequencies measured with damper damper damper (and railbus) perpendicular parallel perpendicular parallel perpendicular parallel =y =x =y =x =y =x Hz Hz Hz Hz Hz Hz SW-3WO 6,25 7,81 5,8 7,24 5,86 7,22 SW-4WO 5,67 6,45 5,32 6,5 5,8 6,25 SW-5WO 4,98 5,71 4,69 5,38 4,3 6,1 SW-6O 4,35 4,98 4,1 4,7 4,6 5,4 SW-5OO 3,71 4,3 3,5 4,5 3,9 4,7 SW-4OO 5,96 7,23 5,59 6,78 5,47 7,4 SW-3OO 6,6 7,72 5,62 7,16 6,26 8,1 SW-3WU 7,52 8,3 6,97 7,7 6,64 7,6 SW-4WU 4,69 5,57 4,4 5,22 4,5 5,27 SW-5WU 5,8 6,25 4,79 5,89 3,6 4,6 SW-6U 5,3 5,96 4,75 5,62 4,6 5,8 SW-5OU 4,79 5,67 4,51 5,34 4,2 5,7 SW-4OU 5,47 6,16 5,13 5,77 5,8 6,74 SW-3OU 6,84 8,5 6,34 7,88 6,25 8,6

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 2 5 Conclusion The damping values with dampers are much large than without damper. The required values at each hanger are reached or exceeded. The maximum safety factor is 2,1 for vibrations perpendicular to the bridges axis and 13, for vibrations parallel to the bridge axis. Due to the mass of the dampers itself and due to the weight of the rail bus, which is much larger than the weight of the tractor, the frequencies are different compared with the results of the first measurements. The influence of the rail bus will increase the frequencies of the hangers. Due to that, the dampers are not working in their optimal design point. Anyway, this will happen every time when trains will pass the bridge. This was the reason why the dampers were designed such, that they are working in a broad band of frequencies. Therefore the effect of the dampers is anytime sufficient, even so when the frequencies of the hangers are not in the optimal range. The conclusion of the measurements is: The required damping values for all hangers are reached or exceeded. Therefore, the performance of the bridge has reached the required value.

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 21 6 References [1] EN 1396-3, Zylindrische Schraubenfedern aus runden Drähten und Stäben Berechnung und Konstruktion Teil 3: Drehfedern, Dezember 25 [2] Hortmanns M., Ljungan Bridge, Ange Sweden Full Scale Measurements, 3.5.5 1.6.5, Report W967/65, PSP-Technologien im Bauwesen GmbH [3] Andersson A., Malm R.; Measurement evaluation and FEM Simulation of Bridge dynamcis A case study of a langer beam bridge, Technical report from Royal Institute of Technology Department of Mechanics, Stockholm Sweden, January 24

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 22 Annex A Detailed Results of manual excitation

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 23 7.5 5 2.5-2.5-5 -7.5 2.5 5 7.5 1 12.5 15.8.7.6.5.4.3.2.1 1 2 3 4 5.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 4 3wo-1k-a Figure A. 1 Hanger 3WO (West, upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 24 3 2 1-1 -2-3 2.5 5 7.5 1 12.5 15.25.2.15.1.5 1 2 3 4 5.175.15.125.1.75.5.25.1.2.3.4.5.6.7.8 3wo-3k-b Figure A. 2 Hanger 3WO (West, upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 25 7.5 5 2.5-2.5-5 -7.5 2 4 6 8 1.6.5.4.3.2.1 1 2 3 4 5.35.3.25.2.15.1.5 1 2 3 4 5 4wo-2n_a Figure A. 3 Hanger 4WO (West, upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 26 6 4 2-2 -4-6 2 4 6 8 1.1.8.6.4.2 1 2 3 4 5.5.4.3.2.1.25.5.75 1 1.25 1.5 1.75 4wo-4n-b Figure A. 4 Hanger 4WO (West, upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 27 3 2 1-1 -2-3 2.5 5 7.5 1 12.5.4.35.3.25.2.15.1.5 1 2 3 4 5.4.35.3.25.2.15.1.5.5 1 1.5 2 2.5 3 5wo-5-bp Figure A. 5 Hanger 5WO (West, upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 28.1.75.5.25 -.25 -.5 -.75 -.1 2.5 5 7.5 1 12.5 3E-5 2.5E-5 2E-5 1.5E-5 1E-5 5E-6 1 2 3 4 5.3.25.2.15.1.5.1.2.3.4.5.6 5wo-4-b-b Figure A. 6 Hanger 5WO (West, upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 29 5 4 3 2 1-1 -2-3 -4 5 1 15 2 25.8.7.6.5.4.3.2.1 1 2 3 4 5.3.25.2.15.1.5.5 1 1.5 2 2.5 3 3.5 6o-1n-a_ Figure A. 7 Hanger 6WO (upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 3 4 3 2 1-1 -2-3 -4 2.5 5 7.5 1 12.5 15.3.25.2.15.1.5 1 2 3 4 5.2.175.15.125.1.75.5.25.25.5.75 1 1.25 1.5 1.75 2 6o-3n-b_ Figure A. 8 Hanger 6WO (upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 31 6 4 2-2 -4-6 2.5 5 7.5 1 12.5 15.8.7.6.5.4.3.2.1 1 2 3 4 5.4.375.35.325.3.275.25.225.2 1 2 3 4 5 6 5oo-2n-a Figure A. 9 Hanger 5OO (East, upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 32 4 3 2 1-1 -2-3 -4 2.5 5 7.5 1 12.5 15.15.125.1.75.5.25 1 2 3 4 5.2.175.15.125.1.75.5.25.5 1 1.5 2 2.5 3 3.5 4 5oo-5n-b Figure A. 1 Hanger 5OO (East, upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 33 1 7.5 5 2.5-2.5-5 -7.5-1 -12.5 2.5 5 7.5 1 12.5.1.8.6.4.2 1 2 3 4 5.7.6.5.4.3.2.1 1 2 3 4 5 6 4o-1n-a Figure A. 11 Hanger 4OO (East, upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 34 6 4 2-2 -4-6 2.5 5 7.5 1 12.5 15.1.8.6.4.2 1 2 3 4 5.2.175.15.125.1.75.5.25.25.5.75 1 1.25 1.5 1.75 2 4oo-3n-b Figure A. 12 Hanger 4OO (East, upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 35 5 2.5-2.5-5 -7.5 1 2 3 4 5.5.4.3.2.1 1 2 3 4 5.45.4.35.3.25.2.15.1.5.5 1 1.5 2 2.5 3 3oo-1n-a Figure A. 13 Hanger 3OO (East, upstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 36 2 1.5 1.5 -.5-1 -1.5-2 1 2 3 4 5 6 7 8.125.1.75.5.25 1 2 3 4 5.15.125.1.75.5.25.1.2.3.4.5.6.7.8 3oo-4n-b Figure A. 14 Hanger 3OO (East, upstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 37 6 4 2-2 -4-6 2.5 5 7.5 1 12.5 15.5.4.3.2.1 1 2 3 4 5.35.3.25.2.15.1.5.25.5.75 1 1.25 3wu-1k-a Figure A. 15 Hanger 3WU (West, downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 38 4 3 2 1-1 -2-3 -4 2 4 6 8 1.3.25.2.15.1.5 1 2 3 4 5.35.3.25.2.15.1.5.25.5.75 1 1.25 1.5 1.75 3wu-3k-b Figure A. 16 Hanger 3WU (West, downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 39 3 2 1-1 -2-3 2 4 6 8 1.2.175.15.125.1.75.5.25 1 2 3 4 5.4.35.3.25.2.15.1.5.5 1 1.5 2 2.5 3 3.5 4wu-2-bp Figure A. 17 Hanger 4WU (West, downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 4 4 3 2 1-1 -2-3 -4 2.5 5 7.5 1 12.5.4.35.3.25.2.15.1.5 1 2 3 4 5.7.6.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 4wu-5-bp Figure A. 18 Hanger 4WU (West, downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 41 7.5 5 2.5-2.5-5 -7.5 2.5 5 7.5 1 12.5 15.25.2.15.1.5 1 2 3 4 5.225.2.175.15.125.1.75.5.25 2 4 6 8 1 5wu-1k-a Figure A. 19 Hanger 5WU (West, downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 42 2 1.5 1.5 -.5-1 -1.5-2 2.5 5 7.5 1 12.5 15.15.125.1.75.5.25 1 2 3 4 5.25.2.15.1.5.5 1 1.5 2 2.5 5wu-3k-b Figure A. 2 Hanger 5WU (West, downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 43 6 4 2-2 -4-6 2.5 5 7.5 1 12.5.1.8.6.4.2 1 2 3 4 5.2.175.15.125.1.75.5.25.5 1 1.5 2 2.5 3 3.5 4 6u-2_a Figure A. 21 Hanger 6U (downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 44 4 3 2 1-1 -2-3 -4 2.5 5 7.5 1 12.5.35.3.25.2.15.1.5 1 2 3 4 5.7.6.5.4.3.2.1.5 1 1.5 2 2.5 3 6u-4-b-bp Figure A. 22 Hanger 6U (downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 45 4 3 2 1-1 -2-3 -4 2.5 5 7.5 1 12.5.6.5.4.3.2.1 1 2 3 4 5.6.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 5ou-1n-a Figure A. 23 Hanger 5OU (East, downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 46 3 2 1-1 -2-3.5 1 1.5 2 2.5 3 3.5.1.8.6.4.2 1 2 3 4 5.5.45.4.35.3.25.2.15.25.5.75 1 1.25 5ou-4n-b Figure A. 24 Hanger 5OU (East, downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 47 7.5 5 2.5-2.5-5 -7.5 1 2 3 4 5 6 7 8.5.4.3.2.1 1 2 3 4 5.4.35.3.25.2.15.1.5 1 2 3 4 5 4ou-1n-a Figure A. 25 Hanger 4OU (East, downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 48 3 2 1-1 -2-3 2.5 5 7.5 1 12.5.25.2.15.1.5 1 2 3 4 5.3.25.2.15.1.5.25.5.75 1 1.25 4ou-3n-b Figure A. 26 Hanger 4OU (East, downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 49 7.5 5 2.5-2.5-5 -7.5.5 1 1.5 2 2.5 3 3.5 4 2 1.75 1.5 1.25 1.75.5.25 1 2 3 4 5.8.7.6.5.4.3.2.1.5 1 1.5 2 2.5 3 3.5 4 3ou-1n-a Figure A. 27 Hanger 3OU (East, downstream, perpendicular) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 5 3 2 1-1 -2-3 1 2 3 4 5 1.8.6.4.2 1 2 3 4 5.175.15.125.1.75.5.1.2.3.4.5.6.7.8.9 3ou-3k-b- Figure A. 28 Hanger 3OU (East, downstream, parallel) with damper

Ljungan Bridge, Ange Schweden W983/95 Design of the Dampers and Verification-measurements, 13.9.5 14.9.5 Page 51 Tragwerksplanung Baudynamik Konstruktiver Glasbau Windingenieurwesen Stahlbau Softwareentwicklung Pauwelsstraße 19 D-5274 Aachen Phone: 49 () 241 / 963 24 8 Fax. - / 963 24 9 e-mail: mail@psp-tech.de Internet: http://www.psp-tech.de