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51 ture increase in a particular cable. Temperature increases The maintenance manual for the James River Bridge in Vir- are meant to represent loss of stiffness of individual ginia included procedures for the repair of longitudinal splits cables without the need to modify the cable stiffness. in PE sheathing. This involves removal of the existing film Future measured cable force changes can then be used tape, cleaning of the damaged area at least 3 ft above and below together with the transformation matrix to identify cables the split, filling of the crack with a suitable polyurethane grout that have suffered stiffness losses. A similar transforma- or other compatible material to obtain a smooth surface, using tion matrix can be formed that is related to deck eleva- 8 mil polyester film tape with fiberglass reinforcement to wrap tions instead of cable forces. Other sources of damage, the cable from 2 ft below to 2 ft above the split with minimum such as support settlements, can also be incorporated. of 50% overlap, and wrapping again with PVF film. There are very few components of the common stay cables The available choices for the repair of steel sheathings (i.e., those that have been designed over the last 30 years) that are far more limited, and there is no known track record for could be considered repairable. Practically, the only items that the effectiveness of such repairs. A report prepared for the the inspectors and maintenance engineers can realistically Delaware DOT recommends application of flexible liquid repair are the HDPE cable sheathings, neoprene boots, and mastic to the cracks on a steel saddle pipe and continual possibly the elastomeric rings. Retrofitting for vibration con- inspections. trol can also be done. However, repair of corrosion or fatigue damage to MTEs in the free length or anchorages of older Figure 66 shows the results of the survey as related to the cables (not the newer designs) is practically impossible, short repair of stay cables. Approximately 30% of cables in the of removal of the entire cable. The removal process itself is a United States and Canada have had some form of repair. major challenge and a significant undertaking, especially on older bridges. The main task of the maintenance engineer and inspectors is therefore prevention, especially control of mois- MITIGATION OF STAY CABLE VIBRATIONS ture (from internal and external sources) and elimination of A wide variety of solutions to the problem of stay cable vibra- excessive vibrations. If preventive measures fail, the mainte- tions have been proposed and/or implemented. These mitiga- nance engineer must then have a reliable tool to determine if tion approaches can be categorized as modifications to the a cable or cables must be replaced and when they should be surface of HDPE pipe, cross cables, viscous dampers, visco- replaced. elastic dampers, friction dampers, tuned mass dampers, semi- active and active dampers, and others. In this section, a brief A number of options are available with regard to repair of summary of each approach is given. damaged or cracked HDPE sheathing. For minor localized damage, conventional wrapping with PVF tape is typically done, although this is believed by some not to be effective. Modifications to the Surface of HDPE Pipes When the HDPE has cracked or has more widespread dam- age, then a more extensive repair must be considered. The As discussed earlier, the formation of rivulets on the surface of options include an elastomeric wrap system and a two-piece the cable is believed to be the cause of rainwind vibrations. HDPE pipe that snaps together to form a cover for the original Therefore, a very popular and effective approach has been to pipe. The elastomeric wrap is installed with an automatic modify the surface of the cable to break up and disrupt the wrapping device with 50% overlap. Within 24 h after wrap- flow of water, thus not allowing the formation of rivulets. A ping, the wrap is heated to fuse the seams and shrink the wrap very common form of this modification is helical or spiral against the cable. The ends of the wrap must be secured firmly marks, fillets, or ribs on the surface of HDPE pipe as shown to prevent lifting. in Figure 67. Figure 68 provides wind tunnel results with and 80.0 70.0 Percent of Bridges 60.0 U.S. Canada 50.0 40.0 30.0 20.0 10.0 0.0 yes no not known no answer Cables Repaired? FIGURE 66 Percentage of bridges that have had cables repaired.
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52 FIGURE 69 Surface modifications on the HDPE FIGURE 67 Spiral strakes on the surface of HDPE pipe to (Matsumoto 2000). control rainwind vibrations. damping effect" from cross ties, which can be increased by without surface modifications. According to the wind tunnel using more flexible and dissipative ties. tests by Larose and Wagner Smitt (1999), in some cases, the rainwind vibrations persisted with limited amplitudes even Cable restrainers have also been used as a temporary solu- with the helical fillets. tion to rainwind vibrations (Poston 2002). Figure 71a shows the restrainer system with three lines of cables, and Figures Other, less frequently used options are dimples or longi- 71b and c, respectively, show the measured vibration ampli- tudinal ribs on the surface (Figure 69). Surface dimples were tudes before and after installation of restrainers. used on the Tatara Bridge in Japan, and Yamaguchi et al. (1999) reported that they were effective in controlling rain During the construction of the Burlington Bridge over wind vibrations. the Mississippi in Iowa, several incidences of rainwind vi- brations were observed with amplitudes of up to 0.6 m (2 ft) Cross Cables (Bierwagen no date). Bierwagen reports that temporary ropes in the form of 25-mm or 1-in.-diameter Manila ropes were first Cross cables, secondary cables, cable restrainers, or cross ties used to help tie the cables down. However, the Manila rope are used to connect different stay cables within a cable plane. broke during a subsequent occurrence of vibrations. There- Figure 70 shows a cross cable installed on SR-46 over the East Fork White River in Indiana. These transverse connections reduce the effective length of the cable and increase cable frequency (Ito 1999). They also somewhat increase cable damping (Lankin et al. 2000). Yamaguchi and Nagahawatta (1995) performed experimental and analytical research on the damping effects of cable cross ties. The experiments consisted of two cables connected with two cross ties. They concluded that "there exists a more or less m Duct dynamic efficiency Vibration amplitude No Filet 1 0.5 Filet 0.05 Wind velocity 5m/s 10m/s 15m/s FIGURE 68 Effect of surface modifications on FIGURE 70 Cross cable installed on a bridge in Indiana vibration amplitudes (Stubler 1999). (courtesy: Indiana DOT).
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53 (a) 4 1-minute RMS acceleration (g) 3.5 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 1-minute mean deck-level wind speed (mph) (b) 4 1-minute RMS acceleration (g) 3.5 3 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 35 40 1-minute mean deck-level wind speed (mph) (c) FIGURE 71 (a) Cable restrainer, (b) vibrations before installation of cross cables, (c) vibrations after installation of restrainers (Poston 2002). fore, a cross cable system was designed and implemented. It is reported that the cross cables should be tensioned pro- Figure 72 shows the layout of cross cables (top) and the perly to prevent slacking of the restrainers (Bournand 1999). method of connection to the cables (bottom). According to Bournand reported that the cross cables on the Fred Hartman Bierwagen, the restraint system included 12.6-mm or 0.5-in.- Bridge in Texas failed one year after installation as a result diameter zinc-coated wire ropes that crisscross through the of fatigue and fretting. He suggests that "the cables must be cables and are attached to them using friction clamps. Similar designed using a flexible wire rope or similar system (with high cross cables have also been used on the Clark Bridge in Alton, internal damping) and with good fatigue and wear resistance." Illinois. This system was installed on the bridge. Some observers also
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54 CABLE TIE-DOWNS (TYPICAL) 660' 405' SPAN MS1 SPAN MS2 FIGURE 72 Cable restraint system for the Burlington Bridge in Iowa (Bierwagen no date). believe that cross cables reduce the aesthetic quality of cable- Viscous Dampers stayed bridges (Johnson et al. 2002). In this section, the application of mechanical viscous dampers Bloomstine and Stoltzner (1999) reported on the failure for suppression of stay cable vibrations is discussed. In gen- of a wire cross cable on the Faroe cable-stayed bridge in eral, the term "viscous damper" used here refers to a mechan- Denmark. The original system consisted of steel brackets with ical damper that generates force proportional to the velocity of neoprene linings attached to the cables with stainless steel wire piston movements (i.e., it can be idealized as a dashpot). Other connected in between them. The wires "were wrapped around investigators sometimes prefer to use the terms "oil damper" a thick washer in the bracket and secured by two wire locks." or "hydraulic damper," and distinguish them from viscous Abrasion between wire and the washer caused the first wire damper. In this discussion, they are all referred to as viscous failure after 4 years. A new system using 10-mm marine grade damper as long as they meet the definition given. stainless steel wire and turnbuckles was used. Viscous dampers for stay cables have been installed on a Many respondents to the survey had positive views con- large number of cable-stayed bridges worldwide, including cerning cross cables, with the ability to inspect them and the Sunshine Skyway Bridge, Cochrane Bridge, and Erasmus know whether they are working given as an important factor. Bridge. Figure 74 shows a schematic of a cable of length L, Figure 73 shows the results of the survey as related to the use with a viscous damper positioned at a distance of Ld from of cross cables. one end.
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55 90.0 80.0 U.S. Canada Percent of Bridges 70.0 60.0 50.0 40.0 30.0 20.0 10.0 0.0 yes - from the yes - retrofitted no no answer beginning to correct vibrations Cross Cables FIGURE 73 Frequency of the use of cross cables. Several researchers have proposed numerical approaches of particular interest, because vibrations occur over a wide for determining the contribution of a viscous damper to the range of cable modes. The influences of sag and bending stiff- overall cable damping. Some of the earlier works were by ness were ignored. Kovacs (1982), Yoneda and Maeda (1989), and Pacheco et al. (1993). Each idealized the cable as a taut string when deriving Main and Jones (2001) discussed the installation of two their formulations. In 1999, Xu et al. presented results of their viscous dampers on the Fred Hartman Bridge in Texas. They experimental study on control of cable vibrations using vis- analyzed the pre- and post-damper installation response of the cous dampers. cables, and showed that although the dampers were designed for the first mode, they were very effective in controlling all Tabatabai and Mehrabi (2000) presented a nondimensio- of the high-amplitude vibrations that had been observed be- nal formulation that included the effects of cable sag and fore damper installation. bending stiffness, and performed parametric studies (using cable parameter ranges from a database of stay cables) to There is a rough "rule-of-thumb" that can be used to esti- develop an equation for calculating the first mode damping mate the maximum achievable damping (in fraction of criti- contribution by a viscous damper. This study indicated that cal damping). The maximum damping is approximated as the influence of cable sag was insignificant for the range of 0.5(Ld/L) (Lankin et al. 2000). Therefore, if a damper is located parameters found in stay cables. However, the influence of at 2% of the length of the cable, then the maximum achievable cable bending stiffness was found to be important, as dampers damping is 1%. It is important to realize that the theoretical are typically located close to the anchorages. Although their end of the cable from which Ld is calculated is generally dif- formulation was applicable to higher modes as well, their ferent from the actual end. The complicating factors are the proposed equation was optimized for the first mode only. varying bending stiffness of the cable at the end, the presence of neoprene dampers, and the presence of steel sockets. Main and Jones (2002) investigated the multi-mode contri- Tabatabai et al. (1998b) presented approximate relationships bution of a linear viscous damper attached to a taut string. that allow determination of an equivalent effective length for They pointed out that damper performance at higher modes is different end conditions. FIGURE 74 Idealized cable with viscous damper (Tabatabai and Mehrabi 2000).
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56 The respondents to the questionnaire indicated seven bridges with viscous dampers, most of which were installed to correct observed vibrations. There is some concern expected about potential leakage of fluids in such dampers. Viscoelastic Dampers The commonly used neoprene ring can essentially serve as a viscoelastic damper; however, because of difficulty with con- sistent installation and their variability, their level of damping contribution is difficult to estimate. Tabatabai and Mehrabi (2000) performed tests on a scale stay cable model with and FIGURE 76 SDR damper (Mizoe et al. 1999). without neoprene rings. The neoprene rings increased damp- ing by more than 10-fold to 0.6% of critical damping. There is at least one cable supplier that is supplying pro- Friction Dampers prietary viscoelastic and hydraulic damping systems. These Bournand (1999) reported on the development of a friction systems are placed between the HDPE and the guide pipe (or damper for stay cables (see Figure 77). This damper system an extension of guide pipe). The viscoelastic damper uses a has two parts; a movable part that is attached to the strands shaped elastomeric material to damp cable vibrations (Fig- by a bolted collar and a fixed part that is bolted to the steel ure 75). It is expected that most suppliers would have their support pipe. The bolted collar has several "friction wings," own damping systems in the near future. and the fixed part has several "spring ring blades supporting several friction screws." The ring blades are deflected to have Another form of viscoelastic damper is the Super High- a steady friction contact of the friction screws. This damper Damping Rubber Damper (SDR). Mizoe et al. (1999) pre- type has reportedly been installed on the Uddevalla Bridge in sented a damping device that is installed between the cable Sweden. and the guide pipe (or anchor pipe). When the cable moves, a relative displacement occurs between the cable and the guide pipe causing shear deformations in the damping ma- Semi-Active Dampers terial. A high-damping material is developed by combining styrene butadiene rubber, high-damping carbon, and some Johnson et al. (2002) presented a theoretical discussion and plastics to achieve its properties. Figure 76 shows the SDR described the development of semi-active damping for stay damper. These dampers were first installed on two cables cables. A semi-active damper can be a variable-orifice vis- of the Meiko East Bridge in Japan for testing. The authors cous damper, a controllable friction damper, or a controllable reported that the damping level achieved was confirmed with fluid damper (Johnson et al. 2000). Computational simula- calculated values. Subsequently, these dampers were installed tions were used to examine the effectiveness of semi-active on most cables of this bridge. They have been in service since damping. The authors reported that the potential for using 1998, and wind-induced vibrations have reportedly not been semi-active dampers to control stay cable vibrations "has been observed. demonstrated" in comparison with passive viscous dampers. FIGURE 75 Viscoelastic and hydraulic dampers (Stubler et al. 1999).
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57 Cable ipe t ayP S 18 MR damper 0. 0.14 0.24 0.30 54° Friction Damper Damper Steel Support Pipe Anchorage Head Support 2.25 FIGURE 77 Friction damper (Bournand 1999). Using an optimal control algorithm, the authors stated that a simulated semi-active damper located at 2% of the distance from the end of cable reduced responses by 71% compared Foundation with an optimal viscous damper and 72% compared with fully active devices. FIGURE 78 MR damper installation on bridge cable in China (Ko et al. 2002). Johnson et al. (2000) reported on laboratory experiments on scaled stay cables with a magnetorheological (MR) fluid damper. MR dampers are a type of semi-active damper (con- trollable fluid) in which the yield stress of the fluid is change- The main advantage of the TMD is that it is not restricted able through variations in magnetic field strength. Laboratory to the cable ends. The main disadvantage is that it can only results indicated that the damper was able to achieve "signif- be tuned to a particular frequency, and its effectiveness is icant" response reductions, but not to the level expected from reduced at other frequencies. simulations. Recommendations were made for addressing this problem in future studies. Jensen et al. (2002) proposed using a TMD between two cables at mid-length. In their article, the authors present an Ko et al. (2002) reported on field tests of stay cables with analytical formulation for their concept. MR dampers on the Dongting Lake Bridge in China. Field measurements were taken before and after damper installa- tions. The equivalent damping level was found to be depen- Other Damping Systems dent on damper location, voltage applied to damper, and the level of vibration. Under optimum voltage input, the damping Tabatabai and Mehrabi (2000) reported on damping tests ratios for the second and third modes can reportedly be greater on a scale model of a stay cable. They tested a number of than 0.8% of critical damping. These semi-active dampers approaches for cable damping including using common are commercially available. Figure 78 shows MR damper neoprene rings, latex grout as filler inside HDPE, a liquid installation on a bridge cable in China. damper, application of spiral adhesive damping tapes around HDPE, and filling of the guide pipes with a low stiffness polyurethane. They concluded that the conventionally used Tuned Mass Dampers neoprene ring improved cable damping significantly to 0.4% to 0.6% of critical damping (compared with a damping The tuned mass damper (TMD) is tuned to a particular fre- of 0.05% for cable without neoprene ring). They suggested quency of interest; for example, the first mode of the cable. that the effectiveness of neoprene rings is influenced by the The TMD, in its basic mathematical representation, consists degree of precompression in the neoprene ring and any re- of a mass, a spring, and a damping component. By changing straint of ring movement in the transverse direction. The the basic properties of the damper, the TMD can be tuned to use of latex grout increased cable damping by 60%, but not the right frequency. TMDs have been applied to a variety of to the level needed for control of rainwind vibrations. They structures including power line cables. Tabatabai and Mehrabi also concluded that the liquid damper and damping tapes (1999) patented a shaped viscoelastic TMD for stay cables. did not significantly improve damping. Filling of guide pipes