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<br />OOlG'79 <br /> <br />Depending on the factors discussed above, if a tie rod vibrates at a resonant condition, cracks will <br />invariably be formed in the welds which attach the tie rod to'the plate. Depending on the length <br />of time for which the resonant condition occurs, the cracks may eventually join up and result in a <br />through crack of the tie rod. Under these conditions, the structural integrity of the tie rod will be <br />lost and failure will occur. <br /> <br />There are two recent instances at Reclamation facilities where this type of failure has occurred. <br />At Palisades Dam in 1980, three tie rods were found to have extensive cracks, and one tie rod had <br />completely broken through its 9-inch diameter. At New Melones Dam in 1997, two tie rods were <br />found to have 360 degree circumferential cracks at both their ends. Since the cracks had <br />penetrated only 2 inches into the 10-inch diameters, " complete failure" had not yet occurred, but <br />it would only have been a matter of time. <br /> <br />In the Spring of 1979, "vibrations" were noted at the main outlet works at Navajo Dam, when <br />the total discharge through the two 72-inch hollow-jet valves was reported to be 3,700 ft3/s. The <br />reservoir water surface was at elevation 6056.07, and the valves were open 67 percent. The valve <br />openings were then reduced to 54 percent, with a resulting discharge of3,500 ft3/s, causing the <br />vibrations to stop. Project personnel indicated that the vibrations were felt in the area above the <br />wye branches, and not in the valve house. <br /> <br />The Reynolds number for a flow velocity of 56 ftls and a rod diameter of8 inches is 2.77xl06. <br />This puts the vortices in the supercritical range, where re-establishment of turbulent vortex streets <br />normally occurs. These vortices can excite either of the two tie rods, the level of response <br />depending on the values of their natural frequencies. Therefore, the vibrations felt at the outlet <br />works area could have been due to either one or both of the tie rods vibrating. When the <br />discharge was reduced to 3,500 ft3/S no vibrations were felt, probably due to the fact that the <br />Reynolds number was then in the critical range. In this range, the vortex streets are narrower and <br />disorganized, and it is unlikely that the tie rods would be excited. <br /> <br />Even though vibrations were reported at 3,700 ft3/s, we would not be able to predict which tie rod <br />was vibrating and whether or not resonance was occurring. It is difficult to calculate the natural <br />frequencies of tie rods when the pipe is embedded in concrete, as is the case here. This is because <br />it is not feasible theoretically to determine the amount of restaint afforded by the concrete <br />interacting with the steel stiffening member. The theoretical analysis must therefore assume a <br />certain degree offixity of each tie rod. However, testing can be performed to determine the <br />natural frequencies of the tie rods and also determine whether the stresses encountered could <br />cause the tie rods to fail. The natural frequencies of both tie rods must be determined in order to <br />make predictions of the possibilities of vibrations occurring at other discharges. <br /> <br />The TSC has performed two recent investigations to determine the natural frequencies of tie rods. <br />The first investigation was at Hoover Dam in the Spring of 1997 [22], when modal surveys were <br />performed on four ll-inch-diameter tie rods in the laterals of the upper Nevada penstock. The <br />second investigation was performed at New Melones Dam in December 1997, when modal <br /> <br />22 <br />