Flow-Induced Vibration of Long-Span Gates: One and Two Degrees-of-Freedom

Flow-Induced Vibration of Long-Span Gates: One and Two Degrees-of-Freedom

DOI: 10.4018/978-1-5225-3079-4.ch007
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In this chapter the theoretical equations for fluctuating pressures due to vertical and streamwise gate motions developed in Chapters 4 and 5 are used to derive equations of motion for long-span gates with underflow, overflow and simultaneous over- and underflow. Theoretical development of analysis methods is supported by laboratory and full-scale measurements. Specifically, this chapter considers long-span gate instabilities including one degree-of-freedom vibration of gates with underflow and free discharge, one degree-of-freedom vibration of a gate with submerged discharge and vortex shedding excitation, a two degree-of-freedom vibration of long-span gates with only underflow, and two degrees-of-freedom vibration of long-span gates with simultaneous over and underflow. A method is developed to predict pressure loading on the crest of the gate with overflow.
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Gates that dam wide upstream reservoirs or wide rivers typically have spans that are much larger than the gate heights, making then relatively elastic in the streamwise direction. They readily undergo elastic streamwise bending. Long-span gates are commonly installed with the weir plate inclined toward the downstream side such that the larger upstream hydrostatic pressure will create a water tight seal as it presses down on the gate in its closed position. While the inclination of long-span gates in the downstream direction may, depending on the gate mounting system, assure a water tight seal, it also makes these gates press-shut devices. As discussed in Chapter 2, press-shut devices, while statically stable, are dynamically unstable. The dynamic instability of a downstream inclined long-span gate results from its streamwise bending displacement.

A conventional long-span gate with a weight of 49 tons, constructed on the Ara River, Japan, is shown in Figure 1. The weir plate is 28 m long and about 3 m high. It is inclined at 30o (relative to vertical) in the downstream direction. The hydraulic load on the weir plate is supported by the gate slots in the concrete piers at the ends of the gate span. The gate is raised along the slot. In contrast, a different type of long-span gate (new at the time of its design) located in Schinznach, close to Zurich, Switzerland, is shown in Figure 2. The weir plate is 22.5 m long and about 3.4 m high and is inclined at 30o in the downstream direction (the same as for the Ara River gate). The gate has a weight of 100 ton. In order to decrease the required force to raise the gate, the hydraulic load exerted on the weir plate is supported by a pair of trunnion pins located on the upstream side of the gate in the piers at the gate ends. The large hydraulic pressure on the gate bottom, creates a moment about the upstream trunnion pins and acts to raise the gate, rotating it about the trunnion pins. Further, the weir plate has a circular arc shape, which increases the hydraulic opening moment on the heavy gate. As a result, the required force needed to raise the gate in rotation about the trunnion pins is drastically reduced. The operation is easily accomplished and the gate opens smoothly despite its very substantial weight. Although the gate opens smoothly, the design makes the gate behave as a press-open, with inherent problems in sealing the gate when it is in its closed position. This type of gate is known as a reversed Tainter gate.

At small openings most, if not all, long-span gates are susceptible to serious gate vibrations as a result of flow beneath the gate, as reported by Petrikat (1980), Ishii et al. (1987), and Ishii (1990a; 1990b; 1990c). The long-span gate constructed on the Ara River, shown in Figure 1, also underwent similar vibrations at a frequency between 3 and 5 Hz, with a water depth of 2.7 m upstream and almost 0 m downstream. The vibration occurred at small gate openings from 8 to 25 mm and the vibration amplitude was about 4 mm at the spanwise center.

Figure 1.

Long-span gate on the Ara River, Japan, with a weight of 49 tons: (a) side view from downstream, (b) cross-sectional view

Figure 2.

Long-span gate at Schinznach, Switzerland, with a weight of 100 tons, showing (a) side view from downstream, (b) cross-sectional view

After Petrikat (1980).

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