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The leg structures of offshore rigs may be several hundred meters long, which makes the rigs capable of operations on depth below a hundred meters. Investigations have been carried out at a particular offshore rig located at a water depth of approximately 80 meters in the Norwegian part of the North Sea.Violent vibrations of members in the leg structures of the rig have been investigated by extensive field measurements of accelerations and strains.  Various solutions were investigated and a customized solution performed. Filling the susceptible tubes with a concrete medium reduced the vibrations to a minimum.