The invention relates to a bearing comprising at least one system for determining the amplitude A of the pseudo-sinusoidal deformations of an area of the fixed race that are induced during rotation, the said system comprising at least three strain gauges (7), a device for measuring three signals Vi depending respectively on the temporal variations of the signal emitted by each gauge (8), the said device being able to form two signals SIN and COS respectively of like angle and like amplitude, and a device for calculating the amplitude A of the deformations of the area (7) as a function of time, the said device being designed to calculate the expression SIN2+COS2 so as to deduce the amplitude A therefrom.