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Be stars are surrounded by outflowing circumstellar matter structured in the form of decretion discs. They are often members of binary systems, where it is expected that the decretion disc interacts both radiatively and gravitationally with the companion. In this work we study how various orbital (period, mass ratio, eccentricity) and disc (viscosity) parameters affect the disc structure in coplanar systems. We simulate such binaries with the use of a smoothed particle hydrodynamics code. The main effects of the secondary on the disc are its truncation and the accumulation of material inwards of truncation. In circular or nearly circular prograde orbits, the disc maintains a rotating, constant in shape, configuration, which is locked to the orbital phase. The disc is smaller in size, more elongated and more massive for low viscosity parameter, small orbital separation and/or high mass ratio. Highly eccentric orbits are more complex, with the disc structure and total mass strongly dependent on the orbital phase. We also studied the effects of binarity in the disc continuum emission. Since the infrared and radio SED are sensitive to the disc size and density slope, the truncation and matter accumulation result in considerable modifications in the emergent spectrum. The decretion disc in circular binaries remains constant in shape and phase-locked. Eccentric binaries exhibit strong dependence on the distance to the secondary. We conclude that binarity can serve as an explanation for the variability exhibited in observations of Be stars, and that our model can be used to detect invisible companions.