MHD avalanches involve small, intensely localized instabilities that spread across neighbouring regions in a magnetic field. Cumulatively, many small events release vast amounts of stored magnetic energy. Straight cylindrical flux tubes, in Parker (1972)’s model of coronal loops, are liable to such avalanches: one unstable flux tube can cause instability to proliferate through reconnection, resulting in an ongoing chain of like events. True coronal loops are curved, arching between different footpoints on one photospheric plane. Using three-dimensional MHD simulations, we here verify the viability of MHD avalanches within the curved magnetic geometry of a multi-threaded coronal arcade. In contrast to the behaviour of straight cylindrical models, a modified ideal MHD kink mode occurs more readily and preferentially upwards in this new geometry. Such instability spreads over a region far wider than the original flux tubes, and wider than their photospheric footpoints. Consequently, substantial and sustained heating is produced, in a series of nanoflare-type events, contributing significantly to coronal heating. Overwhelmingly dominant is viscous heating, attributable to the shocks and jets produced around these small events. Reconnection is not the greatest contributor to heating, but rather the facilitator of those processes that are. Localized and intermittent, the heating shows no strong spatial preference, except for a small bias away from footpoints. Effects of realistic physical plasma parameters and the implications for thermodynamic models, with energetic transport, are discussed.