A turbine ring assembly extending about an axis, includes a plurality of ring sectors made of ceramic matrix composite material forming a turbine ring and a ring support structure held by a turbine casing, each ring sector including a base from which an upstream lug and a downstream lug spaced axially from each other extend radially outwardly, the ring support structure including a spacer having a clamp against which the downstream lug of the ring sectors is held, a first upstream flange against which the upstream lug of the ring sectors is held, and upstream of the first upstream flange, a second upstream flange for absorbing forces against which the first upstream flange is held.