A structural support system is provided in a can annular gas turbine engine having an arrangement including a plurality of integrated exit pieces (IEPs) forming an annular chamber for delivering gases from a plurality of combustors to a first row of turbine blades. A bracket structure is connected between an IEP and an inner support structure on the engine. The bracket structure includes an axial bracket member attached to an IEP and extending axially in a forward direction. A transverse bracket member has an end attached to the inner support structure and extends circumferentially to a connection with a forward end of the axial bracket member. The transverse bracket member provides a fixed radial position for the forward end of the axial bracket member and is flexible in the axial direction to permit axial movement of the axial bracket member.