Methods and apparatus are provided for constructing refractory structures, e.g., glass furnace regenerator structures and/or glass furnace structures formed of refractory components, by positioning opposed pairs of vertically oriented base beams on respective opposite sides of the refractory structure and having a lower end rigidly attached to a foundation of the refractory structure and an upper end which extends vertically above the refractory structure, and attaching cross-support beams to respective ones of the base beams at the upper end thereof so as to latitudinally span the refractory structure. An overhead crane assembly may thus be supported by the cross-support beams.