Abstract: A roof or wall structure incorporating support assemblies of this invention is disclosed. The roof or wall structure comprises an inner sheath secured to plural spaced-apart purlins or girts; an outer sheath; plural spaced-apart support means each assembled from a plurality of the present support means, secured to the inner sheath and to the outer sheath for maintaining the outer sheath spaced from the inner sheath; and thermal insulation filling the space between the inner and outer sheaths. The arrangement is such that the thermal insulation has a substantially uniform thickness throughout the roof or wall structure. The depth of the support means may be varied to accommodate the desired thickness of thermal insulation. The support means accommodate thermal expansion and contraction of the outer sheath independently of the inner sheath, thereby totally eliminating the possibility of leaks associated with prior art structures.