A canopy assembly includes a frame composed of a plurality of elongated elements interconnected to form an array to which a fabric is secured and stretched. Portions of the fabric are secured in tension into corresponding different ones of the elements, and corresponding ends of respective elements are connected together to form the frame. At least some of the elements each respectively have an H-shaped cross-section with space-opposed pairs of each of mutually-spaced legs projecting individually away from respective opposite ends of the crossbar of that cross-section. A variety of different devices may be used alternatively to secure the portions of fabric to the different elements, while creating tension in the fabric. A number of different interconnectors may be used alternatively or in various different combinations to connect corresponding ends of respective different elements in the formation of the frame. Different ones of those devices and interconnectors also are described in use with channel-shaped elements rather than H-shaped elements.