Partially-enclosed racks (with sides but not roofs) were introduced in the early-mid 1970s. Many older open racks had side panels added to them, as shown in the photo above.
Fully enclosed racks were introduced by the late 1970s, becoming more and more common through the 1980s. Open and partially enclosed racks would have remained common through the 1980s, slowly being replaced by fully enclosed versions. By the late 1980s they would certainly be a dying breed, but some examples of partially enclosed racks were still around in the early 1990s.