This is a pdf on the conservation of a 15-inch Rodman gun and barbette carriage, but both this gun's top carriage and the 13-inch mortar bed's cheeks are constructed in the same manner.
NOTES ON THE PRESERVATION OF THE 15 INCH RODMAN GUN, TOP CARRIAGE, AND CHASIS .....
http://www.nps.gov/history/history/online_books/guis/15_rodman.pdfP.8, C. "The TOP CARRIAGE: The assembly consists of the following main subassemblies: Two CHEEK ASSEMBLIES of sandwich construction in a general vertical triangular configuration, of which the major components are two sheet metal CHEEK PLATES, inner and outer, right and left. These are bound together around their circumference by “T” shaped FRONT CAPS, REAR CAPS, and at the bottom by SHOE IRONS. At the very top is the loop-shaped TRUNNION BED which receives the TRUNNIONS of the GUN."
Also read pp.10-11 starting with "CHEEK PLATES: There are four CHEEK PLATES in the TOP CARRIAGE."
Skidmark has already posted this site; but you can clearly see the thin outer plate of the beat up Ft. Moultrie mortar bed in the enlarged photo.
Craig Swain's blog: To the Sound of the Guns, Civil War Artillery, Battlefields and Historical Marke
http://www.flickr.com/photos/50467989@N05/5069720652/sizes/l/in/photostream/Waymarking: The Fort Moultrie mortar from the other side; look at the bottom rear of the cheek. I do believe this is an original bed, and I also think that the second photo skidmark posted in reply # 12 shows the same original bed.
http://www.waymarking.com/gallery/image.aspx?f=1&guid=4ec81720-211f-4ecb-a879-e654966524b0The third photo (enlarged) on this "Hisorical Marker Database" link that I posted before, also clearly shows the two iron plates with the bracing sandwiched in between them (seen from the front).
http://www.hmdb.org/PhotoFullSize.asp?PhotoID=79087