The 4 door convertibles of the 50's and 60's also had full frames under them. The convertible versions of these cars usually had heavier frames under them than the sedan and coupe versions. Source(s):
4 Door Convertible >> 1929 Chevrolet Landau 4 door convertible | Richard Spiegelman | Flickr

4 Door Convertible >> 1929 Chevrolet Landau 4 door convertible | Richard Spiegelman | Flickr

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4 Door Convertible >> File:1954 Cadillac series 62 convertible fvl.jpg - Wikimedia Commons

4 Door Convertible >> File:1954 Cadillac series 62 convertible fvl.jpg - Wikimedia Commons