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Short answer, yes. The 1968-72 convertible frames are boxed in between the front & rear wheel wells where the others are more of a C channel frame along the rocker panel. I've seen convertible frame prices anywhere from $350.00-$1000.00.
They are easy to differentiate with just a quick glance.
You've probably found one and want to know if it's priced right but if you haven't post your state because someone may have one near you. For future readers of this thread Be sure to check the whole frame with an awl looking for soft spots. Check the mount holes for rust out. Get a frame measure diagram and measure between spots to confirm its not bent. I took mine to a body shop to certify it because I did not have that drawing. Best 95.00 I ever spent. A good price is only good if the frame is straight. Hard to tell without measuring. Good luck with the search.
Good advice on taking it to a frame shop if you find a frame. This is a 70 convertible frame that had obviously been hit in the back. The right rear is sticking up several inches. Easy to fix but - later in the process, after painting, someone with a sharp eye noticed a slight 3/16" inward bow on the main right frame rail and a 3/16 outward bow on the left rail. Ugh, not easy to fix. And executing the measurement process in the CSM didn't catch it. This still ended up being a good frame in the end.
The shop I took mine to could put it on a frame straightening rack at a per hour rate. They showed me where it had been straightened before. In the frame are round holes that had been deformed from the chain hooks they use to pull it back into specs. They also told me that ( in spec ) is a plus or minus, not exact measurements because a 40+ year old frame carrying a heavy motor over potholes etc. will not be perfect.
Thanks for the answers and feedback. My friend has a 72 and it was hit hard in the back. The frame damage is behind the wheel, but I explained as you have pointed out that there could be resulting damage further forward. He is getting the frame measured next week but I mentioned he may want to change the frame. He's pulling the motor and trans out for a reseal and doing a disc brake conversion and front suspension rebuild. Plus the left 1/3 of the trunk floor needs to be cut out cause it was just pounded out with a hammer during the repair years ago. He's halfway there to a frame change labor wise so its worth considering. The car is located in the Washington D.C. Metro area.
On mine I asked for a letter to certify the frame is within specs to help later. I now have a frame certified to be within tolerances in case I sell it or use it on a project. Will I ever need the frame? Who knows but it's easier to sell with a certified letter of health if I don't. In your case a future buyer may question if the frame is straight and you could wip out the certificate and end that mystery on the spot.