Shaking problems

Recently I have discovered that my truck shakes pretty bad from the rear when I'm between 35 and 70 mph. I got new tires thinking maybe one of them was bad and it helped a little. Some days its worse than others. The u joints are all new and the carrier bearing is also. Sometimes it gets so bad I can feel it in the steering wheel. Could it possibly be a rear brake problem or something in the rear end? I know these trucks have the famous bed shake but Ive had people follow me and mine doesn't do it so I ruled that out as a possibility. I doubt it's a transmission problem cause as far as shifting and everything I have zero problems and have never heard any noises from that area. I was hoping to get some input if anyone has had the same problem or anything similar.

 

I just had a very similar problem on my 2012 Platinum. I originally thought it was a bent rear wheel. Mine would shake with and without braking, but was worse with hard braking. Turned out to be a right rear warped rotor. I hope your problem is as simple as that. It also didn’t help that the caliper bracket on the same side wasn’t tight.