Or work up to it. The body takes time to adjust.
Never, EVER, use this method. The piano is not a sport, you are not weightlifting or running. If strength were necessary at all, we wouldn't have child prodigies, as their muscles wouldn't be fully developed. Sure, there is a lot of movement in playing the piano, but you are first and foremost training the mind. You are training coordination and speed. The stamina is all in the mind, not in the body. Pain as a result of lengthy practice is a sign of tension, not of weakness.
As others have mentioned, you probably have poor posture. We'd have to see a picture of you to tell you exactly what to do. As far as the idea of sitting lower mentioned before, I doubt that's it, but it may be because I am short and sitting to low at the piano is all too easy. Sitting low at the piano, from my experience, may result in overcompensation by raising the shoulders, which is a large problem. There should be a very slight decline from your elbow to you fingers when sitting at the piano. Some advocate that your forearms should be parallel to the ground, but there should never be an incline. Accentuate the curves in your back. As Barbara Lister-Sink demonstrates, there are four curves in the spine, and I would guess that you may be working against them with your posture. The spine is not straight, and sitting taller doesn't mean straightening it. However, poor posture can invert the curve in your lower back, causing your tailbone to shift forward and your chest to cave in.
If you must think it is muscles, then try an abdominal workout. The back is the antagonist to the abdominals, and if your abs are weak then you back may not be able to fully relax and widen. Get an exercise ball so you can do a good ab workout and hyperextensions as well to make sure the back still develops with the abs. I'd still say muscle strength/stamina is not your problem, though.