The pilot was landing at an off-airport site, which was surrounded by trees. The pilot stated that while on approach, he increased his approach airspeed due to turbulence. The airplane landed hard, and bounced. He added power to abort the landing, but realized he could not climb over the trees at the end of the landing area, and he closed the engine throttle. As the airplane touched down again it continued off the end of the site, and collided with brush. The pilot said there were no mechanical problems with the airplane, and that he should have used a slower approach airspeed or performed a go-around. The airplane sustained substantial damage to the left wing spar and aileron.