On September 12, 1999, about 1330 eastern daylight time, a Piper PA-24-250, N8051P, registered to and operated by Aviation Center of Tampa Bay Incorporated, veered off the runway on landing at Albert Whitted Municipal Airport, St. Petersburg, Florida, while on a Title 14 CFR 91 personal flight. Visual meteorological conditions prevailed at the time and no flight plan was filed. The aircraft received substantial damage, and the private-rated pilot sustained no injuries. The one pilot-rated passenger received minor injuries. The flight originated from Cross City, Florida, the same day, about 1230. The pilot stated that after making a normal landing the airplane was initially tracking down the runway centerline, but about 500 feet after the touchdown point it veered to the right at about a 45-degree angle. The pilot further stated that he applied the handbrake which made the situation worse, and the airplane exited the runway. The pilot-rated passenger said that the landing was not a hard landing. A mechanic who examined the airplane to assess the damage and determine the cost to repair the airplane said that the airplane's hand brake is cable operated and goes to a "Y" that is connected to the toe brake cable. The mechanic said that application of the hand brake locks the rudder pedals, preventing the pilot from applying rudder input to control the airplane. The mechanic also said that the rudder bar is connected to the rudder trim through a worm screw, and that the rudder trim was 1/3 of the way to the right of center, resulting in the rudder pedals being uneven when the handbrake was applied and the pedals were locked. The mechanic also said that the damage to the airplane was not consistent with that of a hard landing, but that the damage was consistent with a sudden stop, such as when the airplane collided with the sand bank. The mechanic said that the pilot told him that it was a normal landing, and during the landing rollout he retracted the flaps, turned off the boost pump, and then applied the hand brake, in that order, when as a result of applying the handbrake, the airplane veered off the runway. The nose gear right drag link exhibited fracture surfaces, so the drag link was sent to the National Transportation Safety Board's Materials Laboratory for analysis. The laboratory report shows that the nose gear right drag link fracture surfaces exhibited a rough, matte gray appearance, consistent with overstress. In addition, the laboratory report shows that the drag link bolt was bent 13 degrees relative to its axis, consistent with an overstress condition.