After an uneventful 30 minute flight the pilot returned to the airport and entered the traffic pattern for a full stop landing on runway 28; the wind at the time was variable at 3 knots. He reported the touchdown was normal, but about 5 to 10 seconds after touchdown, "the plane started rumbling and pulling hard to the left"; he confirmed he was not on the airplane's brakes at that time. He reported the nose steering was not effective, and when the left main landing gear wheel was in the grass, he advanced the left throttle in an attempt to overcome the left turning tendency. The airplane then contacted a temporary rock road and both main landing gears collapsed. All occupants exited the airplane uninjured, and when he deemed it safe, he reentered the airplane and secured the fuel selectors. Postaccident inspection of the airplane by several FAA inspectors revealed the left tire was deflated and a hole was completely worn through the casing on an area of the tread, and also through the tube. Postaccident operational testing of the airplane's brake system revealed no evidence of preimpact failure or malfunction. The brakes released with release of pressure on the brake pedals; no sticking was noted. Damage to a portion of the left wing at the leading edge and main spar was noted. Damage was also noted the main spar of the left aileron, and to structure on the lower fuselage aft of the wing trailing edge.