The flight instructor reported that after conducting maneuvers in the area for about 30 minutes, he returned to the airport to demonstrate the first landing of the flight. He reported that upon touchdown on the grass runway, the brakes “were not effective” and the airplane veered off the runway to the left into a utility trailer that was parked near the runway. The fuselage sustained substantial damage. The private pilot receiving instruction, seated in the rear seat, reported that the approach and landing appeared normal, and the flight instructor completed a 3-point landing. He recalled that the flight instructor was unable to get the airplane to stop, and he believed the brakes were not effective given they had “plenty of runway to stop.” A Federal Aviation Administration inspector examined the airplane and brake system. The left wheel was rotated, and the left brake pedal when actuated, was observed to stop the wheel movement. The right brake pedal was bound and no longer fully functional due to impact related damage. Its actuator plunger was manipulated via a screwdriver, and right wheel movement was stopped, but not with the same amount of force as compared to the functional left brake pedal. The brake system’s fluid was normal. Neither pilot reported any issues with the brakes prior to takeoff. The effectiveness of the brake system could not be determined, due to the damage sustained to the right brake pedal during the impact with the trailer.