Flight Crew Commercial; Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor
Flight Crew Total 431
Aircraft Equipment Problem Less Severe; Ground Event / Encounter Loss Of Aircraft Control
Flight Crew Took Evasive Action
Aircraft
After completing an instrument flight training lesson we returned to the airport for landing and I demonstrated the RNAV Instrument Approach to my student. Normally; I would allow my student to land the aircraft but I elected to land the airplane myself because there was a direct crosswind of 15-25 knots being reported at the airport's surface. The approach and landing occurred without incident. However; after landing the aircraft and receiving instruction from ATC to vacate the runway; I realized that the airplane's left brake had failed. I subsequently was unable to taxi clear of [the] runway due to the aircraft's inability to slow down enough to make the turnoff. I then chose to continue rolling to [the next] taxiway where I again attempted to vacate the runway by making the left turn. The aircraft was slowed sufficiently to turn but upon applying the rudder; it did not turn enough to stay clear of the edge of the taxiway. I managed to bring the aircraft to a full stop by applying full back pressure to the yoke; essentially using the elevator as an air brake. The aircraft came to a rest on the edge of the taxiway. I was unable to make a right turn due to the aircraft's proximity to a taxiway light on the right side. I decided to shut down the aircraft and request assistance from airport operations. Due to the aircraft being disabled on the edge of the runway; [the] runway was closed for approximately 15 minutes; until my student and I were able to manually push the aircraft clear.
C172 instructor pilot reported he was unable to clear the runway as the left brake had locked up during landing roll.