Large Transport
Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP)
Flight Crew Total 13800
Confusion; Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict
Flight Crew Took Evasive Action
Human Factors; Procedure
Climbing through approximately FL280 to the altitude we were cleared to; FL300; we received a TCAS RA. TCAS said 'descend; descend;' so I disengaged the autopilot and initiated descent into green band on V/S. Almost immediately; TCAS changed command to 'climb; climb' so I reversed direction and climbed into the green band until we were clear of traffic. We were IMC. ATC seemed busy and presumably didn't realize they had cleared us to climb through someone else's altitude.
During climbout of DFW on the Harper 3 departure and passing through FL280; we spotted an aircraft on TCAS that was at our altitude coming towards us. We were assigned an altitude of FL300. We shortly thereafter received an RA to descend and a few seconds later to climb. We executed the RA procedure per SOP and then continued to climb to our assigned altitude of FL300. During the RA maneuver; the Controller then told us to turn right 20 degrees. The Air Traffic Controller never warned us about the approaching aircraft. He seemed to be very busy at the time. He never even made a comment about the event after it happened.
Air carrier flight crew reported receiving an RA after ATC cleared them to climb to another aircrafts altitude.