CARJ CREW HAD THE STICK SHAKER; AND STICK PUSHER ACTIVATE WHEN THE CREW ACCEPTED A CLRNC TO CLB FROM FL310 TO FL350 IN 3 MINS.

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THE FO'S LEG. FLT WAS PROCEEDING NORMALLY. LEVEL AT FL310 FOR SEVERAL MINS; EXPERIENCING TURB. WE WERE CLRED TO FL350. DURING THE CLB; ATC QUERIED ABOUT THE ABILITY OF THE FLT TO CLB TO FL350 WITHIN 3 MINS; WHICH WE ACCEPTED. I SELECTED VERT SPD MODE AND PUT IN THE 1500 FPM RATE. AT THIS TIME; THE AIRSPD INDICATED SOMEWHERE IN EXCESS OF .74 MACH; AS A CONSIDERABLE PERIOD OF TIME WAS SPENT AT FL310; WHICH ALLOWED TIME FOR SPD TO BUILD UP. AS AIRSPD DECREASED; WE CONTINUED TO EXPERIENCE TURB. THE CAPT SUGGESTED WE REDUCE CLB RATE TO ABOUT 1000 FPM. THIS WAS ACCOMPLISHED AND THE DECREASE IN AIRSPD WAS REDUCED. AS I FURTHER REDUCED THE CLB RATE; THE AUTOPLT DISCONNECTED; AND THE STICK SHAKER ACTIVATED MOMENTARILY. THE CAPT TOOK THE CTLS AND CONFIRMED MAX THRUST. I GUARDED THE RADIOS AND MONITORED SYS. AS THE CAPT LEVELED THE ACFT; THE STICK PUSHER ACTIVATED. I BELIEVE THIS WAS PARTIALLY DUE TO THE TURB WE CONTINUED TO EXPERIENCE. THE CAPT STAYED WITH THE CTLS; ATTEMPTING TO LEVEL. THE STICK PUSHER ACTIVATED AGAIN. I IMMEDIATELY REQUESTED A DSCNT. ATC ASSIGNED FL310. AUTOPLT WAS ENGAGED. I TOOK THE CTLS AGAIN. THE CAPT CHKED WITH THE FLT ATTENDANT TO NOTIFY HER OF THE CONDITION OF THE FLT. THE FLT CONTINUED TO THE DEST OF GEG WITHOUT FURTHER EVENTS. SUPPLEMENTAL INFO FROM ACN 605397: THE STICK SHAKER ACTIVATED AND THE CAPT TOOK THE CTLS. THE CAPT LEVELED THE ACFT AND THE STICK PUSHER ACTIVATED. THE CAPT LEVELED THE ACFT AGAIN AND THE STICK PUSHER ACTIVATED A SECOND TIME.