A B737-700 ENCOUNTERED SEVERE TURBULENCE AT FL400 WITH CREW AND PAX SEATED. THE ACFT EXCEEDED MMO AND REQUIRED A POST FLT INSPECTION.

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WE WERE ENRTE TO ZZZ AT FL400 NEAR ZZZ1 AND ON A DISPATCH PLANNED WX DEV RTE WHICH WAS BEING FLOWN BY NUMEROUS ACFT. OPTIMUM ALT WAS FL400 OR HIGHER WITH AN AIRSPD ENVELOPE OF ABOUT 40 KTS. ATC RPTED RIDES LOWER WERE WORSE. THE FLT ATTENDANTS HAD BEEN SEATED FOR SOME TIME DUE TO RPTS OF LIGHT TO MODERATE CHOP ENRTE AND OUR PROX TO WX AREAS. SEATBELT SIGN WAS ON AND I HAD WARNED THE PAX 2 OR 3 TIMES STARTING BEFORE PUSHBACK THAT THERE WAS SIGNIFICANT WX NEAR OUR RTE AND THAT 'THE SEATBELT SIGN IS NOT A SUGGESTION TONIGHT. IF IT IS ON; WE INSIST YOU REMAIN BUCKLED IN YOUR SEATS.' WE DEVIATED FARTHER N FROM THE RADAR ECHOES; SO AS TO CLR THE NEAREST STORMS HORIZONTALLY BY AT LEAST 40 NM. ANOTHER ACFT 100 NM NW RPTED MODERATE TURB. THIS WAS THE ONLY OTHER SIGNIFICANT RPT BEYOND LIGHT TO MODERATE TURB. SOON AFTER PASSING W OF THE FIRST RADAR ECHOES WE ENCOUNTERED OCCASIONAL MODERATE TURB; WHICH QUICKLY INCREASED TO MODERATE TO SEVERE; THEN SEVERE TURB. AIRSPD OSCILLATED BTWN .76 AND .79 MACH WITH A BRIEF MMO EXCEEDANCE (1 - 1.5 SECONDS) TO .81 MACH; AS THE AIRSPD DID NOT RESPOND TO PWR REDUCTION. ROLL OSCILLATIONS WERE +15 DEGS FROM HORIZ AND THE ACFT WAS SOMEWHAT UNRESPONSIVE TO CTL INPUTS. WE REQUESTED AND WERE IMMEDIATELY CLRED TO FL360. ONCE WE WERE ABLE TO CTL AIRSPD ENOUGH TO DSND; WE LEFT THE SEVERE TURB LAYER OUT OF FL385 AND ENCOUNTERED LIGHT TO MODERATE CHOP DOWN TO AND INCLUDING FL360. WE WERE IN SEVERE TURB FOR 2-3 MINS. I QUERIED THE PAX AND FLT ATTENDANTS AND THEY RPTED EVERYONE WAS SEATED DURING THE EVENT AND NO ONE HAD BEEN INJURED. WE RPTED THE ENCOUNTER TO DISPATCH WHO COORD MAINT UPON ARR AT ZZZ. ALL SYS WERE NORMAL FOR THE DURATION OF THE FLT. MADE ENTRIES IN ACFT LOGBOOK AND MET MAINT IN ZZZ. OTHER THAN AWAITING BETTER TURB DETECTION TECHNOLOGY; I CANNOT THINK OF ANY WAY THIS COULD HAVE BEEN AVOIDED. I WOULD EMPHASIZE THAT CREWS SHOULD BE TRAINED TO MAKE EMPHATIC PAX ANNOUNCEMENTS WHEN THE RIDE COULD BE ROUGH AND TO FLT ATTENDANTS; THAT THEY MUST REMAIN SEATED WHEN DIRECTED; EVEN IF IT SEEMS IT WILL BE SMOOTH.