INSTRUCTOR WITH SPI LANDS 3 FT SHORT OF RWY; DAMAGED NOSE GEAR STRUT.

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ACFT: PIPER ARCHER. STUDENT AND I HAD JUST FINISHED A LESSON ON STALLS AND WERE HDG BACK TO CENTENNIAL ARPT. WE HAD BEEN IN THE AIR FOR APPROX 1.2 HRS. TWR TOLD US TO RPT 2 MI SE AND WE SET UP FOR A L DOWNWIND FOR RWY 17L. THE DOWNWIND WAS FAIRLY WIDE BUT WE TURNED ONTO FINAL JUST OVER ARAPAHOE RD. THE VASI GS WAS RED OVER WHITE. AFTER MAKING POS IDENT THAT I WAS ON GS; MY ATTN TURNED AWAY FROM THE VASI FOR THE REST OF THE LNDG. STUDENT WAS EXECUTING THE LNDG WITH FULL FLAPS AT 40 DEGS AND 70 KIAS. WE BOTH NOTICED THAT WE WERE SLIGHTLY LOW SO STUDENT ADDED A LITTLE PWR. AT APPROX 300 FT FROM THE EDGE OF THE RWY; I REALIZED THAT THERE WAS A POTENTIAL PROB OF LNDG SHORT OF THE RWY. I TOOK OVER IMMEDIATELY; ADDED PWR AND APPLIED BACK PRESSURE. HOWEVER; THE INERTIAL FORCES OF THE DSCNT WERE THERE; THE ACFT WAS IN THE DIRTY CONFIGN; AND THE DSCNT COULD NOT BE COMPLETELY STOPPED. WE TOUCHED DOWN VERY SMOOTHLY 30 FT FROM THE RWY EDGE. THIS WAS NOTED BY THE TRACKS LEFT IN THE DIRT. THE NOSEWHEEL TOUCHED DOWN 3 FT FROM THE EDGE OF THE RWY ON CTRLINE. ALMOST INSTANTLY I FELT A LARGE JOLT AS THE NOSE GEAR HIT THE LIP AT THE EDGE OF THE RWY. I SAW THE O RING FROM THE NOSE STRUT FLY OUT IN FRONT OF THE ACFT. I APPLIED FULL BACK PRESSURE AND REDUCED PWR TO IDLE. THE NOSE CAME DOWN AND RESTED SAFELY ON THE COLLAPSED STRUT. I TAXIED TO ALPHA 3 AND CONTACTED GND CTL. GND CTL TOLD ME TO CALL THE TWR WHEN I WAS DONE TYING DOWN. I CALLED TWR; IDENTIFYING MYSELF AS CHEROKEE AND TOLD THEM THAT EVERYTHING WAS ALRIGHT AND THAT IT LOOKED LIKE I LOST A LOT OF HYD FLUID OUT OF THE NOSE STRUT. LATER THE NEXT DAY; MAINT LOOKED AT THE STRUT AND DETERMINED THAT THE STRUT NEEDED TO BE REBUILT. THERE WAS ALSO A FLAT SPOT ON THE ALUMINUM PART OF THE WHEEL. NO ONE WAS HURT. 3 DAYS LATER; THE ACFT WAS FIXED AND FLYING AGAIN. TO PREVENT THIS FROM HAPPENING AGAIN; I SUGGEST THAT ALL PLTS FLY ON GS.