Closure to “Collapse of Yielding Structures during Earthquakes”

Abstract

THE EFFECT OF GRAVITY ON THE EARTHQUAKE RESPONSE OF ONE- DEGREE OF FREEDOM YIELDING STRUCTURES IS STUDIED BY SUB- JECTING THEM TO SIMULATED EARTHQUAKE EXCITATION. INTEREST IS CENTERED ON THE TIME REQUIRED FOR YIELDING PROGRESSING TO THE POINT OF COLLAPSE. THE RESULTS SHOW THAT THE EFFECT OF GRAVITY IS TO INCREASE SIGNIFICANTLY THE DEVELOPMENT OF PERMANENT SET, OVER THAT OCCURRING WHEN GRAVITY IS IGNORED. BECAUSE THE GRAVITY EFFECT INCREASES AS THE DEFLECTION GROWS, THE PERMANENT SET INCREASES RAPIDLY JUST PRIOR TO FAILURE. THE RESPONSE STATISTICS FOR ELASTO PLASTIC STRUCTURES INDICATE THAT THE AVERAGE TIME TO FAILURE IS INVERSELY PROPORTIONAL TO THE SQUARE OF THE RATIO OF THE EARTHQUAKE STRENGTH TO THE LATERAL YIELD LEVEL OF THE STRUCTURE, IMPLYING THAT AN EARTHQUAKE OF SHORT DURATION WOULD HAVE TO POSSESS SIGNIFICANTLY HIGHER ACCELERATIONS THAN A LONGER EARTHQUAKE IN ORDER TO CAUSE FAILURE OF A GIVEN STRUCTURE. FOR THE BILINEAR HYSTERETIC STRUCTURE, THE RESULTS SHOW A LARGE INCREASE IN THE AVERAGE TIME OF FAILURE WHEN THE SECOND SLOPE INCREASES FROM ZERO. IT WAS FOUND THAT FOR THE RANGE OF PERIODS CONSIDERED THE AVERAGE TIME TO COLLAPSE FOR THE YIELDING STRUCTURES WAS INDEPENDENT OF THE NATURAL PERIOD OF SMALL VIBRATIONS