RELIABILITY ANALYSIS OF STEEL SMRF AND SCBF STRUCTURES CONSIDERING THE VERTICAL COMPONENT OF NEAR-F AULT GROUND MOTIONS Investigators: 1) Jawad Fayaz; Graduate Student 2) Farzin Zareian; Associate Professor Performance Based Earthquake Engineering Laboratory, University of California Irvine Estimate Type II Parameters u & k Type II Distribution- Curve Fitting - EQ Load Setting up Limit State Equations = − − − BEAMS & BRACES = − + + − + + COLUMNS D, L, E and R represent random variables for EDP due to Dead Load, Live Load, Earthquake Load and corresponding Resistance, respectively. The subscript CA denotes the respective component action Calculate: µ & = 1 − exp =1– = 0 Τ − 1 2 2 2 | 2 Analysis Case Effective Nominal Resistance (R n ) Analyzed Under Case I Τ . + . +. . 2-D Ground Motions Case II Τ . + . +. . 3-D Ground Motions Case III Τ . + . + . +. . 3-D Ground Motions Case IV 2% Drift Based Design 3-D Ground Motions CASES OF ANALYSIS 1 SMRF 2-, 4-, 8- & 12- Story SCBF 3- & 6- Story 140 feet 100 feet 180 feet 120 feet 120 feet 180 feet SCBF 12- & 16- Story 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0 100 200 300 400 500 EDP due to Earthquake Load E RotD50 Spectral Acceleration (Sa) Dead Load - Normal Distribution = µ C.o.V = µ Calculate: µ & Live Load - Gamma Distribution = µ C.o.V = µ Calculate: µ & Resistance – LogNormal Distribution = µ C.o.V = µ Calculate: µ & Limit State Equation FORM b 4 5 6 +. + , + , + r , 2 3 Current b of SMRF Members Current b of SCBF Members Empirical values to upgrade seismic load combinations Empirical values of ‘x’ for the seismic load combinations can be derived from this figure depending on what percentage of members are required to attain Reliability = 1.75 (i.e. Probability of Failure = 4%) CASE I CASE II CASE III Reliability Index (b ) for Braces 1.0 1.2 1.4 1.6 1.8 2.0 CASE I CASE II CASE III Reliability Index (b ) for Columns 1.0 1.2 1.4 1.6 1.8 2.0 1.0 1.2 1.4 2.2 2.4 2.6 2.0 1.8 1.6 Reliability Index (b ) for Beams CASE: MOMENTS SHEAR I II III IV I II III IV CASE III CASE IV 1.0 1.2 1.4 2.2 2.4 2.6 2.0 1.8 1.6 Reliability Index (b ) for Columns CASE II CASE I 0.00% 0.20% 0.40% 0.60% 0.80% 1.00% 0 0.1 0.2 0.3 0.4 0.5 0.6 1.2 1.8 2.4 3 3.6 Frequency Probability Mass Cumulative Probability 0.5 PMF 0.0 0.6 1.2 1.8 2.4 3.0 3.6 CDF x - Values 0.4 0.3 0.2 0.1 0.0 1.0 0.8 0.6 0.4 0.2 0.0