SCHEDULE 8:30 AM 10:30 AM Session I 11:00 AM Break 12:15 PM Session II 1:30 PM Lunch 2:45 PM Session III 3:15 PM 4:30 PM Session IV

ENERGY DIAGRAM

ENERGY DIAGRAM w/ HYSTERETIC

IMPLIED NONLINEAR BEHAVIOR

STEEL STRESS STRAIN RELATIONSHIPS

INELASTIC WORK DONE

HYSTERETIC BEHAVIOR

MOMENT ROTATION RELATIONSHIP

IDEALIZED MOMENT ROTATION

DUCTILITY LATERAL LOAD Partially Ductile Ductile Brittle DRIFT

CAPACITY DESIGN STRONG COLUMNS & WEAK BEAMS IN FRAMES REDUCED BEAM SECTIONS LINK BEAMS IN ECCENTRICALLY BRACED FRAMES BUCKLING RESISTANT BRACES AS FUSES RUBBER-LEAD BASE ISOLATORS HINGED BRIDGE COLUMNS HINGES AT THE BASE LEVEL OF SHEAR WALLS ROCKING FOUNDATIONS OVERDESIGNED COUPLING BEAMS OTHER SACRIFICIAL ELEMENTS

SHEAR LINKS FOR ENERGY DISSIPATION

PERFORMANCE LEVELS Operational Immediate Occupancy Life Safety Collapse Prevention Less Damage More Damage Ref: FEMA 451 B

PERFORMANCE LEVELS

IDEALIZED FORCE DEFORMATION CURVE

ASCE 41 BEAM MODEL

STRENGTH vs. DEFORMATION ELASTIC STRENGTH DESIGN - KEY STEPS   CHOSE DESIGN CODE AND EARTHQUAKE LOADS DESIGN CHECK PARAMETERS Stress/BEAM MOMENT GET ALLOWABLE STRESSES/ULTIMATE– PHI FACTORS CALCULATE STRESSES – Load Factors (ST RS TH) CALCULATE STRESS RATIOS INELASTIC DEFORMATION BASED DESIGN -- KEY STEPS CHOSE PERFORMANCE LEVEL AND DESIGN LOADS – ASCE 41 DEMAND CAPACITY MEASURES – DRIFT/HINGE ROTATION/SHEAR GET DEFORMATION AND FORCE CAPACITIES CALCULATE DEFORMATION AND FORCE DEMANDS (RS OR TH) CALCULATE D/C RATIOS – LIMIT STATES

ASCE 41 ASSESSMENT OPTIONS Linear Static Analysis Linear Dynamic Analysis (Response Spectrum or Time History Analysis) Nonlinear Static Analysis (Pushover Analysis) Nonlinear Dynamic Time History Analysis (NDI or FNA)

STRUCTURAL COMPONENTS

F-D RELATIONSHIP

BACKBONE CURVE

HYSTERESIS LOOPS

ASCE 41 BACKBONE CURVES This can be used for components of all types. It can be used if experimental results are available. ASCE 41 gives capacities for many different components. .

ASCE 41 MOMENT HINGE AUTOMATED

HYSTERESIS LOOPS AUTOMATED

IMPORTANCE OF DUCTILITY LATERAL LOAD Partially Ductile Ductile Brittle DRIFT

ASCE 41 – DUCTILITY

FORCE AND DEFORMATION CONTROL

ASCE 41 BEAM MODEL

STEEL COLUMN AXIAL-BENDING

COLUMN AXIAL-BENDING MODEL

CONCRETE COLUMN AXIAL-BENDING

STEEL STRESS STRAIN RELATIONSHIPS

STEEL COLUMN FIBER MODEL SECTION FIBERS

MATERIAL STRESS-STRAIN CURVES Unconfined and Confined Concrete ( Compared ) Confined Concrete Steel

CONCRETE COLUMN FIBER HINGE MODEL Reinforced Concrete Column Steel Rebar Fibers Confined Concrete Fibers Unconfined Concrete Fibers

MATERIAL STRESS-STRAIN CURVES Unconfined and Confined Concrete ( Compared ) Confined Concrete Steel

SHEAR WALL FIBER HINGE MODEL Reinforcement Layout Steel Fibers Confined Concrete Fibers Unconfined Concrete Fibers

SHEAR WALL FIBER HINGE MODEL Shear Wall Cross Section Rebar Fibers Confined and Unconfined Concrete Fibers

STRAIN AS A PERFORMANCE MEASURE Concrete   Tension Compression IO 0.0001 -0.0015 LS 0.0005 -0.003 CP 0.001 -0.0045 Rebar   Tension Compression IO 0.02 -0.02 LS 0.06 -0.06 CP 0.09 -0.09

STRAIN AND ROTATION MEASURES

CONCRETE WALL MODELING P-M Action With No Shear Coupling Nonlinear Fiber Model P-M Action With Shear Coupling (Multi-layered Nonlinear Darwin-Pecknold Concrete Shell Model )

ENERGY DISSIPATION DEVICES Buckling-Restrained Brace (BRB) Friction Isolator Rubber Isolator Viscous Damper Friction Damper

SHEAR HINGE MODEL

PANEL ZONE ELEMENT

LINEAR vs. NONLINEAR

NONLINEAR SOLUTION SCHEMES ∆ ƒ u 1 2 iteration CONSTANT STIFFNESS ITERATION 3 4 5 6 ∆ ƒ u 1 2 iteration NEWTON – RAPHSON ITERATION

NONLINEAR EVENT TO EVENT ANALYSIS

STEP BY STEP DYNAMIC ANALYSIS

EQUATIONS FOR CAA METHOD

THE POWER OF RITZ VECTORS APPROXIMATELY THREE TIMES FASTER THAN THE CALCULATION OF EXACT EIGENVECTORS IMPROVED ACCURACY WITH A SMALLER NUMBER OF VECTORS CAN BE USED FOR NONLINEAR ANALYSIS TO CAPTURE LOCAL RESPONSE

FAST NONLINEAR ANALYSIS (FNA) DISCRETE NONLINEARITY FRAME AND SHEAR WALL HINGES BASE ISOLATORS (RUBBER & FRICTION) STRUCTURAL DAMPERS STRUCTURAL UPLIFT STRUCTURAL POUNDING BUCKLING RESTRAINED BRACES

RITZ VECTORS

FNA ADVANTAGES MODAL SOLUTION - NO STIFFNESS REDUCTION CLOSED FORM SOLUTION – VERY FAST TIME STEP INDEPENDENT CAPTURES HIGH FREQUENCY RESPONSE RITZ VECTORS CALCULATED ONCE MULTIPLE TIME HISTORIES ARE FAST

FNA KEY POINT The Ritz modes generated by the nonlinear deformation loads are used to modify the basic structural modes whenever the nonlinear elements go nonlinear.

DYNAMIC EQUILIBRIUM EQUATIONS g u - = w + x 2 M Ku C t . .. M C .. .. K .. .. ..

RESPONSE FROM GROUND MOTION A B t u g = + - . 2 x w .. ug .. 2 ug2 ug1 1 t1 t2 t

CLOSED FORM DAMPED RESPONSE { [ . ] cos ( )] sin } e u B t A d = - + xw w 1 2 Bt x [u ) 3

BASIC DYNAMICS WITH DAMPING u & - = w + x 2 M Ku C t C K g u &

RESPONSE MAXIMA u t ) cos( w = 2 - & sin( max

Displacement Response Spectrum RESPONSE SPECTRUM GENERATION -0.40 -0.20 0.00 0.20 0.40 1.00 2.00 3.00 4.00 5.00 6.00 TIME, SECONDS GROUND ACC, g Earthquake Record -4.00 -2.00 DISPL, in. -8.00 8.00 T= 0.6 sec T= 2.0 sec 2 4 6 8 10 12 14 16 PERIOD, Seconds DISPLACEMENT, inches Displacement Response Spectrum 5% damping

SPECTRAL PARAMETERS S PS w = d V a v DISPLACEMENT, in. PERIOD, sec 4 8 12 16 2 6 10 PERIOD, sec DISPLACEMENT, in. 20 30 40 VELOCITY, in/sec 0.00 0.20 0.40 0.60 0.80 1.00 ACCELERATION, g d V S PS w = v a

Spectral Acceleration, Sa THE ADRS SPECTRUM ADRS Curve Spectral Displacement, Sd Spectral Acceleration, Sa 2.0 Seconds 1.0 Seconds 0.5 Seconds Period, T RS Curve

THE ADRS SPECTRUM

THE LINEAR PUSHOVER

EQUIVALENT LINEARIZATION How far to push? The Target Point!

ARTIFICIAL EARTHQUAKES CREATING HISTORIES TO MATCH A SPECTRUM FREQUENCY DOMAIN & TIME DOMAIN MATCHING

SPECTRAL MATCHING IN FREQUENCY DOMAIN FFT Inverse FFT Scaled Cyclic Signals for Each Frequency of Interest De-aggregated Cyclic Signals for Each Frequency of Interest Scale Amplitudes for Each Freq. (Scale factor = At/As) Seed Acceleration Time History Acceleration Time History Matched to Target Spectrum As At Target Spectrum and Spectrum for Seed Acceleration Time History Target Spectrum and Spectrum for Matched Acceleration Time History

SPECTRAL MATCHING IN TIME DOMAIN B C D E F G H I Seed Acceleration Time History Target Spectrum and Spectrum for Seed Acceleration Time History Adjust Wavelet No Yes Misfit < Tol Adjust Wavelet Wavelet for Freq. Band A No Yes Misfit < Tol ADD Wavelet for Freq. Band B ADD . . . . Misfit < Tol for all Freq. Bands Target Spectrum and Spectrum for Matched Acceleration Time History Acceleration Time History Matched to Target Spectrum

CONSEQUENCE BASED DESIGN

RATING FOR SEISMIC PERFORMANCE CoRE Rating Safety Reparability Functionality 5-Star Life Safe Loss <5% Occupiable Immediately Functional < 72 hours 4-Star Loss <10% Occupiable Immediately Functional < 1 month 3-star Loss <20% Occupiable < 1 month Functional < 6 months Certified Not estimated Not Certified Life Safety Hazard