SCHEDULE

8:30 AM 10:30 AM Session I

10:30 AM 11:00 AM Break

11:00 AM 12:15 PM Session II

12:15 PM 1:30 PM Lunch

1:30 PM 2:45 PM Session III

2:45 PM 3:15 PM Break

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 Brittle Ductile

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

Restaurant Restaurant

Resta

urant

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 Brittle Ductile

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 )

Steel Confined Concrete

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 )

Steel Confined Concrete

SHEAR WALL FIBER HINGE MODEL

Reinforcement Layout

Steel Fibers

Confined Concrete Fibers

Unconfined Concrete Fibers

SHEAR WALL FIBER HINGE MODEL

Shear Wall Cross Section Confined and Unconfined Concrete Fibers Rebar Fibers

STRAIN AS A PERFORMANCE MEASURE

Rebar

Tension Compression

IO 0.02 -0.02

LS 0.06 -0.06

CP 0.09 -0.09

Concrete

Tension Compression

IO 0.0001 -0.0015

LS 0.0005 -0.003

CP 0.001 -0.0045

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

Friction Isolator Rubber Isolator Viscous Damper Friction Damper Buckling-Restrained

Brace (BRB)

SHEAR HINGE MODEL

PANEL ZONE ELEMENT

50

LINEAR vs. NONLINEAR

NONLINEAR SOLUTION SCHEMES

NEWTON RAPHSON ITERATION

u u

1 2

iteration

u u

1 2

iteration

CONSTANT STIFFNESS ITERATION

3 4 5 6

52

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 u u u - = w + w x +

2 2

g u M Ku u C u M

Ku u C t

u M . ..

- = + +

= + + 0

.

.

u g

M

K

C

..

..

..

..

..

RESPONSE FROM GROUND MOTION

ug ..

2 ug2 ..

ug1 ..

1

t1

t2 t

A B t u g = + = - . u u u + + 2

2 x w w

.. ..

CLOSED FORM DAMPED RESPONSE

{ [ .

] cos

[ ( .

)] sin }

e u B

t

A u u B

t B

t

t d

d t t d

. u t = -

+ - - + +

- xw

w w

w w xw

w w

w

1 2

2

1 1 2 2

1

e A B

t

u u A B

t

A B Bt

t

t d

d t t d

u t = - +

+ + - + -

+ - +

- xw

w

x

w w

w xw

x

w

x

w w

w

x

w w

{ [u ] cos

[ . ( )

] sin }

[ ]

1 2 3

1 1

2

2

2 3 2

2

1 2 1

2

BASIC DYNAMICS WITH DAMPING

g u u u u & & & & & - = w + w x + 2 2

g u M Ku u C u M

Ku u C t

u M

& & & & &

& & &

- = + +

= + + 0

g u & &

M

K

C

RESPONSE MAXIMA

u t ) cos( 0 t u w =

) cos( 0 2 t u w w - = u t & &

) sin( 0 t u w w - = u t &

max 2 u w - = max u & &

RESPONSE SPECTRUM GENERATION

Displacement Response Spectrum

5% damping

0

2

4

6

8

10

12

14

16

0 2 4 6 8 10

PERIOD, Seconds

DIS

PL

AC

EM

EN

T,

inch

es

-0.40

-0.20

0.00

0.20

0.40

0.00 1.00 2.00 3.00 4.00 5.00 6.00

TIME, SECONDS

GR

OU

ND

AC

C,

g

Earthquake Record

-4.00

-2.00

0.00

2.00

4.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

DIS

PL, in

.

-8.00

-4.00

0.00

4.00

8.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

DIS

PL, in

.

T= 0.6 sec

T= 2.0 sec

SPECTRAL PARAMETERS

0

4

8

12

16

0 2 4 6 8 10

PERIOD, sec

DIS

PL

AC

EM

EN

T, in

.

0

10

20

30

40

0 2 4 6 8 10

PERIOD, sec

VE

LO

CIT

Y, in

/se

c

0.00

0.20

0.40

0.60

0.80

1.00

0 2 4 6 8 10

PERIOD, sec

AC

CE

LE

RA

TIO

N, g

d V S PS w =

v a PS PS w =

THE ADRS SPECTRUM

ADRS Curve

Spectral Displacement, Sd

Spe

ctra

l Acc

ele

rati

on

, Sa

Period, T

Spec

tral

Acc

eler

atio

n, S

a

RS Curve

0.5

Sec

on

ds

1.0

Sec

on

ds

2.0

Sec

on

ds

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

Target Spectrum and Spectrum for Seed Acceleration Time History

Seed Acceleration Time History

De-aggregated Cyclic Signals for Each Frequency of Interest

FFT

At

As

Scaled Cyclic Signals for Each Frequency of Interest

Scal

e A

mp

litu

de

s fo

r Ea

ch F

req

. (Sc

ale

fac

tor

= A

t/A

s)

Target Spectrum and Spectrum for Matched Acceleration Time History

Acceleration Time History Matched to Target Spectrum

Inverse FFT

SPECTRAL MATCHING IN TIME DOMAIN

Target Spectrum and Spectrum for Seed Acceleration Time History

Target Spectrum and Spectrum for Matched Acceleration Time History

Seed Acceleration Time History

A B C D E F G H I

Wavelet for Freq. Band A

Wavelet for Freq. Band B

AD

D

Misfit < Tol

Adjust Wavelet

No

Misfit < Tol

Adjust Wavelet

Acceleration Time History Matched to Target Spectrum

. .

. .

Yes

AD

D

Yes No

Misfit < Tol for all Freq. Bands

Cabinets, 1% Bookcases, 1% Roof Equipment, 1%

Cladding, 2%

Partitions, 27%

Moment Frame, 2%

Ceiling, 32%

Elevators, 21%

Computers, 6%

Servers/Network, 7%

CONSEQUENCE BASED DESIGN

CoRE Rating Safety Reparability Functionality

5-Star Life Safe Loss