2. 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

4. ENERGY DIAGRAM

5. ENERGY DIAGRAM w/ HYSTERETIC

6. IMPLIED NONLINEAR BEHAVIOR

7. STEEL STRESS STRAIN RELATIONSHIPS

8. INELASTIC WORK DONE

9. HYSTERETIC BEHAVIOR

10. MOMENT ROTATION RELATIONSHIP

11. IDEALIZED MOMENT ROTATION

12. DUCTILITY
LATERAL
LOAD
Partially Ductile
Ductile
Brittle
DRIFT

13. 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

14. SHEAR LINKS FOR ENERGY DISSIPATION

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

16. PERFORMANCE LEVELS

17. IDEALIZED FORCE DEFORMATION CURVE

18. ASCE 41 BEAM MODEL

19. 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

20. 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)

22. STRUCTURAL COMPONENTS

23. F-D RELATIONSHIP

24. BACKBONE CURVE

25. HYSTERESIS LOOPS

26. 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. .

27. ASCE 41 MOMENT HINGE AUTOMATED

28. HYSTERESIS LOOPS AUTOMATED

29. IMPORTANCE OF DUCTILITY
LATERAL
LOAD
Partially Ductile
Ductile
Brittle
DRIFT

30. ASCE 41 – DUCTILITY

31. FORCE AND DEFORMATION CONTROL

32. ASCE 41 BEAM MODEL

33. STEEL COLUMN AXIAL-BENDING

34. COLUMN AXIAL-BENDING MODEL

35. CONCRETE COLUMN AXIAL-BENDING

36. STEEL STRESS STRAIN RELATIONSHIPS

37. STEEL COLUMN FIBER MODEL
SECTION
FIBERS

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

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

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

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

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

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

44. STRAIN AND ROTATION MEASURES

45. 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 )

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

47. SHEAR HINGE MODEL

48. PANEL ZONE ELEMENT

50. LINEAR vs. NONLINEAR

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

52. NONLINEAR EVENT TO EVENT ANALYSIS

53. STEP BY STEP DYNAMIC ANALYSIS

54. EQUATIONS FOR CAA METHOD

55. 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

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

57. RITZ VECTORS

58. 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

59. 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.

60. DYNAMIC EQUILIBRIUM EQUATIONSg u - = w + x 2 M Ku C t . .. M C .. .. K .. .. ..

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

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

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

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

65. 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

66. SPECTRAL PARAMETERS S PS w = d V a v DISPLACEMENT, in. PERIOD, sec4 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

67. 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

68. THE ADRS SPECTRUM

69. THE LINEAR PUSHOVER

70. EQUIVALENT LINEARIZATION
How far to push? The Target Point!

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

72. 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

73. SPECTRAL MATCHING IN TIME DOMAINB 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

74. CONSEQUENCE BASED DESIGN

75. 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