1. Seismic Analysis and Design Using Response Spectra
Of Structures
Using Response Spectra Or
Time History Motions BY
Ed Wilson
Professor Emeritus of Civil Engineering
University of California, Berkeley
February 24, 2010 1

2. On Advanced Numerical Modeling and Analytical Techniques
SUMMARY OF PRESENTATION
On Advanced Numerical Modeling and Analytical Techniques
Personal Remarks – 50 years experience of dynamic analysis
Seismic Analysis Using Response Spectra – CQC3
Comparison with Direct Time History Dynamic Analysis
Retrofit of the San Mateo Bridge _-
The Fast Non-Linear Analysis Method – FNA Method
Retrofit of the Richmond San Rafael Bridge
Near Fault Seismic Analysis
Concluding Remarks

3. edwilson.org and ed-wilson1@juno.com
1882
Father Born In San Francisco – Carpenter and
Walked Guard in S.F. after 1906 Earthquake
1931
Ed born in Ferndale CA – Earthquake Capitol of USA
1950
Graduated - Christian Brothers HS in SAC.
Sacramento Jr. College
BS in Civil Eng. – UC Berkeley
DOT CA Bridge Dept. – Ten Mile River Bridge
US Army – Korea – Radio Repairman
M.S. and D. Eng. With Prof. Ray Clough
1960
With Ray, Conducted the first Time-Histories
Earthquake Response of Buildings Bridges & Dams. - Fifty Years Ago
Worked on the Apollo Program at Aerojet in Sacramento - Designed Structures for 10 g Loads
Professor at UC Berkeley

4. NINETEEN SIXTIES IN BERKELEY
1. Cold War - Blast Analysis
2. Earthquake Engineering Research
3. State And Federal Freeway System
4. Manned Space Program
5. Offshore Drilling
6. Nuclear Reactors And Cooling Towers

5. NINETEEN SIXTIES IN BERKELEY
1. Period Of Very High Productivity
2. No Formal Research Institute
3. Free Exchange Of Information – Gave programs to profession prior to publication
4. Worked Closely With Mathematics Group
5. Students Were Very Successful

6. DYNAMIC ANALYSIS USING RESPONSE SPECTRUM SEISMIC LOADING
Before the Existence of Inexpensive Personal Computers, the Response Spectrum Method was the Standard Approach for Linear Seismic Analysis

7. Figure 15.1a Typical Earthquake Ground Acceleration - Percent of Gravity

8. Figure 15.1b Absolute Earthquake Ground Displacements - Inches

9. Figure 15.2b Pseudo-Acceleration Spectrum,
- Percent of Gravity
Figure 15.2a Relative Displacement Spectrum y (T)MAX Inches

10. Figure 15.2b Pseudo-Acceleration Spectrum Percent of Gravity

11. Major Approximation
The loads are applied directly to the structure; whereas, the real earthquake displacements are applied at the foundation of the real structure.

12. Development of the Three Spectrum
In Addition, All Spectrum Values Are Maximum Peak Values
The Time History Details of the Duration of the Earthquake Have Been Lost

13. Examples of Three-Dimensional Spectra Analyses

14. Definition of Earthquake Spectra Input

15. Three-Dimensional Spectra Analyses
Equal Spectrum from any direction – CQC3 Method
Maximum Peak Column Moments - Symmetrical All Values are Positive

16. Three-Dimensional Spectra Analyses 100/30 Spectrum Method
Maximum Peak Column Moments - Not Symmetrical
All Values are Positive

17. Summary of Multi-Component Combination Rules
The 100/30 and 100/40 percent rules have no theoretical basis.
The SRSS combination rule, applied to equal spectra, produces identical results for all reference systems and requires only one analysis to produce all design forces and displacements.

18. The CQC3 method should be used where the horizontal orthogonal components of the seismic input are not equal.
In case of the seismic analysis of structures near a fault, the fault normal and parallel motions are not equal.

19. In 1996 The CQC3 was Proposed by Professor Armen Der Kiureghian
As a Replacement for the
30%, 40% & SRSS Rules
For Multi-Component Seismic Analysis

21. Design Checks of Three-Dimensional Frame Members for Seismic Forces
In order to stratify various building codes, every one-dimensional compression member within a structure must satisfy the following Demand/Capacity Ratio at all points in time:
t = 0 = Static Loads Only

22. Where the forces acting on the frame element cross-section at time “t” are including the static forces prior to the application of the dynamic loads. The empirical constants are code and material dependent and are normally defined as .

23. Design Checks of Three-Dimensional Frame Members for Spectra Forces
For the case maximum peak spectra forces, compression members within a structure must satisfy the following Demand/Capacity Ratio
Where P(max), M2(max) and M3(max) have been
Calculated by the CQC Method

24. The Retrofit of the San Mateo Bridge
Demand/Capacity Ratios were calculated using COC forces using spectrum calculated from several three-dimensional sets of earthquake motions.
Time-dependent Demand/Capacity Ratios were calculated directly from the same set of earthquake motions.
In general, the time-dependent Demand/Capacity Ratios were approximately 50 percent of the ratios using the CQC forces.

25. Limitations of Response Spectrum Analysis
All forces and displacements obtained from a Response Spectrum Analysis are Maximum Peak Values and are all positive numbers.
The specific time the Maximum Peak Values occur is different for every period.
Nonlinear Behavior CANNOT be considered in a Response Spectrum Analysis.
Except for a single degree of freedom, a Response Spectrum Analysis is an APPROXIMATE METHOD
This is not Performance Based Design

26. STRUCTURAL ANALYSIS PROGRAM
S A P
STRUCTURAL ANALYSIS PROGRAM
ALSO A PERSON
“ Who Is Easily Deceived Or Fooled”
“ Who Unquestioningly Serves Another” 5

27. From The Foreword Of The First SAP Manual
"The slang name S A P was selected to remind the user that this program, like all programs, lacks intelligence.
It is the responsibility of the engineer to idealize the structure correctly and assume responsibility for the results.”
Ed Wilson 1970 6

28. The SAP Series of Programs
SAP Used Static Loads to Generate Ritz Vectors
Solid-Sap Rewritten by Ed Wilson
SAP IV Subspace Iteration – Dr. Jűgen Bathe
1973 – 74 NON SAP New Program – The Start of ADINA
1979 Lost All Research and Development Funding
1979 – 80 SAP 80 New Linear Program for Personal Computers
1983 – 1987 SAP 80 CSI added Pre and Post Processing
SAP 90 Significant Modification and Documentation
1997 – Present SAP Nonlinear Elements – More Options –
With Windows Interface

29. FIELD MEASUREMENTS REQUIRED TO VERIFY
1. MODELING ASSUMPTIONS
2. SOIL-STRUCTURE MODEL
3. COMPUTER PROGRAM
4. COMPUTER USER

31. CHECK OF RIGID DIAPHRAGM APPROXIMATION
MECHANICAL VIBRATION DEVICES

32. FIELD MEASUREMENTS OF PERIODS AND MODE SHAPES
MODE TFIELD TANALYSIS Diff. - %
Sec Sec. 0.5

33. FIRST DIAPHRAGM MODE SHAPE
15 th Period
TFIELD = 0.16 Sec.

34. The Fast Nonlinear Analysis Method
The FNA Method was Named in 1996
Designed for the Dynamic Analysis of
Structures with a Limited Number of Predefined Nonlinear Elements

35. BASE ISOLATION
Isolators 25

36. BUILDING
IMPACT
ANALYSIS 26

37. FRICTION
DEVICE
CONCENTRATED
DAMPER
NONLINEAR
ELEMENT 27

38. GAP ELEMENT
BRIDGE DECK ABUTMENT
TENSION ONLY ELEMENT 28

39. Degrading Stiffness Elements are in SAP 2000
P L A S T I C
H I N G E S
2 ROTATIONAL DOF
Degrading Stiffness Elements are in SAP 2000 29

40. Mechanical Damper
F = f (u,v,umax )
F = ku
F = C vN
Mathematical Model

41. First Application of the FNA Method - 1994
103 FEET DIAMETER FEET HEIGHT
NONLINEAR
DIAGONALS
BASE
ISOLATION
Nonlinear Seismic Analysis of
ELEVATED WATER STORAGE TANK 30

42. COMPUTER MODEL 92 NODES 103 ELASTIC FRAME ELEMENTS 56
NONLINEAR DIAGONAL ELEMENTS
600
TIME Seconds 31

43. COMPUTER TIME REQUIREMENTS PROGRAM ANSYS INTEL 486 3 Days
( 4300 Minutes )
ANSYS
CRAY
3 Hours
( 180 Minutes )
SADSAP
INTEL 486
2 Minutes
( B Array was 56 x 20 ) 32

44. EXAMPLE OF FRAME WITH UPLIFTING ALLOWED40

45. Four Static Load Conditions Generation of LDR Vectors
Are Used To Start The
Generation of LDR Vectors
EQ DL Left Right 41

46. 45

47. Column Axial Forces

48. Confirmed by Shaking Table Tests
Summary of Results for Building Uplifting Example
from Two Times the Loma Prieta Earthquake
Uplift
Computer Time
Max. Displace-ment (inches)
Max. Column Force (kips)
Max. Base Shear (kips)
Max. Base Moment (k-in)
Max. Strain Energy (k-in)
Max. Uplift (inches)
Without
14.6 Sec
7.76
924
494
424,000
1,547
0.0
With
15.0 Sec
5.88
620
255
197,000
489
1.16
Percent Diff.
-24%
-33%
-40%
-53%
-68%
Confirmed by Shaking Table Tests
By Ray Clough on Three Story Frame

49. Advantages Of The FNA Method
1. The Method Can Be Used For Both Static And Dynamic Nonlinear Analyses
2. The Method Is Very Efficient And Requires A Small Amount Of Additional Computer Time As Compared To Linear Analysis
2. The Method Can Easily Be Incorporated Into Existing Computer Programs For LINEAR DYNAMIC ANALYSIS. 47

50. 63

52. MULTISUPPORT SEISMIC ANALYSIS (Earthquake Displacements Input )
ANCHOR PIERS
Hayward Fault San Andreas Fault
East West 54

53. 65

54. Eccentrically Braced Towers66

55. Analysis and Design of Structures for Near Fault Earthquake Motions
On the UC Berkeley Campus
Fault Normal and Parallel Foundation Displacements are Significantly Different
Used six different Time-History Earthquake Motions for Nonlinear Dynamic Analyses

56. Base Isolated in 2004 Hearst Mining Building – Built in 1905 to 07
50 Yards from the Hayward Fault
Base Isolated in 2004

57. Near Fault Analysis and Design - SRC

58. Concluding Remarks
The 100/30 percent Rule should replaced by the SRSS Rule - Until the CQC3 is implemented in SAP 2000.
Response Spectra Seismic Analysis is an Approximate Method and is restricted to linear structural behavior and may satisfy a design code. However, it may not produce a Performance Based Design
In general, Nonlinear Time-History Analyses produce more realistic results and can produce Performance Based Design

59. Nonlinear Seismic Analyses are possible due to:
Performance Based Design is using all the information about the seismic displacement loading on the structure and to the accurately predict the nonlinear behavior and damage to the structure.
All Code Based Designed Structures appear to be based on Linear Analysis.
Nonlinear Seismic Analyses are possible due to:
New Methods of nonlinear analysis have been developed.
New Nonlinear Energy Dissipation and Simple Isolation Device can be used.
The new inexpensive personal computer can easily conduct the required calculations.

60. Floating-Point Speeds of Computer Systems
Definition of one Operation A = B + C*D 64 bits - REAL*8
Year
Computer or CPU
Operations Per Second
Relative Speed
1962
CDC-6400
50,000 1
1964
CDC-6600
100,000 2
1974
CRAY-1
3,000,000 60
1981
IBM-3090
20,000,000
400
CRAY-XMP
40,000,000
800
1994
Pentium-90
3,500,000 70
1995
Pentium-133
5,200,000
104
DEC-5000 upgrade
14,000,000
280
1998
Pentium II - 333
37,500,000
750
1999
Pentium III - 450
69,000,000
1,380
2003
Pentium IV – 2,000
220,000,000
4,400
2006
AMD - Athlon
440,000,000
8,800
2009
Intel – Core 2 Duo
1,200,000,000
25,000