1. Seismic Analysis Concepts - Prof SH Lodi
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Prof. Sarosh H Lodi

2. Seismic Analysis Concepts?
How to estimate internal forces due to seismic excitation
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3. Earthquake Protective Design Philosophical Issues
High probability of “Failure”
“Failure” redefined to permit behavior (yielding) that would be considered failure under other loads.
High Uncertainty
Importance of Details
“In dealing with earthquakes we must contend with appreciable probabilities that failure will occur in the near future. Otherwise, all the wealth of the world would prove insufficient… We must also face uncertainty on a large scale… In a way, earthquake engineering is a cartoon… Earthquakes systematically bring out the mistakes made in design and construction, even the minutest mistakes.” Newmark & Rosenblueth

4. Elastic vs Inelastic Response
The red line shows the force and displacement that would be reached if the structure responded elastically.
The green line shows the actual force vs. displacement response of the structure
The pink line indicates the minimum strength required to hold everything together during inelastic behavior
The blue line is the force level that we design for.
We rely on the ductility of the system to prevent collapse.
From 1997 NEHRP Provisions

5. mu(t) + cu(t) + ku(t) = -mug(t)
Dynamic Concept
Time History Analysis
Mathematical Model .. . ..
mu(t) + cu(t) + ku(t) = -mug(t)
Two storied building

6. Response Spectrum Concept
Dynamic Concept
Response Spectrum Concept

7. Equivalent Force Method
Base Shear Determination
Base Shear, V = CsW
where:
Cs = seismic response coefficient
W = the effective seismic weight, including applicable portions of other storage and snow loads
Total ELASTIC earthquake force (in each direction): VEQ can be calculated

8. Equivalent Force Method Seismic Response Coefficient, Cs
Cs = SDS /(R/I)
Cs need not exceed
SD1/(T(R/I)) for T < TL
SD1TL/(T2(R/I)) for T > TL
Cs shall not be taken less than
Max[0.044SDSI, 0.01] for S1 < 0.6g
0.5S1/(R/I) for S1 > 0.6g

9. Equivalent Force Method Response Modification Coefficient, R
The response modification factor, R, accounts for the dynamic characteristics, lateral force resistance, and energy dissipation capacity of the structural system.
Can be different for different directions.

10. Equivalent Force Method Fundamental Period, T
May be computed by analytical means
May be computed by approximate means, Ta
Where analysis is used to compute T:
T < Cu Ta
May also use Ta in place of actual T
ASCE 7-05 Seismic Provisions - A Beginner's Guide to ASCE 7-05 10

11. Equivalent Force Method Approximate Fundamental Period, Ta
An approximate means may be used.
Ta = CThnx
Where:
CT = Building period coefficient.
hn = height above the base to the highest level of the building
for moment frames not exceeding 12 stories and having a minimum story height of 10 ft, Ta may be taken as 0.1N, where N = number of stories.
For masonry or concrete shear wall buildings use eq
Ta may be different in each direction.

12. Equivalent Force Method Building Period Coefficient, CT

13. Equivalent Force Method Base Shear Summary
V = CsW
From Design Spectrum
W = Building Seismic Weight
Max[0.044SDSI,0.01] or 0.5S1/(R/I) < SDS/(R/I) < SD1/(T(R/I)) or TLSD1/(T2(R/I))
From map
Numerical Analysis or Ta = CThnx or Ta = 0.1N
R from Table based on the Basic Seismic-Force-Resisting System
CT = 0.028, 0.016, 0.030, or 0.020
hn = building height
N = number of storys
I from Table based on Occupancy Category

14. Equivalent Force Method Vertical Distribution of Base Shear
For short period buildings the vertical distribution follows generally follows the first mode of vibration in which the force increases linearly with height for evenly distributed mass.
For long period buildings the force is shifted upwards to account for the whipping action associated with increased flexibility

15. Equivalent Force Method Story Force, Fx
Fx = CvxV
Where Cvx = Vertical Distribution Factor
Wx = Weight at level x
hx = elevation of level x above the base
k = exponent related to structure period
When T < 0.5 s, k =1, When T > 2.5 s, k =2,
Linearly interpolate when 0.5 < T < 2.5 s

16. Equivalent Force Method Story Shear, Vx
Story shear, Vx, is the shear force at a given story level
Vx is the sum of all the forces above that level.

17. Equivalent Force Method Horizontal Distribution
Being an inertial force, the Story Force, Fx, is distributed in accordance with the distribution of the mass at each level.
The Story Shear, Vx, is distributed to the vertical lateral force resisting elements based on the relative lateral stiffnesses of the vertical resisting elements and the diaphragm.

18. Performance Levels Hazard Levels Occasional Incipient Collapse Rare
50% in 50 years
Rare
10% in 50 years
Very Rare
5% in 50 years
Max Considered
2% in 50 years
Incipient Collapse
Life Safety
Immediate Reoccupancy
Fully Operational

19. Design Objective Defined
A specific performance level given a specific earthquake hazard level
Stated basis of current codes:
Life safety (+some damage control) at 10% in 50 year event (nominally)

20. Development of Performance-based Seismic Design Standards and Criteria

21. Advantages of Performance-Based Approach
Specifically Addresses:
Unique Building Features
Client Needs
Building Use Considerations
Proposed Alternatives
Assessment of Code Requirements
Increased Engineering Rigor / Peer Review
Comprehensive Systems Overview
Integration of Systems
Cost Effectiveness
Improved Knowledge of Loss Potential

22. Disadvantages of Performance-Based Approach
Reluctance to Approve PB Approach
Unfamiliar with Methodology
Lack of Knowledge of Science Creates Tendency to Disagree with or be Skeptical of:
Approach, Objectives, Certainty
Perception that Anything Less than Code is not “Safe”
Qualifications of Designer / Reviewer
More Design/Engineering Time
Occupancy Changes May Require Re-analysis

23. Code Procedures Require buildings have complete structural systems
Require systems have sufficient strength to resist specified forces
Limit permissible drifts under specified forces
Require members and connections be “detailed” prescriptively
2003

24. Building Codes Imply Performance
100 yrs
Ability to resist frequent, minor earthquakes without damage
Ability to resist infrequent, moderate earthquakes with limited structural and nonstructural damage
Ability to resist worst earthquakes ever likely to occur without collapse or major life safety endangerment
500 yrs
2003
2,500 yrs
Performance is not guaranteed

25. Building Codes & Performance Warranties
If a building is affected by an extreme event and performs poorly:
There is an expectation of how the building should have performed but no implied warranty
The only warranty is that the engineer complied with the standard of care
For most buildings, demonstration that a design was performed in accordance with the building code will provide adequate proof of conformance to the standard of care

26. First Generation Standards are Available
Seismic
Evaluation of Buildings
ASCE/SEI has standardized FEMA guideline documents on::
Seismic Evaluation
Predict types of damage a building would experience in future events (based on FEMA178)
Rehabilitation
Procedures to design building upgrades to achieve desired performance (based on FEMA 356)
Though not directly recognized by the building codes, these standards are being used as the basis for Performance-based design of new buildings and seismic retrofit
ASCE-31
Seismic
Rehabilitation of Buildings
ASCE-41

27. Selecting Performance Present Generation
Bata
BBQ!
Food!
Operational
Operational – negligible impact on building
Beer!
Food!
Joe’s
BBQ!
Bata
Life
Safety
Life Safe – building is safe during event but possibly not afterward
Collapse
Prevention
Collapse Prevention – building is on verge of collapse, probable total loss
Beer!
Food!
Joe’s
BBQ!
Bata
Immediate
Occupancy
Immediate Occupancy – building is safe to occupy but possibly not useful until cleanup and repair has occurred

28. Code-equivalent Performance
Seismic Analysis Concepts - Prof SH Lodi
Code-equivalent Performance
Beer!
Food!
Joe’s
BBQ!
Bata
Immediate
Occupancy
Frequent event (varying between 50- and 100-
year return periods)
Beer!
Food!
Joe’s
BBQ!
Bata
Life
Safety
Collapse
Prevention
DBE
MCE

29. Risk Assessment and Performance Based Design

30. Thank you