Seismic Analysis Concepts
Prof. Sarosh H Lodi
1
Seismic Analysis Concepts
How
to
estimate
internal forces due to
seismic excitation
?
F=ma
or
Acceleration vs Time, File ELCENTRO
F=
Translation Acceleration (INCHES/SECONDS^2)
200
100
0
5
10
15
20
25
30
35
40
45
50
55
2
-100
-200
Time (SECONDS)
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
3
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
4
Dynamic Concept
Time History Analysis
Mathematical Model
.
..
..
mu(t) + cu(t) + ku(t) = -mug(t)
200
Translation Acceleration (INCHES/SECONDS^2)
Two storied
building
Acceleration vs Time, File ELCENTRO
100
0
5
10
15
20
25
30
35
40
45
50
55
-100
5
-200
Dynamic Concept
Response Spectrum Concept
Acceleration vs Time, File ELCENTRO
Translation Acceleration (IN/SEC^2)
200
100
0
5
10
15
20
25
30
35
40
45
50
55
-100
-200
Time (SEC)
6
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
7
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
8
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.
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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
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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 12.8-9
 Ta may be different in each direction.
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Equivalent Force Method
Building Period Coefficient, CT
12
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
R from Table 12.2-1 based
on the Basic Seismic-ForceResisting System
I from Table 11.5-1 based on
Occupancy Category
Numerical Analysis or Ta
= CThnx or Ta = 0.1N
CT = 0.028, 0.016, 0.030, or
0.020
hn = building height
N = number of storys13
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
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Equivalent Force Method
Story Force, Fx
Fx = CvxV
Where Cvx = Vertical Distribution Factor
Cvx
W x hx
k
n
W i hi
k
i= 1
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
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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.
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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.
17
Performance Levels
 Incipient Collapse
Hazard Levels
 Occasional

50% in 50 years
 Life Safety
 Rare
 Immediate

Reoccupancy
 Fully Operational
10% in 50 years
 Very Rare

5% in 50 years
 Max Considered

2% in 50 years
18
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)
19
Development of Performance-based
Seismic Design Standards and Criteria
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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
21
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
22
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
23
Building Codes Imply Performance
• Ability to resist frequent, minor
earthquakes without damage
2003
100 yrs
• Ability to resist infrequent,
moderate earthquakes with
limited structural and
nonstructural damage
500 yrs
• Ability to resist worst
earthquakes ever likely to occur
without collapse or major life
safety endangerment
2,500 yrs
Performance is not guaranteed
24
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
25
First Generation Standards are Available
• ASCE/SEI has standardized FEMA guideline
documents on::
• Seismic Evaluation
– Predict types of damage a building would
experience in
future events (based on FEMA178)
Seismic
Evaluation of
Buildings
ASCE-31
• 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
Seismic
Rehabilitation of
Buildings
ASCE-41
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Selecting Performance
Present Generation
Bata
Joe’s
Bata
BBQ!
Food!
Operational
Beer!
BBQ!
Food!
Immediate
Occupancy
Beer!
BBQ!
Food!
Life
Safety
Collapse
Prevention
Operational – negligible impact on building
Immediate Occupancy – building is safe to occupy but
possibly not useful until cleanup and repair has occurred
Life Safe – building is safe during event but possibly not
afterward
Collapse Prevention – building is on verge of
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collapse, probable total loss
Code-equivalent Performance
Frequent event (varying between 50- and 100year return periods)
Joe’s
Bata
Beer!
BBQ!
Food!
Immediate
Occupancy
DBE
MCE
Beer!
BBQ!
Food!
Life
Safety
Collapse
Prevention
28
Risk Assessment and Performance Based
Design
29
Thank you
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