Design-of-Structures-for-EQ-Loads.pdf

Classifying the Earthquakes
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CE 623 - High Rise Buildings - Dr. J. A. S. C. Jayasinghe

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Terminology used to
defined Earthquakes
Maximum Credible Earthquake (MCE)
Maximum Design Earthquake (MDE)
Safe Shutdown Earthquake (SSE)
Contingency Level Earthquake (CLE)
Ductility Level Earthquake (DLE)
Operating Basis Earthquake (OBE)
Maximum Probable Earthquake (MPE)
Strength Level Earthquake (SLE)

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❖ Maximum Credible Earthquake (MCE)
• Earthquake associated with specific seismotectonic structures, source areas, or
provinces that would cause the most severe vibratory ground motion or foundation
dislocation capable of being produced at the site under the currently known tectonic
framework
• Determined by judgment based on all known regional and local
geological and seismological data
• Little regard is given to its probability of occurrence, which may vary
from a less than a hundred to several tens of thousands of years

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❖ Maximum Design Earthquake (MDE)
• Represents the maximum level of ground motion for which the structure should be
designed or analysed
❖ Safe Shutdown Earthquake (SSE)
• The maximum earthquake potential for which certain structures, systems, and
components, important to safety, are designed to sustain and remain functional (used
in the design of nuclear power plants)
❖ Contingency Level Earthquake (CLE)
• Earthquake that produces motion with a 10% probability of exceedance in 50 years
• For this event, the structure may suffer damage, however life safety is protected

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❖ Operating Basis Earthquake (OBE)
• EQ for which the structure is designed to resist and remain operational
• The OBE is usually taken as an:
a) EQ producing the maximum motions at the site once in 110 years (recurrence
interval)
b) EQ with half the peak acceleration of SSE
c) EQ that produces motion with a 50% probability of exceedances in 50 years

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❖ Maximum Probable Earthquake (MPE)
• The maximum EQ that is likely to occur during a 100 year interval
❖ Strength Level Earthquake (SLE)
• The maximum earthquake that is likely to occur during a 200 year interval
• This earthquake is not anticipated to induce significant damage or inelastic response in
the structural elements

Seismic Hazard Analysis Process
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1. Study the geology of the region
2. Study the past EQ records
3. Prepare general soil profile
4. Potential site amplification of
ground motion
5. Estimation of soil shear wave
velocity (SWV)
6. Soil classification based on SWV
7. Estimation of soil dynamic properties
8. Collect information about existing
building
9. Estimate/measure time period of
buildings
10. Classify the building in terms of
risk
11. Develop design response spectra

Seismic Code and Design Method
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Seismic Analysis
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𝑀 ሷ
𝑢 + 𝐶 ሶ
𝑢 + 𝐾𝑢 + 𝐹𝑁𝐿 = 𝐹
𝑀 ሷ
𝑢 + 𝐶 ሶ
𝑢 + 𝐾𝑢 = −𝑀 ሷ
𝑢𝑔
𝐾𝑢 = 𝐹𝐸𝑄
𝐾𝑢 = 𝐹𝐸𝑄
𝐾𝑢 + 𝐹𝑁𝐿 = 𝐹𝐸𝑄
𝑀 ሷ
𝑢 + 𝐾𝑢 = 0
Time History Analysis
General Equation
Equivalent Static
Analysis
Pushover Analysis
Modal Response
Spectrum Analysis
Response Spectrum
Acceleration Records

Basic Dynamic for Ground Motion
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𝑐
𝑘
𝑚
ሷ
𝑢𝑔
𝜔 =
𝑘
𝑚
𝑐 = 2𝜉𝜔𝑚
𝑚 ሷ
𝑢 + 𝑐 ሶ
𝑢 + 𝑘𝑢 = 𝐹
𝐹 = −𝑚 ሷ
𝑢𝑔
𝑚 ሷ
𝑢 + 𝑐 ሶ
𝑢 + 𝑘𝑢 = −𝑚 ሷ
𝑢𝑔
𝑚 ሷ
𝑢 + 2𝜉𝜔𝑚 ሶ
𝑢 + 𝑚𝜔2𝑢 = −𝑚 ሷ
𝑢𝑔
ሷ
𝑢 + 2𝜉𝜔 ሶ
𝑢 + 𝜔2𝑢 = − ሷ
𝑢𝑔

Ground Motion
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❖ The input variables are ground acceleration ( ሷ
𝑢𝑔), damping ratio (𝜉) and circular frequency (𝜔)
ሷ
𝑢 + 𝜔2
𝑢 = − ሷ
𝑢𝑔
❖ The final unknown is displacement (and its derivatives – velocity and acceleration)
𝑎 𝑣 𝑢

Response Spectrum
13

What is Response Spectrum?
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❖ For a ground acceleration at particular time, for a given time period and damping ratio, a
single value of displacement, velocity and acceleration can be obtained
❖ Output of the above (𝑢, 𝑣, 𝑎) equation are the dynamic response to the ground motion for
a structure considered as a SDOF
❖ A plot of the “maximum” response for different ground motion history, different time
period and damping ratio give the “Spectrum of Response”
ሷ
𝑢 + 𝜔2
𝑢 = − ሷ
𝑢𝑔

Response Spectrum Generation
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Response Spectrum for Different Damping Ratios
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Response Spectrum for Different Ground Motions
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𝝃 = 𝟓%

Spectra for Different Soils
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Eurocode (EC8): Lateral Force Method
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Force Based Seismic Design Procedure as in
Eurocode - (EC8)
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❖ With regard to the implications of structural regularity on design, separate consideration
is given to the regularity characteristics of the building in plan and in elevation
Regularity Allowed Simplification
Plan Elevation Model Linear-elastic analysis
Yes Yes Planar Lateral force method
Yes No Planar Model response spectrum analysis
No Yes Spatial Lateral force method
No No Spatial Model response spectrum analysis
Table 4.1: Consequences of structural regularity on seismic analysis and design

Lateral Force Method
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1. The structural geometry, including member sizes is estimated. In many cases these may be
dictated by non-seismic load considerations
2. Member elastic stiffnesses are estimated, based on preliminary estimates of member size.
Different assumptions are made in different seismic codes about appropriate stiffnesses for
members. In some cases gross (uncracked section) stiffnesses are used, while in some codes
about the stiffnesses are taken, to reflect the softening caused by expected cracking at yield-
level response (Eurocode 08 - cracked)
3. Based on the assumed member stiffnesses, the fundamental period (equivalent lateral force
approach) or periods (multi-mode dynamic analysis) are calculated. In some building codes
a height-dependent fundamental period is specified, independent of member stiffness, mass
distribution, or structural geometry
75
.
0
1
1 )
( n
H
C
T =

Lateral Force Method - (EC8)
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Lateral Force Method (EC8)
23

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4. The design elastic base shear FBE for the structure corresponding to elastic response with
no allowance for ductility is given by an equation of the form:

m
T
S
F b
BE )
( 1
=
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Period/(s)
Spectral
acceleration/(g)
Design response spectrum

25

26

27

Lateral Force Method - EC8
28

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(Total Dead Load) + (Self Weight)
+ (0.6) × (0.5) × (Total live load)
෍ 𝐺𝑘,𝑗" + " ෍ Ψ𝐸,𝑖 . 𝑄𝑘,𝑖

Design Spectra as in EC8 for Different Soil Classes
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Response Spectrum – Sri Lanka
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Seismic Zonation Map (Sri Lanka)
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(Seneviratne et al., 2016)
𝑅 Sri Lanka = 1.5

Proposed Normalized Response Spectrum
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(Seneviratne et al., 2016)
SA =
1+10T
( )* PGA
2.5PGA
1.25/ T * PGA
ì
í
ï
î
ï
ü
ý
ï
þ
ï
0 £ T £ 0.15
0.15 £ T £ 0.5
0.5 £ T £ 4.0
𝑇𝐶
𝝃 = 𝟓%

Force Reduction Factor (R) / Behavior Factor (q)
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5. The appropriate force-reduction factor R corresponding to the assessed ductility
capacity (μ) of the structural system and material is selected. Generally R is specified by
the design code and is not a design choice, though the designer may select to use a lesser
value than the code specified one
)
1
2
( 2
/
1
−
=
= 
y
e
F
F
R

=
=
y
e
F
F
R
Energy based approach
Displacement based approach

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y
d
2
/
1
,
)
1
2
(


=
−
=
= 

y
e
F
F
R
Fe
Fy
Δy Δd
Fe
Fy
Δy Δd
❖ The conservation of energy, or velocity, has been proposed
as a means to allow computation of the reduction of the
applied force. An energy conservation principle leads to the
following relationship in terms of force reduction and
structural ductility:
❖ The equal displacement rule specify that the force reduction
factor can be considered equal to the available ductility:

=
=
y
e
F
F
R

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❖ The above figures enables us to introduce the concepts of “force-reduction factors” and
“ductility”, which are fundamental tools in current seismic design
❖ For a structure with linear elastic response to the design earthquake, the maximum force
developed at peak displacement is Fe
❖ We label Fy as reduced ultimate strength and related to the elastic response level by the
force-reduction Factors

Behavior Factor (q) - (EC8)
37

Behavior Factor (q) - (EC8)
38

Force Reduction Factor (R)
39

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6. The design base shear force is then found from:
R
F
V BE
BR =
❖ The base shear force is then distributed to different parts of the structure to provide a
vector of applied seismic forces
❖ For building structures, the distribution is typically proportional to the product of the
height and mass at different levels, which is compatible with the displaced shape of
the preferred inelastic mechanism (beam-end plastic hinges plus column-base plastic
hinges for frames; wall-base plastic hinges for wall structures)
❖ The total seismic force is distributed between different lateral force-resisting
elements, such as frames and structural walls, in proportion to their elastic stiffness

41

42

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7. The structure is then analyzed under the vector of lateral seismic design forces, and the
required moment capacities at potential locations of inelastic action (plastic hinges) is
determined. The final design values will depend on the member stiffnesses

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8. Structural design of the member sections at plastic hinge locations is carried out and the
displacements under the seismic action are estimated.
9. The displacements are compared with code-specified displacement limits
10. If the calculated displacements exceed the code limits, redesign is required. This is
normally effected by increasing member sizes, to increase member stiffness
11. If the displacements are satisfactory, the final step of the design is to determine the
required strength of actions and members that are not subject to plastic hinging
12.The process known as capacity design (Ensures that the dependable strength in shear,
and the the moment capacity of sections where plastic hinging must not occur, exceed the
maximum possible input corresponding to maximum feasible strength of the potential
plastic hinges)
e
s Rd
d =

45

46

Design of Irregular Structures for Earthquake Loading
47

Modal Response Spectra Analysis
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❖For most earthquake analyses, and particularly for design, the time-history analyses are not
applicable
❖For design, most engineers use response spectra, those associated with real earthquakes or
those set out in seismic design codes
❖Response spectra are generated for single degree of freedom structures and give the
maximum response of a structure with a given natural period of free-vibration and
specified fraction of critical damping
❖ This means that they can only be used to give the maximum response of each mode
seperately
❖As the times at which each mode reaches its peak response is unknown then statistical
techniques must be used to obtained the maximum response of the structure

Response Spectrum Analysis Using SAP2000
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Response Spectrum Analysis Using SAP2000
50

Modal Combination Rules
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❖ ABS SUM Rule
Add the absolute maximum value from each mode Not
so popular and not used in practice
❖ SRSS
Square Root of Sum of Squares of the peak response
from each mode. Suitable for well separated natural
frequencies
❖ CQC
Complete Quadric Combination is applicable to large
range of structural response and gives better results than
SRSS
𝑟𝑚𝑎𝑥 = ෍
𝑖=1
𝑛
𝑟𝑖
𝑖=1
𝑛
𝑟𝑖
2
𝑖=1
𝑛
෍
𝑗=1
𝑛
𝑟𝑖 𝛼𝑖𝑗𝑟
𝑗

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