CE 72.32 (January 2016 Semester) Lecture 8 - Structural Analysis for Lateral Loads

Dr. Naveed Anwar
Executive Director, AIT Consulting
Affiliated Faculty, Structural Engineering
Director, ACECOMS
Design of Tall Buildings
AIT Hybrid Learning System

Dr. Naveed Anwar
Director, ACECOMS
Lecture 9: Structural Analysis
for Lateral Loads
Design of Tall Buildings

Design of Tall Buildings: Hybrid Learning System, Dr. Naveed Anwar
• Analysis for Earthquake
– Basic Elements of Seismology
– The Seismic Analysis Problem
– Forces generated by Earthquakes
– Vertical and Horizontal Regularity
– Seismic Analysis Methods
• Analysis Using Equivalent Static
Load
• Analysis Using Response Spectrum
• Analysis Using Acceleration Time
History
– Capacity Design Approach
– Earthquake Analysis using ETABS
and SAP 2000
Lecture Contents
• Analysis for Wind
– The Wind Analysis Problem
– Bluff Body Aerodynamics
– Wind Effects on Tall Buildings
– Analysis Using Equivalent Static
Load
– Combining Response for Member
Design
3

Analysis for Earthquake
4

Basic Elements of Seismology
5

The Earth
Inside the EarthSource: Murty (2004)
6

Dip Slip (normal or thrust) Strike Slip (right or left lateral)
Four Basic Types of Faults
A fault is a fracture along which the blocks of
crust on either side have moved relative to one
another parallel to the fracture.
Source: Murty (2004)
7

Theory of Continental Drift
An earthquake is caused by the
rebound of elastically strained rock.
Elastic Rebound Theory
Source: httap://www.seismo.unr.edu
8

Plate Tectonics
9

Convergence plate boundary: Subduction zone, etc.
Divergence plate boundary: Plates diverges at mid-ocean ridges
Transform fault: Plates move laterally past each other
Earth’s 14 Lithospheric Plates
and Their Movements
10
Earth’s Changing Landscape

Seismic Waves
Body Wave
Surface Wave
11

Design of Tall Buildings: Hybrid Learning System, Dr. Naveed Anwar 12

Arrival of Seismic Waves at a Site

Basic Terminology
Reducing illumination with distance
from an electric bulb
Electric Bulb Analogy

Classifying the Earthquakes
Terminology used to
define earthquake
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)
15

• 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 less
than a hundred to several tens of thousands of years
Classifying the Earthquake

• Maximum Design Earthquake (MDE)
– Represents the maximum level of ground motion for which the structure
should be designed or analyzed.
• 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.

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

• 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

The Seismic Analysis Problem
20

The Basic Equilibrium Equations
• Linear-Static Elastic
• Linear-Dynamic Elastic
• Nonlinear - Static Elastic OR Inelastic
• Nonlinear-Dynamic Elastic OR Inelastic
1FKu 
2)()()()( tFtKutuCtuM  
4)()()()()( tFtFtKutuCtuM NL  
3FFKu NL 
21

Linear and Nonlinear
• Linear, Static and Dynamic
• Nonlinear, Static and Dynamic
Non Linear Equilibrium
FKu 
)()()()( tFtKutuCtuM  
)()()()()( tFtFtKutuCtuM NL  
FFKu NL 
22

Basic Analysis Types
Excitation Structure Response Basic Analysis Type
Static Elastic Linear
Linear-Elastic-
Static Analysis
Static Elastic Nonlinear
Nonlinear-Elastic-
Static Analysis
Static Inelastic Linear
Linear-Inelastic-
Static Analysis
Static Inelastic Nonlinear
Nonlinear-Inelastic-
Static Analysis
Dynamic Elastic Linear
Linear-Elastic-
Dynamic Analysis
Dynamic Elastic Nonlinear
Nonlinear-Elastic-
Dynamic Analysis
Dynamic Inelastic Linear
Linear-Inelastic-
Dynamic Analysis
Dynamic Inelastic Nonlinear
Nonlinear-Inelastic-
Dynamic Analysis
23

• Non-linear Analysis
– P-Delta Analysis
– Buckling Analysis
– Static Pushover Analysis
– Fast Non-Linear Analysis (FNA)
– Large Displacement Analysis
• Dynamic Analysis
– Free Vibration and Modal Analysis
– Response Spectrum Analysis
– Steady State Dynamic Analysis
Special Analysis Types

Comprehensive Equilibrium Equation
)()()()()( tFtFtKutuCtuM NL  
• Cover all Static, Dynamic, Elastic, Non Elastic, Damped, Un-damped,
Linear, Non-Linear cases and their combinations
• Handles response for:
– Basic Dead and Live Loads
– Seismic, Wind, Vibration and Fire Analysis
25

Comprehensive Equilibrium Equation
FFKuuCuM NL  
Damping-Velocity
Mass-Acceleration Stiffness-Displacement
Nonlinearity
External Force
KuuCuM  
The basic variable is displacement and its derivatives
26

Static Part
Dynamic Part
Static and Dynamic
27

• Static Excitation
– When the excitation (load) does not vary rapidly with time
– When the load can be assumed to be applied “slowly”
• Dynamic Excitation
– When the excitation varies rapidly with time
– When the “inertial force” becomes significant
• Most Real Excitation are Dynamic but are considered “Quasi Static”
• Most Dynamic Excitation can be converted to “Equivalent Static Loads”
Static versus Dynamic

Linear and Non-Linear
Linear Part
Non-Linear Part
29

The Structure Stiffness - K
Section Stiffness
Member Stiffness
Structure Stiffness
Material Stiffness
Cross-section Geometry
Member Geometry
Structure Geometry
Linear
Non-Linear
30

Seismic Analysis
Time History Analysis
0 KuuM 
EQNL FFKu 
Free Vibration
Pushover
Analysis
EQFKu 
Equivalent
Static Analysis
EQFKu 
Response Spectrums
Response Spectrum
Analysis
Acceleration Records
guMKuuCuM  
31

A SDOF System
32
Idealized SDOF system
Un-damped free vibrations of SDOF system Damped free vibrations of SDOF system

A MDOF System
33
Representation of a multi-
mass system by a single-
mass system:
(a) fundamental mode of a
multi-mass system and
(b) equivalent single-mass
system.

Forces Generated by
Earthquakes
34

Schematic Representation of Seismic
Forces

Concept of 100% g (1g)
Linear Viscous Damper

Force Reversal
37
Bilinear Force–displacement Hysteresis Loop

Inertial Forces
38
Effect of Inertia in a building when
shaken at its base
Flow of seismic inertia forces
through all structural
components
Source: Murty, (2004)
Inertia force and relative
motion within a building

The natural period values are only indicative; depending on
actual properties of the structure, natural period may vary
considerably.
Fundamental natural periods of
structures differ over a large
range. Source: Murty (2004)
Free vibration
response of a
building: the
back-and-
forth motion is
periodic.

Different Buildings Respond Differently
to Same Ground Vibration
Building Behavior during
Earthquakes

Vertical and Horizontal
Regularity
41

Simple plan shape buildings do well
during earthquakes
Buildings with one of their overall sizes much larger or
much smaller than the other two, do not perform well
during earthquakes
Identical vertical members placed
uniformly in plan of building cause all
points on the floor to move by the same
amount.

Sudden deviations in load transfer path along the height lead to poor
performance of buildings. Source: Murty (2004)

Rope swings and buildings: both swing back-
and-forth when shaken horizontally. The former
are hung from the top, while the latter are
raised from the ground.
Even if vertical members are placed uniformly in
plan of building, more mass on one side causes
the floors to twist.

Buildings have unequal vertical
members; they cause the building
to twist about a vertical axis

Vertical members of buildings that
move more horizontally sustain
more damage
Pounding can occur between
adjoining buildings due to
horizontal vibrations of the two
buildings

This is what earthquakes do … (Click to watch)
47

The Tragic Side…
48
On 8 October 2005, an earthquake of
magnitude 7.6 hit Islamabad,
Pakistan, killing 30, 000 and seriously
injuring another 60, 000 people.
Some structures collapsed next to
others of the same age that
remained intact.
This zone was classified as to be
considered as only moderate. UBC 97
was applied by private consultants.
Courtesy: L. A. Prieto Portar (2008), University of Florida

Kashmir Earthquake (Oct 8, 2005)
Magnitude = 7.7
Death Toll > 80,000
49

Haiti Earthquake (2010)
Magnitude = 7.0
Death Toll: 100,000 ~ 200,000
50

Upper storeys of open ground
storey buildings move together as
a single block – such buildings are
like inverted pendulums.
Soft Story Mechanism

Open ground storey building - assumptions made in current design practice are
not consistent with the actual structure.

Soft Story Failures
53

Seismic Analysis
Methods
54

• Linear Static Procedures
– Equivalent Static Analysis
• Nonlinear Static Procedures
– Capacity Spectrum Method
– Displacement Coefficient Method
– Various Other Pushover Analysis Methods
• Linear Dynamic Procedures
– Response Spectrum Analysis
– Linear Response History Analysis
• Nonlinear Dynamic Procedures
– Nonlinear Response History Analysis
Seismic Analysis Procedures

• Study the Geology of the Region
• Study the Past EQ Records
• Prepare General Soil Profile
• Potential Site Amplification of Ground Motion
• Estimation of Soil Shear Wave Velocity (SWV)
• Soil Classification Based on SWV
• Estimation of Soil Dynamic Properties
• Collect Information about Existing Buildings
• Estimate/Measure Time Period of Buildings
• Classify the Buildings in Terms of Risk
• Develop Design Response Spectra
Seismic Hazard Analysis Process

Seismic Hazard Curve
Seismic hazard curve for Bangkok (Warnitchai & Lisantono, 1996)
57

Typical Dynamic Analysis
Typical Dynamic Analysis
Free Vibration Response
Response to Harmonic Forces
Response to Periodical
Loading
Response to Impulse Loading
Ambient Vibration Response
Response to
Direct Dynamic Force
Response to
Earthquake Excitation
58

• Definition
– Natural vibration of a structure released from initial condition and subjected
to no external load or damping
• Main governing equation - Eigenvalue Problem
• Solution gives
– Natural Frequencies
– Associated mode shapes
– An insight into the dynamic behavior and response of the
structure
Free Vibration Analysis
         tt
tt
PuKucuM 












 

Mode Shapes
• A mode shape is a set of relative (not absolute) nodal displacement for a particular
mode of free vibration for a specific natural frequency
• There are as many modes as there are DOF in the system
• Not all of the modes are significant
• Local modes may disrupt the modal mass participation
60

The Modal Analysis
• The modal analysis determines the inherent natural frequencies of vibration
• Each natural frequency is related to a time period and a mode shape
• Time Period is the time it takes to complete one cycle of vibration
• The Mode Shape is normalized deformation pattern
• The number of Modes is typically equal to the number of Degrees of Freedom
• The Time Period and Mode Shapes are inherent properties of the structure
and do not depend on the applied loads
61

The Modal Analysis
• The Modal Analysis should be run before applying loads any other analysis to check
the model and to understand the response of the structure.
• Modal analysis is precursor to most types of analysis including Response Spectrum,
Time History, Push-over analysis, etc.
• Modal analysis is a useful tool even if full Dynamic Analysis is not performed.
• Modal analysis is easy to run and is fun to watch when animated.
62

• The Time Period and Mode Shapes, together with animation
immediately exhibit the strengths and weaknesses of the structure.
• Modal analysis can be used to check the accuracy of the structural model
– The Time Period should be within reasonable range,
• (Ex: 0.1 x number of stories seconds)
– The disconnected members are identified
– Local modes are identified that may need suppression
Application of Modal Analysis

• The symmetry of the structure can be determined
– For doubly symmetrical buildings, generally the first two modes are
translational and the third mode is rotational
– If the first mode is rotational, the structural is un-symmetrical
• The resonance with the applied loads or excitation can be avoided
– The natural frequency of the structure should not be close to excitation
frequency
Application of Modal Analysis

Modal Analysis Results
65
Translationin
Minordirection
TranslationinMajor
direction
Torsional
• T1=5.32 sec
• 60% in
Minor
direction
• T6=1.28 sec
• 18% in
Minor
direction
• T9=5.32 sec
• 6.5% in
Minor
direction
• T2=4.96 sec
• 66% in
Major
direction
• T7=0.81 sec
• 5.2% in
Major
direction
• T4=1.56 sec
• 15% in
Major
direction
T3=4.12 sec T8=0.65secT5=1.30 sec

Eccentric and Concentric Response
Mode-1 Mode-2 Mode-3
Symmetrical Mass
and Stiffness
Unsymmetrical Mass
and Stiffness
66

• Damper is an energy absorbing
element
• Viscous damper is the most common
• Energy is lost by heat, friction,
damages, etc.
• Free vibration of a damped system
dies out gradually
Damped System
67

Damped Dynamic Response
68
Easy to Remember: 1, 2, 4 Cycle for 10, 5, 2.5
0
1
2
3
4
5
6
7
0.02 0.04 0.06 0.08 0.1
NoofCyclestoReducePeakAmplitudeby50%
Damping Ratio
Effect of Damping (Approximate)

Basic Dynamic for Ground Motion
g
g
g
g
uuuu
umumumum
umkuucum
mc
m
k
ummgumF
Fkuucum











2
2
2
2
2;



69

• The input Variables are ground
acceleration, damping ratio and
circular frequency
• The final unknown is displacement
(and its derivatives)
Ground Motion
guuuu   2
2 
70

Modal Displacements
71

• Code based, Equivalent Static Methods
– Uses single mode, single DOF approach
• Modal Analysis
– Determines the basic, inherent dynamic response indicators
• Response Spectrum Methods
– Linear, using modal combination and “Response Reduction Factor”
– Nonlinear Static Pushover Methods
• Time History Methods
– Linear Time History method and “Response Reduction Factor”
– Nonlinear Time History Analysis
Estimating Seismic Response

Analysis Using Equivalent Static
Load

• Model Code
– IBC 2000
• International Building Codes
• NEHRP Provisions
• FEMA 368-369 Provisions
• Incorporates most recent (1996) USGS Hazard Maps
• Guidelines
– ATC -40
• Applied Technology Council
– FEMA
• Federal Emergency Management Agency
Model Codes and Guidelines

The Basic Notion
• Convert the Seismic Excitation to an “Equivalent Static Force” applied at the base of
the building, called the Base Shear. Then Distribute the Base Shear to various parts
of the Building by using:
V = W C ( from F = m a)
• This formula is based on the assumption that the structure will undergo several
cycles of inelastic deformation and energy dissipation without collapse. Force and
displacements in the structure are derived assuming linear behavior.
75

• The old equation: V = (Z K C S I) W
• The new equation:
– I = Importance factor, for a specific occupancy category, from UBC Table
16-K
– Cv = Velocity based ground response coefficient, for a specific seismic zone
and soil profile, from UBC Table 16-R
– R = Response modification factor, for a specific structural system, from UBC
Table 16-N
– T = Fundamental, period of vibration, from UBC Formula (30-8) or (30-10)
The UBC-97 Form of Equation
RT
ICv
s
s
C
WCV



• Maximum Inelastic Displacement (Eq. 30-17)
– ∆M = 0.7 R ∆s
– ∆M = maximum inelastic displacement
– R = overstrength factor
– ∆s = design level displacement by design seismic forces
• Drift Limit
– For structures having a time period of < 0.7s, Drift limit = 0.025 x story height
– For structures having a time period of ≥ 0.7s, Drift limit = 0.02 x story height
– Actual time period calculated by Method B shall be used to calculate the
design lateral force for story drift and neglect the 30% or 40% limitations in
Section 1630.2.2.
– Design base shear minimum limit formula (30-6) will also be neglected.
Inelastic Displacement and Drift (UBC 97)

The IBC-06 Form of Equation
CsWV 







E
DS
S
I
R
S
C
MSDS SS
3
2
 SaMS SFS 
Fa = Site coefficient short period , Table 1615.1.2(1)
Ss = Spectral accelerations for short periods, Maps
R = The response modification factor, Table 1617.6
T
I
R
S
C
E
DI
S







EDSS ISC 044.0







E
S
I
R
S
C 15.0
IE = The occupancy importance factor, Section 1616.2
Cs does not
need to be
greater than
T = Fundamental period (in seconds) of the structure
11
3
2
MD SS  11 SFS VM 
FV = Site coefficient, 1 sec period, Table 1615.1.2(2).
S1 = Spectral accelerations for a 1-second period, Maps
Cs must be greater than
78

• W includes:
– In areas used for storage, a minimum of 25% of the reduced floor live load
(floor live load in public garages and open parking structures does not have to
be included.
– Where an allowance for partition weight or a minimum weight of 50 kg/m2 of
floor area, whichever is greater.
– Total operating weight of permanent equipment.
– 20 % of flat roof snow load where the flat roof snow load exceeds 150 kg/m2

• R is dependent on structural system and ranges from 1.5 to 8 (bad to good)
• Fa is site modification for short period spectrum and ranges from 0.8 to 2.5 (good
to bad)
• Fv is a site modification for 1 sec period spectrum and ranges from 0.8 to 3.5 (good
to bad)
• I ranges from 1.0 to 1.5 (Normal to important)
80

IBC-2006: General Procedure
• Maximum Considered Earthquake (MCE) based on 2005 USGS probabilistic hazard
maps
• Deterministic limits used in high seismicity areas where the hazard can be driven by
tails of distributions
• Hazard maps provide spectral accelerations for
– T = 0.2 Sec called Ss
– T= 1.0 Sec called S1
• Local soil conditions considered using site coefficients
– Fa for short duration
– Fv for longer duration
• Develop the design spectrum using “S” and ‘F
81

The Overall Procedure
• Step 1: Determine Seismic Zone Factor, Z
• Step 2: Determine Seismic Source Type
• Step 3: Determine Near Source Factor
• Step 4: Determine Soil Profile Type
• Step 5: Determine Ground Response Coefficients, Ca and Cv
• Step 6: Determine Fundamental period, T
82

The Overall Procedure
• Step7: Classify the Structural System and determine the Response Modification
Factor, R
• Step 8: Determine the Occupancy Categories and Importance Factor, I
• Step 9: Determine the Seismic Response Coefficient, Cs
• Step 10: Determine the Base Shear
• Step 11: Vertical Distribution of Base Shear into Lateral Forces
83

Equivalent Lateral Load Procedure
• Calculation of seismic response coefficient ,
where







I
R
S
C DS
S
factoronmodificatiresponseTheR
periodshortatparameteronacceleratiresponsespectraldesignDSS
factorimportanceoccupancyTheI
84

• Upper limit of seismic response coefficient,
• Lower limit of seismic response coefficient,
R = response modification factor
SD1 = design spectral response acceleration parameter at a period of 1s
TL = long-period transition period
T = fundamental period of building
I = importance factor
L
D
S TT
I
R
T
S
C 






 for1
L
LD
S TT
I
R
T
TS
C 






 for
2
1
01.0SC
85

• Buildings and structure for which the 1-second spectral response, S1 , is
equal to or greater than 0.6 g, the value of the seismic response
coefficient, Cs , shall not be taken as less than:
R = response modification factor
S1 = spectral response acceleration parameter at a period of 1s
I = importance factor
IR
S
CS
/
5.0 1

86

• Computing Time Period, T:
– The fundamental period of the building, T , in the direction under
consideration shall be established using the structural properties and
deformational characteristics of the resisting elements in a properly
substantiated analysis
• Or
– Shall be taken as the approximate fundamental period, Ta. The calculated
fundamental period, T, shall not exceed the product of the coefficient for upper
limit on calculation period, Cu, and the approximate fundamental period , Ta.
87

• Approximate fundamental period
N = number of stories
h = height in feet
stories)12exceedingnot(buildings1.0 NTa 
x
nt hCTa 
88

• Vertical distribution of seismic forces:
• The lateral force, (kip or kN) , induced at any level:
where
– Cvx =Vertical distribution factor.
– k = A distribution exponent related to the buildings period as follows:
• For buildings having a period of 0.5 second or less, k = 1
• For buildings having a period of 2.5 seconds or more, k = 2
• For building having a period between 0.5 and 2.5 seconds or more, k shall be 2 or
shall be determined by linear interpolation
VCF vxx 

 n
i
k
ii
k
xx
vx
hw
hw
C
1
89

Hazard Maps for Determining Ss, S1
90

• Adjust Maximum Considered
Earthquake (MCE) values of Ss
and S1 for local site effects
– SMs = Fa x Ss
– SM1 = Fv x S1
• Calculate the spectral
design values
– SDS = 2/3 x SMS
– SD1 = 2/3 x SM1
Design Spectral Values

Site Classification Characteristics
• Soil conditions at the site should be determined.
• They modify the ground motion
• Based on the site soil properties, the site shall be classified as either Site Class A, B,
C, D, E or F in accordance with Table 1613.5.2
• When the soil properties are not known in sufficient detail to determine the site
class, Site Class D shall be used unless the building official or geotechnical data
determines that Site Class E or F soil is likely to be present at the site
92

Site Classification Characteristics
93

Site Coefficients
• To adjust maximum considered earthquake spectral response acceleration
according to soil conditions
SMS =Fa Ss
SM1 = Fv S1
94

Site Coefficients
95

Seismic Design Category
• The structure must be assigned a seismic design category.
• Determines the permissible structural systems
• Determines limitations on height and irregularity.
• Determines those components of the structure that must be designed for seismic
• loads, and the types of analysis required.
• The seismic design categories, designated A through F
• They depend on the seismic use group and the design spectral acceleration
coefficients, SDS and SD1. The structure is assigned the more severe of the two
values taken from these tables
96

Seismic Design Category
97

• Seismic Design Category are used to select:
– Type of analysis
• Very Simplified
• Equivalent Lateral Load Procedure
• Response Spectrum
• Time-history
– Type of design and detailing
• Special Detailing
• Intermediate Detailing
• Ordinary Detailing
– Many other checks/requirements
Why Seismic Design Categories?

Response Modification Coefficient
• It reduces the design loads to account for the damping and ductility of the
structural system. An abbreviated set for values for R is found in Table
below.
99

• Typical Values
3.0 Ductile steel frames (Special Case)
2.5 Ductile concrete frames
2.5 Ordinary concrete frames
2.5 RC shear walls
2.5 Reinforced masonry shear walls
2.5 Unreinforced masonry shear walls
2.0 Ordinary steel frames
Over Strength Factor (Ω0)

Flow Chart
101

• Ss and S1, mapped MCE
spectral accelerations are
0% to 300% and 0% to
100% in the map.
• For example, if the map
value is 125%g, it should
be input as 1.25g
Using ETABS For EQ Static Analysis (IBC 2006)
102

• UBC-97
Summary: UBC-97 versus IBC2006
• IBC-2000
RT
ICv
s
s
C
WCV

 CsWV 
R
IS
I
R
S
C EDS
E
DS
S 







RT
IS
T
I
R
S
C DI
E
DI
S 







Cv = 0.05 to 0.5
I = 1.0 to 1.5
R =
SDS = 0.13 to nearly 1.0
IE = 1 to 1.5
R = 4 to 8
SD1 = 0.05 to nearly 0.5
103

Analysis Using
Response Spectrum
104

What are Response Spectra?
• 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
• The output of the above (u, v, a) equation are the dynamic response to the ground
motion for a structure considered as a single DOF
• A plot of the “maximum” response for different ground motion history, different
time period and damping ratio give the “Spectrum of Response”
guuuu   2
2 
105

Response Spectrum –
A picture is worth a concept
106
Graphical description of a response spectrum

What is Response Spectrum?
107

The Overall Picture …
108
Combined DVA response for El Centro ground motion, β = 2%

Response Spectrum Generation
109

Spectral Parameters
• Spectral Displacement Sd
• Pseudo Spectral Velocity Sv
• Pseudo Spectral Acceleration Sa
2
2
dt
ud
uva
dt
du
uv
u




dva
dv
SSS
SS
2




110

Spectra for Different Soils
111

How to Use Response Spectra
• For each mode of free vibration, the corresponding Time Period is obtained.
• For each Time Period and specified damping ratio, the specified Response
Spectrum is read to obtain the corresponding Acceleration
• For each Spectral Acceleration, the corresponding velocity and displacements
response for the particular degree of freedom is obtained
• The displacement response is then used to obtain the corresponding stress
resultants
• The stress resultants for each mode are then added using some combination rule to
obtain the final response envelope
112

• ABS SUM Rule
Add the absolute maximum value
from each mode. Not so popular
and not used so much used
• 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.


N
n
no rr
1
0
Modal Combination Rules


N
n
no rr
1
2
0
 

N
i
N
n
niino rrr
1 1
00
113

Response Spectrum Analysis


n
i
imi
m g
w
M
1
2

1. Develop the Mathematical Model of the Structure
2. Determine Mode Shapes by Eigen Value Analysis
3. For Each Mode m, determine:


n
i
imi
m g
w
L
1

Eq Participation Factor
Modal Mass
114



n
i
iwW
1
g
M
L
W
m
m
m
2

WM
gL
PM
m
m
2

Effective Weight
Participating Mass
Where;
115

4. Determine the Number of Modes to be Considered to represent at least
90% of the participating mass of Structure
5. Determine the Spectral Acceleration and Seismic Design Coefficients for
each mode:
a. For Design response spectrum (UBC) determine Sam for Tm
b. Determine modal Seismic design coefficient
I = Importance Factor; R = Response Modification Factor
R
I
SC amm 
  





 9.0
W
W
PM m
116

6. Determine the modal Base Shears, Vm, and Total Dynamic Shear Vd
7. Determine the Design Base Shear from Static Procedures and compare
base shear with dynamic results
m
m
m W
g
C
V 
 22
3
2
2
2
1 ... nd VVVVV 
117

8. Scale Dynamic Analysis Results
9. Distribute base shear for each mode over the height of Structure
10. Perform Lateral analysis for each mode
11. Combine Dynamic Analysis results for all considered modes using SRSS
m
imi
imi
im V
w
w
F




118

Design Spectrum PRA = 0.025g
119

0 41 2 3
Period (s)
0
0.8
0.2
0.4
0.6
SpectralAcceleration(g)
0 1 2 3
Period (s)
0
0.8
0.2
0.4
0.6
PRA = 0 .0 25g PRA = 0 .0 5g
Class A1
Class A2
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A1
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A2
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
SpectralAcceleration(g) 0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
0 41 2 3
Period(s)
0
0.8
0.2
0.4
0.6
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A3
Acceleration Spectra
120

0 41 2 3
Period (s)
0
120
40
80
Spectralvelocity(cm/s)
0 41 2 3
Period (s)
0
120
40
80
0
0
120
40
80
PRA = 0.025g PRA = 0.05g
Class A1
Class A2
0 41 2 3
Period (s)
0
120
40
80
Spectralvelocity(cm/s)
0 41 2 3
Period (s)
0
120
40
80
0 41 2 3
Period (s)
0
120
40
80
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A1
0 41 2 3
Period (s)
0
120
40
80
SpectralVelocity(cm/s)
0 41 2 3
Period (s)
0
120
40
80
0 41 2 3
Period (s)
0
120
40
80
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A2
0 41 2 3
Period (s)
0
120
40
80
SpectralVelocity(cm/s)
0 41 2 3
Period (s)
0
120
40
80
0 41 2 3
Period (s)
0
120
40
80
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A3
Velocity Spectra
121

0 41 2 3
Period (s)
0
40
10
20
30
Spectraldisplacement(cm)
0 41 2 3
Period (s)
0
40
10
20
30
PRA = 0.0 25g PRA = 0.05g
Class A1
Class A2
0 41 2 3
Period (s)
0
40
10
20
30
0 41 2 3
Period (s)
0
40
10
20
30
0 41 2 3
Period (s)
0
40
10
20
30
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A1
0 41 2 3
Period (s)
0
40
10
20
30
0 41 2 3
Period (s)
0
40
10
20
30
0 41 2 3
Period (s)
0
40
10
20
30
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A2
0 41 2 3
Period (s)
0
40
10
20
30
0 41 2 3
Period (s)
0
40
10
20
30
0 41 2 3
Period (s)
0
40
10
20
30
PRA = 0.025g PRA = 0.05g PRA = 0.075g
Class A3
Displacement Spectra
122

• Input needed for Response Spectrum Analysis
– Mass and stiffness distribution
– A Specified Response Spectrum Curve
– The Response Input Direction
– The Response Scaling Factors
– The modes to be included
• Output From Response Spectrum Analysis
– Unsigned displacements, stress resultants and stresses, etc.
The Input – Output Summary

Analysis Using
Acceleration Time History
124

The Time History Analysis
• The full dynamic equilibrium equation is solved for each time step on the
acceleration-time curve
• The History of the deformations resulting from previous time step calculation is
considered in computing the response for the current time step
• The time-history analysis is in-fact a piece wise solution of the entire force
histogram
125

Earthquake Records
Cliff Station from 1989 Loma Preita, USA
CUIP Station from 1985 Michoacan, Mexico
126

Ground Motion
guuuu   2
2 
• The input Variables are ground
acceleration, damping ratio and
circular frequency
• The final unknown is displacement
(and its derivatives)
127

• Input
– Mass and stiffness distribution
– The acceleration-time record
– The scaling factors
– Directional factors
– Analysis time step, etc.
• Output
– Displacements, stress resultants and stresses in each time step
– The envelop values of response
Input-Output for Time History Analysis

Capacity Design Approach
129

Performance objectives under different intensities of earthquake shaking –
seeking low repairable damage under minor shaking and collapse-prevention
under strong shaking.

Ductile and brittle structures – seismic design attempts to avoid structures of the
latter kind.

The beams must be the weakest links and not the columns – this can be achieved by
appropriately sizing the members and providing correct amount of steel
reinforcement in them.

Ductile Link Analogy
133
Ductile Chain Design Source: Murty (2004)

Two distinct design of buildings that result in different earthquake performances –
Columns should be stronger than beams

Earthquake shaking reverses
tension and compression in
members – Reinforcement is
required on both faces of the
members.

Building on flexible supports shakes lesser
– this technique is called Base Isolation.

View of Basement in a
Hospital building
– built with base isolators
after the original building
collapsed during the 2001
Bhuj earthquake.
Source: EERI, USA
Seismic
Energy
Dissipation
Devices:
each device is
suitable for a
certain
building.

4 Commandments of Seismic Design
138
• Thou shall select an overall layout of a lateral force–
resisting system appropriate to the anticipated level of
ground shaking (providing a redundant and continuous
load path)
• Thou shall determine code-prescribed forces and
deformations generated by the ground motion, and
distribute the forces vertically to the lateral force–
resisting system.
• Thou shall analyze the building for the combined effects of gravity and seismic
loads to satisfy the structural performance and acceptable deformation levels
prescribed in the governing building code.
• Thou shall provide details to assure that the structure has sufficient inelastic
deformability to undergo large deformations when subjected to a major
earthquake.

Earthquake Analysis using
ETABS and SAP 2000
139

• Use the define load case option
and select the appropriate code
• Structure can be analyzed for
several codes at the same time
Using ETABS for EQ Static Analysis (UBC
97)
140

• For rigid diaphragm, the total
force will be applied as the center
of mass
• For semi-rigid diaphragm, the
force will be distributed at each
node of the elements
97)
Rigid diaphragm Semi-rigid diaphragm
141

97)
Direction and Eccentricity
X dir
X dir + Eccen Y X dir - Eccen Y
142

97)
• Method A
– Ct value shall be input according to the structure type
• Program Calculated
– Calculate the mode which has the largest participation factor in the direction of
load.
– Compare with the Method A period and determine the time period to be used.
143

• User Defined
– Use the user input time period and do not compare against the Method A
period.
Using ETABS for EQ Static Analysis
(UBC 97)

• Overstrength Factor (Table 16-N)
– Global ductility capacity of lateral force-resisting system
• Soil Profile Types
– SA, SB, SC, SD, SE
– Ranging from hard rock to soft soil
– Ground vibration tends to be greater on soft soil than hard rock
• Seismic Zone Factor (Table 16-I)
– Zone 1, 2A, 2B, 3, 4
– Effective peak ground acceleration as a function of g
– Recurrence interval of 475 years which gives a 10% probability exceeded in a
fifty years period
(UBC 97)

• Seismic Source Type (Table 16-U)
– Depends on maximum moment magnitude potential of a fault and slip rate
• Distance to Source (Table 16-T)
– Ground acceleration increases near the fault in Zone 4
• Importance Factor (Table 16-K)
– Depends on occupancy categories
(UBC 97)

• Step 1
– Use “Define Function” option to
define a Response Spectrum
Curve
– Chose from list of Standard
Curves or use User Defined
Using ETABS For RS Analysis

• Step 2
– Use “Define Response Spectrum Case”
option to define a case using one of the
Defined RS Curves
– Use the scale factor equal to g for the
analysis.
– Analysis for several RS curves can be
done at the same time

• Step 3
– After analyzing with the scale factor equal to
g, the base shear from the RS analysis shall
be compared with the static base shear and
scaled.
– Scale factor shall be calculated and
reanalyzed.
– 30% of the loading shall be applied in
orthogonal direction.

• Step 1
– Use “Define Time History
Function” option to define a
Value Vs Time Function
– Analysis for several Time
History curves can be done at
the same time
Time History Analysis Using SAP2000

• Step 2
– Use “Define Analysis Case”
option to define a Analysis Case
using one of the Defined TH
Curve
– TH can be attached to any Load
Case
Time History Analysis Using SAP2000

Time-History Analysis Using SAP2000
152

Arya, S., O’Neil, M., & Pincus G. (1979). Design of Structures and Foundations for Vibrating
Machines. Gulf Publishing Company.
Clough, R.W., & Penzien, J. (1993). Dynamics of Structures (2nd ed.). McGraw-Hill Publishers.
Chopra, A.K. (2001). Dynamics of Structures-Theory and Applications to Earthquake
Engineering (2nd ed.). Prentice Hall.
Kolousek, V. (1984). Wind Effects on Civil Engineering Structures. Elsevier.
Ghosh, S.K. (2002). Seismic Design using Structural Dynamics. ICBO
Kong, F.K., Evans, R.H, Cohen, E., & Roll, F. (1983). Handbook of Structural Concrete. Pitman
Advance Publishing Program.
Warnitchai, P. (n.d.). Structural Dynamics, Wind Engineering and Earthquake Engineering:
Course notes. Thailand: Asian Institute of Technology
Sources and References

Analysis for Wind
154

The Wind
Analysis Problem
155

Wind Analysis
Full Dynamic
Analysis
WFKu  Equivalent
Static Analysis
Wind-Time Records
)(tFKuuCuM  
FFKu NL  Equivalent Static
Nonlinear Analysis
0 KuuM 
Free Vibration
WFKu 
Matched Analysis
156

Analysis of Wind Effects
Wind
Loading on
the Structure
Structural
Respose
Check Safety/
Serviceability
Influence of Deformation
on Loading
Metrology Aerodynamics Theory of Structures
Material science,
codes, regulations
Aeroelasticity
157

• Using Equivalent Static Load derived from pressure due to wind
– Uses simplified parameters and coefficients
– Methods based on Projected Area
– Methods based on Exposed Surfaces
• Using Simplified Wind Dynamics
– Considers gust, resonance, vortex shedding, structures modes of vibration,
etc.
– Similar to Response Spectrum for earthquake
• Using full Dynamic Analysis
– Wind time and space history
– Interaction between wind and structure
Analysis for Wind

• Following information is required
– Wind Direction
– Gradient Wind Speed
– Maximum Wind Speed
– Separation between the constant wind speed and the fluctuation
– Turbulence Intensity
• Basic Concepts
– Mean Velocity and Gust Factor
– Vortex Shedding
Basic Wind Characteristics

Classification of Wind Effects
Static
Effects
Deformation Due to Time Averaged Aerodynamic Force
Stress Due to Wind Induced Pressure or Force
Static Instability
Torsional Divergence (negative stiffness)
Lateral Buckling
Dynamic
Effects
Forced
Vibration
Buffering
(random
vibration)
Due to
Atmospheric
Turbulence
Limited Amplitude
ResponseDue to Body-
induced
Turbulence
(Wake)
Vortex Excitation
Dynamic
Instability
(negative
damping)
Galloping
Divergent
Amplitude
Response
Wake Galloping
Torsional Flutter
Coupled Flutter
Rain Induced Vibrations
160

Bluff Body Aerodynamics
161

• Characteristic of Civil Engineering Aerodynamics
– Low Speed (<100m/s)
– Incompressible flow phenomena
– Turbulent flows in atmospheric boundary layer
– Bluff form of structures (non-streamline shapes)
Bluff Body Aerodynamics

Wind Profiles
163

Velocity - Time Variations
Variation of Wind Velocity with Time
164

2D Flow of Wind-Simplified
165

Vortex Shedding
166

Wind Loads - Pressure Variations
Face under
Pressure
Faces
under Suction
167

Pressure, Lift, Drag and Moment
CG
Resultant Force
Lift, Drag and Moment
CG
Wind Flow
Direction
Lift
Drag
Moment
168

Drag and Lift Coefficient
• Two-dimensional
drag and lift
coefficients for
structural
shapes.
Source: "Wind Forces on Structures,"
Trans. ASCE, 126 (1961), 1124-1198
and [12-2]
169

Lift, Drag and Moment
where:
CL, CM, CD are non-dimensional lift, moment, and drag coefficients
 
 
  M
DD
LL
CBBUM
CBUF
CBUF
.1
2
1
.1
2
1
.1
2
1
2
2
2









170

Strouhal Number
Source: Strouhal Number for a variety of shapes From "Wind Forces on Structures,"Trans. ASCE, 126 (1961), 1124-1198
• Strouhal Number =Ns D/U
relates the Vortex Shedding with Wind Velocity, Primary Frequency and Across-
Wind Dimensions
171

Reynolds and Strouhal Relationship
Reynolds Number is a measure of inertial to viscous flow
172

Aero - Elastic Phenomenon
• Vortex Shedding and Lock in Phenomenon
• Across Wind Galloping
• Wake Galloping
• Torsional Divergence
• Flutter
173

Wind Effects on Tall Buildings
174

Flow Around a Tall Building
175

Cross-wind vibrations are usually greater than along-wind vibrations
for buildings of heights greater than 100m (330 feet)
along wind
cross wind
Overall loading and dynamic response
176

Cladding pressures:
Four values of pressure coefficients:
2
ha
0
p
Uρ
2
1
pp
C


2
ha
0
p
Uρ
2
1
ppˆ
Cˆ 
 2
ha
0
p
Uρ
2
1
pp
C



2
ha
2
Cpp
Uρ
2
1
p
σC


Time
Cp (t)
Cp
ˆ
Cp
C p
Cp

177

Square cross section - height/width = 2.1
0.8
0.6
0.4
0.2 0.2
0.0
-0.2 -0.2
-0.4 -0.4
1.8
1.6
1.4
1.21.0 1.0
pC pCˆpC

stagnation
point  0.8h
minimum maximum
Windward wall:
178

mean Cp’s :
-0.6 to -0.8
Side wall (wind from left) :
-0.9
-0.9
-0.5
-0.6
-0.8
-0.8
-0.7
-0.6
-0.5
-2.2-2.4
-2.0
-2.0
-1.8 -2.2
-2.4
-2.6
-2.8
-3.2
-3.8
-3.4
-3.0
-2.8
-2.6
-2.4
0.6
0.4
0.2
0.0
pC pCˆpC

largest minimum Cp : -3.8
179

mean Cp’s :
-0.35 to -0.45
largest minimum Cp : -1.6
Leeward wall :
-0.45 -0.45
-0.4
-0.35
-1.6
-1.6
-1.4 -1.4
-1.2
-1.6 -1.6
-0.1
pC pC

pCˆ
180

Overall Loading and Dynamic Response
along wind
Standard deviation of deflections at top of a tall building:
η
1
bn
U
ρ
ρ
A
h
σ
kx
1
h
b
a
x
x













η
1
bn
U
ρ
ρ
A
h
σ
ky
1
h
b
a
y
y












 cross wind
Ax and Ay - depend on building shape
kx - 2 to 2.5 ky - 2.5 to 3.5 (cross-wind)
b - average building density
n1 - first mode frequency  - critical damping ratio
181

Overall Loading and Dynamic Response
Standard deviation of deflections at top of a tall building :
Circular cross section :
10
1
5
2
100
5
2
10
- 1
5
2 3 5 7 10 15
windX
Y
x
cross wind
1000 x deflection
height
sy
h
sx
h
1
182

Deflections at the Top of a Tall Building
Effect of cross section :
Peakdeflection
height
0
.001
.002
.003
.004
30 50 100 500 1000
Return period/years
Directionofmotion
Modification of corners are effective in reducing response
183

Torsional Loading and Response
Two mechanisms:
• Applied moments from aerodynamic forces produced by non-uniform pressure
distributions or non-symmetric cross-sections
• Structural eccentricity between elastic center and geometric center (a 10%
eccentricity on a square building: doubled mean twist and increased dynamic
twist by 40-50%)
184

Torsional Loading and Response
Mean Torque Coefficient :
depends on ratio between minimum and maximum projected widths of the
cross section
0.2
0.1
0 0.2 0.4 0.6 0.8 1.0
f = 2
max
min








b
b
185

Interference Effects
Surrounding buildings can produce increases or decreases in peak wind loads:
shows percentage change in peak cross-wind response of building B, due
to a similar building A at position (X, Y)
10b 8b 6b 4b 2b -2b
b
Building B
Wind direction
(X,Y)
Building A
V
b
2b
3b
4b
0%
+30%
+20% +10%
-10%
+10%
+20%
X
Y
0%
-20%
increases
increases
decreases
186

Damping
Damping is the mechanism for dissipation of vibration energy
Structural damping (Japanese buildings) :
0018.0470014.0 11 






h
x
n t

0029.0400013.0 11 






h
x
n t

reinforced concrete
steel frame
n1 = first mode natural frequency xt = amplitude of vibration
187

Analysis Using
Equivalent Static Load
188

Wind Loads-ASCE 7-05 Approach
The Main Equation:
where:
qz = Velocity pressure evaluated at height z
Kz = Velocity pressure exposure coefficient evaluated at height z
Kzt = Topographic factor
Kd = Wind directionality factor
V = Basic wind speed
I = Importance factor
 2 2
0.00256 lb/ftz z zt dq K K K V I
189

Wind Loads-ASCE 7-05 Approach
The wind pressure, p, at any point on the surface of the vertical projected
area is
190

Cp Coefficients
191

• Exposure from rigid diaphragm
– Exposure width is calculated from the extent of the diaphragm perpendicular
to the wind direction
– For rigid diaphragm, wind load is applied as a point load at the center of mass
– For semi rigid diaphragm, wind load is applied by tributary area basis along
the edge of the diaphragm
Static Analysis Using ETABS
Rigid DiaphragmSemi-rigid Diaphragm

Calculation of Exposure Width and Height
193

• Exposure from Area Objects
– Include area objects
• Cp coefficients shall be assigned separately on the area objects with
respect to the wind direction.

• Exposure from Area Objects
– Include frame objects
• If the structure is open structure, the wind load on the frames required to be
considered. Force coefficients shall be assigned separately on the frame objects.

Combining
Response for
Member Design
196

• At least 3 basic Wind Load Cases should be considered
– Along X-Direction
– Along Y Direction
– Along Diagonal
• Each Basic Wind Load Case should be entered separately into load
combinations twice, once with (+ve) and once with (-ve) sign
• Total of 6 Wind Load Cases should considered in Combinations, but only
3 Load Cases need to be defined and analyzed
Applying Wind Loads

Applying Wind Loads
• At least 3 basic load case for wind
load should be considered
• Diagonal wind load may be
critical for special types and
layouts of buildings
Wx
Wy
Wxy
198

Wind Load Combinations
• “f” is the load factor specified for
wind in the design codes
• Six additional load combinations are
required where ever “wind” is
mentioned in the basic load
combinations
Comb1 Comb2 Comb3 Comb4 Comb5 Comb6
Wx +f -f 0 0 0 0
Wy 0 0 +f -f 0 0
Wxy 0 0 0 0 +f -f
Example:
Comb = 0.75 (1.4D + 1.7W) will need
Six Actual Combinations
Comb1v= 0.75 (1.4D + 1.7Wx)
Comb2 = 0.75 (1.4D - 1.7Wx)
Comb3 = 0.75 (1.4D + 1.7Wy)
Comb4 = 0.75 (1.4D - 1.7Wy)
Comb5 = 0.75 (1.4D + 1.7Wxy)
Comb6 = 0.75 (1.4D - 1.7Wxy)
199

Obtaining Envelop Results
200

• Actions Interact with each other, effecting the
stresses
• For Column Design: P, Mx, My
• For Beam Design: Mx, Vy, Tz
• For Slabs: Mx, My, Mxy
• At least 3 actions from each combination must
be considered together as set
• Therefore, envelop results can not be used
• Every load combinations must be used for
design with complete “action set”
Can Envelop Results be Used?
P
Mx
My

• For static loads, Design Actions
are obtained as the cumulative
result from each load
combination, as set for all
interacting actions
• The final or critical results
from design of all load
combinations are adopted
Design Actions For Static Loads
202

For a Single Action
Static, Dynamic and Nonlinear Results
Static Load Case
Response Spectrum Load Case
Time History Load Case
Static Non-linear Load Case
1
+
-
1 for each Time Step
OR 1 for envelop
1 for each Load Step
Load
Combination
Table
OR 1 for Envelop

Response Spectrum Case
• All response spectrum cases are assumed to be earthquake load cases
• The output from a response spectrum is all positive.
• Design load combination that includes a response spectrum load case is checked
for all possible combinations of signs (+, -) on the response spectrum values
• A 3D element will have eight possible combinations of P, M2 and M3 and eight
combinations for M3, V, T
204

Response Spectrum Results
• Design Actions needed for Columns:
+P, +Mx, +My
+P, +Mx, -My
+P, -Mx, +My
+P, -Mx, -My
-P, +Mx, +My
-P, +Mx, -My
-P, -Mx, +My
-P, -Mx, -My
Maximum Results obtained by:
SRSS, CQC, etc.
P, Mx, My>
LoadCombinationTable
205

Time History Analysis Results
Response Curve for One Action
206

Time History Results
• The default design load combinations do not include any time history results.
• Define the load combination to include time history forces in a design load
combination
• It is possible to perform a design for each step of Time History or design for
envelops for those results
• For envelope design, the design is for the maximum of each response quantity
(axial load, moment, etc.) as if they occurred simultaneously.
• Designing for each step of a time history gives correct correspondence between
different response quantities
207

Time History Results
• The program gets a maximum and a minimum value for each response quantity
from the envelope results for a time history.
• For a design load combination, any load combination that includes a time history
load case in it is checked for all possible combinations of maximum and minimum
time history design values.
• If a single design load combination has more than one time history case in it, that
design load combination is designed for the envelopes of the time histories,
regardless of what is specified for the Time History Design item in the preferences.
208

Static Nonlinear Results
• The default design load combinations do not include any Static Nonlinear results
• Define the load combination to include Static Nonlinear Results in a design load
combination
• For a single static nonlinear load case, the design is performed for each step of the
static nonlinear analysis.
209

The Result Combination
• The result combination does not consider the interaction of earthquake,
wind, vibration and fire.
• That would be really complex and probably not a realistic scenario.
210

Arya, S., O’Neil, M., & Pincus G. (1979). Design of Structures and Foundations for Vibrating
Machines. Gulf Publishing Company.
Clough, R.W., & Penzien, J. (1993). Dynamics of Structures (2nd ed.). McGraw-Hill Publishers.
Chopra, A.K. (2001). Dynamics of Structures-Theory and Applications to Earthquake
Engineering (2nd ed.). Prentice Hall.
Kolousek, V. (1984). Wind Effects on Civil Engineering Structures. Elsevier.
Ghosh, S.K. (2002). Seismic Design using Structural Dynamics. ICBO
Kong, F.K., Evans, R.H, Cohen, E., & Roll, F. (1983). Handbook of Structural Concrete. Pitman
Advance Publishing Program.
Warnitchai, P. (n.d.). Structural Dynamics, Wind Engineering and Earthquake Engineering:
Course notes. Thailand: Asian Institute of Technology
Sources and References

Dr. Naveed Anwar
Director, ACECOMS
Thank You

CE 72.32 (January 2016 Semester) Lecture 8 - Structural Analysis for Lateral Loads

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