This document discusses the dynamic response design of tall buildings, emphasizing the importance of modal analysis for understanding structural performance under loads such as wind and earthquakes. It highlights concepts like natural frequencies, modes of vibration, and factors influencing stiffness estimation, while also addressing the use of various analysis methods including linear and nonlinear dynamic procedures. The analysis aids in assessing the strengths and weaknesses of building structures, ensuring reliable performance during dynamic events.

1. Dr. Naveed Anwar
Dynamic Response
Design of Tall Buildings: Trends and Achievements for
Structural Performance
Bangkok-Thailand
November 7-11, 2016
Naveed Anwar, PhD

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What is the first thing
a doctor does before
seeing a patient

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Check Blood
Pressure and
Heart Rate

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This is an indicator of the body’s
state and potential for any
problems due to other cause

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Dynamic Response
is the Heartbeat
(and blood pressure )
of the structure

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Basic Physics of Dynamics
• Newton’s View, for rigid bodies
F = ma

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Structural engineer’s View
FKuuCuM  
for linear elastic, deformable bodies

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Structural as a Linear Spring
FKuuCuM  

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The Structure Stiffness - K
Material Stiffness
Section Stiffness
Member Stiffness
Structure Stiffness
Cross-Section Geometry
Member Geometry
Structure Geometry
FKuuCuM  

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The Structure Stiffness - K
Material Stiffness
Section Stiffness
Member Stiffness
Structure Stiffness
Cross-Section Geometry
Member Geometry
Structure Geometry
Non-Linear
Linear
FKuuCuM  

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Linear Vs
Non Linear
Response

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

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Source of Nonlinear Force
Non Linear Equilibrium
FFKuuCuM NL  

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The ‘Natural Free’ Dynamics
FFKuuCuM NL  
0 KuuM 
Free Vibration
Natural Frequencies and Mode Shape

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The Modal Dynamic Response

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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

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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.

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Application of Modal Analysis
• 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,
– The disconnected members are identified
– Local modes are identified that may need suppression
• 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

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Natural Periods or Frequency
• The heartbeat of the structure
• Indicates the “stiffness” and “mass” relationship
• Basis for damping, resonance and amplification effects
• Many relationships for tall buildings (0.1 N, with Height etc,)

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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

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

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Modal Analysis ResultsTranslationin
Minor
direction
Translationin
Major
direction
Torsional
• T1=5.32 sec
• 60% in Minor
direction
• T6=1.28 sec
• 18% in Minor
direction
• T9=0.75 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

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Higher Mode Effects in Tall Buildings
• The contribution of higher
modes on reposes of Tall
Buildings for earthquakes (and
wind) is one the most important
difference between the low rise
and tall buildings

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Effect of Modes on Story Moment
24

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Effect of Modes on Story Moment
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Building 50 Story
50%30%10%

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Building 25 Story
80%15%4%

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Modal Response Influenced by
• Structure
• Attachments
• Occupants
Mass
• Tower
• Podium
• Basement
• Foundation
• Soil
Stiffness

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Elastic Stiffness Estimation Influenced by
• Material modeling
• Cross-section Modeling
• Member Modeling
• Foundation Modeling

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“Actual” Stiffness Estimation Influenced by
• The state of the
structure at any given
time
• Damage
• Deformation
• Cracking
• Creep/Shrinkage
• Stress-state

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Estimating Stiffness through “Cracking Factors”
• Code specified cracking factors
• Typical applied to all members
• At all locations
• For all load cases
• Not realistic, and subject to
considerable variation and
debate

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Estimating Natural Period at States
• Use Non-linear models
• Apply gravity loads, incrementally as a non linear case
• Determine Modal Properties at the end of the Gravity Case
• Use Gravity case and Modal properties as a start for other cases

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

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

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Seismic Analysis Procedures
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

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Nonlinear Dynamic Time History
• Nonlinear Dynamic Time History Advantage
 It applies to structures of all types
 It accounts directly for the dynamic nature of earthquakes loads
 It accounts directly for hysteretic loops and energy dissipation
 More accurate than pushover analysis
• Nonlinear Dynamic Time History Disadvantage
 More complex, needs more information, tools, skills
 Response spectrum cannot use. Uses ground motions.
 The Response can be sensitive to changes in the ground motion. Analysis must
be carried out for a number of earthquakes
 Requires more computer time than pushover

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Initial Conditions
• The initial conditions describe the state of the structure at the
beginning of a time-history case. These include:
• Displacements and velocities
• Internal forces and stresses
• Internal state variables for nonlinear elements
• Energy values for the structure
• External loads
• The accelerations are not considered initial conditions, but are
computed from the equilibrium equation.

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Additional Information Required for NDA
Appropriate Hysteretic Response of either Material or Structural Components has to be Provided
(At present, there is no clear recommendations)

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Estimating, understanding and including
dynamic response in the design
is the key for high and reliable performance of
structures for Wind and Earthquakes
It all starts with Modal Analysis

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