design of tall buildings: trends and achievements for...
TRANSCRIPT
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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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Dr. Naveed Anwar2
2
What is the first thing a doctor does before seeing a patient
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Dr. Naveed Anwar
Check Blood Pressure and Heart Rate
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Dr. Naveed Anwar4
4
This is an indicator of the body’s state and potential for any problems due to other cause
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Dr. Naveed Anwar5
Dynamic Response is the Heartbeat (and blood pressure )
of the structure
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Dr. Naveed Anwar6
Basic Physics of Dynamics
• Newton’s View, for rigid bodies
F = ma
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Dr. Naveed Anwar7
Structural engineer’s View
FKuuCuM
for linear elastic, deformable bodies
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Dr. Naveed Anwar8
Structural as a Linear Spring
FKuuCuM
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Dr. Naveed Anwar9
The Structure Stiffness - K
Material Stiffness
Section Stiffness
Member Stiffness
Structure Stiffness
Cross-Section Geometry
Member Geometry
Structure Geometry
FKuuCuM
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Dr. Naveed Anwar10
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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Dr. Naveed Anwar11
Linear Vs Non Linear
Response
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Dr. Naveed Anwar12
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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Dr. Naveed Anwar13
Source of Nonlinear Force
Non Linear Equilibrium
FFKuuCuM NL
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Dr. Naveed Anwar14
The ‘Natural Free’ Dynamics
FFKuuCuM NL
0KuuM Free Vibration
Natural Frequencies and Mode Shape
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Dr. Naveed Anwar
The Modal Dynamic Response
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Dr. Naveed Anwar16
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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Dr. Naveed Anwar17
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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Dr. Naveed Anwar18
Application of Modal Analysis
• The Time Period and Mode Shapes, together with animation immediately exhibit thestrengths 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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Dr. Naveed Anwar19
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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Dr. Naveed Anwar20
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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Dr. Naveed Anwar21
Eccentric and Concentric Response
Mode-1 Mode-2 Mode-3
Symmetrical Mass
and Stiffness
Unsymmetrical
Mass and Stiffness
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Dr. Naveed Anwar22
Modal Analysis ResultsTr
ansl
atio
nin
M
ino
r d
ire
ctio
n
Tran
slat
ion
in
Maj
or
dir
ect
ion
Tors
ion
al
• 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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Dr. Naveed Anwar23
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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Dr. Naveed Anwar24
Effect of Modes on Story Moment
24
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Dr. Naveed Anwar25
Effect of Modes on Story Moment
25
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Dr. Naveed Anwar26
Building 50 Story
50%30%10%
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Dr. Naveed Anwar27
Building 25 Story
80%15%4%
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Dr. Naveed Anwar28
Modal Response Influenced by
• Structure
• Attachments
• OccupantsMass
• Tower
• Podium
• Basement
• Foundation
• Soil
Stiffness
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Dr. Naveed Anwar29
Elastic Stiffness Estimation Influenced by
• Material modeling
• Cross-section Modeling
• Member Modeling
• Foundation Modeling
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Dr. Naveed Anwar30
“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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Dr. Naveed Anwar31
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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Dr. Naveed Anwar32
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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Dr. Naveed Anwar33
Seismic Response
FFKuuCuM NL
Time History Analysis
0KuuM
EQNL FFKu
Free Vibration
Pushover
Analysis
EQFKu Equivalent
Static Analysis
EQFKu
Response Spectrums
Response Spectrum
Analysis
Acceleration RecordsguMKuuCuM
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Dr. Naveed Anwar34
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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Dr. Naveed Anwar35
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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Dr. Naveed Anwar36
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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Dr. Naveed Anwar37
Initial Conditions
• The initial conditions describe the state of the structure at thebeginning 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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Dr. Naveed Anwar38
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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Dr. Naveed Anwar39
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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Dr. Naveed Anwar40
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Dr. Naveed Anwar41