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

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for linear elastic, deformable bodies

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Structural as a Linear Spring

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The Structure Stiffness - K

Material Stiffness

Section Stiffness

Member Stiffness

Structure Stiffness

Cross-Section Geometry

Member Geometry

Structure Geometry

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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

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Linear Vs Non Linear

Response

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Dynamic Equilibrium

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Damping-Velocity

Mass-Acceleration Stiffness-Displacement

Nonlinearity

External Force

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The basic variable is displacement and its derivatives

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Source of Nonlinear Force

Non Linear Equilibrium

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The ‘Natural Free’ Dynamics

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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 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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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 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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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

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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

• OccupantsMass

• 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

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Time History Analysis

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EQNL FFKu

Free Vibration

Pushover

Analysis

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Static Analysis

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Response Spectrums

Response Spectrum

Analysis

Acceleration RecordsguMKuuCuM

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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 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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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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