Dynamic Response of Tall Buildings, Its Evaluation, and Mitigation by Effective...

Dr. Munir Ahmed, Doctor of Engineering (AIT)

Associate Professor,

Capital University of Science

and Technology, Islamabad

Past

Experience:-

NESPAK, about

12 Years

Past Experience:- AIT

Solution at Asian

Institute of

Technology, about 03

Years

Dynamic Response of Tall Buildings,

Its Evaluation, and Mitigation by

Effective Control Mechanisms

Presentation Outline

Earthquake Characteristics and Tall Building Response

Dynamic Response Evaluation Procedures-Linear and

Non-Linear

Seismic Demands at the Design Basis Earthquake (DBE)

Level (Code Based Design)-Response Spectrum Analysis

Seismic Demands at the Maximum Considered Earthquake

(MCE) Level-Non Linear Time History Analysis

Control Measures using Plastic Hinge Mechanism

2

Dr. Munir Ahmed, CUST

Basic Difference between Gravity, Wind and

Earthquake Response of Tall Buildings3

The heavier the

Building, the

greater the

pressure on its

foundation

The Lateral

Force results in

Gradually

Decreasing

Deflection

Ground Shaking

Creates often an

Undulated Motions

Earthquake

Response of the

Tall Building shall

be Main Focus of

this Presentation


Seismic Waves, Accelograph, and Building

Responses

4

Dr. Munir Ahmed,

CUST

Newton’s Second Law

F = ma

where m = mass of building

a = acceleration of ground

F is known as an inertial force,

created by building's tendency to remain at rest, in its

original position, although the ground beneath it is

moving

F

Engineering representation

of earthquake force

What is really happening?

5


Ground Motion Histories

Signal

Processing

and

Frequency

Filtration

Accelograph Records to Ground Motions

Histories6


Frequency (f) = number of complete cycles of vibration

per second of a point on the ground or mass in the

building

Period (T) = time needed to complete one full cycle of

vibration of a point on the ground or mass in the Building

T = 1 / f

Frequency and Time Periods

k

m

T = 2πk

m

One Complete Cycle

One Complete Cycle

SDoF

system

7


Frequency Content Parameters

The Dynamic Response of Structural Systems, Facilities and

soil is very sensitive to the frequency content of the ground

motions.

The frequency content describes how the amplitude of a

ground motion is distributed among different frequencies.

The frequency content strongly influences the effects of the

motion.

Using Fourier Transformation (a Mathematical Technique) we

can find the frequency content of seismic waves by shifting

from time domain to the frequency domain.

8


The ground motion can be expressed as

sum of harmonics (sinusoidal) waves with

different frequencies and arrival times.

The amplitude of waves for

different frequencies are

expressed in Fourier Amplitude

Spectra.

Dominant Frequency Content of Ground Motions

=++

++

9


T1,h1T2,h1

T3,h1

Acceleration

Tim

e

(Sa)1

(Sa)2

(Sa)3

Resp

onse

Acc

ele

art

ion

Peak A

ccele

ration

Period(s)

h0

h1

h2

T1

T2

T3

(a)

(b)

(c)(d)

Response Spectrum

10


Resonance

Resonance = frequency content of the ground motion is

close to any one of building's natural frequency

tends to increase or amplify building response

building suffers the greatest damage from ground motion at a

frequency close or equal to its own natural frequency

• Example: Mexico City earthquake of September 19, 1985

– majority of buildings that collapsed were around 20 stories tall

– natural period of around 2.0 seconds

– other buildings, of different heights and different natural frequencies, were undamaged even though located right next to damaged 20 story buildings

Phenomenon of Resonance

11


H

λ = VT

λ = Wave Length

V=velocity of the wave

T=time period of the Wave/Building

H= Height of the Building

Waves with “λ,s>=2H”, excite only fundamental

mode of the building

Waves with “λ,s<=2H/n”, excite “n” number of

modes of the building

Deformation Modes of the Buildings with

reference to Seismic Waves

Build

ing S

tructu

re-

De

form

ation

Mo

de

Seis

mic

Waves

P- Wave

S- Wave

Surface-

Waves

12


The red line shows the force and displacement that would be reached if the structure responded elastically.

The green line shows the actual force vs. displacement response of the structure

The pink line indicates the minimum strength required to hold everything together during inelastic behavior

The blue line is the force level that we design for.

We rely on the ductility of the system to prevent collapse.

From 1997 NEHRP Provisions

13


Elastic vs. Inelastic Response-Earthquake

Resistant Design philosophy

V

Newton’s View, for rigid bodies

F = ma

Structural engineer’s View

for linear elastic, deformable bodies

Newton’s 2nd Law for Rigid Bodies and Equation

of Dynamic Equilibrium

14


Structures as Linear SpringStructure as Linear Spring-Equation of Dynamic

Equilibrium

15

Load (F)


Dynamic Equilibrium

16

The Basic Variable is displacement and its

derivativeDr. Munir Ahmed, CUST

Equation of Dynamic Equilibrium and Different

Type of Analysis

Non-linear Time

History Analysis

Undamped Free Vibration

Analysis

Linear Time History

Analysis

17


Concept of Modal Analysis

18

Modal analysis is used to determine Building’s vibration

characteristics — natural frequencies and mode shapes.

It is the most fundamental of all dynamic analysis types and is

generally the starting point for other, more detailed dynamic

analyses.

02 ii MK

natural circular frequencies i

(Heart Beat of the Structure)

and mode shapes i (Blood

Pressure of the Structure)

i= 2 π fi,


Concept of Response Spectrum Analysis-Valid for

Linear Elastic System and Fundamental Mode

Dominant Systems

Sullivan

et. al.

(2008)

19


Concept of Multi Modal Pushover Analysis

Procedure- For Non-Linear Inelastic Systems

where only Peak Response is Required

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di

Cyclic Pushover Analysis

Flag shaped Hysteretic

Model (Raumoko 2D )

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di



Model (Raumoko 2D )

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di



Model (Raumoko 2D )

Determine Base Shear vs.

Top Displacement

No

n-lin

ea

r

pro

pe

rtie

s o

f E

q.

SD

oF

syste

m

Determine Target

Displacement

Push the structure to

target displacement

and get the peak

responses

20

0

1,000

2,000

3,000

4,000

5,000

0 50 100

Ba

se S

hea

r (

Kip

s)

Top displacement (inches)

Consider as many

modes as significant

and add the peak

modal responses

statistically


Concept of Uncoupled Modal Response History

Analysis Procedure-Chopra Procedure Extended

to High Rise Buildings

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di



Model (Raumoko 2D )

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di



Model (Raumoko 2D )

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di



Model (Raumoko 2D )

Determine Base Shear vs.

Top Displacement

No

n-lin

ea

r

pro

pe

rtie

s o

f E

q.

Sp

oo

f syste

m

Determine Target

Displacement

Convert the SDOF Responses to

MDoF system using Formulas and

addition of different mode responses

in time domain to get the total

response

21

Consider as many


and add the modal

responses in time

domain

Time

Respons

e


Concept of Modal Pushover Analysis-Simplified

MMPA procedure using Elastic Displacement as

Target Dispalcement

Pushover Force

f =α M ϕi

xri

Vbi Fsi

Di



Model (Raumoko 2D )

0

1,000

2,000

3,000

4,000

5,000

0 50 100

Ba

se S

hea

r (

Kip

s)

Top displacement (inches)

Push the structure to

target displacement

and get the peak

responses

Plastic Hinge may be modeled using non-

linear shell elements in SAP, 2000.

The paper about this procedure was submitted in ISI Impact Factor

International Journal and Comments have been received.

22

Consider as many


and add the peak

modal responses

statistically


40 Storied Tall Case Studied Building

X

Y

23

A 40 –story Building

RC Central Core Wall

with Perimeter Columns,

Located in High Seismic

Hazard Zone—UBC

Zone 4

Soil Type: SD

Designed by

Magnusson

Klemencic

Associates and

ARUP using

LATBSDC’s Design

ProcedureDr. Munir Ahmed, CUST

40 Storied Tall Case Studied Building24

DBE design criteria

Parameter Value as Per UBC

Seismic Zone 4 Z=0.4

Soil Type SD

Seismic Coff. Acc. Ca=0.44

Seismic Coff. Vel. Cv=0.64

Response Modification factor R=5.5

Importance factor I=1.0

Time Period as per Method B

in UBC-97Tb=3.58 sec

Weight W=89700 kips


Plan

Elevation of

the building

Inherently Torsional Mode exist in the

Structures, however, for regular

structure like this will activate only if

ground motions has torsional

component

Mode Shape of 40 Storied Tall Building From

Modal Analysis-First Ten Modes

X

Y

Tra

nsla

tion-X

Tra

nsla

tion-Y

Tors

ional

T=4.89 sec

T=0.90 sec

T=0.36 sec

T=0.24 sec

T=3.89sec

T=0.84sec

T=0.40 secT=0.23 sec

T1=2.6 secT6=0.85sec

Mode-1 Mode-4 Mode-8 Mode-9

Mode-2 Mode-6 Mode-7 Mode-9

Mode-3 Mode-5

25


-5

0

5

10

15

20

25

30

35

40

45

-1 -0.5 0 0.5 1

Lev

el n

o.

Modal Value

Mode 1

Mode 2

-5

0

5

10

15

20

25

30

35

40

45

-1 -0.5 0 0.5 1

Lev

el n

o.

Modal value

Mode 3

Mode4

Mode

No.

Natural

Period (T)

Freq.

(f=1/T)

Mass

Participation

1 4.9 0.2 0.661

2 0.9 1.1 0.203

3 0.36 2.8 0.068

4 0.20 5.0 0.031

Mode Shape Values for 40 Storied Tall Building from

Modal Analysis-X-Direction only

The mass participation is higher

for modes in which net floor

mass translation/acceleration

from original position is more.

26


Elastic and design demands at the Design Basis

Earthquake Level Using Response Spectrum

(RS) method (UBC-97)

-5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6

Lev

el N

o.

Moment (kips-in x 107)

Combined

Mode 1

Mode 2

Mode 3

Mode 4

-5

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6

Lev

el N

o.

Moment (kips-in x 107)

Elastic Demands

Design Demands=Elastic/R

Elastic Demands

Moment Demands

27


Elastic and design demands at the Design Basis

Earthquake Level Using RS method (UBC-97)

-5

0

5

10

15

20

25

30

35

40

0 10 20 30

Lev

el N

o.

Shear (kips x 103)

Combined

Mode 1

Mode 2

Mode 3

Mode 4

-5

0

5

10

15

20

25

30

35

40

0 10 20 30

Lev

el N

o.

Shear (kips-in x 103)

Elastic Demands

Design Demands=Elastic/R

Elastic Demands

Shear Demands

28


Seismic Demands at the Maximum Considered

Earthquake Level Using NLRHA

29



Earthquake Level-NLRHA

The case study building, previously designed for the codebased DBE design demands, was verified at the MCE levelusing NLRHA procedure.

30



Earthquake-Selection and Scaling of Ground

Motions

Selected Ground Motions

are Spectrally Matched

using RSPMATCH, 2005

Software (Hancock et al.

(2006) ).

A Time domain spectral

matching technique, in

which wavelets are added

to the time series near the

time of peak response, is

used.

0

0.5

1

1.5

2

2.5

3

3.5

0 1 2 3 4 5

Response spectra

SH-PR-360 x 3.0

HM-H-090 x 4.0

LP-HSP-000 x 1.5

CM-EUR-090 x4.0

Hon-MGH-EW x 4.0

Chichi-Taipei-090 x 6.0

Imp-Ch-012 x 4.0

Target Spectra

DBE Spectrum (UBC-97, Zone 4, SD)

MCE Spectrum (DBE Spectrum x 1.5)

0

0.5

1

1.5

2

0 1 2 3 4 5Natural Period (Sec)

Comparison of (a) Scaled and (b) Spectrum

matched ground motion records with MCE

Response spectra of

sclaed ground motions

Target spectra

Sa

(g

)

31


Accele

ration (

g)

Time (sec)

Scaled Time History

Adjustment

Modified Time History



Motions32


Velo

city (

cm

/s)

Dis

p. (

cm

)

Time (sec.)



Motions33


Inelastic concrete and steel fibers for

modeling flexural behavior of the

wall at plastic hinge location.

Linear elastic flexure and shear

behavior for wall outside plastic

hinge location, columns, and slabs.

A bilinear hysteretic model of non-

degrading type for modeling the

steel fiber.

Mander’s stress-strain model for

making concrete fiber

Damping Ratio is 1-5% from Mode

1 to 6.

Seismic Demands at the Maximum

Considered Earthquake-Non-linear Model

Core Wall

ColumnsPlastic

Hinge at

the baseSlabs

Core Wall with Plastic Hinge

34

Basements


Park Envelope

Perform -3D

Cyclic

fy

fu

ξy ξsh ξu

Str

ess

Strain

fy = Rebar yield stress , fu = Rebar ultimate stress capacity

ξy = Rebar yield strain, ξsh = Strain in rebar at the onset of strain hardening,

ξu= Rebar ultimate strain capacity, Eo=Modulus of elasticity

Eo

Mander Envelope

Perform -3D

Unloading

ft

f’cc

ξ'c ξ'cc ξcu

Str

ess

Strain

fc’ = Compressive strength of unconfined concrete

fcc’ = Compressive strength of confined concrete

ξ'c =Concrete strain at fc’

ξ'c c =Concrete strain at fcc’

ξcu= Ultimate strain capacity for confined concrete

Eo= Tangent modulus of elasticity, dc=energy dissipation factor for the reloading stiffness.

ft =Tensile strength of concrete= ( fc’ is in psi)

Reloading

Eo

Eo

dcEo

Unloading and reloading are

the same in case of tension

f’c

Steel Material Concrete Material

Seismic Demands at the Maximum

Considered Earthquake-Non-linear Model35


Comparison of the DBE demands and MCE

demands

Comparison shows that MCE demands are significantly higher

than the DBE demands as well as their distribution pattern is

different than DBE demands. So Code Based RS procedure

is not valid for Tall Buildings (Where higher mode are

dominant)

Proper control measures need to be identified and designed

to suppress these large seismic demands.

-5

0

5

10

15

20

25

30

35

40

0 10 20 30 40

Lev

el N

o.

Shear (kips x 103)

Lower-bound

Mean

Upper-bound

Series5

Design Demands

-5

0

5

10

15

20

25

30

35

40

0 1 2 3

Moment (kip-in x 107)

NLRHA & MCE

RSA & DBE

-5

0

5

10

15

20

25

30

35

40

0 50 100 150

Disp. (inches)

36


Effective Control Mechanism Using Multiple

Plastic Hinge Concept

37


Conventional Approach DW Approach by Rad

and Adebar (2008)

DPH Approach by Panagiotou

and Restrepo (2009)

Core Wall Showing Plastic Hinges Location

Plastic

Hinges

Plastic

Hinge

Design Strategy Based on the Plastic

Hinges-Brief Review of Existing Approaches

Plastic

Hinges all

along the

wall height

38


There are some disavantages associted with the existingapproaches.

For the DW (ductile wall) approach, the seismic design willbe uneconomical due to the stringent requirements ofductile detailing throughout the wall height.

The repair cost will also be high since the damage can occurat various locations.

On the other hand, DPH (dual plastic hinge) approach maynot be effective for some of the higher modes, which maysignificantly contribute to the seismic demands.

Design Strategy Based on the Plastic

Hinges-Brief Review of Existing Approaches39


A new approach to reduce the inelastic seismic demands in

the core walls of high rise buildings is proposed.

The approach allows flexural plastic hinges to form at

effective locations along the wall height.

The effective locations are those where the bending

moments induced by important vibration modes reach their

maximum values.

The flexural strength at these locations is based on the DBE

moments.

The effectiveness of this proposed approach on a case study

building has been verified by using the NLRHA procedure.

New Design Approach Based on the Identification

of the Higher Modes40



of the Higher Modes

Several Plastic Hinges are placed based on the dominanthigher modes such as 2nd and 3rd modes.

41


Back Ground and Problem Statement

Conventional Approach Proposed Approach

Basements

Core Wall

Columns

Plastic

Hinge at the baseSlabs


Plastic

Hinges

Comparison with the conventional approach

42


Comparison with the conventional approach

using NLRHA

-5

0

5

10

15

20

25

30

35

40

0 10 20 30

Lev

el N

o.

Shear (kips x 103)

-5

0

5

10

15

20

25

30

35

40

0 1 2 3

Moment (kip-in x 107)

0

5

10

15

20

25

30

35

40

0 0.02 0.04

Sto

rey N

o.

Shear Def. Angle (radian)

-5

0

5

10

15

20

25

30

35

40

0 25 50 75 100

Lev

el N

o

Disp (in )

NLRHA is performedwith PHs at severallocations

There is 60%reduction in themoment demand atthe mid height.

Whereas sheardemand is reducedby 33% using theproposed approach.

43


Proposed Approach DW Approach by Rad

and Adebar (2008)

DPH Approach by Panagiotou

and Restrepo (2009)


Plastic

Hinges

Plastic

Hinges

Comparison with the existing approaches

Plastic

Hinges all

along the

wall height

44


Comparison with the existing approaches

-5

0

5

10

15

20

25

30

35

40

0 1 2 3

Conventional approach

Proposed approach

DW approach

DPH approach

0 10 20 30

Moment (Kips-in x 107) Shear (Kips x 103)

Lev

el N

o.

The comparison shows that proposed approach is as

effective as DW approach and slightly more effective than

the DPH approach

45


The seismic demands can be greatly reduced by the

proposed approach, and its effectiveness is as good as the

DW approach and is superior to the DPH approach.

Since the proposed approach is more economical than

the DW approach but slightly less economical than the

DPH approach, the building designer will have more options

to choose for handling the problem of high seismic force

demands in the core wall.


of the Higher Modes-Conclusions46


THANK YOU FOR YOUR ATTENTION

47


Q&A

Questions from the audience

48


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