A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND A SEISMIC DESIGN APPROACH USING TARGET DRIFT AND YIELD MECHANISM AS PERFORMANCE OBJECTIVESYIELD MECHANISM AS PERFORMANCE OBJECTIVES

(PERFORMANCE-BASED PLASTIC DESIGN)(PERFORMANCE-BASED PLASTIC DESIGN)

DESIGN BASE SHEAR & VERTICAL DISTRIBUTIONDESIGN BASE SHEAR & VERTICAL DISTRIBUTION

Subhash C. GoelSubhash C. GoelSutat LeelataviwatSutat Leelataviwat

Bozidar StojadinovicBozidar StojadinovicSoon-Sik LeeSoon-Sik Lee

Prabuddha DasguptaPrabuddha DasguptaShih-Ho ChaoShih-Ho Chao

Department of Civil and Environmental Engineering Department of Civil and Environmental Engineering The University of MichiganThe University of Michigan

Ann Arbor, MIAnn Arbor, MI

CURRENT DESIGN PRACTICE

• Design Base Shear

V = Ce W/R• Elastic Design/Analysis• Drift Check

Cd Δ < Δlimit

• Prescribed Ductility Detailing

(Works most of the time – But not always!)

CONCEPTCONCEPT

Ve

Vu = ΩoV

V = Ve /R

Δ CdΔ ≤ Δu

Base Shear

Displacement (Story Drift)

Selected Mechanism at Target DriftSelected Mechanism at Target Drift

i pbrMb

pcMpq pq

1( )i i i nF Fb b

u

ih

DESIGN BASE SHEARWork needed to “ push” the system monotonically up to the target drift = Energy needed for an equivalent SDOF to be monotonically “ pushed” up to the target ductility level ( )

For the given system,

Using Newmark-Hall Inelastic Spectra (Rµ-µs-T) for E-P SDOF,

Ref: Housner (1956, 1960)

Solution of Work-Energy Equation gives Design Base Shear

Ductility Reduction Factors Ductility Reduction Factors Proposed by Newmark and Proposed by Newmark and Hall [1973]Hall [1973]

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3

Period (sec)

s=2

s=6

s=5

s=4

s=3

R

Modification Factor for Modification Factor for Energy Equation versus Energy Equation versus PeriodPeriod

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5 3

Period (sec)

s=2

s=6

s=5

s=4

s=3

Acceleration Region

Velocity, Displacement Region

Acceleration Region

Velocity, Displacement Region

Effect of Target Inelastic DriftEffect of Target Inelastic Drift

0.2

0.4

0.6

0.8

1.2

0 0.5 1 1.5 2 2.5

Period (T)

V/W

0 0.5 1 1.5 2 2.5

Period (T)

V/W

=0.000pq

0.005

0.0100.0150.020

1.0

0.0

Elastic

Comparison of the Design Base Shear Comparison of the Design Base Shear Coefficients at Ultimate Strength LevelCoefficients at Ultimate Strength Level

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.5 1 1.5 2 2.5

Period (T)

V/W

Modified Energy

2.8(1.4UBC-94)

2.8UBC-97

Comparison of Base shear-Roof drift curves of two frames Comparison of Base shear-Roof drift curves of two frames

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.00

500

1000

1500

2000

2500

3000

Roof Drift (%)

Bas

e S

hear

(K

ips)

10-Story PPD FrameOverstrength = 1.81

Design Base Shear according to IBC 2000 Approach V=1600 kips

Design Base Shear according to Proposed Approach V=1358 kips

10-Story IBC FrameOverstrength = 1.74

   

 Design Lateral Force Distribution Based on Inelastic Response

  Lateral Force Distributions in Current Building Codes :

First-Mode Dynamic Solution of Lumped MDOF System

Elastic Response

(Clough and Penzien 1993; Chopra 2000; NEHRP 2001)

Close to a straight line (k =1) when the T is 0.5 second or less;

Close to a parabola (k = 2) when T period is 2.5 seconds or more

IBC 2003

A New Lateral Force Distribution Based on Inelastic Response of Structures (Lee and Goel, 2001; Chao and Goel, 2005):

was originally proposed as 0.5, which was revised to 0.75 based on more extensive nonlinear dynamic analyses on EBFs, CBFs, and STMFs.

Story Shear Distribution Factor

Lateral Force at level i

Lateral Force at Top level n

 Justification of the New Lateral Force Distribution

1. Relative Story Shear Distributions

Relative Distribution of Story Shear Vi / Vn

0 1 2 3 4 50.5 1.5 2.5 3.5 4.51

2

3

4

5

6

7

8

9

Sto

ry L

eve

l

El Centro

Newhall

Sylmar

Synthetic

IBC 2003

Eq. 4

9-Story SMF

UBC 97

0.5

Eq. 4 0.75

0 1 2 3 4 50.5 1.5 2.5 3.5 4.5

1

2

3

4

5

6

7

8

9LA02 (El Centro)LA04 (Array #05)

LA07 (Barstow)

LA09 (Yermo)

LA12 (Loma Prieta)LA13 (Newhall)LA17 (Sylmar)

LA18 (Sylmar-2)LA19 (North Palm)

LA21(Kobe_2%in50yr)

LA23 (Loma Prieta_2%in50yr)LA26 (Rinaldi_2%in50yr)

LA27 (Sylmar_2%in50yr)

LA30 (Tabas_2%in50yr)

Sto

ry L

evel

Relative Distribution of Story Shear Vi / Vn

NEHRP 2000 (IBC 2003)

Eq. 4 0.75

9-Story STMF

Eq. 4 0.5

0 1 2 3 4 50.5 1.5 2.5 3.5 4.51

2

3

4

5

6

7

8

9

10

IBC 2003

la01la02la09la12la13la16la17la19

Sto

ry L

evel

Relative Distribution of Story Shear Vi / Vn

10-Story EBF

Eq. 4 0.5

Eq. 4 0.75

0 1 2 3 40.5 1.5 2.5 3.51

2

3

4

5

6

Sto

ry L

evel

La02

La04

La09

La16

La17

La20

NEHRP 2003

Relative Distribution of Story Shear Vi / Vn

Eq. 4 0.75

6-Story CBF

0 1 2 3 4 50.5 1.5 2.5 3.5 4.51

2

3

4

5

6

7

8

9

10

Sto

ry L

eve

l

Relative Distribution of Story Shear Vi / Vn

Taft Event (1952)

Elastic AnalysisInelastic Analysis

10-Story SMF (Goel, 1967)

IBC 2003

Eq. 4 0.5

Eq. 4 0.75

0 1 2 3 4 50.5 1.5 2.5 3.5 4.51

2

3

4

5

6

7

8

9

10

IBC 2003

LA01 Earthquake

Sto

ry L

evel

Relative Distribution of Story Shear Vi / Vn

Elastic AnalysisInelastic Analysis

10-Story EBF

Eq. 4 0.75

Relative Story Shear Distributions (comparison between elastic and inelastic responses):

0 1 2 3 4 50.5 1.5 2.5 3.5 4.51

2

3

4

5

6

7

8

9

10

IBC 2003

LA09 Earthquake

Sto

ry L

evel

Relative Distribution of Story Shear Vi / Vn

Elastic AnalysisInelastic Analysis

10-Story EBF

Eq. 4 0.75

4. Higher Mode Effect Accentuated by Inelastic Behavior

Beams impose no restraint on joint rotations

(Chopra, 2005)

Beams impose complete restraint on joint rotations

2. Maximum Interstory Drift Distributions

Sto

ry L

evel

Maximum Interstory Drift (%)

Interstory DriftIBCPPD

-2.0 -1.0 0.0 1.0 2.0-1.5 -0.5 0.5 1.50

2

4

6

8

10

1

3

5

7

9

10-Story EBF

LA16 Earthquake

pcM

i pbiMiuF

pcM

cM h

ih

3. Column Design Moments

Free body diagram of an exterior “column tree”

0

1

2

3

4

5

6

7

8

9

Moment (kip-ft)

Sto

ry

0

1

2

3

4

5

6

7

8

9

Moment (kip-ft)

Sto

ryDesign Moment

Design Moment(UBC Distribution)El Centro

New hall

Sylmar

Synthetic

(Lee and Goel, 2001)

Exterior column Interior column

0123456789

1011121314151617181920

Moment (kip-ft)

Sto

ry

0123456789

1011121314151617181920

Moment (kip-ft)

Sto

ry

Design Moment

Design Moment(UBC Distribution)El Centro

New hall

Synthetic

Sylmar

(a) Exterior (b) Interior

(Lee and Goel, 2001)

SOME RESULTS

Plastic Hinge Plastic Hinge Distribution in 3-Story Distribution in 3-Story

SMRF and 9-Story SMRF and 9-Story SMRFSMRF

(b) 9-Story

(a) 3-Story

Sylmar

El Centro

Sylmar

El Centro

Newhall

Synthetic

Synthetic

Newhall

Rotational Ductility Demands: 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0

Sylmar

El Centro

Synthetic

Newhall

Rotational Ductility Demands : 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0

Plastic Hinge Plastic Hinge Distribution in 20-Story Distribution in 20-Story

SMRFSMRF

0

5

10

15

20

0 1 2 3 4

Story Drift (%)

Stor

y

4

20- Story

0123456789

10

Stor

y

0

1

2

3

Stor

y

0 1 2 3 4

0 1 2 3 4

Story Drift (%)

3- Story

9- Story

El Centro NewhallSylmar Synthetic

Maximum Story Drift due to Selected Earthquake Records

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4

Story Drift (%)

Sto

ry

Ta

rge

t D

rift

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4

Story Drift (%)

Sto

ry

El Centro Newhall Synthetic Sylmar

Ta

rge

t D

rift

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4

Story Drift (%)

Sto

ry

Ta

rge

t D

rift

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4

Story Drift (%)

Sto

ry

Ta

rge

t D

rift

(a) 1.5% Target Drift (b) 2.0% Target Drift

(c) 2.5% Target Drift (d) 3.0% Target Drift

Maximum Story Drifts of Four 20-Story Frames Designed with (a) 1.5% Target Drift, (b) 2.0% Target Drift, (c) 2.5% Target Drift, and (d) 3.0% Target Drift under Four Earthquakes