DIRECT DISPLACEMENT-BASED SEISMIC DESIGN OF …canterbury.royalcommission.govt.nz/documents-by... · DIRECT DISPLACEMENT-BASED SEISMIC DESIGN OF ... susceptibility to shear failure.

1

DIRECT DISPLACEMENT-BASED SEISMIC DESIGN OF

STRUCTURES

Nigel Priestley

European School for Advanced Studies in Reduction of Seismic Risk

(“Rose”

School), Pavia, Italy

ENG.PRI.0003.1

2

•

WHAT SHOULD BE THE STRUCTURAL STRENGTH? (BASE SHEAR FORCE)?

•

HOW SHOULD THIS STRENGTH BE DISTRIBUTED?

•

IS CURRENT DESIGN PHILOSOPHY ADEQUATE, PARTICULARLY WITH REFERENCE TO NEW TECHNOLOGY SYSTEMS?

WITHIN A PERFORMANCE-BASED ENVIRONMENT:

ENG.PRI.0003.2

3

1. The Need for DDBD

(Problems with Force-based Design)

• Estimating Elastic Stiffness

•

Distribution of Required Strength based on Elastic Stiffness

• Displacement-Equivalence Rules (equal displacement)

• Specified Ductility of Force-Reduction Factors

•

Assumption that Increased Strength Reduces potential for damage

Note: Damage is strain or drift (not strength) related

ENG.PRI.0003.3

HA HB HC

A

B

C

Period T (seconds)

Spec

tral

Acc

eler

atio

n S

A(T

)

Elastic

Ductile

Structure

Acceleration Response Spectrum

Concrete Bridge under Longitudinal Seismic Excitation

CBA

CBAlong HEIKKKK

,,3

12Stiffness:

Period:

longKmT /2

Base shear force:

RSgm

F TA )(

Pier Shear Force:

long

ii K

KFF

Design Displacement:

gSTTAlong )(2

2

4

ENG.PRI.0003.4

HA HB HC

A

B

C

Concrete Bridge Under Longitudinal Response

CBA

CBAlong HEIKKKK

,,3

12

longKmT /2

longKmT /2

Stiffness:

Period:

Pier Strength:long

ii K

KFF

What value for EI? What force-reduction factor? Is the strength distribution logical?

ENG.PRI.0003.5

6

0 0.002 0.004 0.006Curvature (1/m)

0

10000

20000

30000

40000M

omen

t (k

Nm

)

Nu/f'cAg = 0

Nu/f'cAg = 0.1

Nu/f'cAg = 0.2

Nu/f'cAg = 0.3

Nu/f'cAg = 0.4

(a) Reinforcement Ratio = 1%

0 0.002 0.004 0.006Curvature (1/m)

0

10000

20000

30000

40000

50000

Mom

ent

(kN

m)

Nu/f'cAg = 0

Nu/f'cAg = 0.1

Nu/f'cAg = 0.2

Nu/f'cAg = 0.3

Nu/f'cAg = 0.4

(b) Reinforcement Ratio = 3%

SELECTED MOMENT-CURVATURE CURVES FOR CIRCULAR COLUMNS (D=2m,f’c

= 35MPa, fy

= 450MPa)

ENG.PRI.0003.6

7

0 0.1 0.2 0.3 0.4Axial Load Ratio (Nu/f'cAg)

0

0.2

0.4

0.6

0.8

1

Stif

fnes

s R

atio

(E

I/E

I gro

ss)

l = 0.04

l = 0.03

l = 0.02

l = 0.01

l = 0.005

EFFECTIVE STIFFNESS RATIO FOR CIRCULAR COLUMNS

EIeff

= MN

/y

EIeff

/EIgross

=MN

/y

EIgross

ENG.PRI.0003.7

8

INTERDEPENDENCY OF STRENGTH AND STIFFNESS

Stiffness EI = M/

M M

y3

y2

y1

y

M1

M2

M3

M1

M2

M3

(a) Design assumption (constant stiffness)

(b) Realistic assumption (constant yield curvature)

INFLUENCE OF STRENGTH ON MOMENT-CURVATURE RESPONSE

ENG.PRI.0003.8

9

HA HB HC

A

B

C

Bridge Under Longitudinal Response

CBA

CBAlong HEIKKKK

,,3

12

longKmT /2

longKmT /2

Stiffness:

Period:

Pier Strength:long

ii K

KFF

What value to use for EI? What ductility?

ENG.PRI.0003.9

10

Column C

Column A

Column B

Force

yC

Displacement 4yC

,yA yB

Column height ratios: hA

:hB

:hC

= 2.0:2.75:1.0

Yield displacement ratio: yA

:yB

:yC

= 4.0:7.56:1.0

Strength distribution: VA

:VB

:VC

= 0.125:0.048:1.0

y

= y

h2/3

=2.25y

h2/(3D)

Force-Based Design of Bridge

ENG.PRI.0003.10

11

BRIDGE WITH UNEQUAL COLUMN HEIGHTS

•

Shortest piers are stiffest. Shear is in proportion to 1/h3. Therefore moments (and, approximately reinforcement ratio) are in proportion to 1/h2. Increasing the reinforcement ratio of the short piers relative to the long piers increases the relative stiffness of the short piers, attracting still higher shear in elastic response.

•

Allocating high shear to the short column increases its susceptibility to shear failure.

•

Displacement capacity of the short pier is DECREASED by increasing its reinforcement ratio

•

It doesn’t make sense to have a higher reinforcement ratio for the shorter columns than the longest columns (and in practice, they would probably have the same reinforcement ratio, for simplicity of construction)

ENG.PRI.0003.11

12

YIELD DRIFTS OF CONCRETE FRAMES

ELASTIC DEFORMATION CONTRIBUTIONS TO DRIFT

OF A BEAM/COLUMN JOINT SUBASSEMBLAGE

Beam flexure and shear deform.Column flexure and shear deform.Joint shear deformation

ENG.PRI.0003.12

13

Column height/beam length aspect ratio (lc/lb) : 0.4 – 0.86 Concrete compression strength (f’c) : 22.5MPa – 88MPa Beam Reinforcement yield strength (fy) : 276MPa – 611MPa Maximum beam reinforcement ratio (A’s/bwd) : 0.53% – 3.9% Column axial load ratio (Nu/f’cAg) : 0 – 0.483 Beam aspect ratio (lb/hb) : 5.4 – 12.6

CONCRETE FRAME DRIFT EQUATION

y = 0.5y (lb /hb )

Equation Checked against test data with:

ENG.PRI.0003.13

14

y = 0.5y (lb /hb )

EXPERIMENTAL DRIFTS OF BEAM/COLUMN TEST UNITS COMPARED WITH EQUATION

ENG.PRI.0003.14

15

Circular column: Dyy /25.2

Rectangular column: cyy h/10.2

Rectangular cantilever walls: wyy l/00.2

T-Section Beams: byy h/70.1

b

byy h

l 5.0Concrete Frames:

DIMENSIONLESS YIELD CURVATURES AND DRIFTS

Steel Frames:b

byy h

l 65.0

ENG.PRI.0003.15

16

FRAME DUCTILITY LIMITS

NOTE: CODES LIMIT DRIFT TO 0.02-0.025

b

byy h

l 5.0Yield Drift:

Example: lb

= 6m, hb

=0.6m, fy

= 500MPa

y = 500/200,000 = 0.0025;

y = 0.5*0.0025*6.0/0.6 = 0.0125

Thus ductility limit is 1.6 to 2.0

Note: using high-strength reinforcement provides no benefit in reduced steel content!

ENG.PRI.0003.16

FORCE-BASED DESIGN – ASSUMPTIONS OF SYSTEM DUCTILITY

AND CONSEQUENT FORCE-REDUCTION FACTOR

•

In current force-based design it is assumed that structural systems have a unique ductility capacity, and hence a unique force-reduction factor

e.g.

Concrete Frame Building: R

= 6 (depends on country)

Concrete Wall Building: R

= 4

(::)

Concrete Bridge:

R

= 3

(::)

ENG.PRI.0003.17

Structural Type and Material

US West Coast Japan New** Zealand

Europe

Concrete Frame 8 1.8-3.3 9 5.85 Conc. Struct. Wall 5 1.8-3.3 7.5 4.4

Steel Frame 8 2.0-4.0 9 6.3 Steel EBF* 8 2.0-4.0 9 6.0

Masonry Walls 3.5 6 3.0 Timber (struct. Wall) 2.0-4.0 6 5.0

Prestressed Wall 1.5 - - - Dual Wall/Frame 8 1.8-3.3 6 5.85

Bridges 3-4 3.0 6 3.5 * Eccentrically Braced Frame **SP factor of 0.67 incorporated.

FORCE-REDUCTION FACTORS IN DIFFERENT COUNTRIES

ENG.PRI.0003.18

A B C

STRUCTURE Column Moment-Curvature Relationships

INFLUENCE OF AXIAL LOAD ON COLUMN STIFFNESS

REFINED ANALYSIS MYTH

A

C

ENG.PRI.0003.19

20

INFLUENCE OF ELASTIC DAMPING ON DISPLACEMENT-EQUIVALENCE RULE

Displacement-equivalence rules are based on Inelastic Time History Analysis (ITHA). The representation of the initial response has a considerable influence on the results:

“Elastic damping” is typically added to represent the initial stages,and expressed as a % of critical damping – typically 5%. There are two main ways this could be modelled: as initial-stiffness proportional damping, or tangent-stiffness proportional damping:

Initial-stiffness: damping always proportional to this slope

Tangent stiffness: damping force reduces when stiffness reduces; increases when stiffness increases

ENG.PRI.0003.20

IS HIGH STRENGTH NECESSARY OR EVEN DESIRABLE?

High Strength:

•

SESOC recommends high strength to reduce damage to frame buildings (mu

= 1.25)

• Reduces damage in small or moderate earthquakes

•

Does not necessarily reduce damage in Design or Extreme EQ

• Does not necessarily reduce displacements

•

Subjects contents to higher accelerations (increased contents damage)

•Increases foundation forces and cost

ENG.PRI.0003.21

0 1 2 3 4Reinforcement Ratio (%)

0

0.5

1

1.5

2

Par

amet

er R

atio

Displacement

Stre

ngt

h

uy1 y2

u/y

Strength

StiffnessDuctilityCapacityDispl.

Capacityu Demand/Capacity

(a) Strength vs Ductility (b) Influence of Rebar % on Parameters

S1

S2

INFLUENCE OF STRENGTH ON DAMAGE

ENG.PRI.0003.22

23

2. DIRECT DISPLACEMENT - BASED SEISMIC DESIGN

A RATIONAL SEISMIC DESIGN APPROACH

ENG.PRI.0003.23

Force

Displacement

Ki Ks

First cycle

Subsequent cycle

Secant Elastic

CHARACTERIZING STRUCTURE BY ELASTIC OR SECANT STIFFNESS

Maximum

Residual

ENG.PRI.0003.24

25

FORMULATION OF THE DIRECT DISPLACEMENT-BASED (DDBD)

APPROACH

DDBD is based on the observation that damage is directly related to strain (structural effects) or drift (non-

structural effects), and both can be integrated to obtain displacements. Hence damage and displacement can be directly related. The design approach ACHIEVES a specified damage limit state.

It is not possible to formulate an equivalent relationship between strength (force) and damage. This is one of the major deficiencies of current force-based seismic design). The level of damage is uncertain

ENG.PRI.0003.25

DIRECT DISPLACEMENT-BASED

SEISMIC DESIGN FUNDAMENTALS

• Based on fundamental inelastic modes of response

•

Hysteretic response represented by equivalent viscous damping

•

Higher modes considered by new capacity design provisions

ENG.PRI.0003.26

me Fu

F Fn rKi

He Ki Ke

y d

(a) SDOF Simulation (b) Effective Stiffness Ke

0 2 4 6Displacement Ductility

0

0.05

0.1

0.15

0.2

0.25

Dam

pin

g R

atio

,

0 1 2 3 4 5Period (seconds)

0

0.1

0.2

0.3

0.4

0.5

Dis

pla

cem

ent

(m)

0.05

=0.10

=0.15

=0.20

=0.30

d

Te

Elasto-Plastic

Steel Frame

Concrete Frame

Hybrid Prestress

(c) Equivalent damping vs. ductility (d) Design Displacement Spectra

Concrete Bridge

FUNDAMENTALS OF DDBDENG.PRI.0003.27

28

Fme

He

Fu

Fn

Ki

rKi

Ke

y D

(a) SDOF Simulation (b) Initial and Secant Stiffness

INITIAL AND SECANT STIFFNESS

Initial Stiffness: Ki with (5%) elastic damping (traditional)

Secant Stiffness: Ke with effective (e.g.16%) damping (new)

ENG.PRI.0003.28

29

0 2 4 6Displacement Ductility

0

0.05

0.1

0.15

0.2

0.25

Dam

pin

g (

%)

0 1 2 3 4 5Period (seconds)

0

0.1

0.2

0.3

0.4

0.5

Dis

pla

cem

ent

(m)

5%

10%

15%

20%

30%

d

Te

Elasto-Plastic

Steel Frame

Concrete Frame

Hybrid Prestress

(c) Equivalent damping vs. ductility (d) Design Displacement Spectra

Concrete Bridge

(c) Equivalent Damping vs Ductility (d) Design Displacement Spectra

ASPECTS OF DDBD

Ductility Damping; Damping+Displacement Period Te

Fu =KeD224

ee T

MK

ENG.PRI.0003.29

MDOF STRUCTURES

DDBD is a SDOF Design method, based on fundamental inelastic mode. With MDOF structure:

• Determine displaced shape, and characteristic disp.

• Determine effective Mass

• Determine effective Ductility and Damping

• Determine Effective Stiffness & Base shear

• Distribute Base shear to mass locations

•

Analyze structure to determine moments at plastic hinges

• Use capacity design to determine forces elsewhere

ENG.PRI.0003.30

1. DESIGN DISPLACEMENT FOR S.D.O.F STRUCTURES

• Depends on Design Limit State

• Structural displacement limit: Strain related

• Non-structural displacement limit: Drift related

•

chose critical of structural and non-structural limit displacements

ENG.PRI.0003.31

EXAMPLE OF STRAIN LIMIT STATES

Curvature from concrete compression:

mc

= cm

/cCurvature from reinforcement tension:

ms

= sm

/(d-c)

Chose lesser of mc

and ms

,Design Displacement is:

ds

=

y

+

p

= y

H2/3 + (m

-y

)Lp

H

Lp

= plastic hinge length.

ENG.PRI.0003.32

DRIFT LIMIT STATE

Code-specified non-structural drift limit = d

Displacement Limit d

=

d

.H

The lesser of the structural and non-structural displacement is chosen as the design value.

NOTE: Design approach will often be to design for a specified drift limit, and detail the critical sections to ensure strain limits are satisfied (this is particularly appropriate at the damage-control limit state).

NOTE: If the relationship between maximum and residual drift is known, the DDBD approach can be adapted to design for residual drift limits.

ENG.PRI.0003.33

CRITICAL DISPLACEMENTS

•Frames:

normally governed by structural or non- structural drift in beams of lowest storey

•

Cantilever Wall buildings: normally governed by plastic rotation at the wall base (for longest wall), or drift in top storey

•

Bridges: normally governed by plastic rotation, or drift limit, of the shortest column

ENG.PRI.0003.34

35

22 /4 eee TmK Effective Stiffness:

deBase KVF Base Shear Force:

n

iii

n

iiid mm

11

2 /MDOF Design Displacement:

d

n

iiie mm

/1

ELEMENTS OF DDBD: Multi-storey Building

Effective Mass:

n

iii

n

iiiie mHmH

11

/Effective Height:

ENG.PRI.0003.35

3.EQUIVALENT VISCOUS DAMPING

The design procedure requires relationships between displacement ductility and equivalent viscous damping.

Damping is the sum of elastic and hysteretic damping, and is determined by inelastic time-history analysis for different hysteretic rules:

hysteleq

Elastic damping, and the way that this has been modelled

in time-history analysis in the past:

refer

Ch.4 pp 203-210 for details

ENG.PRI.0003.36

37

Concrete Wall Building, Bridges (TT):

1444.005.0eq

Concrete Frame Building (TF):

1565.005.0eq

Steel Frame Building (RO):

1577.005.0eq

Hybrid Prestressed Frame (FS,=0.35):

1186.005.0eq

Friction Slider (EPP):

1670.005.0eq

Bilinear Isolation System (BI, r=0.2):

1519.005.0eq

RELATIONSHIPS FOR TANGENT-STIFFNESS DAMPING

ENG.PRI.0003.37

DAMPING FOR WALL BUILDING

Walls have different ductilities

(d

yA

, d

/yB

), hence damping.

System Damping:

Note: chose wall strength

Proportional to lw2:

m

jj

m

jjje VV

11

/

m

jwj

m

jjwje ll

1

2

1

2 /

ENG.PRI.0003.38

F1 F2 F3 F4 F5

V1

V2 V3

V4

V5

displaced shape

H2 H3

H4

1444.005.0pier damping:

Proportion of forces carried to abutments = x, hence:

Pier shear forces:

5

151

iiFxVV

4

2

5

1

1/11i iii

ii HHFxV Assumes all

piers yield

Inertia forcespier shears

abutment shear

ENG.PRI.0003.39

40

4. SEISMIC INPUT FOR DDBD

0 1 2 3 4 5Period T (seconds)

0

0.2

0.4

0.6

0.8

1

Acc

eler

atio

n a

(T)

(g)

0 1 2 3 4 5Period T (seconds)

0

0.1

0.2

0.3

0.4

0.5

Dis

pla

cem

ent

(T

) (

m)

(a) Acceleration Spectrum for 5% damping (b Displacement Spectrum for 5% damping

Force-based design

DDBD

ENG.PRI.0003.40

41

max

TC Period TD TE

PG

max

PG

TC Period TD TE

Displac

emen

t

GENERAL FORM OF ELASTIC 5% DISPLACEMENT SPECTRUM, FROM EC8

Corner Period

Linear

Plateau

ENG.PRI.0003.41

42

DESIGN DISPLACEMENT SPECTRA (4)

• Based on Faccioli’s observations,the corner period Tcappears to increase almost linearly with moment magnitude. For earthquakes with MW > 5.7, the following expression seems conservative:

7.55.20.1 wc MT

• Peak displacement at the corner period can be estimated from the following expression (firm ground):

r

WM )2.3(

max10

seconds

mm r = nearest distance to fault plane (km)

ENG.PRI.0003.42

43

0 2 4 6 8 10Period (seconds)

0

400

800

1200

1600

2000

Spec

tral

Dis

pla

cem

ent

(mm

)

M = 7.5

M = 7.0

M = 6.5M = 6.0

5% Damped Spectra Resulting from the Equations, at r = 10km

ENG.PRI.0003.43

44

0 1 2 3 4 5 6Period (seconds)

0

400

800

1200

1600

2000

Spec

tral

Dis

pla

cem

ent

(mm

)

0 1 2 3 4 5 6Period (seconds)

0

0.4

0.8

1.2

1.6

2

Spec

tral

Acc

eler

atio

n (

xg)Life

safety

Damagecontrol

Serviceability

Lifesafety

Damagecontrol

Serviceability

(a) Displacement Spectra (b) Acceleration Spectra

Elastic Spectra for Different Limit States

ENG.PRI.0003.44

45

0 1 2 3 4 5Period T (seconds)

0

0.2

0.4

0.6

0.8

1

Rel

ativ

e D

isp

lace

men

t

T,

0 1 2 3 4 5Period T (seconds)

0

0.2

0.4

0.6

0.8

1

Rel

ativ

e D

isp

lace

men

t

T,

4,5%

0.05

0.10

0.15

0.20

0.30

0.30

(a) "Normal" Conditions (b) Velocity Pulse Conditions

0.20 0.15

0.10

0.05

(Eq.(2.8)) (Eq.(2.11))

Recommended Spectral correction for Damping

ENG.PRI.0003.45

46

Note that designing for “Velocity Pulse”

spectra of the type in the previous slide using Direct Displacement-Based Design automatically results in a reduced effective period, and hence an increased seismic design force to limit the displacements to the design value.

This is one of the advantages of Direct Displacement-Based Design

ENG.PRI.0003.46

47

F4 VB4 VB4

Level 4 Base Overturning Moment F3 VB3 VB3 Level 3 F2 Level 2 H3

VB1 VB1

F1 Level 1 Level 0 MC1 MC2 MC3

T C Lbase

CjbaseBi

Cjb

ii

MLVOTM

MLTOTM

HFOTM

VB2 VB2

VC1 VC2 VC3

ANALYSIS OF FRAMES UNDER LATERAL FORCES

n

iiiiiBi mmVF

1

/

Lateral force distribution

0.6H1

ENG.PRI.0003.47

0.6H1

H1

0.15H1

VC

0.325VCH1

0.6VCH1

Level 0

Level 1

FIRST STOREY COLUMN MOMENTS

ENG.PRI.0003.48

49

COMBINATION OF GRAVITY AND SEISMIC MOMENTS AT FRAME PLASTIC HINGES

0 100 200 300Seismic Moment (kNm)

0

100

200

300

Des

ign

Mom

ent

(kN

m)

Gravity Moment

Seismic alone

RedistributedSeismic+Gravity

Design for higher of factored gravity moments OR design seismic moments (not a combination of both). Displacement demand is not influenced.

ENG.PRI.0003.49

50

TORSIONAL RESPONSE OF WALL BUILDINGS WITH STRENGTH AND STIFFNESS ECCENTRICITY

Wall Wall 2

Wall 3

Wall 4 Z

X kZ1, kZ2

ktrans

ktrans

CM CV CR

eVX eRX

LX = 25 m

LZ=15m

VB

V1 V2 Strength eccentricity

Stiffness eccentricity

Both strength and stiffness eccentricity affect torsional

response. In DDBD the design displacement at centre of mass is reduced to account for torsional

response

ENG.PRI.0003.50

51

HIGHER MODE EFFECTS

Two effects in DDBD

1. Drift amplification –

A reduction to the design drift is applied to frames higher than about 10 storeys

2. Moment and Shear amplification for capacity- protected actions and members. These have been

extensively researched by inelastic time-history analysis. Results are found to depend on the effective structural displacement ductility demand. New design equations and simplified design approaches have been developed for different structural systems.

ENG.PRI.0003.51

52

(e.g.) Design Column Moments in Frames

f,t

f,c

0.75H

0.25H

1.0

H

first storey

Efo

Nf MM

113.015.1, ocf

1 oo

ENG.PRI.0003.52

53

0 2000 4000 6000 8000 10000Moment (kNm)

0

5

10

15

20

Hei

gh

t (m

)

IR= 0.5 1.0 1.5 2.0

SRSS/

Cap.Des

0 4000 8000 12000 16000 20000Moment (kNm)

0

10

20

30

Hei

ght(

m)

IR=0.5 1.0 1.5 2.0

Cap.Des

SRSS/

30

40

t (m

)

IR=0 5 1 0 1 5 2 0

40

60t

(m)

IR=0 5 1 0 1 5 2 0

( ) y ( ) y

(c) Eight-Storey Wall (d) Twelve-Storey Wall

Capacity Design Moments and Time History Results for Different Seismic Intensity Ratios (IR=1=Design Intensity)

CANTILEVER WALL MOMENTS

ENG.PRI.0003.53

54

0 400 800 1200 1600 2000Shear Force (kN)

0

5

10

15

20

Hei

gh

t (m

)

IR= 0.5 1.0 1.5 2.0

SRSS/

Cap.Des

0 500 1000 1500 2000 2500Shear Force (kN)

0

10

20

30

Hei

gh

t (m

)

IR= 0.5 1.0 1.5 2.0

SRSS/

Cap.Des

30

40

t (m

) 40

60t

(m)

(c) Eight-Storey Wall (d) Twelve-Storey Wall

Capacity Design Shears and Time History Results for Different Seismic Intensity Ratios (IR=1=Design Intensity)

ENG.PRI.0003.54

78 Park Tce. Typical internal shear wall.

2 layers rebar, high %, compression failure? Lack of cross linking. Higher mode shear forces?

ENG.PRI.0003.55

56

MODIFIED MODAL SUPERPOSITION (MMS)

Extension to Method suggested by Eibl

and Keintzel,1988

SHEAR FORCE PROFILES5.02

32

22

1 ...)( EiEii VVVViV1i

= Inelastic

first-mode shear force at level i (from DBD forces) or elastic shear force, if lower

V2Ei

(etc) = elastic

2nd (etc) mode shear force at level i

THUS FORCE REDUCTION FOR DUCTILITY IS ONLY APPLIED TO FIRST MODE

ENG.PRI.0003.56

57

0 4000 8000 12000 16000 20000Moment (kNm)

0

10

20

30

Hei

gh

t (m

)

0 4000 8000 12000 16000 20000Moment (kNm)

0

10

20

30

Hei

gh

t (m

)

0 10000 20000 30000Moment (kNm)

0

10

20

30

40

Hei

gh

t (m

)

0 10000 20000 30000Moment (kNm)

0

10

20

30

40

Hei

gh

t (m

)

0 10000 20000 30000 40000Moment (kNm)

0

20

40

60

Hei

gh

t (m

)

0 10000 20000 30000 40000Moment (kNm)

0

20

40

60

Hei

gh

t (m

)

THA MMS THA MMSTHA MMS

(n) Twelve-Storey Wall, IR=1.0

(o) Twelve-Storey Wall, IR=1.5

(p) Twelve-Storey Wall, IR=2.0

(r) Sixteen Storey Wall, IR 1.0 (v) Twenty Storey Wall, IR 1.0

(s) Sixteen-Storey Wall, IR=1.5 (w) Twenty-Storey Wall, IR=1.5

(t) Sixteen-Storey Wall, IR=2.0 (x) Twenty-Storey Wall, IR=2.0

THA MMS

THA MMS

THA MMS

MMS Moment Envelopes Compared with Time History Results for Different Seismic Intensity Ratios (IR=1=Design)

ENG.PRI.0003.57

58

20

30

ht

(m)

0 500 1000 1500 2000 2500 3000Shear Force (kN)

0

10

20

30

Hei

ght

(m)

0 500 1000 1500 2000 2500 3000Shear Force (kN)

0

10

20

30

Hei

gh

t (m

)

30

40

ht

(m)

0 1000 2000 3000 4000Shear Force (kN)

0

10

20

30

40

Hei

gh

t (m

)

0 1000 2000 3000 4000Shear Force (kN)

0

10

20

30

40

Hei

gh

t (m

)

40

60

ht (

m)

0 1000 2000 3000 4000Shear Force (kN)

0

20

40

60

Hei

ght

(m)

0 1000 2000 3000 4000Shear Force (kN)

0

20

40

60

Hei

gh

t (m

)

MMS THA MMS THA MMS THA

MMS THA

THA MMS

THA MMS

(m) Twelve-Storey Wall, IR=0.5 (q) Sixteen-Storey Wall, IR=0.5 (u) Twenty-Storey Wall, IR=0.5

(n) Twelve-Storey Wall, IR=1.0 (r) Sixteen-Storey Wall, IR=1.0 (v) Twenty-Storey Wall, IR=1.0

MMS Shear Envelopes Compared with Time History Results for Different Seismic Intensity Ratios (IR=1= Design)

ENG.PRI.0003.58

59

Hei

ght

MF oMF

oMB

Mo0.5Hn

Tension shift

VF oVF

VoBase=oVVBase

Von

Capacity envelope

Capacity envelope

(a) Moment Capacity Envelope (b) Shear Force Capacity

Bo

To

Hn MCM ,15.0 4.01075.04.0,1

oiT TC

Moment: where

SIMPLIFIED WALL CAPACITY-DESIGN EQUATIONS

,BaseVoo

Base VV ToV C ,21 15.1)5.0(4.0067.0,2 iT TC

ENG.PRI.0003.59

60

DOES DDBD MAKE A DIFFERENCE?

•

Determining moment demand by elastic modal analysis is inappropriate, resulting in poor distributions of lateral strength;

•

Force-based design uses elastic stiffness which is not known at the start of the design. DDBD uses yield displacement or drift which IS known at the start of the design.

•

DDBD achieves a specified limit state at the design intensity (uniform risk); force-based design, at best, is bounded by the limit state, and vulnerability to damage is variable.

•

The design effort with DDBD is less than with force-based design.

ENG.PRI.0003.60

61

INFLUENCE OF SEISMIC INTENSITY ON DESIGN FORCES

Force-Based Design Displacement-Based Design

1

212 Z

ZVV bb 2

112 Z

ZTT ee , but22 /4 eee TmK

Hence:2

1

212

ZZKK ee

Hence:2

1

212

ZZVV BB

If Z2

= 0.5Z1

, Vb2

= 0.5Vb1 : Vb2

= 0.25Vb1

ENG.PRI.0003.61

62

BASE SHEAR AS FUNCTION OF BUILDING HEIGHT

• Assume shape function is linear (i.e. dual wall/frame)

• Assume story mass constant at m per storey.

• Effective mass:

me

= k1

nm

• Design displacement: d

= k2

n

• Effective period:

Te

= k3

d

= k2

k3

n

• Effective Stiffness: !Ke

= 42me

/Te2

= k4

m/n

• Base Shear: VB

= ke

d

= k4

m/n.k2

n = k5

m

•Thus base shear force is independent of building height (!)

Heff,1

Heff,2

m

m

m

m

m

m

m

m

m

VB1 VB2

d2

d1

(a) Building 1 (b) Building 2 (c) Design Displacements

ENG.PRI.0003.62

63

HA HB HC

C A

B

Force-Based Design Displacement-Based Design

Stiffness: prop. to 1/H3

prop. to 1/H

Shear Force: prop. to 1/H3

prop. to 1/H

Moments: prop. to 1/H2

equal

Rebar: prop. to 1/H2

equal

Ductility: equal (!)

prop. to 1/H2

BRIDGE COLUMNS OF UNEQUAL HEIGHT

` F Hc HA HB

ENG.PRI.0003.63

CONCLUSIONNew Zealand needs a measured and rational response to the Christchurch earthquake experience. A knee-

jerk band-aid repair to the existing force-based design approach is, in my view, inadequate.

Displacement-based design codes have been developed, and should be considered as a preferred alternative for NZ design.

ENG.PRI.0003.64