BUILDING TORSION DUE TO EARTHQUAKES:RECENT DEVELOPMENTS

Keynote Lecture

S. A. Anagnostopoulos1 and M.T. Kyrkos2

The 5th National Conference on Earthquake Engineering and the 1st

National Conference on Earthquake Engineering and Seismology

BUILDING TORSION DUE TO EARTHQUAKES:RECENT DEVELOPMENTS

Keynote Lecture

S. A. Anagnostopoulos1 and M.T. Kyrkos2

1Professor, Dept. of Civil Engineering University of Patras,2Structural Engr. Ph.D., Attica Region, Athens,

CONTENTS-OBJECTIVES• Make a general introduction to the problem of earthquake

induced torsion in buildings, including its causes andrelated code provisions

• Review the pertinent literature and point out shortcomingsin many of the past studies as well as some contradictingresults and conclusions debated for many years

• Briefly discuss our research and results pertaining:(a) To improved design of asymmetric buildings for

uniform ductility demand distribution(b) To the code specified accidental design eccentricity

• Make a general introduction to the problem of earthquakeinduced torsion in buildings, including its causes andrelated code provisions

• Review the pertinent literature and point out shortcomingsin many of the past studies as well as some contradictingresults and conclusions debated for many years

• Briefly discuss our research and results pertaining:(a) To improved design of asymmetric buildings for

uniform ductility demand distribution(b) To the code specified accidental design eccentricity

PAST RESEARCH ACTIVITY

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PAST RESEARCH ACTIVITY

• The majority (~ 65%) of the pertinent published work isbased on simplified, one-story, shear-beam models

• About ~ 30% of the published work is based onsimplified, elastic multi-story models

• Very rare (< 5%) is the use of inelastic dynamicanalyses of realistic buildings modeled with detailedplastic hinge idealizations. (Yet the building responseunder design level earthquakes is always inelastic)

• The majority (~ 65%) of the pertinent published work isbased on simplified, one-story, shear-beam models

• About ~ 30% of the published work is based onsimplified, elastic multi-story models

• Very rare (< 5%) is the use of inelastic dynamicanalyses of realistic buildings modeled with detailedplastic hinge idealizations. (Yet the building responseunder design level earthquakes is always inelastic)

Causes of earthquake induced torsion in buildings

1. Non-symmetric arrangement of the load resistingelements (stiffness eccentricity) or non-symmetricdistribution of masses

2. Torsional motion in the ground caused by seismicwave passage and by ground motion incoherency

3. Other reasons that are not explicitly accounted for instructural design (stiffness of non-structural elementssuch as brick infill walls, non-symmetric yielding of theload resisting elements, etc.).

1. Non-symmetric arrangement of the load resistingelements (stiffness eccentricity) or non-symmetricdistribution of masses

2. Torsional motion in the ground caused by seismicwave passage and by ground motion incoherency

3. Other reasons that are not explicitly accounted for instructural design (stiffness of non-structural elementssuch as brick infill walls, non-symmetric yielding of theload resisting elements, etc.).

TORSION RELATED CLAUSES IN CODES

Regularity Criteria: Structural and geometrical

Torsional Sensitivity: Usually limits on dmax/davg

Accidental Eccentricity (eacc) Usually 0.05L ÷ 0.10L

Torsional effects Usually by moving masses by eaccor by applying a static torque

Amplification of static eccentricity Not any more

TORSION RELATED CLAUSES IN CODES

Regularity Criteria: Structural and geometrical

Torsional Sensitivity: Usually limits on dmax/davg

Accidental Eccentricity (eacc) Usually 0.05L ÷ 0.10L

Torsional effects Usually by moving masses by eaccor by applying a static torque

Amplification of static eccentricity Not any more

SIMPLIFIED, ONE-STORY SHEAR BEAM MODEL(The most general case used)

Ly

emy

esy

ey

CM

GC

x

yEL4

EL5

EL2

EL3EL1

MassEccentricity

εmx = emx / Lxεmy = emy / Ly

Lx

emxesx

ex

CR

EL6

StiffnessEccentricity

εsx = esx / Lxεsy = esy / Ly

Physicaleccentricities:

ex=esx+ emxey=esy+ emy

TYPES OF SIMPLIFIED, ONE-STORY MODELS USED

(a) (b) (c)(a) (b) (c)

(d) (e) (f)BidirectionalEccentricity

“STIFF” AND “FLEXIBLE” EDGES OF A NON SYMMETRICBUILDING (Meaningful only for static loadings)

Stiff edge: Displacement from translation and rotation aresubtracted

Flexible edge: Displacement from translation and rotationare added

Shear or Stiffnesscenter (CS or CR):Point through whicha lateral force willcause no rotation

Motion in Y direction

Shear or Stiffnesscenter (CS or CR):Point through whicha lateral force willcause no rotation

PROBLEMS OF THE SIMPLIFIED SHEAR-BEAMMODELS USED IN PAST STUDIES

1. They cannot match ALL the important properties forthe inelastic dynamic response of real, non-symmetric multistory buildings

2. Stiffness and strength of the resisting elements of theshear-beam model are typically specified andcalculated independently and only for seismic loads.In real buildings, stiffness and strength coming fromgravity loads and other design requirements lead tosignificant differences in relative strength andstiffness distributions.

1. They cannot match ALL the important properties forthe inelastic dynamic response of real, non-symmetric multistory buildings

2. Stiffness and strength of the resisting elements of theshear-beam model are typically specified andcalculated independently and only for seismic loads.In real buildings, stiffness and strength coming fromgravity loads and other design requirements lead tosignificant differences in relative strength andstiffness distributions.

3. Yielding of one element in the simplified model isequivalent to the formation of a mechanism in a framestory in real buildings, prevented in modern Codesthrough capacity design provisions.

4. Higher mode effects cannot be accounted for in thesimplified models

5. Incorrect extrapolation of conclusions to real buildings

3. Yielding of one element in the simplified model isequivalent to the formation of a mechanism in a framestory in real buildings, prevented in modern Codesthrough capacity design provisions.

4. Higher mode effects cannot be accounted for in thesimplified models

5. Incorrect extrapolation of conclusions to real buildings

CONSEQUENCES OF SUCH SHORTCOMINGS

• Contradictory results by different researchers• Persisting controversies – questionable results• Conclusions applicable ONLY to the very specific

models used and hence extrapolation to realbuildings is at best questionable• Little benefit from a very large volume of research

• Contradictory results by different researchers• Persisting controversies – questionable results• Conclusions applicable ONLY to the very specific

models used and hence extrapolation to realbuildings is at best questionable• Little benefit from a very large volume of research

CONTROVERCIES AND CONTRADICTING RESULTS

• Rutenberg, A. (1992) (review paper)“The picture emerging from the foregoing review is somewhatconfusing”…..“Several discrepancies and inconsistencies amonginvestigators have been reported in the preceding sections”.

• Chandler et al (1996) (review paper) … listed “ten areas of concernwhere the use of differing definitions or the making of divergingassumptions has resulted in a basic lack of agreement between theresults and conclusions of the research”.

• De Stefano, M. and Pintucchi, B. (2008) (review paper)“Many studies adopting more realistic multi-story models haveevidenced the shortcomings of simplified one-story models,especially in predicting qualitative features of inelastic response.”

• Rutenberg, A. (1992) (review paper)“The picture emerging from the foregoing review is somewhatconfusing”…..“Several discrepancies and inconsistencies amonginvestigators have been reported in the preceding sections”.

• Chandler et al (1996) (review paper) … listed “ten areas of concernwhere the use of differing definitions or the making of divergingassumptions has resulted in a basic lack of agreement between theresults and conclusions of the research”.

• De Stefano, M. and Pintucchi, B. (2008) (review paper)“Many studies adopting more realistic multi-story models haveevidenced the shortcomings of simplified one-story models,especially in predicting qualitative features of inelastic response.”

Classic example:

For code designed buildings, which of the two edges, thestiff or the flexible is the critical one?? (where criticalmeans “ penalized most due to torsion”, in terms ofductility demands)

Conclusions divided between the two optionswhile in some papers the answer is parameter

dependent !!!

Classic example:

For code designed buildings, which of the two edges, thestiff or the flexible is the critical one?? (where criticalmeans “ penalized most due to torsion”, in terms ofductility demands)

Conclusions divided between the two optionswhile in some papers the answer is parameter

dependent !!!

OUR VIEW1. Problem complexity - many parameters2. Failure or unwillingness of most authors to

recognize the problems and shortcomings oftheir oversimplified 1-story shear beammodel (1ST-INSB)

3. Failure of most authors to clearly state thattheir results were applicable ONLY to thespecific models used and subject to theunderlying assumptions. Instead, unjustifiedgeneralizations were made.

1. Problem complexity - many parameters2. Failure or unwillingness of most authors to

recognize the problems and shortcomings oftheir oversimplified 1-story shear beammodel (1ST-INSB)

3. Failure of most authors to clearly state thattheir results were applicable ONLY to thespecific models used and subject to theunderlying assumptions. Instead, unjustifiedgeneralizations were made.

GC

CR

x

y

CM

Ly=12m

Lx=18m

ey

ex

1 2 3 4

6 7 8

9 10 11 12

5

FR1 FR2 FR3

FR4

FR5

FR6

ANSWER TO THE CRITICAL ELEMENT CONTROVERSY

3-STORY, PH MODEL 1-STORY, SHEAR BEAM MODEL3-STORY, PH MODEL 1-STORY, SHEAR BEAM MODEL

ELEMENT PROPERTIES DETERMINATION FOR THE 1ST-INSB MODEL

BUILDINGS WITH PLASTIC HINGE IDEALIZATION

Type: one, three and five-story reinforced concretebuildings (fundamental period: 0.30s < Τ < 1.32s)

Design: according to EC2 and EC8 and also UBC97(equiv. static and dynamic response spectrumanalysis)

Idealization: each member is idealized with theplastic hinge model

Analysis: inelastic, time-history for groups of earthquakemotions matching the design spectrum

Basic Parameter: Biaxial eccentricities 0.0 , 0.10 , 0.20 , 0.30

Type: one, three and five-story reinforced concretebuildings (fundamental period: 0.30s < Τ < 1.32s)

Design: according to EC2 and EC8 and also UBC97(equiv. static and dynamic response spectrumanalysis)

Idealization: each member is idealized with theplastic hinge model

Analysis: inelastic, time-history for groups of earthquakemotions matching the design spectrum

Basic Parameter: Biaxial eccentricities 0.0 , 0.10 , 0.20 , 0.30

3-St. Bldg/ Beams / Dir. y : -------- Frame 1 (“stiff” side), -------- Frame 3 (“flexible” side)

ROTATIONAL DUCTILITY FACTORS BEAMS,3 – STORY, PH MODEL : (Results for x and y directions)

3-St. Bldg / Beams / Dir x : -------- Frame 6 (“stiff” side), -------- Frame 4 (“flexible” side)

ROTATIONAL DUCTILITY FACTORS BEAMS,5 – STORY, PH MODEL : (Results for x and y directions)

5-St. Bldg/ Beams / Dir. y : -------- Frame 1 (“stiff” side), -------- Frame 3 (“flexible” side)

5-St. Bldg / Beams / Dir x : -------- Frame 6 (“stiff” side), -------- Frame 4 (“flexible” side)

DERIVATION OF PROPERTIES OF THE SIMPLIFIED MODELS

1. MODEL SIMP1 : MATCHES PROPERTIES OF REAL BUILDING(From the properties of the PH models)

3 Lowest periods, element stiffnesses AND element strengthsStrengths from ALL loading conditions

2. MODEL SIMP3 ( Design only for earthquake, as typically

done in the past)

Identical to SIMP1 except that element strengths determinedas done in the past from earthquake loading only

1. MODEL SIMP1 : MATCHES PROPERTIES OF REAL BUILDING(From the properties of the PH models)

3 Lowest periods, element stiffnesses AND element strengthsStrengths from ALL loading conditions

2. MODEL SIMP3 ( Design only for earthquake, as typically

done in the past)

Identical to SIMP1 except that element strengths determinedas done in the past from earthquake loading only

DUCTILITY FACTOR COMPARISONS: PH, SIMP1, SIMP3 MODELS

3 story _ P-H model_Displ. Ductilities

1,000

1,300

1,600

1,900

0,00 0,10 0,20 0,30ε=e/L

Duc

tiliti

es

Fr1 (Stif f side) Fr3 (Flex side)3 story _ P-H model_Displ. Ductilities

0,500

0,800

1,100

1,400

1,700

2,000

0,00 0,10 0,20 0,30ε=e/L

Duc

tiliti

es

Fr6 (Stif f side) Fr4 (Flex side)

3 story _ SIMP1 model

0,00

0,50

1,001,50

2,00

2,50

3,00

0,00 0,10 0,20 0,30ε=e/L

Duc

tility

Fr1 (Stif f side) Fr3 (Flex side)3 story _ SIMP1 model

0,00

0,50

1,001,50

2,00

2,50

3,00

0,00 0,10 0,20 0,30ε=e/L

Duc

tility

Fr6 (Stif f side) Fr4 (Flex side)

Y-DIRECTION X-DIRECTION

3 story _ SIMP1 model

0,00

0,50

1,001,50

2,00

2,50

3,00

0,00 0,10 0,20 0,30ε=e/L

Duc

tility

Fr1 (Stif f side) Fr3 (Flex side)3 story _ SIMP1 model

0,00

0,50

1,001,50

2,00

2,50

3,00

0,00 0,10 0,20 0,30ε=e/L

Duc

tility

Fr6 (Stif f side) Fr4 (Flex side)

3 story _ SIMP3 model_eacc=0.05

1,00

1,50

2,00

2,50

3,00

3,50

0,00 0,10 0,20 0,30ε=e/L

Duc

tility

Fr1 (Stif f side) Fr3 (Flex side)3 story _ SIMP3 model_eacc=0.05

1,00

1,50

2,00

2,50

3,00

3,50

0,00 0,10 0,20 0,30ε=e/L

Duc

tility

Fr6 (Stif f side) Fr4 (Flex side)

ANSWER TO THE CONTROVERSY

• For code designed eccentric structures the“flexible” edge of is penalized more by strongearthquakes due to torsion• The oversimplified one-story model can only

predict the correct trends ONLY if its 3periods, element stiffness AND strengthsmatch those of the real buildings

• For code designed eccentric structures the“flexible” edge of is penalized more by strongearthquakes due to torsion• The oversimplified one-story model can only

predict the correct trends ONLY if its 3periods, element stiffness AND strengthsmatch those of the real buildings

DUCTILITY DEMAND DISTRUBUTION INCODE DESIGNED REAL BUILDINGS AND

PROPOSED IMPROVEMENT

LAYOUT OF IRREGULAR BUILDINGS EXAMINED

TORSIONALLY STIFF

TORSIONALLY FLEXIBLE

LAYOUT OF 3-STORY IRREGULAR STEEL BUILDINGS

TORSIONALLY STIFF

TORSIONALLY FLEXIBLE(Uniformly distributed masses)TORSIONALLY FLEXIBLE(Uniformly distributed masses)

DETAILED , REALISTIC PLASTIC HINGE MODEL OF ABUILDING AND NON LINEAR MEMBER BEHAVIOR

y

M1

p M

y

ΔΜμ=1+p.Μ

M-θ Relationship and interaction diagramof Beam-Column members

F-δ relationship for bracing members

plu

y

u1

u

DESIGN AND MEAN SPECTRUMOF 10 SEMI-ARTIFICIAL MOTIONS

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.00 1.00 2.00 3.00 4.00 5.00

Period (sec)

Spec

tral A

ccel

erat

ion

(g) MEAN

EC8, Ag,max=0.24g

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.00 1.00 2.00 3.00 4.00 5.00

Period (sec)

Spec

tral A

ccel

erat

ion

(g) MEAN

EC8, Ag,max=0.24g

Modification procedure for torsionally stiff& flexible buildings

uy,stiff = top story displacement of the “stiff” edgeuy,flex = top story displacement of the “flexible” edgeuyO = mean story displacement

(computed by equivalent static method)

yo

stiffystiffy u

uf ,

, yo

flexyflexy u

uf ,

,

EFFECTS OF DESIGN MODIFICATIONS ON ECCENTRICITIES(Buildings with initial mass eccentricity εm=0.20)

TorsionallySTIFF

TorsionallyFLEXIBLE

MEAN NATURAL ECCENTRICITYINITIAL DESIGN MODIFIED DESIGN

εx εy εx εyTorsionallySTIFF

0.115 0.135 0.04 0.05

TorsionallyFLEXIBLE

0.165 0.145 0.10 0.10

TorsionallyFLEXIBLE

MODIFIED TORSIONALLY STIFF BUILDINGInitial mass eccentricity εm=0.20

DIRECTION X DIRECTION YAXIAL STRAIN DUCTILITY FACTOR IN BRACES

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ryFlex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

ROTATIONAL DUCTILITY FACTORS IN BEAMS

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ryFlex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2Rotational ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3Rotational ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

MODIFIED TORSIONALLY FLEXIBLE BUILDINGInitial mass eccentricity εm=0.20

DIRECTION X DIRECTION Y

AXIAL STRAIN DUCTILITY FACTOR IN BRACES

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ryFlex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

ROTATIONAL DUCTILITY FACTORS IN BEAMS

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ryFlex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3 4Axial strain ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3Rotational ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

1

2

3

1 2 3Rotational ductility factor

Sto

ry

Flex-mod Stiff-modFlex-init Stiff-init

ACCIDENTAL DESIGN ECCENTRICITY

THREE AND FIVE-STORYFRAME TYPE BUILDINGS

GC

CR

x

y

CM

Ly=12m

Lx=18m

ey

ex

1 2 3 4

6 7 8

9 10 11 12

5

FR1 FR2 FR3

FR4

FR5

FR6

• frame type buildings with plastic hinge idealization• simultaneous biaxial mass and stiffness eccentricity

ey

ex

CM

GCCR

x

y

Ly=15m

Lx=21m

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

FR1 FR2 FR3

FR6

FR5

FR4

GC

CR

x

y

CM

Ly=12m

Lx=18m

ey

ex

1 2 3 4

6 7 8

9 10 11 12

5

FR1 FR2 FR3

FR4

FR5

FR6

ey

ex

CM

GCCR

x

y

Ly=15m

Lx=21m

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

FR1 FR2 FR3

FR6

FR5

FR4

3-STORY 5-STORY

PARAMETRIC ANALYSES

Variants of the 3 and 5-story buildings which are analysedwith accidental eccentricity: ± 5%

Original-physicalmass eccentricity

Inelastic analysismass eccentricity

Original-physicalmass eccentricity

Inelastic analysismass eccentricity

εm εm,1 εm,0 εm,2

0.00 -0.05 0.00 0.05

0.10 0.05 0.10 0.15

0.20 0.15 0.20 0.25

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

Design: e = 0.00L+/-eaccAnalyzed variants:

ε=0.00 : __________

ε=0.05 : ___ __O__ ___

eacc=0.00

Design: e = 0.20L+/-eaccAnalyzed variants:ε=0.15 : _ _ __ _ _

ε=0.20 : __________

ε=0.25 : ___ __O__ ___

Design: e = 0.10L+/-eaccAnalyzed variants:ε=0.05 : _ _ __ _ _

ε=0.10 : __________

ε=0.15 : ___ __O__ ___

DUCTILITY FACTORS FOR THE BEAMS OF THETHE 5-STORY BUILDINGS, STIFF SIDE (Fr1, Dir-y)

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'St if f 'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

eacc=0.05L

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00 6.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00 6.00 7.00

Design: e = 0.00L+/-eaccAnalyzed variants:

ε=0.00 : __________

ε=0.05 : ___ __O__ ___

eacc=0.00

Design: e = 0.20L+/-eaccAnalyzed variants:ε=0.15 : _ _ __ _ _

ε=0.20 : __________

ε=0.25 : ___ __O__ ___

Design: e = 0.10L+/-eaccAnalyzed variants:ε=0.05 : _ _ __ _ _

ε=0.10 : __________

ε=0.15 : ___ __O__ ___

DUCTILITY FACTORS FOR THE BEAMS OF THETHE 5-STORY BUILDINGS, FLEXIBLE SIDE (Fr3, Dir-y)

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00 6.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00 6.00 7.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00 6.00

'Flex'side

1

2

3

4

5

1.00 2.00 3.00 4.00 5.00 6.00 7.00

eacc=0.05L

CONCLUSIONS• The many conflicting conclusions and controversies in

past publications are due to the failure of many authorsto recognize the shortcomings of their over-simplifiedmodels and from unjustified generalizations orextensions of their conclusions to real buildings

• Simplified one-story models can provide usefulqualitative results ONLY when their properties arerationally selected to match most of the basicproperties of actual buildings

• The many conflicting conclusions and controversies inpast publications are due to the failure of many authorsto recognize the shortcomings of their over-simplifiedmodels and from unjustified generalizations orextensions of their conclusions to real buildings

• Simplified one-story models can provide usefulqualitative results ONLY when their properties arerationally selected to match most of the basicproperties of actual buildings

CONCLUSIONS (Cont.)

• When asymmetric buildings, designed according toEC8, are subjected to strong earthquake motions,the ductility demands at the “flexible” edges aresubstantially and consistently greater than those atthe “stiff” edges

• A simple, one step design modification has beenproposed, improving the building’s seismicperformance significantly. This suggests that a codeimprovement is possible.

• When asymmetric buildings, designed according toEC8, are subjected to strong earthquake motions,the ductility demands at the “flexible” edges aresubstantially and consistently greater than those atthe “stiff” edges

• A simple, one step design modification has beenproposed, improving the building’s seismicperformance significantly. This suggests that a codeimprovement is possible.

CONCLUSIONS (Cont.)

• The accidental design eccentricity is not veryeffective in reducing ductility demands inasymmetric frame type buildings. In fact, in somebuilding locations the designs with zero accidentaleccentricity exhibited ductility demands, less thanthose with accidental eccentricity.

• These findings suggest that accidental eccentricityprovisions in codes, should be re-examined, in viewof the great additional computational requirementsthey impose on designers

• The accidental design eccentricity is not veryeffective in reducing ductility demands inasymmetric frame type buildings. In fact, in somebuilding locations the designs with zero accidentaleccentricity exhibited ductility demands, less thanthose with accidental eccentricity.

• These findings suggest that accidental eccentricityprovisions in codes, should be re-examined, in viewof the great additional computational requirementsthey impose on designers

THANK YOU FOR YOURATTENTION

THANK YOU FOR YOURATTENTION