Torsion in buildings the Mexican research experience after the 1985 earthquake Gustavo Ayala

Torsion in buildings the Mexican research experience after the 1985 earthquake

Gustavo Ayala

TORSION

Causes No coincidence of acting and resisting forces in structures with asymmetric plan distibutions of masses, stiffnesses and/or strengths.

Kinematic effectsCoupling between lateral and rotational displacements of the levels.

Consequences Non-contemplated damage in asymmetric structures subjected intense earthquakes.

DAMAGE STATISTICS

19th SEPTEMBER 1985, MEXICO EARTHQUAKE

DESIGN PHYLOSOPHYTorsion DesignElastic models of single storey shear buildings. DESIGN RECOMMENDATIONS FOR TORSIONIt is formally accepted that under intense seismic events structural damage (non-linear behaviour) may occur.

SPATIAL VARIATION OF THE TORSION CENTRE IN MULTI-STOREY BUILDINGS WITH IN-PLAN AND ELEVATION ASYMMETRY ( SHEAR AND BENDING MODELS)

CENTRE OF TORSION The Centre of Torsion of a buuilding is defined as the loci on its levels or inter-storeys at which the seismic force or shear must be applied to produce only translations with no rotations

PARAMETERS WHICH DEFINE THE LOCATION OF THE CENTRE OF TORSION. Stiffness Location of the elements Distribution of lateral loads The CENTRE OF TORSION is not an INVARIANT

SHEAR MODELS

EXACT .

Infinite stiffnesses of beams Plane frames

TRADITIONAL.

Bending on beams Inter-storey stiffnesses of plane frames

THREE DIMENSIONAL MATRIX FORMULATION

LOCATION OF THE CENTRE OF TORSION

BUILDING MODELS 4 levels


Model

L ( m )

Cols. in black ( cm )

Cols. in white ( cm )

W( Ton / m2 )

I

5.0

60 x 60

40 x 40

0.8

II

5.0

40 x 40

60 x 60

1.0

III

5.0

40 x 40

40 x 40

0.8

Model

Cols. ( cm )

Wall

W ( Ton / m2 )

IV

60 x 60

Concrete, fc =200 kg/cm2, 8 cm thick

1.304 y 1.152

V

60 x 60

Masonry, f*m = 15 kg/cm2, 10 cm thick

1.304 y 1.152


Model

Brick wall, f*m = 15 kg/cm2, 15cm thick

Level 1to 14

Level 15

I

Entre Eje 1 - 2 y A B

690 kg/m2

450 kg/m2

II

Entre Eje 1 - 3 y A C

690 kg/m2

450 kg/m2

III

Entre Eje 1 - 5 y A E

690 kg/m2

450 kg/m2

IV

Entre Eje 1 - 7 y A G

690 kg/m2

450 kg/m2

Model

Concrete wall, fc = 250 kg/cm2, 15 cm thick

Level 1 to 14

Level 15

V

Entre Eje 1 - 2 y A B

690 kg/m2

450 kg/m2

VI

Entre Eje 1 - 3 y A C

690 kg/m2

450 kg/m2

VII

Entre Eje 1 - 4 y A D

690 kg/m2

450 kg/m2

VIII

Entre Eje 1 - 5 y A E

690 kg/m2

450 kg/m2

Location of the torsion centre4 levelsModel IModel II

Location of the torsion centre4 levelsModel IIIModel IV

Location of the torsion centre15 levels4 levelsModel VModel I

Location of the torsion centre15 levelsModel IIModel III

Location of the torsion centre15 levelsModel IVModel V

Location of the torsion centre15 levelsModel VIModel VII

Location of the torsion centre15 levelsModel VIII

INELASTIC TORSION

Parametric studies based on single storey models

Distribucin en planta de las rigideces y resistencias. Excentricidad esttica Relacin de aspecto de la planta Cociente Rr/ Rn Periodo fundamental de vibrar ( T ) Relacin de frecuencias desacopladas ( W ) Evaluacin del criterio de diseo por Torsin del RCDF BACKGROUND

BACKGROUND1 ) Gmez, Ayala and Jaramillo, 19872) Barrn, Ayala and Zapata, 1991

BACKGROUND3) Garca and Ayala, 19914) Zapata and Ayala,1993

Relationships of Maximum Ductility Ratios vs. Strength Distribution in shear models with resisting elements in two orthogonal directions.

SOME RESULTS OBTAINED FROMSINGLE STOREY MODELS

Relationships of Maximum Ductility Ratios vs. Strength DistributionSOME RESULTS OBTAINED FROMSINGLE STOREY MODELS

STUDY OF THE RESPONSE OF 3D BUILDING MODELS TORSIONALLY COUPLED

INVESTIGATED MODEL

CONSIDERED PARAMETERSMASS AND STIFFNESS ASYMMETRIC.DYNAMICA AMPLIFICATION FACTOR. FAdin = Mt Me

Design Eccentricity : ed1 = a es + b b ed2 = d es - b b

TYPES AND LEVELS OF STRUCTURAL ASYMMETRYMASS ASYMMETRIC MODELSSTIFFNESS ASYMMETRIC MODELSmean values

Eccentricity

Model I

Model II

Model III

Mass

0.10 b

0.15 b

0.20 b

Eccentricity

Model I

Model II

Model III

Stiffness

0.106 b

0.176 b

0.224 b

Symmetric ModelINSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)Model I Mass AsymmetricInterstorey 01

Symmetric ModelModel I Mass AsymmetricInterstorey 01INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

Model III Mass AsymmetricModel II Mass AsymmetricInterstorey 01INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

Modelo II Asimtrico en RigidezModelo I Asimtrico en RigidezInterstorey 01INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

Model III Stiffness AsymmetricInterstorey 01INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

SYMMETRIC MODELINSTANTANEOUS CENTRE OF STIFFNESS (CIR)Interstorey 01

MODEL I MASS ASYMMETRICInterstorey 01INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

MODEL II MASS ASYMMETRICInterstorey 01INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

MODEL III MASS ASYMMETRICInterstorey 01INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

MODEL I STIFFNESS ASYMMETRICInterstorey 01INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

MODEL II STIFFNESS ASYMMETRICInterstorey 01INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

MODEL III STIFFNESS ASYMMETRICInterstorey 01INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

SYMMETRIC MODELInterstorey 01SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

MODEL I MASS ASYMMETRICInterstorey 01SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

Interstorey 01MODEL II MASS ASYMMETRICSHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

Interstorey 01MODEL III MASS ASYMMETRICSHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

MODEL I STIFFNESS ASYMMETRICInterstorey 01SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

Interstorey 01MODEL II STIFFNESS ASYMMETRICSHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCTInterstorey 01MODEL III STIFFNESS ASYMMETRIC

DYNAMIC AMPLIFICATION FACTOR

Inelastic Dynamic Eccentricity ( e din )

MODEL

Interstorey

1

5

15

Symmetric

0.050 - 0.093b

0.036 - 0.067b

0.076 - 0.141b

Inelastic DynamicAmplification Factor ( FA din )

Mass asymmetric

Model I

2.09 - 3.89

1.38 - 2.56

1.25 - 2.33

Model II

1.02 - 1.89

0.99 - 1.83

0.87 - 1.62

Model III

1.06 - 1.97

0.82- 1.53

0.83 - 1.54

Siffness asymmetric

Model I

2.16 - 4.02

1.23 - 2.28

0.52 - 0.97

Model II

1.54 - 2.86

0.87 - 1.61

0.13 - 0.24

Model III

1.19 - 2.21

0.70 - 1.30

0.13 - 0.23

EEFECT OF FUNDAMENTAL PERIOD

STRUCTURAL MODELS Group 1 (Models 4 levels) Group 2 (Models 8 levels) Group 3 (Models 15 levels)

SIMTRICOS Y ASIMTRICOS EN MASAS

ASIMTRICOS EN RIGIDECES

STIFFNESS ASYMMETRIC

CONSIDERACIONES PARA EL ANLISIS NO LINEAL Se asume que los modelos poseen base rgidaSe desprecian los efectos P-DeltaSe asume que el sistema de piso es indeformable en su planoLas uniones viga-columna se suponen rgidasLa masa del nivel se supone concentrada en un punto (CM)La estructura no pierde su geometra inicial durante el anlisis y hasta antes del colapso Excitacin ssmica

BEHAVIOUR PARAMETERS

CIR (Instantaneous Stiffness Centre)

Centro instantneo de torsin de entrepiso obtenido en cada paso de anlisis

CICS (Instantaneous Sismic Shear Centre)

Es un punto que define la ubicacin en planta de la demanda de fuerza cortante en cada paso de anlisis.

SUCT (ltimate Shear - Torsion Surface)

Locus de las combinaciones de fuerza cortante y momento torsionante de entrepiso, que aplicadas estticamente a la estructura, producen su colapso.

RESULTSInterstorey 014 levelsMEM411MEM402CICSCIR

RESULTSInterstorey 014 levelsMEM402MEM411

Universidad Nacional Autnoma de MxicoPOR MI RAZA HABLARA EL ESPIRITU

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Torsion in buildings the Mexican research experience after the 1985 earthquake Gustavo Ayala