Sin ttulo de diapositiva

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

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TORSION

• Causes
• No coincidence of acting and resisting forces in
  structures with asymmetric plan distibutions of
  masses, stiffnesses and/or strengths.
• Kinematic effects
• Coupling between lateral and rotational
  displacements of the levels.
• Consequences
• Non-contemplated damage in asymmetric structures
  subjected intense earthquakes.

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DAMAGE STATISTICS
19th SEPTEMBER 1985, MEXICO EARTHQUAKE
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Torsion Design
DESIGN RECOMMENDATIONS FOR TORSION
Elastic models of single storey shear buildings.
DESIGN PHYLOSOPHY
It is formally accepted that under intense
seismic events structural damage (non-linear
behaviour) may occur.
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SPATIAL VARIATION OF THE TORSION CENTRE IN
MULTI-STOREY BUILDINGS WITH IN-PLAN AND ELEVATION
ASYMMETRY ( SHEAR AND BENDING MODELS)
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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
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LOCATION OF THE CENTRE OF TORSION

• SHEAR MODELS
• EXACT .
• Infinite stiffnesses of beams
• Plane frames
• TRADITIONAL.
• Bending on beams
• Inter-storey stiffnesses of plane frames
• THREE DIMENSIONAL MATRIX FORMULATION

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BUILDING MODELS
4 levels
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BUILDING MODELS
15 levels
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BUILDING MODELS
4 levels
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BUILDING MODELS
15 levels
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Location of the torsion centre
4 levels
Model I
Model II
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Location of the torsion centre
4 levels
Model III
Model IV
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Location of the torsion centre
15 levels
4 levels
Model V
Model I
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Location of the torsion centre
15 levels
Model II
Model III
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Location of the torsion centre
15 levels
Model IV
Model V
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Location of the torsion centre
15 levels
Model VI
Model VII
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Location of the torsion centre
15 levels
Model VIII
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INELASTIC TORSION
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BACKGROUND

• Parametric studies based on single storey models
• Distribución en planta de las rigideces y
  resistencias.
• Excentricidad estática
• Relación de aspecto de la planta
• Cociente Rr/ Rn
• Periodo fundamental de vibrar ( T )
• Relación de frecuencias desacopladas ( W )
• Evaluación del criterio de diseño por Torsión
  del RCDF

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BACKGROUND
1 ) Gómez, Ayala and Jaramillo, 1987 2) Barrón,
Ayala and Zapata, 1991
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BACKGROUND
3) García and Ayala, 1991 4) Zapata and Ayala,1993
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SOME RESULTS OBTAINED FROMSINGLE STOREY MODELS

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

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SOME RESULTS OBTAINED FROMSINGLE STOREY MODELS
Relationships of Maximum Ductility Ratios vs.
Strength Distribution
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STUDY OF THE RESPONSE OF 3D BUILDING MODELS
TORSIONALLY COUPLED
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INVESTIGATED MODEL
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CONSIDERED PARAMETERS

• MASS AND STIFFNESS ASYMMETRIC.

• DYNAMICA AMPLIFICATION FACTOR. FAdin Mt
• 
  Me
• Design Eccentricity ed1 a es b b
  ed2 d es - b b

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TYPES AND LEVELS OF STRUCTURAL ASYMMETRY
MASS ASYMMETRIC MODELS
STIFFNESS ASYMMETRIC MODELS
mean values
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INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)
Symmetric Model
Model I Mass Asymmetric
Interstorey 01
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INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)
Symmetric Model
Model I Mass Asymmetric
Interstorey 01
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INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)
Model III Mass Asymmetric
Model II Mass Asymmetric
Interstorey 01
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INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)
Interstorey 01
Modelo II Asimétrico en Rigidez
Modelo I Asimétrico en Rigidez
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INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)
Model III Stiffness Asymmetric
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
SYMMETRIC MODEL
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
MODEL I MASS ASYMMETRIC
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
MODEL II MASS ASYMMETRIC
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
MODEL III MASS ASYMMETRIC
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
MODEL I STIFFNESS ASYMMETRIC
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
MODEL II STIFFNESS ASYMMETRIC
Interstorey 01
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INSTANTANEOUS CENTRE OF STIFFNESS (CIR)
MODEL III STIFFNESS ASYMMETRIC
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
SYMMETRIC MODEL
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
MODEL I MASS ASYMMETRIC
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
MODEL II MASS ASYMMETRIC
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
MODEL III MASS ASYMMETRIC
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
MODEL I STIFFNESS ASYMMETRIC
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
MODEL II STIFFNESS ASYMMETRIC
Interstorey 01
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SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON
THE SUCT
MODEL III STIFFNESS ASYMMETRIC
Interstorey 01
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DYNAMIC AMPLIFICATION FACTOR
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EEFECT OF FUNDAMENTAL PERIOD
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STRUCTURAL MODELS

• Group 1 (Models 4 levels)
• Group 2 (Models 8 levels)
• Group 3 (Models 15 levels)

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SIMÉTRICOS Y ASIMÉTRICOS EN MASAS
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ASIMÉTRICOS EN RIGIDECES
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STIFFNESS ASYMMETRIC
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CONSIDERACIONES PARA EL ANÁLISIS NO LINEAL

• Se asume que los modelos poseen base rígida
• Se desprecian los efectos P-Delta
• Se asume que el sistema de piso es indeformable
  en su plano
• Las uniones viga-columna se suponen rígidas
• La masa del nivel se supone concentrada en un
  punto (CM)
• La estructura no pierde su geometría inicial
  durante el análisis y hasta antes del colapso
• Excitación sísmica

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BEHAVIOUR PARAMETERS

• CIR (Instantaneous Stiffness Centre)
• Centro instantáneo de torsión de entrepiso
  obtenido en cada paso de análisis
• CICS (Instantaneous Sismic Shear Centre)
• Es un punto que define la ubicación en planta de
  la demanda de fuerza cortante en cada paso de
  análisis.
• SUCT (Últimate Shear - Torsion Surface)
• Locus de las combinaciones de fuerza cortante y
  momento torsionante de entrepiso, que aplicadas
  estáticamente a la estructura, producen su
  colapso.

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RESULTS
CICS
CIR
MEM402
Interstorey 01 4 levels
MEM411
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RESULTS
MEM411
MEM402
Interstorey 01 4 levels
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RESULTS
MEM802
CICS
CIR
Interstorey 01 8 levels
MEM822
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RESULTS
MEM802
MEM822
Interstorey 01 8 levels
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RESULTS
CICS
MEM1502
CIR
Interstorey 01 15 levels
MEM1522
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RESULTS
MEM1522
MEM1502
Interstorey 01 15 levels
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Thank you
Universidad Nacional Autónoma de México
POR MI RAZA HABLARA EL ESPIRITU