1

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

3 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.

4 DAMAGE STATISTICS 19th SEPTEMBER 1985, MEXICO EARTHQUAKE

5 DESIGN PHYLOSOPHY Torsion Design Elastic models of single storey shear buildings. DESIGN RECOMMENDATIONS FOR TORSION It is formally accepted that under intense seismic events structural damage (non-linear behaviour) may occur.

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

7 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“

8 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

9 BUILDING MODELS 4 levels

10 BUILDING MODELS 15 levels

11 BUILDING MODELS 4 levels

12 BUILDING MODELS 15 levels

13 Location of the torsion centre 4 levels Model I Model II

14 Location of the torsion centre 4 levels Model III Model IV

15 Location of the torsion centre 15 levels 4 levels Model V Model I

16 Location of the torsion centre 15 levels Model II Model III

17 Location of the torsion centre 15 levels Model IV Model V

18 Location of the torsion centre 15 levels Model VI Model VII

19 Location of the torsion centre 15 levels Model VIII

20 INELASTIC TORSION

21 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 BACKGROUND

22 1 ) Gómez, Ayala and Jaramillo, 1987 2) Barrón, Ayala and Zapata, 1991

23 BACKGROUND 3) García and Ayala, 1991 4) Zapata and Ayala,1993

24 Relationships of Maximum Ductility Ratios vs. Strength Distribution in shear models with resisting elements in two orthogonal directions. SOME RESULTS OBTAINED FROM SINGLE STOREY MODELS

25 Relationships of Maximum Ductility Ratios vs. Strength Distribution SOME RESULTS OBTAINED FROM SINGLE STOREY MODELS

26 STUDY OF THE RESPONSE OF 3D BUILDING MODELS TORSIONALLY COUPLED

27 INVESTIGATED MODEL

28 CONSIDERED PARAMETERS MASS AND STIFFNESS ASYMMETRIC. DYNAMICA AMPLIFICATION FACTOR. FA din = Mt Me Design Eccentricity : e d1 =  e s +  b e d2 =  e s -  b

29 MASS ASYMMETRIC MODELS TYPES AND LEVELS OF STRUCTURAL ASYMMETRY STIFFNESS ASYMMETRIC MODELS mean values

30 Symmetric Model INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS) Model I Mass Asymmetric Interstorey 01

31 Symmetric Model Model I Mass Asymmetric Interstorey 01 INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

32 Model III Mass Asymmetric Model II Mass Asymmetric Interstorey 01 INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

33 Modelo II Asimétrico en Rigidez Modelo I Asimétrico en Rigidez Interstorey 01 INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

34 Model III Stiffness Asymmetric Interstorey 01 INSTANTANEOUS CENTRE OF SEISMIC SHEAR (CICS)

35 SYMMETRIC MODEL INSTANTANEOUS CENTRE OF STIFFNESS (CIR) Interstorey 01

36 MODEL I MASS ASYMMETRIC Interstorey 01 INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

37 MODEL II MASS ASYMMETRIC Interstorey 01 INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

38 MODEL III MASS ASYMMETRIC Interstorey 01 INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

39 MODEL I STIFFNESS ASYMMETRIC Interstorey 01 INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

40 MODEL II STIFFNESS ASYMMETRIC Interstorey 01 INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

41 MODEL III STIFFNESS ASYMMETRIC Interstorey 01 INSTANTANEOUS CENTRE OF STIFFNESS (CIR)

42 SYMMETRIC MODEL Interstorey 01 SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

43 MODEL I MASS ASYMMETRIC Interstorey 01 SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

44 Interstorey 01 MODEL II MASS ASYMMETRIC SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

45 Interstorey 01 MODEL III MASS ASYMMETRIC SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

46 MODEL I STIFFNESS ASYMMETRIC Interstorey 01 SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

47 Interstorey 01 MODEL II STIFFNESS ASYMMETRIC SHEAR - TORSIONAL MOMENT HISTORY SUPERPOSED ON THE SUCT

48 Interstorey 01 MODEL III STIFFNESS ASYMMETRIC

49 DYNAMIC AMPLIFICATION FACTOR

50 EEFECT OF FUNDAMENTAL PERIOD

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

52 SIMÉTRICOS Y ASIMÉTRICOS EN MASAS

53 ASIMÉTRICOS EN RIGIDECES

54 STIFFNESS ASYMMETRIC

55 CONSIDERACIONES PARA EL ANÁLISIS NO LINEAL 4 4Se asume que los modelos poseen base rígida 4 4Se desprecian los efectos P-Delta 4 4Se asume que el sistema de piso es indeformable en su plano 4 4Las uniones viga-columna se suponen rígidas 4 4La masa del nivel se supone concentrada en un punto (CM) 4 4La estructura no pierde su geometría inicial durante el análisis y hasta antes del colapso 4 4 Excitación sísmica

56 * * 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. BEHAVIOUR PARAMETERS

57 RESULTS Interstorey 01 4 levels MEM411 MEM402 CICSCIR

58 RESULTS Interstorey 01 4 levels MEM402 MEM411

59 RESULTS Interstorey 01 8 levels MEM802 MEM822 CICS CIR

60 RESULTS Interstorey 01 8 levels MEM802 MEM822

61 RESULTS Interstorey 01 15 levels MEM1502 MEM1522 CICS CIR

62 RESULTS Interstorey 01 15 levels MEM1522MEM1502

63 Universidad Nacional Autónoma de México POR MI RAZA HABLARA EL ESPIRITU