Presentation is loading. Please wait.

Presentation is loading. Please wait.

Nonlinear Analysis & Performance Based Design. CALCULATED vs MEASURED.

Similar presentations


Presentation on theme: "Nonlinear Analysis & Performance Based Design. CALCULATED vs MEASURED."— Presentation transcript:

1 Nonlinear Analysis & Performance Based Design

2

3 CALCULATED vs MEASURED

4 Nonlinear Analysis & Performance Based Design ENERGY DISSIPATION

5 Nonlinear Analysis & Performance Based Design

6

7

8 IMPLICIT NONLINEAR BEHAVIOR

9 Nonlinear Analysis & Performance Based Design STEEL STRESS STRAIN RELATIONSHIPS

10 Nonlinear Analysis & Performance Based Design INELASTIC WORK DONE!

11 Nonlinear Analysis & Performance Based Design CAPACITY DESIGN STRONG COLUMNS & WEAK BEAMS IN FRAMES REDUCED BEAM SECTIONS LINK BEAMS IN ECCENTRICALLY BRACED FRAMES BUCKLING RESISTANT BRACES AS FUSES RUBBER-LEAD BASE ISOLATORS HINGED BRIDGE COLUMNS HINGES AT THE BASE LEVEL OF SHEAR WALLS ROCKING FOUNDATIONS OVERDESIGNED COUPLING BEAMS OTHER SACRIFICIAL ELEMENTS

12 Nonlinear Analysis & Performance Based Design STRUCTURAL COMPONENTS

13 Nonlinear Analysis & Performance Based Design MOMENT ROTATION RELATIONSHIP

14 Nonlinear Analysis & Performance Based Design IDEALIZED MOMENT ROTATION

15 Nonlinear Analysis & Performance Based Design PERFORMANCE LEVELS

16 Nonlinear Analysis & Performance Based Design IDEALIZED FORCE DEFORMATION CURVE

17 Nonlinear Analysis & Performance Based Design 17 ASCE 41 BEAM MODEL

18 Nonlinear Analysis & Performance Based Design Linear Static Analysis Linear Dynamic Analysis (Response Spectrum or Time History Analysis) Nonlinear Static Analysis (Pushover Analysis) Nonlinear Dynamic Time History Analysis (NDI or FNA) ASCE 41 ASSESSMENT OPTIONS

19 Nonlinear Analysis & Performance Based Design ELASTIC STRENGTH DESIGN - KEY STEPS CHOSE DESIGN CODE AND EARTHQUAKE LOADS DESIGN CHECK PARAMETERS STRESS/BEAM MOMENT GET ALLOWABLE STRESSES/ULTIMATE– PHI FACTORS CALCULATE STRESSES – LOAD FACTORS (ST RS TH) CALCULATE STRESS RATIOS INELASTIC DEFORMATION BASED DESIGN -- KEY STEPS CHOSE PERFORMANCE LEVEL AND DESIGN LOADS – ASCE 41 DEMAND CAPACITY MEASURES – DRIFT/HINGE ROTATION/SHEAR GET DEFORMATION AND FORCE CAPACITIES CALCULATE DEFORMATION AND FORCE DEMANDS (RS OR TH) CALCULATE D/C RATIOS – LIMIT STATES STRENGTH vs DEFORMATION

20 Nonlinear Analysis & Performance Based Design STRUCTURE and MEMBERS For a structure, F = load, D = deflection. For a component, F depends on the component type, D is the corresponding deformation. The component F-D relationships must be known. The structure F-D relationship is obtained by structural analysis.

21 Nonlinear Analysis & Performance Based Design FRAME COMPONENTS For each component type we need : Reasonably accurate nonlinear F-D relationships. Reasonable deformation and/or strength capacities. We must choose realistic demand-capacity measures, and it must be feasible to calculate the demand values. The best model is the simplest model that will do the job.

22 Nonlinear Analysis & Performance Based Design F-D RELATIONSHIP

23 Nonlinear Analysis & Performance Based Design LATERAL LOAD Partially Ductile Brittle Ductile DRIFT DUCTILITY

24 Nonlinear Analysis & Performance Based Design ASCE 41 - DUCTILE AND BRITTLE

25 Nonlinear Analysis & Performance Based Design FORCE AND DEFORMATION CONTROL

26 Nonlinear Analysis & Performance Based Design BACKBONE CURVE

27 Nonlinear Analysis & Performance Based Design HYSTERESIS LOOP MODELS

28 Nonlinear Analysis & Performance Based Design STRENGTH DEGRADATION

29 Nonlinear Analysis & Performance Based Design ASCE 41 DEFORMATION CAPACITIES This can be used for components of all types. It can be used if experimental results are available. ASCE 41 gives capacities for many different components. For beams and columns, ASCE 41 gives capacities only for the chord rotation model.

30 Nonlinear Analysis & Performance Based Design BEAM END ROTATION MODEL

31 Nonlinear Analysis & Performance Based Design PLASTIC HINGE MODEL It is assumed that all inelastic deformation is concentrated in zero- length plastic hinges. The deformation measure for D/C is hinge rotation.

32 Nonlinear Analysis & Performance Based Design PLASTIC ZONE MODEL The inelastic behavior occurs in finite length plastic zones. Actual plastic zones usually change length, but models that have variable lengths are too complex. The deformation measure for D/C can be : - Average curvature in plastic zone. - Rotation over plastic zone ( = average curvature x plastic zone length).

33 Nonlinear Analysis & Performance Based Design ASCE 41 CHORD ROTATION CAPACITIES IOLSCP Steel Beam p / y = 1 p / y = 6 p / y = 8 RC Beam Low shear High shear p = 0.01 p = p = 0.02 p = 0.01 p = p = 0.02

34 Nonlinear Analysis & Performance Based Design COLUMN AXIAL-BENDING MODEL

35 Nonlinear Analysis & Performance Based Design STEEL COLUMN AXIAL-BENDING

36 Nonlinear Analysis & Performance Based Design CONCRETE COLUMN AXIAL-BENDING

37 Nonlinear Analysis & Performance Based Design SHEAR HINGE MODEL

38 Nonlinear Analysis & Performance Based Design PANEL ZONE ELEMENT Deformation, D = spring rotation = shear strain in panel zone. Force, F = moment in spring = moment transferred from beam to column elements. Also, F = (panel zone horizontal shear force) x (beam depth).

39 Nonlinear Analysis & Performance Based Design BUCKLING-RESTRAINED BRACE The BRB element includes isotropic hardening. The D-C measure is axial deformation.

40 Nonlinear Analysis & Performance Based Design BEAM/COLUMN FIBER MODEL The cross section is represented by a number of uni-axial fibers. The M- relationship follows from the fiber properties, areas and locations. Stress-strain relationships reflect the effects of confinement

41 Nonlinear Analysis & Performance Based Design WALL FIBER MODEL

42 Nonlinear Analysis & Performance Based Design ALTERNATIVE MEASURE - STRAIN

43 Nonlinear Analysis & Performance Based Design ƒ ƒ u u 1 2 iteration NEWTON – RAPHSON ITERATION ƒ ƒ u u 12 iteration CONSTANT STIFFNESS ITERATION NONLINEAR SOLUTION SCHEMES

44 Nonlinear Analysis & Performance Based Design Y +Y -Y 0 Radius, R CIRCULAR FREQUENCY

45 Nonlinear Analysis & Performance Based Design u. t u t1... Slope = u t1.. t1t1 u t1t1 t Slope = u t1. u u t1.. t1t1 t THE D, V & A RELATIONSHIP

46 Nonlinear Analysis & Performance Based Design UNDAMPED FREE VIBRATION )cos( 0 tuu t 0 ukum m k where

47 Nonlinear Analysis & Performance Based Design RESPONSE MAXIMA u t )cos( 0 tu )cos( 0 2 tu u t )sin( 0 tu u t max 2 u max u

48 Nonlinear Analysis & Performance Based Design BASIC DYNAMICS WITH DAMPING g uuuu 2 2 g uMKuuCuM uC t uM 0 g u M K C

49 Nonlinear Analysis & Performance Based Design ug.. 2 ug2ug2 ug1ug1 1 t1t1 t2t2 Time t ABtu g u u u 2 2 RESPONSE FROM GROUND MOTION

50 Nonlinear Analysis & Performance Based Design DAMPED RESPONSE

51 Nonlinear Analysis & Performance Based Design SDOF DAMPED RESPONSE

52 Nonlinear Analysis & Performance Based Design RESPONSE SPECTRUM GENERATION TIME, SECONDS GROUND ACC, g Earthquake Record Displacement Response Spectrum 5% damping DISPL, in DISPL, in PERIOD, Seconds DISPLACEMENT, inches T= 0.6 sec T= 2.0 sec

53 Nonlinear Analysis & Performance Based Design SPECTRAL PARAMETERS

54 Nonlinear Analysis & Performance Based Design THE ADRS SPECTRUM ADRS Curve Spectral Displacement, Sd Spectral Acceleration, Sa 2.0 Seconds 1.0 Seconds 0.5 Seconds Period, T Spectral Acceleration, Sa RS Curve 0.5 Seconds1.0 Seconds2.0 Seconds

55 Nonlinear Analysis & Performance Based Design THE ADRS SPECTRUM

56 Nonlinear Analysis & Performance Based Design ASCE 7 RESPONSE SPECTRUM

57 Nonlinear Analysis & Performance Based Design PUSHOVER

58 Nonlinear Analysis & Performance Based Design THE LINEAR PUSHOVER

59 Nonlinear Analysis & Performance Based Design EQUIVALENT LINEARIZATION How far to push? The Target Point!

60 Nonlinear Analysis & Performance Based Design DISPLACEMENT MODIFICATION

61 Nonlinear Analysis & Performance Based Design Calculating the Target Displacement DISPLACEMENT MODIFICATION C 0 Relates spectral to roof displacement C 1 Modifier for inelastic displacement C 2 Modifier for hysteresis loop shape C 0 C 1 C 2 S a T e 2 / 2

62 Nonlinear Analysis & Performance Based Design LOAD CONTROL AND DISPLACEMENT CONTROL

63 Nonlinear Analysis & Performance Based Design P-DELTA ANALYSIS

64 Nonlinear Analysis & Performance Based Design P-DELTA DEGRADES STRENGTH

65 Nonlinear Analysis & Performance Based Design P-DELTA EFFECTS ON F-D CURVES

66 Nonlinear Analysis & Performance Based Design THE FAST NONLINEAR ANALYSIS METHOD (FNA) NON LINEAR FRAME AND SHEAR WALL HINGES BASE ISOLATORS (RUBBER & FRICTION) STRUCTURAL DAMPERS STRUCTURAL UPLIFT STRUCTURAL POUNDING BUCKLING RESTRAINED BRACES

67 Nonlinear Analysis & Performance Based Design RITZ VECTORS

68 Nonlinear Analysis & Performance Based Design FNA KEY POINT The Ritz modes generated by the nonlinear deformation loads are used to modify the basic structural modes whenever the nonlinear elements go nonlinear.

69 Nonlinear Analysis & Performance Based Design CREATING HISTORIES TO MATCH A SPECTRUM FREQUENCY CONTENTS OF EARTHQUAKES FOURIER TRANSFORMS ARTIFICIAL EARTHQUAKES

70 Nonlinear Analysis & Performance Based Design ARTIFICIAL EARTHQUAKES

71 Nonlinear Analysis & Performance Based Design 71 MESH REFINEMENT

72 Nonlinear Analysis & Performance Based Design 72 This is for a coupling beam. A slender pier is similar. APPROXIMATING BENDING BEHAVIOR

73 Nonlinear Analysis & Performance Based Design 73 ACCURACY OF MESH REFINEMENT

74 Nonlinear Analysis & Performance Based Design 74 PIER / SPANDREL MODELS

75 Nonlinear Analysis & Performance Based Design 75 STRAIN & ROTATION MEASURES

76 Nonlinear Analysis & Performance Based Design 76 Compare calculated strains and rotations for the 3 cases. STRAIN CONCENTRATION STUDY

77 Nonlinear Analysis & Performance Based Design 77 The strain over the story height is insensitive to the number of elements. Also, the rotation over the story height is insensitive to the number of elements. Therefore these are good choices for D/C measures. No. of elems Roof drift Strain in bottom element Strain over story height Rotation over story height 12.32%2.39% 1.99% 22.32%3.66%2.36%1.97% 32.32%4.17%2.35%1.96% STRAIN CONCENTRATION STUDY

78 Nonlinear Analysis & Performance Based Design DISCONTINUOUS SHEAR WALLS

79 Nonlinear Analysis & Performance Based Design 79 PIER AND SPANDREL FIBER MODELS Vertical and horizontal fiber models

80 Nonlinear Analysis & Performance Based Design 80 RAYLEIGH DAMPING The M dampers connect the masses to the ground. They exert external damping forces. Units of are 1/T. The K dampers act in parallel with the elements. They exert internal damping forces. Units of are T. The damping matrix is C = M + K.

81 Nonlinear Analysis & Performance Based Design 81 For linear analysis, the coefficients and can be chosen to give essentially constant damping over a range of mode periods, as shown. A possible method is as follows : Choose T B = 0.9 times the first mode period. Choose T A = 0.2 times the first mode period. Calculate and to give 5% damping at these two values. The damping ratio is essentially constant in the first few modes. The damping ratio is higher for the higher modes. RAYLEIGH DAMPING

82 Nonlinear Analysis & Performance Based Design KuuC t uM 0 Kuu 0 M K u C M u M u K 0 2 u u M C C M 2 C M M K 2 C M K 2 M K M K t uM u ; 2 M K RAYLEIGH DAMPING

83 Nonlinear Analysis & Performance Based Design Higher Modes high Lower Modes low To get from & for any M K To get & from two values of ; Solve for & RAYLEIGH DAMPING

84 Nonlinear Analysis & Performance Based Design DAMPING COEFFICIENT FROM HYSTERESIS

85 Nonlinear Analysis & Performance Based Design DAMPING COEFFICIENT FROM HYSTERESIS

86 Nonlinear Analysis & Performance Based Design A BIG THANK YOU!!!


Download ppt "Nonlinear Analysis & Performance Based Design. CALCULATED vs MEASURED."

Similar presentations


Ads by Google