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CALCULATED vs MEASURED

CALCULATED vs MEASURED. ENERGY DISSIPATION. IMPLICIT NONLINEAR BEHAVIOR. STEEL STRESS STRAIN RELATIONSHIPS. INELASTIC WORK DONE!. CAPACITY DESIGN. STRONG COLUMNS & WEAK BEAMS IN FRAMES REDUCED BEAM SECTIONS LINK BEAMS IN ECCENTRICALLY BRACED FRAMES BUCKLING RESISTANT BRACES AS FUSES

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CALCULATED vs MEASURED

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  1. CALCULATED vs MEASURED

  2. ENERGY DISSIPATION

  3. IMPLICIT NONLINEAR BEHAVIOR

  4. STEEL STRESS STRAIN RELATIONSHIPS

  5. INELASTIC WORK DONE!

  6. 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

  7. STRUCTURAL COMPONENTS

  8. MOMENT ROTATION RELATIONSHIP

  9. IDEALIZED MOMENT ROTATION

  10. PERFORMANCE LEVELS

  11. IDEALIZED FORCE DEFORMATION CURVE

  12. ASCE 41 BEAM MODEL

  13. 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

  14. STRENGTH vs DEFORMATION 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

  15. 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.

  16. 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.

  17. F-D RELATIONSHIP

  18. DUCTILITY LATERAL LOAD Ductile Partially Ductile Brittle DRIFT

  19. ASCE 41 - DUCTILE AND BRITTLE

  20. FORCE AND DEFORMATION CONTROL

  21. BACKBONE CURVE

  22. HYSTERESIS LOOP MODELS

  23. STRENGTH DEGRADATION

  24. 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.

  25. BEAM END ROTATION MODEL

  26. 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.

  27. 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).

  28. ASCE 41 CHORD ROTATION CAPACITIES

  29. COLUMN AXIAL-BENDING MODEL

  30. STEEL COLUMN AXIAL-BENDING

  31. CONCRETE COLUMN AXIAL-BENDING

  32. SHEAR HINGE MODEL

  33. 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).

  34. BUCKLING-RESTRAINED BRACE The BRBelement includes “isotropic” hardening. The D-C measure is axial deformation.

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

  36. WALL FIBER MODEL

  37. ALTERNATIVE MEASURE - STRAIN

  38. NONLINEAR SOLUTION SCHEMES ƒ iteration ƒ iteration 2 3 4 5 1 1 2 6 ∆ ∆ ƒ ƒ u u u u ∆ ∆ NEWTON – RAPHSON ITERATION CONSTANT STIFFNESS ITERATION

  39. CIRCULAR FREQUENCY +Y Y q 0 Radius, R -Y

  40. THE D, V & A RELATIONSHIP u . Slope = ut1 t t1 . u . .. ut1 Slope = ut1 t t1 .. u .. ut1 t t1

  41. UNDAMPED FREE VIBRATION + = & & m u k u 0 = w u u cos( t ) t 0 k w = where m

  42. RESPONSE MAXIMA = w u u cos( t ) t 0 w w = - & u u sin( t ) t 0 = w - w 2 u u cos( t ) & & t 0 = - w 2 u u & & max max

  43. BASIC DYNAMICS WITH DAMPING & + + = & & M u C u Ku 0 M t C & + + = - & & & & M u C u Ku M u g K 2 & + x w + w = - & & & & u u u u 2 g & & u g

  44. RESPONSE FROM GROUND MOTION & & & & & + x w + w = + = - 2 u 2 u A B t u u g .. ug 2 .. ug2 t1 t2 .. Time t ug1 1

  45. DAMPED RESPONSE B xw t - & & = - w u e { [ u ] cos t t t d 2 1 w 1 B B 2 & + - w - xw + w + [ A u ( u )] sin t } t t d w 2 2 1 1 w w d x A 2 B xw t - = - + w u e { [u ] cos t t t d 2 3 1 w w 2 x x - 1 A B ( 2 1 ) & + + xw - + w [ u u ] sin t } t t d w w 2 1 1 w d x A 2 B Bt + - + [ ] 2 3 2 w w w

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