energy diagram - ait solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/csi-manilla-ppt.pdf ·...
TRANSCRIPT
![Page 1: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/1.jpg)
![Page 2: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/2.jpg)
![Page 3: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/3.jpg)
ENERGY DIAGRAM
![Page 4: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/4.jpg)
ENERGY DIAGRAM w/ HYSTERETIC
![Page 5: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/5.jpg)
IMPLIED NONLINEAR BEHAVIOR
![Page 6: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/6.jpg)
STEEL STRESS STRAIN RELATIONSHIPS
![Page 7: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/7.jpg)
INELASTIC WORK DONE
![Page 8: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/8.jpg)
HYSTERETIC BEHAVIOR
![Page 9: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/9.jpg)
MOMENT ROTATION RELATIONSHIP
![Page 10: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/10.jpg)
IDEALIZED MOMENT ROTATION
![Page 11: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/11.jpg)
DUCTILITY
LATERALLOAD
Partially DuctileBrittle Ductile
DRIFT
![Page 12: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/12.jpg)
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
![Page 13: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/13.jpg)
PERFORMANCE LEVELS
Restaurant Restaurant
Resta
urant
Operational Immediate
Occupancy
Life Safety Collapse
Prevention
Less Damage More Damage
Ref: FEMA 451 B
![Page 14: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/14.jpg)
PERFORMANCE LEVELS
![Page 15: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/15.jpg)
IDEALIZED FORCE DEFORMATION CURVE
![Page 16: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/16.jpg)
ASCE 41 BEAM MODEL
![Page 17: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/17.jpg)
ASCE 41 MOMENT HINGE
![Page 18: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/18.jpg)
STRENGTH vs. DEFORMATION
ELASTIC STRENGTH DESIGN - KEY STEPS
CHOSE DESIGN CODE AND EARTHQUAKE LOADSDESIGN CHECK PARAMETERS STRESS/BEAM MOMENTGET 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 41DEMAND CAPACITY MEASURES – DRIFT/HINGE ROTATION/SHEAR
GET DEFORMATION AND FORCE CAPACITIESCALCULATE DEFORMATION AND FORCE DEMANDS (RS OR TH)
CALCULATE D/C RATIOS – LIMIT STATES
![Page 19: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/19.jpg)
ASCE 41 ASSESSMENT OPTIONS
• 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)
![Page 20: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/20.jpg)
PERFORMANCE PARAMETERSBRIDGE CATEGORIES
LIFELINE BRIDGES
MAJOR-ROUTE BRIDGES
OTHER BRIDGES
GROUND MOTION LEVELSPROBABILITY IN 50 YEARS RETURN PERIOD
10%
5%
2%
475 YEARS
975 YEARS
2475 YEARS
PERFORMANCE LEVELS
SERVICE DAMAGE
IMMEDIATE
LIMITED
SERVICE DISRUPTION
LIFE SAFETY
MINIMAL DAMAGE
REPAIRABLE DAMAGE
EXTENSIVE DAMAGE
PROBABLE REPLACEMENT
![Page 21: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/21.jpg)
STRUCTURAL COMPONENTS
![Page 22: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/22.jpg)
F-D RELATIONSHIP
![Page 23: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/23.jpg)
DUCTILITY
LATERALLOAD
Partially DuctileBrittle Ductile
DRIFT
![Page 24: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/24.jpg)
ASCE 41 – DUCTILE AND BRITTLE
![Page 25: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/25.jpg)
FORCE AND DEFORMATION CONTROL
![Page 26: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/26.jpg)
BACKBONE CURVE
![Page 27: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/27.jpg)
HYSTERESIS LOOP MODELS
![Page 28: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/28.jpg)
STRENGTH AND DEGRADATION
![Page 29: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/29.jpg)
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.
![Page 30: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/30.jpg)
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.
![Page 31: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/31.jpg)
ASCE 41 ROTATION 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. .
![Page 32: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/32.jpg)
STEEL COLUMN AXIAL-BENDING
![Page 33: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/33.jpg)
COLUMN AXIAL-BENDING MODEL
![Page 34: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/34.jpg)
CONCRETE COLUMN AXIAL-BENDING
![Page 35: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/35.jpg)
FEMA PMM HINGE
![Page 36: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/36.jpg)
CONCRETE COLUMN FIBER HINGE MODEL
Reinforced Concrete Column Steel Rebar Fibers
Confined Concrete Fibers Unconfined Concrete Fibers
![Page 37: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/37.jpg)
SHEAR WALL FIBER HINGE MODEL
Reinforcement Layout
Steel Fibers
Confined Concrete Fibers
Unconfined Concrete Fibers
![Page 38: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/38.jpg)
MATERIAL STRESS-STRAIN CURVES
Unconfined and Confined Concrete( Compared )
SteelConfined Concrete
![Page 39: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/39.jpg)
STRAIN AS PERFORMANCE MEASURE
Strain Limit
Fully confined concrete compressive strain 0.015
Unconfined concrete compressive strain 0.005
Rebar tensile strain 0.05
Rebar compressive strain 0.02
![Page 40: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/40.jpg)
PIER AND SPANDREL FIBER MODELS
![Page 41: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/41.jpg)
BRIDGE SECTIONS AND FIBER MODELS
B R I D G E C R O S S S E C T I O N S
F I B E R M O D E L S OF C R O S S S E C T I O N S
![Page 42: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/42.jpg)
SHEAR HINGE MODEL
![Page 43: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/43.jpg)
PANEL ZONE ELEMENT
![Page 44: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/44.jpg)
NONLINEAR SOLUTION SCHEMES
NEWTON – RAPHSONITERATION
∆ƒ
ƒ
∆ u u
1 2
iteration
∆ƒ
ƒ
∆ u u
1 2
iteration
CONSTANT STIFFNESSITERATION
3 4 5 6
![Page 45: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/45.jpg)
THE POWER OF RITZ VECTORS
APPROXIMATELY THREE TIMES FASTER THANTHE CALCULATION OF EXACT EIGENVECTORS
IMPROVED ACCURACY WITHA SMALLER NUMBER OF VECTORS
CAN BE USED FOR NONLINEAR ANALYSISTO CAPTURE LOCAL RESPONSE
![Page 46: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/46.jpg)
FAST NONLINEAR ANALYSIS (FNA)
DISCRETE NONLINEARITY
FRAME AND SHEAR WALL HINGESBASE ISOLATORS (RUBBER & FRICTION)
STRUCTURAL DAMPERSSTRUCTURAL UPLIFT
STRUCTURAL POUNDINGBUCKLING RESTRAINED BRACES
![Page 47: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/47.jpg)
RITZ VECTORS
![Page 48: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/48.jpg)
FNA ADVANTAGES
MODAL SOLUTION - NO STIFFNESS REDUCTIONCLOSED FORM SOLUTION – VERY FAST
TIME STEP INDEPENDENTCAPTURES HIGH FREQUENCY RESPONSE
RITZ VECTORS CALCULATED ONCEMULTIPLE TIME HISTORIES ARE FAST
![Page 49: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/49.jpg)
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.
![Page 50: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/50.jpg)
DYNAMIC EQUILIBRIUM EQUATIONS
guuuu -=w+wx+2
2
guMKuuCuM
KuuCt
uM...
-=++
=++ 0
.
.
ug
M
K
C
..
..
..
..
..
![Page 51: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/51.jpg)
RESPONSE FROM GROUND MOTION
ug..
2ug2
..
ug1
..
1
t1
t2t
A B t ug= + = -.
u u u+ +22
xw w.. ..
![Page 52: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/52.jpg)
CLOSED FORM DAMPED RESPONSE
{ [.
] cos
[ (.
)] sin }
e uB
t
A u uB
tB
t
t d
dt t d
.ut = -
+ - - + +
- xw
ww
ww xw
ww
w
1 2
2
1 1 2 2
1
eA B
t
u uA B
t
A B Bt
t
t d
dt t d
ut = - +
+ + - +-
+ - +
- xw
w
x
ww
wxw
x
w
x
ww
w
x
w w
{ [u ] cos
[. ( )
] sin }
[ ]
1 2 3
1 1
2
2
2 3 2
2
1 2 1
2
![Page 53: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/53.jpg)
UNDAMPED RESPONSE
)(][ BtAtsinB
u
u
1t
t
++-+
=
22
11
ww
ww
.
][ tcosA
u1
t-
2
2
2
2
1 BtsinuA
tcosB
uu
1
1
t
tt
+-+
-=
][
][.
w
w
w
w
www
w
![Page 54: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/54.jpg)
STEP BY STEP DYNAMIC ANALYSIS
At any point in time, dynamic equilibrium is :
Over a time step, Dt, dynamic equilibrium is :
This equation can be solved by step-by-step methods.
There is one equation with three unknowns (Du, Du, Du),so assumptions must be made and the solution is approximate.
Mu + Cu + Ku = R
M Du + C Du + K Du = DR
Effective load =
Displ = uVeloc = uAccn = u
R = -Mu g
K
M
GroundAccn = ug
C
![Page 55: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/55.jpg)
u0
R0
Dt
DR
Du
Du
Du
u1
u1
u0
u0
u0
R 1
Equilibrium :
From Kinematics :
Hence get effective stiffness and load :
Solve Then :
Du = Dt2
Dt2
(u + u ) =0 1
(2u + Du ) 0
Du = Dt2
Dt2
(u + u ) =0 1
(2u + Du ) 0
4Dt
M + 2Dt2 C + KK =eff
4Dt
) + 2CDR =eff -Mu +g
M(2u +0
u 0 u
0
DReffKeff Du =
Du = -2u + Du2Dt
Du = -2u + Du2Dt
0
0
M Du + C Du + K Du = DR
STEP-BY-STEP INTEGRATION (CAA)
![Page 56: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/56.jpg)
BASIC DYNAMICS WITH DAMPING
guuuu &&&&& -=w+wx+ 2
2
guMKuuCuM
KuuCt
uM
&&&&&
&&&
-=++
=++ 0
gu&&
M
K
C
![Page 57: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/57.jpg)
RESPONSE MAXIMA
u t )cos(0
tu w=
)cos(0
2 tu ww-=u t&&
)sin(0
tu ww-=u t&
max2uw-=maxu&&
![Page 58: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/58.jpg)
RESPONSE SPECTRUM GENERATION
Displacement
Response Spectrum
5% damping
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10
PERIOD, Seconds
DIS
PL
AC
EM
EN
T,
inch
es
-0.40
-0.20
0.00
0.20
0.40
0.00 1.00 2.00 3.00 4.00 5.00 6.00
TIME, SECONDS
GR
OU
ND
AC
C,
g
Earthquake Record
-4.00
-2.00
0.00
2.00
4.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00
DIS
PL, in
.
-8.00
-4.00
0.00
4.00
8.00
0.00 1.00 2.00 3.00 4.00 5.00 6.00
DIS
PL, in
.
T= 0.6 sec
T= 2.0 sec
![Page 59: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/59.jpg)
SPECTRAL PARAMETERS
0
4
8
12
16
0 2 4 6 8 10
PERIOD, sec
DIS
PL
AC
EM
EN
T, in
.
0
10
20
30
40
0 2 4 6 8 10
PERIOD, sec
VE
LO
CIT
Y, in
/se
c
0.00
0.20
0.40
0.60
0.80
1.00
0 2 4 6 8 10
PERIOD, sec
AC
CE
LE
RA
TIO
N, g
dV SPS w=
va PSPS w=
![Page 60: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/60.jpg)
THE ADRS SPECTRUM
ADRS Curve
Spectral Displacement, Sd
Spe
ctra
l Acc
ele
rati
on
, Sa
Period, T
Spec
tral
Acc
eler
atio
n, S
a
RS Curve
0.5
Sec
on
ds
1.0
Sec
on
ds
2.0
Sec
on
ds
![Page 61: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/61.jpg)
THE ADRS SPECTRUM
![Page 62: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/62.jpg)
ASCE 7 RESPONSE SPECTRUM
![Page 63: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/63.jpg)
PUSHOVER
![Page 64: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/64.jpg)
THE LINEAR PUSHOVER
![Page 65: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/65.jpg)
EQUIVALENT LINEARIZATION
How far to push? The Target Point!
![Page 66: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/66.jpg)
DAMPING COEFICIENT FROM HYSTERESIS
![Page 67: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/67.jpg)
DAMPING COEFICIENT FROM HYSTERESIS
![Page 68: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/68.jpg)
DISPLACEMENT MODFICATION
Calculating the Target Displacement
C0 Relates spectral to roof displacementC1 Modifier for inelastic displacementC2 Modifier for hysteresis loop shape
d = C0C
1C
2S
aT
e
2 / (4p2)
![Page 69: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/69.jpg)
ARTIFICIAL EARTHQUAKES
CREATING HISTORIES TO MATCH A SPECTRUM
FREQUENCY CONTENTS OF EARTHQUAKES
FOURIER TRANSFORMS
![Page 70: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/70.jpg)
MATCHING THE SPECTRUM
![Page 71: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/71.jpg)
FOURIER TRANSFORMS
![Page 72: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/72.jpg)
ENERGY DISSIPATION DEVICES
Friction Isolator Rubber Isolator Oil Damper Friction DamperBuckling-Restrained
Brace (BRB)
![Page 73: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/73.jpg)
CoRE Rating Safety Reparability Functionality
5-Star Life Safe Loss <5%Occupiable Immediately
Functional < 72 hours
4-Star Life Safe Loss <10%Occupiable Immediately
Functional < 1 month
3-star Life Safe Loss <20%Occupiable < 1 month
Functional < 6 months
Certified Life Safe Not estimated Not estimated
Not CertifiedLife Safety
HazardNot estimated Not estimated
RATING FOR SEISMIC PERFORMANCE
![Page 74: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/74.jpg)
Cabinets, 1% Bookcases, 1% Roof Equipment, 1%
Cladding, 2%
Partitions, 27%
Moment Frame, 2%
Ceiling, 32%
Elevators, 21%
Computers, 6%
Servers/Network, 7%
DAMAGE ANALYSIS
![Page 75: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/75.jpg)
NONLINEAR ANALYSIS SURVEY
![Page 76: ENERGY DIAGRAM - AIT Solutionssolutions.ait.ac.th/wp-content/uploads/2018/06/CSI-Manilla-ppt.pdf · • Nonlinear Static Analysis (Pushover Analysis) • Nonlinear Dynamic Time History](https://reader030.vdocument.in/reader030/viewer/2022040913/5e88f28ff219a31a8707e8f1/html5/thumbnails/76.jpg)