Pushover Analysis Procedure_part2
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Transcript of Pushover Analysis Procedure_part2
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Pushover Analysis Procedure
using SAP2000
PART 2
PUSHOVER EXAMPLE
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Pushover Analysis in SAP2000:
Steps Sequence
1. Create the model.2. Define frame hinges properties and assign them to the frame
elements.
3. Define the parameters to calculate the demand for each performancelevel (f.e.: acceleration response spectra, ATC-40, FEMA; MRSA).
4. Define the load patterns which are needed for pushover: gravity loadsand any other load acting on the structure before lateral seismicloading.
5. Define the Non-Linear Static load cases and the Modal load case to beused for pushover analysis.
6. Run the Pushover load cases and check the results (Pushover curve).
7. Determine the target displacement by an appropriate method (ATC-40, FEMA, other).
8. Evaluate the number and state of plastic hinges in the structure, andthen check the maximum strains for the most critical hinge.
9. Change structural configuration (additional piles, modified pile layout)
if needed and repeat the process.
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Model Description
Trestle 105 m length.
7 spans 15 m length.
Bents with three steel
pipe (= 1.42 m) piles. Steel box section cap
beam (H=1.20).
5 steel I-Wide section
longitudinal beams. Concrete slab thickness =
0.30 m.
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Model Description
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Discretization
Elements discretizationSprings for soil-
structure interaction
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Mass Source Definition
DEAD load.
Piping load (permanently
attached equipment).
5KPa (10% of uniform live
load)
Vehicle load (part of the
crane above the deck)
MASS_ADD_MG
(additional mass due to
marine growth)
MASS_ADD_WATER
(Hydrodynamic mass
internal and external to
the pile)
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Marine Growth Load
Pile diameter Dp = 1.42 m
MG thk = 0.20 m
MG = 12.75 KN/m3
Distrib. Load = (/4) [(Dp + 2*thk)2- Dp2] = 13 KN/m
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Hydrodynamic Added Mass
Pile diameter Dp = 1.42 m
Water = 9.81 KN/m3
Distrib. Load = 2**(/4)*Dp2
= 31 KN/m
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Pile Cross-Section Geometry
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Nonlinear material definition
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Pile Moment-Curvature Analysis
Three levels of axial load: P1 = -10000 KN (max compression),
P2 = -1700 KN (DEAD load), P3 = 5000 (max tension).
One bending angle: 0 (symmetrical section)
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Pile Moment-Curvature Analysis
Determination of the bilinear M-Phi
diagram for:
P = -1700 KN
Angle = 0
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Pile Moment-Curvature Analysis
Bilinear M-Phi diagram for: P = -1700 KN, Angle = 0
Mne = 18700 KN-m
Mp = 21000 KN-m
Mp/Mne = 1.12
Y= 0.012
u= 0.237
p = uY= 0.225
The same procedure should be repeated for the other two levels of
axial force!
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Pile Hinge Definition 1
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Pile Hinge Definition 2
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Pile Hinge Definition 3
Assign the defined hinge to the frame elements
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Pile Hinge Definition 4
Display the names of the generated hinges
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Pile Hinge Definition 5
Show generated hinge property 11H1
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Pile Hinge Definition 6
Calculating the SF of the hinge PILE-ST52
To define the Moment-Curvature Curve of hinge PILE-ST52, it is
required to calculate the yielding curvature (SF) used by the program:
SF = y / Lp = 5.016E-3 / 1.5 = 3.344E-3
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Pile Hinge Definition 7
M-Phi curve and Interaction surface definition for PILE-ST52
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Pile Hinge Definition 8
M-Phi curve definition for PILE-ST52
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Pile Hinge Definition 9
M-Phi curve definition for PILE-ST52
From bilinear M-Phi:
Mp/Mne = 1.12
0.20 Mp/Mne = 0.22
p = 0.225
SF = 3.344E-3
p / SF = 67
Notice that only plastic curvatures over SF have to be specified in the right column.
In the left column the Mp/Mne (obtained from M-Phi bilinear diagram) is assigned
to point C and a 20% of that value to point D.
Due to numerical stability it is highly recommendable that line CD has a negative
slope (not vertical) and line DE a positive slope (not horizontal).
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Pile Hinge Definition 10
Interaction surface definition for PILE-ST52
Automatically defined for each generated hinge.
It is only used to determine the exact yielding moment (Mne2, Mne3)
and the angle of bending (tg = Mne3 / Mne2).
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1. The described procedure has to be repeated for the
definition of hinges in the cap beam and longitudinalbeam.
2. Due to the lower importance of beam hinges, they canbe defined faster by means of the Automatic Hinges if
the conditions for type of material and cross-sectiongeometry are met (See Part 1 of this guide).
3. It is very likely that in the hinge length for beams is notthe same as the total length of the frame element but a
fraction. This should be taken into account when definingthe hinge length (Lp) relative to the frame elementlength. This is an important parameter for the correctdetermination of the SF (yield curvature) from the yield
rotation automatically calculated by the program.
Beam Hinge Definition
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1. Sudden strength loss is not recommended (segment C-D)2. Reduce the mesh size helps when using sudden strength
loss.
3. It is possible to define hinges along the whole frame
length (e.g.: 10 hinges spaced every tenth part of thetotal length).
4. Repeat the described process for all the combinations ofbending angles and axial loads.
5. For bi-axial or asymmetrical cross-sections, define M-Phifor intermediate bending angles (e.g.: 45).
6. Once the plastic hinge definition is concluded (SFcalulated by the program determined), the property has
to be newly assigned to all the corresponding frames.
Hinge Definition: Final Recommendations
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Parameters for ATC-40 Capacity-Spectrum
Method
Definition of response spectrumfunction (without scaling) for
each demand level (OLE-D1, CLE-
D2, DE-D3)
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Parameters for ATC-40 Capacity-Spectrum
Method
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DEAD Load Case Definition
Constitutes the starting point of pushover analysis.
Non-linear geometric P-Delta analysis is performed for all the
gravity loads present before earthquake
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MODAL Load Case Definition
The results of MODAL load case are used in the definition of the ATC-40
capacity spectrum (ADRS format) and the equivalent period required to
obtain the performance point (target displacement).
Besides, the mode shapes are used in the definition of the MODE load
pattern for pushover analysis.
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Pushover MODE Load Pattern
1. More critical pushover load pattern. Preferred
over uniform ACCEL load pattern.
2. Modal analysis has to be performed first.
3. The two fundamental modes with higher modal
mass participation in directions X and Y,
respectively, are selected for the definition of
MODE load pattern.
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Pushover MODE Load Pattern
Vibration modes selection for X and Y directions
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Pushover MODE Load Pattern
Vibration modes selection for X and Y directions
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Pushover MODE Load Pattern
Pushover Load Case Definition in Y direction
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Pushover Load control application
P h N b f d t f
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Pushover: Number of saved steps for
results analysis
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Pushover Non-Linear Analysis Parameters
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1. Keep using the same type of geometric non-linearity (e.g.: P-Delta) through all the non-linear load case defined in themodel.
2. Start the model with as few hinges as possible. then graduallyincrement the number of hinges as necessary.
3. The first run may no include any type of geometric non-linearity. Then, after checking results and analysisperformance, add P-Delta and may be Large Displacements.
4. Start with modest target displacements and limited numberof steps (saved and total). The idea is always have thepossibility of first perform a quickly analysis. Afterwards thenon-linear behavior could be incremented.
5. Consider more than two loading directions (or loadingmodes) to evaluate the structure under different loadingsituations.
Pushover Analysis:
Final Important Considerations
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
ATC-40 Capacity Spectrum display parameters.D2 Performance Level.
h l l
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Target displacement. D2 Performance Level.
h l l
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
ATC-40 Capacity Spectrum display parameters.D3 Performance Level.
Besides the elastic
period and damping
ratio, the effective
inelastic parameters
are also displayed.
h l A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Target displacement. D3 Performance Level.
P h R l A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Load steps corresponding to target displacements.
Level D2: Step 34 Level D3: Step 49
P h R l A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Identification of first hinge that yields (hinge with maximumdeformations through all the pushover analysis load history.)
First plastic in-ground hinge appears in the bottom part of the pile
at load step 32
P h R lt A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Results display of first plastic hinge at yielding point (step 32).
P h R lt A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Extract information for yielding (step 32), level D2 (step 34) and levelD3 (step 49)
P h R lt A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Extract information for yielding (step 32), level D2 (step 34) and levelD3 (step 49)
P h R lt A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Yield curvature calculation
My = 11085 KN.m
y = 2.282E-3 m-1(aprox.)
P h R lt A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Steel strain calculation for level D2
P h R lt A l i
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Steel strain calculation for level D3
Pushover Results Analysis
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Pushover Results Analysis
Pushover in Y direction (Mode 1 load pattern).
Tensile steel strain for level D2 and D3 are smaller than Strain limitsfor CLE and DE performance levels, respectively. Therefore, the
seismic capacity of the piles is verified.
Table 4-1 POLB