Pushover Analysis Procedure using SAP2000 PART 2 PUSHOVER EXAMPLE
Pushover Analysis in SAP2000: Steps Sequence 1. 2. 3. 4. 5. 6. 7. 8. 9.
Create the model. Define frame hinges properties and assign them to the frame elements. Define the parameters to calculate the demand for each performance level (f.e.: acceleration response spectra, ATC-40, FEMA; MRSA). Define the load patterns which are needed for pushover: gravity loads and any other load acting on the structure before lateral seismic loading. Define the Non-Linear Static load cases and the Modal load case to be used for pushover analysis. Run the Pushover load cases and check the results (Pushover curve). Determine the target displacement by an appropriate method (ATC40, FEMA, other). Evaluate the number and state of plastic hinges in the structure, and then check the maximum strains for the most critical hinge. Change structural configuration (additional piles, modified pile layout) if needed and repeat the process.
Model Description • • • • •
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Trestle 105 m length. 7 spans 15 m length. Bents with three steel pipe (φ = 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.
Model Description
Discretization Elements discretization
Springs for soilstructure interaction
Mass Source Definition • • • • •
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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)
Marine Growth Load
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Pile diameter Dp = 1.42 m MG thk = 0.20 m MG γ = 12.75 KN/m3 Distrib. Load = γ (π/4) [(Dp + 2*thk)2 - Dp2] = 13 KN/m
Hydrodynamic Added Mass
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Pile diameter Dp = 1.42 m Water γ = 9.81 KN/m3 Distrib. Load = 2*γ*(π/4)*Dp2 = 31 KN/m
Pile Cross-Section Geometry
Nonlinear material definition
Pile Moment-Curvature Analysis
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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)
Pile Moment-Curvature Analysis Determination of the bilinear M-Phi diagram for: P = -1700 KN Angle = 0°
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 φY = 0.012 φu = 0.237 φp = φu – φY = 0.225 The same procedure should be repeated for the other two levels of axial force!
Pile Hinge Definition 1
Pile Hinge Definition 2
Pile Hinge Definition 3 •
Assign the defined hinge to the frame elements
Pile Hinge Definition 4 •
Display the names of the generated hinges
Pile Hinge Definition 5 •
Show generated hinge property 11H1
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 = θy / Lp = 5.016E-3 / 1.5 = 3.344E-3
Pile Hinge Definition 7 •
M-Phi curve and Interaction surface definition for PILE-ST52
Pile Hinge Definition 8 •
M-Phi curve definition for PILE-ST52
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 φp = 0.225 SF = 3.344E-3 φp / 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).
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 α= Mne3 / Mne2).
Beam Hinge Definition 1. The described procedure has to be repeated for the definition of hinges in the cap beam and longitudinal beam. 2. Due to the lower importance of beam hinges, they can be defined faster by means of the “Automatic Hinges” if the conditions for type of material and cross-section geometry are met (See Part 1 of this guide). 3. It is very likely that in the hinge length for beams is not the same as the total length of the frame element but a fraction. This should be taken into account when defining the hinge length (Lp) relative to the frame element length. This is an important parameter for the correct determination of the SF (yield curvature) from the yield rotation automatically calculated by the program.
Hinge Definition: Final Recommendations 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 the total length). 4. Repeat the described process for all the combinations of bending angles and axial loads. 5. For bi-axial or asymmetrical cross-sections, define M-Phi for intermediate bending angles (e.g.: 45°). 6. Once the plastic hinge definition is concluded (SF calulated by the program determined), the property has to be newly assigned to all the corresponding frames.
Parameters for ATC-40 Capacity-Spectrum Method Definition of response spectrum function (without scaling) for each demand level (OLE-D1, CLED2, DE-D3)
Parameters for ATC-40 Capacity-Spectrum Method
DEAD Load Case Definition
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Constitutes the starting point of pushover analysis. Non-linear geometric P-Delta analysis is performed for all the gravity loads present before earthquake
MODAL Load Case Definition
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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.
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.
Pushover MODE Load Pattern • Vibration modes selection for X and Y directions
Pushover MODE Load Pattern • Vibration modes selection for X and Y directions
Pushover MODE Load Pattern • Pushover Load Case Definition in Y direction
Pushover Load control application
Pushover: Number of saved steps for results analysis
Pushover Non-Linear Analysis Parameters
Pushover Analysis: Final Important Considerations 1. Keep using the same type of geometric non-linearity (e.g.: PDelta) through all the non-linear load case defined in the model. 2. Start the model with as few hinges as possible. then gradually increment the number of hinges as necessary. 3. The first run may no include any type of geometric nonlinearity. Then, after checking results and analysis performance, add P-Delta and may be Large Displacements. 4. Start with modest target displacements and limited number of steps (saved and total). The idea is always have the possibility of first perform a quickly analysis. Afterwards the non-linear behavior could be incremented. 5. Consider more than two loading directions (or loading modes) to evaluate the structure under different loading situations.
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). ATC-40 Capacity Spectrum display parameters. D2 Performance Level.
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Target displacement. D2 Performance Level.
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.
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Target displacement. D3 Performance Level.
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
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Identification of first hinge that yields (hinge with maximum deformations through all the pushover analysis load history.)
First plastic in-ground hinge appears in the bottom part of the pile at load step 32
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Results display of first plastic hinge at yielding point (step 32).
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Extract information for yielding (step 32), level D2 (step 34) and level D3 (step 49)
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Extract information for yielding (step 32), level D2 (step 34) and level D3 (step 49)
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Yield curvature calculation
My = 11085 KN.m φy = 2.282E-3 m-1 (aprox.)
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Steel strain calculation for level D2
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Steel strain calculation for level D3
Pushover Results Analysis Pushover in Y direction (Mode 1 load pattern). Tensile steel strain for level D2 and D3 are smaller than Strain limits for CLE and DE performance levels, respectively. Therefore, the seismic capacity of the piles is verified. Table 4-1 POLB
