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ALL YOU ALWAYS WANTED TO KNOW ABOUT PUSH-OVER ANALYSIS, BUT WERE AFRAID TO ASK Farzad Naeim, Ph.D., S.E. Director of Research and Development John A. Martin & Associates, Inc. Los Angeles, California

What are we going to talk about? What is push-over analysis What are its fundamental techniques What are its advantages and shortcomings What tools can be used Common Pitfalls in push-over analysis Examples of push-over analysis application

What Qualifications?

Temperament is the key Push-over analysis usually requires more effort than you think. Takes more time than you think. Is more complex than you think. So be patient and do not panic.

Seismic Codes and Guidelines    for New Buildings

Retrofit Guidelines with Nonlinear Methods FEMA 273/274 All Building Types Based on ATC-33 Case studies and calibrations in progress SSC 96-01 (Proposition 122) or ATC-40 Concrete Buildings Only

Comparison of New and Existing Building Criteria

Choice of Method for Design Seismic design is not rocket science It is more of an art than science

Choice of Methods for Design

Push-over Curve or Capacity Spectrum

Design Spectra Representation Ordinary Design

Why Push-Over Analysis? Static Nonlinear Analysis technique, also known as sequential yield analysis, or simply "push-over" analysis has gained significant popularity during the past few years. It is one of the three analysis techniques recommended by FEMA 273/274 and a main component of the Spectrum Capacity Analysis method (ATC-40). Proper application can provide valuable insights into the expected performance of structural systems and components Misuse can lead to an erroneous understanding of the performance characteristics. Unfortunately, many engineers are unaware of the subtle details that have to observed in order to obtain useful results from such analysis. This presentation is an attempt to identify the most important considerations necessary for a push-over analysis to provide meaningful results.

What is Push-Over Analysis? Push-over analysis is a technique by which a computer model of the building is subjected to a lateral load of a certain shape (i.e., inverted triangular or uniform). The intensity of the lateral load is slowly increased and the sequence of cracks, yielding, plastic hinge formations, and failure of various structural components is recorded. Push-over analysis can provide a significant insight into the weak links in seismic performance of a structure. A series of iterations are usually required during which, the structural deficiencies observed in one iteration, are rectified and followed by another. This iterative analysis and design process continues until the design satisfies a pre-established performance criteria. The performance criteria for push-over analysis is generally established as the desired state of the building given a roof-top or spectral displacement amplitude.

What Tools Can Be Used? Nonlinear Analysis software with built-in push-over analysis capabilities DRAIN-2DX, DRAIN-3DX ANSR IDARC-2D, IDARC-3D NL-PUSH ?? Sequential application of linear analysis software

Using Linear Analysis Software Each analysis reflects the state  of building at the end of previous analysis. All component actions are actually action increments They have to be added up to reflect the analysis results. Generally, a substantial amount of manual bookkeeping is involved. Results obtained by  successive linear analyses are inherently approximate, incapable of accurate modeling of the P-D effects and weak in assessment of true member forces. Despite these facts, if used properly, it can provide a good approximation to the global force-displacement curve for the building.

Establishing the Performance Point No building can be pushed to eternity without failure. Performance point is where the Seismic Capacity and the Seismic Demand curves meet. if it exists, it may be established by The Explicit R Factor Method (Reinhorn and others) The Displacement Coefficient Method (FEMA-273) The Capacity Spectrum Method (ATC-40) If the performance point exists and damage state at that point is acceptable, we have a building that satisfies the push-over criterion. If not, we have to fix the building.

The Explicit R-Factor Method

FEMA-273 Method Here an estimate of elastic displacement is obtained first.

FEMA-273 Coefficients

FEMA-273 Coefficients

FEMA-273 Coefficients

FEMA-273 Coefficients

FEMA-273 Coefficients

FEMA-273 Component Curves

ATC-40 Method This is an iterative procedure involving several analyses.

What if Performance Point Does Not Exist?

What if Performance Point Does Not Exist?

What if Performance Point Does Not Exist?

What if Performance Point Does Not Exist? Upgrade the system by adding Strength Stiffness Ductility or any combination of the above Reduce seismic demand by Adding damping God forbid, base isolation Still cannot do it? Combine the above two categories. Still Cannot do it?  Either the building is doomed, or you better look for another job.

Our Next Focus Our next focus in this presentation is on common mistakes committed during a direct push-over analysis. Many of the observations made here, however, are equally well (if not more profoundly) applicable to push-over analysis by successive application of linear analysis techniques. Ten of the most important considerations for a meaningful push-over analysis are summarized as "commandments".

The Ten Commandments of Push-over Analysis

The Ten Commandments 1. Do not underestimate the importance of the loading or displacement shape function. 2. Know your performance objectives before you push the building. 3. If it is not designed, it cannot be pushed. 4. Do not ignore gravity loads. 5. Do not push beyond failure unless otherwise you can model failure. 6. Pay attention to rebar development and lap lengths. 7. Do not ignore shear failure mechanisms 8. P-Delta effects may be more important than you think. 9. Do not confuse the Push-over with the real earthquake loading. 10. Three-dimensional buildings may require more than a planar push.

1. Do not underestimate the importance of the loading shape function. The loading or deformation shape function is selected to represent the predominant dynamic mode shape of the building. Quite often, an inverted triangular shape is used consistent with the codified static lateral force distribution. It is most common to keep the load shape constant during the push. Use of adaptive load shapes is  on the increase. No consistent guidelines exist for definition and application of adaptive load functions exist. Loading shape importance increases for tall buildings whose earthquake response is not dominated by a single mode shape. For these buildings, a loading shape function based on the first mode shape may seriously underestimate the seismic demand on the intermediate floor levels.

1. Do not underestimate the importance of the loading shape function.

1. Do not underestimate the importance of the loading shape function.

2. Know your performance objectives before you push the building. No building can be displaced to infinity without damage. Since the objective of push-over analysis to assess the status of building and its components in a damaged state, it is of paramount importance to understand the specific performance objectives desired for the building. Performance objectives such as collapse prevention, life safety, or immediate occupancy have to be translated into technical terms such as: (a) a given set of design spectra, and (b) specific limit states acceptable for various structural components when subjected to the seismic demand embodied in these design spectra. A push-over analysis without a clearly defined performance objectives is of little use.

3. If it is not designed, it cannot be pushed. E, I, and A are not sufficient. Push-over characteristics are strong functions of force-displacement characteristics of individual members and their connections.  If detailed characteristics are not known, the push-over analysis will be an exercise in futility. Examples: Force-deformation properties of R/C are vastly different from that of steel and care should be taken to determine the initial stiffness, the cracking and the yielding moments and also the post yield behavior. For steel structures, the moment curvature is primarily bilinear or trilinear The possible failure mechanisms in the joint panel zones should be considered in the analysis.  Possible premature weld fractures at the joints will prevent adjoining members from achieving their full plastic capacities. If such fractures are anticipated, they should be given their due consideration.

4. Do not ignore gravity loads. Inclusion or exclusion of the gravity loads can have a pronounced effect on the shape of the push-over curve and the member yielding and failure sequence. Example: Due to the unsymmetric distribution of + and - reinforcements in R/C beams, gravity load delays the onset of yielding and cracking in the beams, resulting in a stiffer structure at lower magnitudes of base shear. The ultimate capacity of the structure, is usually reduced with increasing gravity load.

4. Do not ignore gravity loads.

5. Do not push beyond failure unless otherwise you can model failure.

6. Pay attention to rebar development and lap lengths. For R/C members of existing structures, it is very important to note the development lengths when calculating member capacities. If inadequate development lengths are present, as they are in most of the older buildings, the contributing steel area should be reduced to account for this inadequacy. Failure to do so will result in overestimating the actual capacity of the members and results in an inaccurate push-over curve.

7. Do not ignore shear failure mechanisms If the shear capacity of structural members is not sufficient to permit the formation of flexural plastic hinges, shear failure will precede the formation of plastic hinges at the end of the member. In R/C members, even if the shear capacity is sufficient, but lateral reinforcement is not spaced close enough at the plastic hinge zones, the concrete may crush in the absence of sufficient confinement. If this happens, the plastic capacity is suddenly dropped to what can be provided by the longitudinal steel alone. Very few of the computer programs used routinely for push-over analysis consider either of the above two scenarios. As a consequence, designers should be aware of these problems and deal with them manually, if the computer program they are using cannot address these issues automatically.

8. P-D effects may be more important than you think. The P-D effects become increasingly significant with larger lateral displacements and larger axial column forces. Strong column - weak girder design strategy commonly deals with the moment capacity of columns in the undeformed state. In a substantially deformed state, the moment capacity of columns may be sufficiently reduced to counteract the strong column - weak girder behavior envisioned by the design. Cases of plastic hinge formations during a push-over analysis in columns "designed" to be stronger than the girders are not rare.

8. P-D effects may be more important than you think. 10 story frame  example

9. Do not confuse the Push-over with the real earthquake loading. The push-over load is monotonically increased The earthquake generated forces continually change in amplitude and direction during the duration of earthquake ground motion. Push-over loads and structural response are in phase Earthquake excitations and building response are not necessarily in phase. This is particularly true for near-fault ground motions which tend to concentrate the damage on the lower floors, an effect which is difficult to model by the push-over loads. The best that can be hoped for is for the push-over curve to effectively envelope the earthquake generated forces and displacements.

9. Do not confuse the Push-over with the real earthquake loading.

10. Three-dimensional buildings may require more than a planar push. For building with strong asymmetry in plan, or with numerous non-orthogonal elements, a planar (two dimensional) push-over analysis may not suffice. For such cases a 3D model of the building must be constructed and subjected to push-over analysis. Three dimensional buildings may be pushed in the principal directions independently, or pushed simultaneously in orthogonal directions.

10. Three-dimensional buildings may require more than a planar push.

If done properly, valuable information is obtained

Representative Push-over Analysis at JAMA MWD Irvine Center Tower An unidentified Office Building in West LA UCLA Hospital South Parking Knudsen Hall (UCLA) Saint Vincent Hospital Tollman Hall (UCB)

Seismic Upgrade of the UCLA Knudsen Hall

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The Building Structural System Past Performance

Upgrade Objective Improve building so that it satisfies a "fair" to "good" seismic rating for the building according to the seismic rating system adopted by the University of California Work within a very limited budget Work within a very tight schedule

Alternatives Considered Increase Capacity Adding Shear Walls Adding Steel Braced Frames Fiber-wrapping of columns Converting the exterior frames to ductile moment frames Reduce Demand Base Isolation Damping Devices

Performance Objectives Enhance life-safety potential of the building Limit interstory drift ratios to 0.015 under the EQ-II event Assign Damage indices (DI) to individual components and story levels and keep DI values lower than values deemed acceptable.

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Earthquake Ground Motions Damage Level Site Specific: 50% probability of being exceeded in the next 50 years Design Basis Site Specific: 10% probability of being exceeded in the next 50 years

Selected Suite of Time Histories

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Analytical Models Models of building constructed in existing and upgraded states for Dynamic Analysis using a Three Dimensional Elastic Model (ETABS) Dynamic Analysis using 2-D and 3-D Nonlinear Models (IDARC-2D and IDARC-3D) Nonlinear Static Analysis (IDARC-2D)

Damage Indices

Limits on Inelastic Damage Index Damage index for shear is binary (0 or 1). Except for shear, damage indices for push-over analysis are defined as the ratio of actual curvature to the ultimate curvature capacity DI for individual members < 0.90 DI for floor levels < 0.70

Design of Diaphragm Chords and Drags Diaphragm chord and drag forces shall be established by rational analysis If results of unscaled elastic analysis is used (10% in 50 years) a reduction factor of R < 3 may be applied.

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Initial Damper Characteristics

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Selection and Spatial Distribution of Dampers

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Maximum Interstory Drifts (in.) from Nonlinear Analysis

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Push-over Analysis with NL-PUSH

Push-over Analysis with NL-PUSH

Push-over Analysis with NL-PUSH

Push-over Analysis with NL-PUSH

Push-over Analysis with NL-PUSH

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QUESTIONS?

Thank you.