Performing Pushover Analysis in Etabs

Performing Pushover Analysis in ETABSPerforming Pushover Analysis in ETABSPerforming Pushover Analysis in ETABS

AIT AIT -- ThailandThailand ACECOMSCivil/Structural EngineerPERFORMANCE BASED SEISMIC DESIGN BkneeBknee

ETABS is a software for linear and nonlinear , static and dynamic analysis and design of buildings in 3D. It can create computer model of a building in the same fashion as a real building.

Frame and Shear WallsLateral Load Resisting Elements

Building Structure

Floor Slab ElementsGravity Load Resisting Elements

ETABS offers a powerful 3D nonlinear static pushover analysis option which tracks hinge formation and helps identify the failure mode of the structure that can be performed either on existing or new construction.

Floor DiaphragmLateral Load Transmitting

Element

About ETABSAbout ETABS


Building Structural SystemBuilding Structural System

The Gravity Load Resisting Elements –

The structural system (beams, slab, girders, columns, etc) that act primarily to support the gravity or vertical loads.

The Lateral Load Resisting Elements–

The structural system (columns, shear walls, bracing, etc) that primarily acts to resist the lateral loads.

The Floor Diaphragm–

The structural system that transfers lateral loads to the lateral load resisting system and provides in-plane floor stiffness.


Modeling of Structural GeometryModeling of Structural Geometry

(b) Solid Model (c) 3D Plate-Frame (d) 3D Frame

(a) Real Structure

(e) 2D Frame

Fig. 1 Various Ways to Model a Real StrutureVarious Ways to Model a Real Structure


Computers assist the structural designer in the creative phase of the design process, but it is the designer who rearranges system components so as to optimize both cost and behavior. Therefore any structural software is not a substitute for informed human judgment and should only be used by competent designer with the training and experience necessary to evaluate and verify any information generated by the software tools like ETABS.

WARNING:


Example Application: 3D Concrete Building Example Application: 3D Concrete Building Building Description

The building is a seven-story three dimensional (3D) symmetrical concrete building frame.

Typical Floor Plan and Elevation

6.0m

6.0m

6 @

3.0

m3.

75m

6.0m 5.0m 6.0m

Columns: 70cm x 70cm

W-E beams: 45cm x 55cm

N-S beams: 45cm x 60cm

Slabs: 135mm


Seismic Design Criteria and Design Earthquake LevelsUnderstanding the fundamentals of the Code requirements in terms

of strength and ductility

and the behavior of the proposed structural system, two sets of design parameters were developed for the proposed structural system’s seismic performance.

The first design parameter is an explicit set of quantifiable acceptable Design Criteria defining performance levels, as shown in Table 1.

Design EarthquakeLevel 1

(Moderate Earthquake)Level 2

(Major Earthquake)Level 3

(Severe Earthquake)

Performance Level No Damage Repairable Damage No Collapse

Column Deformation (FEMA 273 p. 6-20)Beam Deformation (FEMA 273 p. 6-19)

Elastic

Elastic

Rotation < 0.01 radians




Allowable Drift Index 0.005 0.010 0.020

Table 1 Design Criteria

Note: Drift index is the ratio of the horizontal roof displacement to the height of the building relative to the ground.


The second set of design parameter is the Design Earthquake Levels

(see next slide), that relates the seismic load design levels stated in the Table 1 of Design Criteria

to the effective

peak ground motion based on the seismic zones. The values of this seismic zone factor related to the seismic zones from the UBC 1997 can be considered to represent the effective peak ground acceleration (associated with an earthquake that has a 10% probability of being exceeded in 50 years) expressed as a function of the acceleration due to gravity. In the absence of site specific study, the following effective peak ground acceleration (PGA) can be used, as shown in Table 2.

Seismic Risk Seismic Damage

Zone 1Minor damage; maximum ground acceleration is 0.07g; corresponds to magnitude 4 to 4.9 of Richter Scale

Zone 2 Moderate damage; maximum ground acceleration is 0.15g; corresponds to magnitude 5 to 5.9 of Richter Scale

Zone 3 Major damage; maximum ground acceleration is 0.30g; corresponds to magnitude 6 to 6.9 of Richter Scale

Zone 4 No collapse; maximum ground acceleration is estimated to be approximately 0.55g; corresponds to magnitude 7 and higher of Richter Scale

Table 2 Effective PGA


Levels of Earthquake Loads by their Intensities

FEMA Qualitative Description

Probability of Occurrence in

50 years

Return Period (Year)

Corresponding Effective PGA

(g)Level 1: MMI VII

Frequently levelOccasional 50% 72 0.12

Level 2: MMI VIIIDesign Intensity level

Rare 10% 475 0.25

Level 3: MMI IXSeverity level

Very Rare 2% 2475 0.50

Table 3 Design Earthquake Level

The level 1 earthquake is similar in magnitude to the Code level

elastic design in a moderate earthquake, which is the serviceability state event (Immediate Occupancy). The level 2 earthquake correspond to the Code ultimate state level in a major earthquake (Life Safety). The level 3 earthquake correspond to the Code inelastic state level in a severe earthquake (Collapse Prevention).

The approximate empirical correlations between Modified Mercalli

Intensity (MMI) and the PGA is shown on next slide.


One often asks: Can my building withstand a magnitude 7.2 earthquake?

But, the M7.2 earthquake causes different shaking intensities at different locations, and the damage induced in buildings at these locations is different. Thus, indeed it is particular levels of intensity of shaking that buildings and structures are designed to resist, and not so much the magnitude. The peak ground acceleration (PGA), i.e., maximum acceleration experienced by the ground during shaking, is one way the engineers and scientists quantify the severity of the ground shaking (seismic intensity).

Approximate Empirical Correlations Between the MMI Intensities and the PGA


Seismic Design Loading

Seismic Coefficient Cv

= 0.672Response spectrum: UBC 1997 Seismic Coefficient Ca

= 0.40

Using the above-mentioned performance based approach; a Code based equivalent static lateral force analysis and response spectrum analysis were used to size all the structural members. Following this initial stage of design, the nonlinear pushover analysis was used to understand the global behavior of the structural system for its compliance with the design criteria.


Note:Ca

and Cv

are the earthquake near-source effect that defines ground motion response within the acceleration and velocity-controlled ranges of the design response spectrum.

Ground motion response within acceleration controlled range of the spectrum

Ground motion response within velocity controlled range of the spectrum


Static seismic load: UBC 1997 Soil Profile Type = ScSeismic Zone Factor = 0.40 Seismic Source Type = A Distance To Known Seismic Source = 10 km


MaterialsConcrete: 24.131 MPa

Reinforcing steel: ASTM Grade 60 fy

= 415 Mpa

Make sure that you read through the sections of the FEMA-273 Guidelines and Commentary or its updated version FEMA 356 before

you attempt to apply the NSP. The procedures discussed here automate the process but you still need a thorough knowledge of the method to ensure valid results. Finally, it is emphasized that the ETABS documentation for the pushover is not intended to, and does not,

document the pushover analysis method, but rather is intended to document the pushover analysis capabilities of ETABS.

Design Gravity Loading

Live Load: Roof LL = 1.0 kPa

Floor LL = 2.4 kPaDead Load: Toppings = 420 Pa

Partitions = 1 kPa


ETABS Screen Shots

The following ETABS screen shots outlines the basic flow from creating a structural model to analysis and design, and to viewing the results of nonlinear static pushover analysis.1.

Create an elastic building model just like you would for any other analysis.

Modeling PhaseModeling Phase


2. Define and assign rigid diaphragm.

Note:

A rigid floor diaphragm simulates the in-plane rigidity produce by the RC floor slab.

A Diaphragm Constraint causes all of its contrained

joints to translate and rotate together as a planar diaphragm that is rigid against membrane deformation.


3. Define static load cases.


4. Modify lateral loads EQX and EQY.


5. Assign

gravity loads.


6. Define mass source.


7. Define acceleration response spectrum function(s).

Spectrum is a curve showing amplitude (the size of the wiggles on an earthquake recording)

as a function of frequency or period (the time interval required for one

full cycle of a wave). Design response spectrum is a specification of the level of seismic design force, or displacement, as a function of natural period of vibration and damping level.


Dynamic Analysis Using Response Spectrum Seismic Loading

Orthogonal Effects in Spectral Analysis (ORTHOGONAL EFFECTS

are the earthquake load effects on structural elements common to the lateral-force-resisting systems along two orthogonal axes).

A well designed structure should be capable of equally resisting

earthquake motions from all possible directions. One option in existing design codes for buildings requires that

members be designed for "100 percent of the prescribed seismic forces in one direction plus 30 percent of the prescribed forces in the perpendicular direction". However, they give no indication on how the directions are to be

determined for complex structures. For structures that are rectangular and have clearly defined principal directions, these "percentage" rules yield approximately the same results as the SRSS method of directional combination. For rectangle building ETABS and SAP2000 can handle the percentage rule automatically by ABS directional combination with orthogonal scale factor of 1. The SRSS method can be both used in rectangular or arbitrarily shaped building.


Definition of Earthquake Spectra Input Applied at Arbitrary Angle

өA weakness in the current code is the lack of definition of the “principal horizontal directions”

for a general three dimensional structure. If each engineer is allowed to select an arbitrary reference system, the “dynamic base shear”

will not be unique and each reference system could result in a different design. One solution to this problem that will result in a unique design base shear is to use the direction of the base shear associated with the fundamental mode of vibration 1 and 2 (by performing modal analysis in SAP2000) as the definition of the “major principal direction”

for the structure. The “minor principal direction”

will be, by definition, 90 degrees from the major axis. This approach has some rational basis because it is valid for regular structures. Therefore, this definition of the principal directions will be used for the method of analysis presented in this presentation..

Angle өө

= arctan

(Modal Base Shear Y / Modal Base Shear X)


Recommendations On Orthogonal Effects

The required design seismic forces may come from any horizontal direction and, for the purpose of design, they may be assumed to act non-concurrently in the direction of each principal axis of the structure.

For three dimensional response spectra analyses, it has been shown that the "design of elements for 100 percent of the prescribed seismic forces in one direction plus 30 or 40 percent of the prescribed forces applied in the perpendicular direction" is dependent on the user's selection of

the reference system. These commonly used "percentage combination rules" are empirical and can underestimate the design forces in certain members and produce a member design which is relatively weak in one direction. It has been shown that the alternate building code approved method, in which an SRSS combination of two 100 percent spectra analyses with respect to any user defined orthogonal axes, will produce design forces that are not a function of the reference system. Therefore, the resulting structural design has equal resistance to seismic motions from all directions.


8. Define response cases in X and Y direction. Consider orthogonal effect.

Initial scale factor = 1

Using a scale factor equals to 1 has two purpose:

1.

The response spectra need not be scaled to match the site specific spectra and structure specific criteria.

2.

To obtain the unscaled

RSA elastic response

base shear.


9. Set analysis options.


10.

Run analysis and compare response spectrum RSP base shear with EQX and EQY base shear.


Response spectrum final scale factor = VEQ/VRSp

Where:

VEQ= Static base shear

VRSp

= Response spectrum base shear

Scaling of ResultsAfter “dynamic base shear”

are calculated in the major and minor principal direction. The next step is to scale the previously used spectra shapes by the ratio of “static design base shear”

to the minimum value of the “dynamic base shear.”

This approach is more conservative than proposed by the current

requirements because only the scaling factor that produces the largest response is used. However, this approach is far more rational because it results in the same design earthquake in all directions.

The current code allows the use of different scale factors for a

design spectra in two different directions. This will result in a design that has a weak direction relative to the other principal direction.

The reasons for having to calculate scaling factors are twofold.

1.

If a “normalized”

or “acceleration”

spectra was used to calculate the spectral results, the spectral results must be scaled to match the site specific spectra and structure specific criteria.

2.

The UBC sets minimum values for the design base shear.



Analysis PhaseAnalysis PhaseThe task in the analysis phase can be divided into Structural Analysis

tasks, Behavior

Assessment tasks, and Demand-Capacity

tasks. The Structural Analysis

tasks are for

running structural analyses and design/check the structure. The Behavior Assessment

tasks allow you to examine and check the behavior of the analysis model. The Demand-Capacity

tasks allow you to calculate performance point, and hence make decisions about the performance of the structure.


1. Run and review the results of the basic linear and dynamic analysis to verify the behavior of the building prior to running pushover analysis.

Structural Analysis Tasks


2. Start the design/check of structure.


3. Unlock model and assign the reinforcement for columns to be checked.


4. Assign the reinforcement overrides for beams which are specified areas of longitudinal steel that occurs at the top and bottom of the left and right ends of the beam.

Note:

Refer to the ETABS User Manual how these overrides are used by ETABS.


Note:

Refer to the ETABS User Manual how these overrides are used by ETABS.


•

Phenomenological

•

Microscopic

Note: RC structures

can be modeled for Nonlinear Response Analysis by:

Incre

asin

g

leve

l of

Refin

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ent

and C

om

ple

xity


Phenomenological

Lumped Nonlinearity

Distributed Nonlinearity

Inelastic Hinges

F

D

KINEMATIC

F

D

ORIGIN-ORIENTED

F

D

PEAK-ORIENTED

F

D

CLOUGH DEGRADING TRILINEARTAKEDA

HYSTERESIS MODEL ARE:KINEMATIC ORIGIN-ORIENTEDPEAK-

ORIENTED CLOUGH DEGRADING TRILINEARTAKEDA


Microscopic

Fiber Models

Fiber Section

Concrete Cell Steel Cell


•

Phenomenological

•

Microscopic

Incre

asin

g

leve

l of

Refin

em

ent

and C

om

ple

xity

Lumped Nonlinearity (used in the presentation)Distributed Nonlinearity

Fiber Models ; the most promising model~ Adequate Accuracy & Efficiency


5. Define hinges to columns if the default hinge is not used.

Note: There are three types of hinge properties in

ETABS. They are default hinge properties, user-defined hinge properties and generated hinge properties. Only default hinge properties and user-defined hinge properties can be assigned to frame elements. (Currently, hinges can be introduced into frame objects only and assigned at any location along the frame

object). When these hinge properties are assigned to a

frame element, the program automatically creates a different generated hinge property for each and every hinge.

The built-in default hinge properties are typically based on FEMA-273 and/or ATC-40 criteria and cannot be modified.

The generated hinge properties are used in the analysis. They can be viewed, but they can not be modified.


Assign hinges to columns to generate an inelastic building model.

Note:

Relative distance is measured from the I-end of the beam, and is based on the clear length between rigid end offsets. A “0”

relative distance indicates the hinge is

at the I-end of the beam. A “1”

relative distance indicates the hinge is at the J-end of the beam. Hinges may be located anywhere along the length of the beam.


6. Define hinges to beams if the default hinge is not used.


Assign hinges to beams to generate an inelastic building model.


7. Rerun the analysis and the design/check of structure.


8. Define the static nonlinear load cases. (Note: Typically the Load to Level Defined By Pattern option is used to apply gravity load, and the Push To Displacement Magnitude of option is used to apply lateral pushes. Pushover analysis takes time. Since it is a step-wise linear analysis, analysis time and results is very much dependent on the number of analysis cycle. Whenever there is load increment on the structure, a new analysis cycle starts.)


9. Run the static nonlinear analysis.

Pushover analysis will continue until any of the following three

conditions is satisfied:

a) Cumulative base shear is less than or equal to the base shear defined

by the user.

b) Displacement at the control joint in the specified direction exceeds specified displacement.

c) The structure becomes unstable.


Behavior Assessment Tasks

Push 2 (Load Pattern Acceleration X-direction)

1. Deflected shapes. Display the pushover deformed shape on step-by-step basis to view the pushover displacement shape and sequence of hinge formation (hinges appear when they yield and are color coded based on their state).


Note: The color of the hinges indicates the state of the hinge, i.e, where it is along its force displacement curve.

In step 7 the building deformed at Life Safety performance level.

Click


Note: To view the displacements of individual nodes right click them.

Click


In step 8 the building deformed beyond

ductile limit point (Collapse Prevention performance level). It is at this level where significant strength loss begins in the second story beams.

Click


Click


Demand-Capacity Tasks

Push 2 (Load Pattern Acceleration X-direction)

1. Display the pushover curve to view the building responses according to the performance point or to adjust the intensity of ground shaking and the damping ratio to determine the appropriate levels of ground motion and performance objectives for the building in order to meet the owner’s expectation.


The pushover analysis provides a Shear vs. Displacement pushover curve to indicate the inelastic limit as well as lateral load capacity of the building. The changes in slope of this curve gives an indication of

yielding of various structural elements. When the slope of the curve does not change it means that structural elements remains elastic.

Click


Pushover curve when Ca = 0.4 and Cv

= 0.672.

The Shear vs

Displacement pushover curve is converted to the Acceleration vs

Displacement Response Spectrum. The pushover curve also shows the demand spectrum, and various performance points. The performance point represents the global response of the building.


2. Adjust the intensity of ground shaking and the damping ratio to determine the appropriate levels of ground motion and performance objectives for the building in order to meet the owner’s expectation.

The pushover curve when Ca = 0.4 and Cv

= 0.9


Notes:When the capacity spectrum option is chosen, the pushover

curve is displayed in

ADRS(Acceleration-Displacement Response Spectrum) format. Refer to ATC-40 for a discussion of this format which is essentially a plot of spectral acceleration versus spectral displacement. In ETABS, the force-displacement pushover curve is converted to the ADRS format by converting the resultant base shear to a spectral acceleration , Sa, and the control displacement in the control direction to a spectral displacement, Sd, generally based on equations 8-1 thru 8-4 in ATC-40.

The single demand spectrum (variable damping) curve is constructed by doing the following for each point on the ADRS pushover curve:

Draw a radial line through the point on the ADRS pushover curve.

This is a line of constant period.

Calculate the damping associated with the point on the curve based on the area under the curve up to that point.

Construct the demand spectrum, plotting it for the same damping level as associated with the point on the pushover curve.


The intersection point of the radial line and the associated demand spectrum represents a point on the Single Demand Spectrum (Variable Damping) curve.


Structural Behavior Type is classified in the table below.

Select A, B or C to obtain a reduction factor applicable for effective damping

Shaking Duration

Essentially New

Building

Average Existing Building

Poor Existing Building

Short Type A Type B Type C

Long Type B Type C Type C


3. Since the performance point (intersection of the ADRS pushover curve and the single demand spectrum (variable damping)) represent the

global

response of the building, display the pushover capacity/demand comparison table to determine what step that the structural member begin to reached its limit state on the particular ground motion and damping ratio.

Ca = 0.40 Cv

= 0.672


Ca = 0.40 Cv

= 0.90

In the Pushover Capacity/Demand Comparison table take note of the following:•

Step identifies the step number in the pushover curve.

•

Teff

is the effective period at the associated step.•

βeff

is the effective damping at the associated step.

•

Sd(C) and Sa(C) define a point on the ADRS capacity curve for the associated step.•

Sd(D) and Sa(D) define a point on the single demand spectrum (variable damping) curve for the associated step.

•

Alpha is the factor used in converting the base shear to spectral acceleration at the associated step.

•

PF*φ is the factor used in converting the displacement to spectral displacement at the associated step.


Damping is a measure of the dissipation of energy in the structure. It represent the frictional characteristics and energy losses of the structure. Typically, a

reinforced concrete building

will have 1 to 2% damping prior to an earthquake. As cracking and structural and nonstructural damage develop during earthquake, this increase to

about 5%.


Evaluation of PerformanceEvaluation of Performance

Displacement Response•

Looking at the Pushover curve, the inelastic roof displacement of 0.190 meter at the performance point generated by the severe earthquake with seismic design level

coefficient Ca = 0.4 and Cv

= 0.672 represents the reliable displacement capacity of a building.

•

Looking at deflected shape of Life Safety limit state the highest inelastic roof displacement is 0.270 meter as it is about to reach its ductile limit state (Collapse Prevention), where significant strength loss begins.

•

When Cv

= 0.9 in the Pushover curve, the performance point changed to an inelastic roof displacement of 0.251 meter, which represents the highest reliable roof displacement capacity of a building as it reaches its limit of structural stability when the specified ground motion is exceeded.

Push2 (Load Pattern Acceleration X-Dir)


Design Implication

•

Structural Damage Objective –

Typically the threshold of structural damage is associated with some inelastic behavior. From a displacement perspective, the building highest inelastic drift δ

of 0.251 meter when the specified earthquake magnitude is exceeded

is

about to produce permanent inelastic deformation. If laterally deformed beyond 0.251 meter, the structure can experience instability and collapse.

•

Life Safety Objective – The highest earthquake design level performance inelastic

building drift δ

is 0.190 meter giving a drift ratio of δ/H = 0.190/21.75 = 0.009 and this is

less than

idealized inelastic drift index of 0.01.

•

Collapse Prevention Objective –

The highest inelastic performance building drift δ

when the earthquake

design level is exceeded

is 0.262 meter giving a drift ratio of

δ/H =

0.251/21.75 = 0.012 and this is less than

idealized inelastic drift index of 0.02.


Design Implication (Continued)

•

Capacity –

Pushover deformed shape shows that life safety is reached in step 7 and collapsed in the second story beams in step 8.

•

Ductility - In the Pushover curve the severe event of earthquake design level

performance base shear is 4633 kN

and the severe event of earthquake design level inelastic roof displacement is 0.190 meter, while the Code design elastic base shear is 1467 kN

and the Code design elastic roof displacement is 0.059 meter.


Conclusion

•

There is a possibility that the beams in the second story will be damaged in step 8 to an earthquake intensity with earthquake near source effect Ca = 0.4

and Cv

= 0.672, that

defines the ground motion response within the acceleration and

velocity controlled ranges of the design response spectrum.

•

Since the computed drift ratio (δ/H) = 0.012) when the specified earthquake magnitude is exceeded

is less than

idealized inelastic drift index of 0.02 and the inelastic response

of the building in the earthquake design level shows life safety

capacity, the design of the building is within Life Safety and Collapse Prevention performance objectives.

•

The building reliable inelastic displacement of 0.190 meter has increased to 0.251 meter when the specified earthquake magnitude is exceeded,

that is, when Ca and

Cv

are 0.4 and 0.9 respectively.

•

The roof displacement corresponding to the severe event of earthquake design level is 0.190/0.059 = 3.22 times the roof displacement at Code elastic design level.


•

The overall result of the pushover analysis in X-direction indicated that the capacity and ductility of the seven story RC building is adequate to sustain the severe earthquake excitation, and some members of the moment resisting frame remain elastic and thus maintain the stability of the building structure.

Analysis results for other load pattern will be demonstrated by running ETABS

Conclusion (Continued)

Documents

Performing Pushover Analysis in Etabs