STR 614: Seismic StructuralAnalysis

(Pushover Analysis)

CUFE, Postgraduate studies2014/ 2014, Spring Semester

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 2

Evaluation of seismic designHistorical Approach:

Traditional Code Basis:

Current Trend:Design based on displacement

RVVbase max

weight theof%10~5baseV

PushoverAnalysis

In-between thetwo procedures ofanalysis

Only concern withthe maximumdisplacement.

Time HistoryAnalysis

Accurate andconsider strengthdegradation

Can take intoaccount highermode effect

PerformanceBased seismic

Long Time

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 3

Seismic Structural AnalysisResponseSpectrum

Simple and Quick Only consider thefirst mode

Inaccurate due tothe stiffness

SeismicDemand

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 4

Seismic Structural Analysis

CapacitySpectrum

PushoverAnalysis

Capacity is a representationof the structural ability.Demand is a representation ofthe EQ ground motion

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 5

Capacity Vs. Demand As displacements increase, the period of the structure lengthens. Inelastic displacements increase damping and reduce demand.

At the performance point,capacity and demand are equal.

The maximumdisplacement implies aunique damage state forthe building relateddirectly to a specific EQ.

Life SafetyDS-III

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 6

Building Performance LevelsPerformance

Point

OperationalDS-I

The post-EQdamage is limitedand safe.Cosmeticrepairing isneeded

ImmediateOccupancyDS- IIMost widely used

criteria foressential facilitiesReasonableusable

CollapsePreventionDS-IV

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 7

Capacity Curve Capacity Spectrum is derivate from an approximate nonlinear,

inelastic static analysis for the structure. In the process of performing this incremental nonlinear static

analysis, a capacity curve is developed for the building.DS

-I

DS-II

DS-II

I

DS-IV

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 8

Factors affecting Capacity CurveLateral Load Pattern Uniform *

Equivalent lateral force pattern

First (or any other) mode shape*

ii mf

kiii hmf

2.5sec.for0.20.5sec.for0.1

T

Tk

Mf iii mf

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 9

Developing Capacity curve1. Develop a nonlinear computer model of the structure.

Dimensioning and reinforcement of the beams and columnsare input in the section properties.

Stress-strain relationships are input in the materialdefinitions.

Moment-curvature and moment-axial plastic hinges aredefined and assigned.

Soil-structure interaction can be accounted in the analysis.

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 10

Developing Capacity curve (cont)2. Apply lateral story force in the proportion to the product the

mass and fundamental mode shape. (first mode shape loadpattern is used herein) This analysis should include gravity loads. The result from this step is the capacity curve (pushover

curve).

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 11

Developing Capacity curve (cont)2. Apply lateral story force in the proportion to the product the

mass and fundamental mode shape. (first mode shape loadpattern is used herein) This analysis should include gravity loads. The result from this step is the capacity curve (pushover

curve).

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 12

Transforming the capacity curve toAcceleration Displacement ResponseSpectrum (ADRS)The capacity spectrum is obtained by transforming the capacitycurve from base shear (VBase) vs. lateral displacement (d)coordinates to spectral acceleration (Sa) vs. spectral displacement(Sd)

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 13

Pushover analysis in seismicregulations

N2 (FEMA-365) and Capacity Spectrum methods (ATC 40)FEMA 365:

https://www.wbdg.org/ccb/DHS/ARCHIVES/fema356.pdf

ATC 40: chapters 6 and 8http://www.civil.iitb.ac.in/~p0saurabhrs/ATC-40.pdf

Capacity Spectrum is a method that allows a graphical comparisonbetween the lateral structural capacity of the building and theseismic demand of the EQ ground motion.

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 14

Capacity Spectrum Method

Totalbasea

MVS

TotalM

top

roofdS

Ni

ii

N

iii

m

m

12

1

Modal Mass

Participation factor

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 15

Capacity Spectrum Methodad STS 2

2

4

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 16

Calculating the Demand usingCapacity Spectrum MethodThe location of the performance point must satisfy tworelationships:

The point must lie on the capacityspectrum curve in order to representthe structure at a given displacement.

The point must lie on the spectraldemand curve, reduced from theelastic and 5% damping isconsidered, to represent thenonlinear demand at the samestructural displacement

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 17

Fragility In order to design a certain structure

to withstand seismic loads, thestructure is modeled to obtain itscapacity spectrum.

On the other hand, a specific Earth-Quake ground motion (or a designresponse spectrum) is used for theanalysis.

This is Not accurate

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 18

Fragility For numerous EQ, with the same PGA, there is a lot of

performance points.

There is a mean (average) and astandard deviation for all thesepeak displacements.

In accordance to these twovalues, the probability ofexceeding a certain roof driftvalue can be obtained.

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 19

Fragility

STR 614: Seismic Structural Analysis Spring Semester (2014/2015) 20

FragilityProbabilit

y of ex

ceedin

g Dam

age St

ate

Peak Ground Acceleration

DS - IDS - II

DS - III

DS - IV