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DEPARTMENT OF CIVIL ENGINEERINGMANIPAL INSTITUTE OF TECHNOLOGY

Deepak S BashettyReg.No:060918003

PERFORMANCE BASED SEISMIC ANALYSIS OF RC BUILDINGS

Under the Guidance of  

Mr.S.VEERAMANI Dr.KRISHNAMOORTHY

Chief Engineering Manager (Civil) Professor,

Engineering Design Research Centre Department of Civil Engineering

(Building & Factories Sector) Manipal Institute of Technology,

ECC Division L&T, Chennai – 600089 Manipal –576 104

External Guide Internal Guide

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Contents

1. Introduction2. Methods of analysis3. Modeling Approach4. Details of Analysis5. Result and Discussion6. Conclusion7. References

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Introduction

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Performance-based Design The basic concept of performance based seismic

design is to provide engineers with the capability to design buildings that have a predictable and reliable performance in earthquakes.

Thus the Performance-based seismic design is a process that permits design of new buildings or upgrade of existing buildings with a realistic understanding of the risk of life, occupancy and economic loss that may occur as a result of future earthquakes.

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Performance-based design begins with the selection of design criteria stated in the form of one or more

performance objectives. Each performance objective is a statement of the acceptable risk of incurring specific levels of damage, and the consequential losses that occur as a result of this damage, at a

specified level of seismic hazard.

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Performance ObjectivesFully Operational, OperationalImmediate-occupancy,life-safety and collapse-prevention

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Selecting Performance Present Generation

Beer!Beer!Food!

Operational

Operational – negligible impact on building

Beer!Beer!Food!Food!

Joe’sBeer!Beer!Food!Food!Beer!Beer!Food!

Joe’s

ImmediateOccupancy

Immediate Occupancy – building is safe to occupy butpossibly not useful until cleanup and repair has occurred

Beer!Beer!Food!Food!

Joe’s

Beer!Beer!Food!Food!Beer!Beer!Food!

LifeSafety

Life Safe – building is safe during event but possibly notafterward

Collapse

Prevention

Collapse Prevention – building is on verge of collapse, probable total loss

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Performance based design

Performance Levels

Building Damage States

Immediate occupancy

Life safety

Collapse prevention

Displacement parameter

Forceparameter

Demand for specific hazard level

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A simple flow chart explaining the “Performance based design”

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Determination of Performance Point

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Generally, a team of decision makers, including the building owner, design professionals, and

building officials, will participate in the selection of performance objectives for a building.

Once the performance objectives are set, a series of simulations (analyses of building response to loading) are performed to estimate the probable performance of the building under various

design scenario events.

If the simulated performance meets or exceeds the performance objectives, the design is complete otherwise it has to be redesigned.

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Advantages of Performance Based Seismic Design

Systematic methodology for assessing the performance capability of a building

Design individual buildings with a higher level of confidence

Design individual buildings to achieve higher performance and lower potential losses.

Design individual buildings that fall outside of code-prescribed limits with regard to configuration, materials, and systems to meet the performance intended by present building codes

Assess the potential seismic performance of existing structures and estimate potential losses in the event of a seismic event.

Performance-based seismic design offers society the potential to be both more efficient and effective in the investment of financial resources to avoid future earthquake losses

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Differences between traditional approach and performance based approach

1) Conventional limit-states design is typically a two-level design approach having concern for the service operational and ultimate-strength limit states for a building, performance-based design can be viewed as a multi-level design approach that additionally has explicit concern for the performance of a building at intermediate limit states related to such issues as occupancy and life-safety standards.

2) The performance based analysis is based on quantifying the deformation of the members and the building as a whole, under the lateral forces of an earthquake of a certain level of seismic hazard. Traditional Approach-Force based Design has no measure of the deformation capability of members or of building.

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3) The deformation or strains are better quantities to assess damage than stress or forces. Since the deformation are expected to go beyond the elastic values.

4) The performance based analysis gives the analyst more choice of ‘performance’ of the building as compared to the limit states of collapse and serviceability in a design based on limit state method.

5)Traditional based design uses Elastic behavior where as Performance based design uses inelastic behavior

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Methods of analysis

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Methods of analysisGenerally for analyzing the structure the following analysis

methods are used depending upon the requirements.

1) Linear static procedure2) Linear dynamic procedure3) Nonlinear static procedure

1. Pushover analysis2. Capacity spectrum method

4) Nonlinear dynamic procedure1. Time history Analysis

Push-over and Time History analyses tools to perform non-linear analysis are considered.

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pushover analysis is the one which is suitable for the performance based seismic design, because elastic analyses are insufficient, therefore they cannot realistically predict the force and deformation distributions after the initiation of damage in the building.

Inelastic analytical procedures become necessary to identify the modes of failure and the potential for progressive collapse.

Inelastic time-history analysis are most realistic analytical approach for evaluating the performance of a building. However, the inelastic time-history analysis is usually too complex and time- consuming in the design of most buildings.

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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., parabolic, inverted triangular or uniform).

• Building is pushed in one horizontal direction. 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.

• Proportion of applied force on each floor is constant , only its magnitude is increased gradually (i.e., Load pattern may be 1st mode shape, parabolic, uniform, inverted triangular etc.).

• Material nonlinearity is modeled by inserting plastic hinge at potential location.

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Continued…• 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.

• Push over analysis requires a large number of assumptions and member response curves are to be provided to the program before it can analyze.

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VB

Δroof

Δroof

VB

Continued…Continued…

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Why Push-Over Analysis?• Static Nonlinear Analysis technique, also known as sequential yield

analysis, or simply "push-over" analysis.

• To get the performance level of structure in case of seismic load.

• Elastic analysis cannot predict failure mechanism and account for redistribution of forces during progressive yielding.

• The use of inelastic procedure for design and evolution is an attempt to help engineer better understand how structures will behave when subjected to major EQ, where it is assumed that the elastic capacity of the structure will be exceeded.

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What is Time History Analysis?

• Time History analysis is a step by step analysis of the dynamical response of a structure to a specified loading that may vary with time.

• The performance analysis may be– Linear – Non-linear

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Why Linear Time History Analysis? • To get the variation of forces at each time step and to get the maximum

response under the the particular time history.

• To verify the design of structure. If forces in the member are within the design forces, then no need to do Non- Linear time history analysis.

• If the forces are exceeding the design forces, then Non-Linear time history analysis is required to understand the performance of structure.

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Why Non-Linear Time History Analysis?

• Elastic analysis cannot predict failure mechanism and account for redistribution of forces during progressive yielding.

• Certain part may yield when subject to major earthquake.

• To get the performance level of structure in case of seismic load.

• The use of inelastic procedure for design and evolution is an attempt to help engineer to better understand how the structures will behave when subjected to major EQ.

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Pushover Analysis Procedure

Create 2D/3D Model

Assign end offsets

Design Structure

Assign Hinge propertiesBeams – M3, V2Columns –PMM, V2

Define Static Pushover Cases

Gravity Pushover (Force controlled)Lateral Pushover(Displacement controlled)

Define Load case(Lateral Load at centre of mass)

Analyze

Run analysis, Run Now

Establish Performance pointBase shear Vs Roof DisplacementSequential Hinge Formation

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Performance Analysis Create Model as Designed

Define Time History Function

Define Linear Time History cases

Analyze

CheckMember Forces ≤ Design Force

Define Non linear Time History Case

Assign Plastic Hinges (Material Nonlinearity)

Define Geometric Nonlinearity

Analyze

Results

Check the performance of the structure and if required, redesign

YES

No

Material nonlinearity is modeled by inserting plastic hinge at potential location.

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Modeling

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Modeling of Beams and Columns

• 3D Frame Elements

• Cross Sectional dimensions, reinforcement details, material type

• Effective moment of inertia (As per ATC 40)

Beams Rectangular 0.5 Ig

T-Beam 0.7 Ig

L-Beam 0.6 Ig

Columns 0.7 Ig

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Modeling approach

Lp = 0.5H

Location of hinges in beams and columns:

• Beam & column elements - nonlinear frame elements with lumped plasticity - defining plastic hinges at both ends of the beams and columns.

lcolumn

Dcolumn

lbeam

Dbeam

Moment and shear hingeAxial-moment and shear hinge

L = Critical distance from critical section of plastic hinge to point of contra flexurefye = yield strength of transverse reinforcementdbl= diameter of transverse reinforcement

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Modelling Approach• Plastic hinge is defined in terms of Force-deformation behaviour

of the member.

• Values are depend on type of element, material properties, longitudinal and transverse steel content - axial load level on the element.

• For beam, flexural hinge is assigned

• For Column, axial and flexural hinges are assigned

• A-unloaded condition, B-effective yield, C-ultimate strength, D- residual strength and E-maximum deformation

Force-deformation Relationship of a Typical Plastic Hinge

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EXAMPLE-1

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Description of Structure

Building Type RC frame without brick infillConcrete compressive strength Yield Strength of reinforcement

– 25 MPa– 415 MPa

Number of stories Ground + 5 Storey

Plan dimensions 16 m 12 m

Building height 24.775 m above plinth level

Type of footing Raft footing (fixed)

•Seismic performance - inter-storey drift ratio, ductility, maximum base shear, roof displacement and plastic hinge formation.

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Column Dimensions and Area of Longitudinal Reinforcement

Column Label

Cross Section

mm x mm

Acol

(mm2)

1 & 9 300 x 500 5892

2 & 10 300 x 500 4020

3 & 11 300 x 400 3216

4 & 12 300 x 300 3080

21& 23 300 x 300 1232

24& 26 300 x 300 905

27& 29 300 x 300 905

5 650 x 650 14784

6 600 x 600 12744

7 550 x 550 10620

8 500 x 500 7856

22 450 x 450 6372

25 300 x 300 4928

28 300 x 300 804Acol = Area of longitudinal reinforcement in column

The beam in all storey levels is of size 300mm x 600mm with tension and compression reinforcements of 3885mm2 and 2412mm2 respectively. The column dimensions and area of longitudinal reinforcement (Acol) details are presented in Table

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Details of Analysis• Pushover Analysis

Gravity analysis is an Force controlled. Pushover analysis is a Displacement controlled. Behaviour of structure characterized by capacity curve (base shear force Vs. roof displacement)

• Time-History Analysis Step by step analysis of the dynamical response of structure

to a time varying load. 7 sets of strong ground motion in the magnitude range of

6.5-7.5 were selected. The peak displacement from NTH is not correspond to

ultimate displacement from pushover analysis. To facilitate comparison the ground motion records scaled

according to peak roof displacement =target displacement

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Input Ground Motions

EQ

No.

Year Earthquake Recording Station

Magnitude

PGA in g

EQ. Scale FactorDBE MCE

1 1979 El Centro Array #7 7.0 0.338 0.45 0.785

2 1999 Duzce Turkey 7.1 0.348 0.8 1.15

3 1971 San Fernando Old Ridge 6.5 0.268 1.7 1.9

4 1995 Kobe KJM 6.9 0.343 0.35 0.5

5 1976 Friuli Tolmezzo 6.5 0.315 0.95 1.2

6 1994 Northridge Arleta 6.7 0.344 0.6 1.0

7 1989 Loma Prieta Gilroy #2 7.1 0.322 0.35 0.515

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Base shear• Maximum base shear -

571kN - 10% of seismic weight - displacement corresponding to base shear - 1.02m.

• Displacement ductility - 2.32.

• Base shear values - DBE & MCE levels from Pushover analysis - 116 kN & 171kN

• From NTH - 151kN & 51kN.

• Results from NTH are 23% & 32% higher than pushover analysis.

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Target Displacement• Represent the maximum displacement likely to be experienced

during the design earthquake • Performance levels are calculated based on equation from FEMA

356.

C0 = Modification factor to relate spectral displacement of an equivalent SDOF system to the roof displacement of building MDOF systemC1 = Modification factor to relate expected maximum inelastic displacements to displacements calculated for linear elastic responseC2 = Modification factor to represent the effect of pinched hysteretic shape, stiffness degradation and strength deterioration on maximum displacement responseC3 = Modification factor to represent increased displacements due to dynamic P- ∆ effectsTe = Effective fundamental period of building, secSa = Response Spectrum Acceleration at effective fundamental period and damping ratio of buildingg = Acceleration due to gravity

g4T

SCCCC 2

2e

a3210t

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Performance Point

• Intersection of capacity & demand spectrum.• Performance assessed for two levels of performance - Life

Safety (LS) under Design Basis Earthquake (DBE) & Collapse Prevention (CP) under Maximum Considered Earthquake (MCE).

• Base shear, roof displacement, spectral acceleration, spectral displacement, effective time period and effective damping - performance point - shown.

• Displacement @ performance point in DBE level - 123mm greater than target displacement 119mm.

• Displacement @performance point in MCE level - 171mm lesser than target displacement 177mm.

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Demand Vs Capacity Spectrum

DBE Level

MCE Level

Demand SpectrumDemand SpectrumCapacity SpectrumCapacity Spectrum

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• Important indicator of building performance.

• 3rd storey level- the largest interstorey drift values -0.58% and 0.85% at both DBE and MCE levels.

• Interstorey drift ratio - increased with increase in storey level up to first 4 stories - thereafter - reverse trend at both levels of earthquake.

• DBE level - pushover analysis over-estimated - interstorey drift ratio - lower storey levels - underestimated - upper storey levels.

• MCE level -pushover analysis -over-estimated - interstorey drift ratio - all storey levels.

Interstorey Drift

htStoreyHeigntfloorsntofadjaceDisplaceme

izontallativedHorRe

ydriftInterstore

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0

1

2

3

4

5

6

7

0.00 0.20 0.40 0.60 0.80 1.00

Interstorey drift in %

Stor

ey L

evel

DBE

MCE

(a) Results from Pushover Analysis at DBE & MCE Levels

0

1

2

3

4

5

6

7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Intersotrey drift in %

Stor

ey L

evel

NTH-DBE

NSP-MCE

NSP-DBE

NTH-MCE

(b) Comparison between Pushover & Time-history Results at DBE & MCE Levels

0

1

2

3

4

5

6

7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Interstorey Drift Ratio in %

Stor

ey L

evel

Elcentro

Duzce

San Fernando

Friuli,Italy

Kobe

Northridge

LomaPrieta

Average 0

1

2

3

4

5

6

7

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

Interstorey Drift Ratio in %

Stor

ey L

evel

Elcentro

Duzce

San Fernando

Friuli,Italy

Kobe

Northridge

LomaPrieta

Average

(a) Results from Time-history Analysis at DBE Level

(b) Results from Time-history Analysis at MCE Level

Figure 8.6 Interstorey Drift Ratios from Time – history Analysis

Figure 8.5 Interstorey Drift Ratios

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Plastic Hinge Pattern

• Pushover analysis • Outer columns at all storey level yielded first • Beams showing hinges in yielding stage at one end only in

the DBE level • Beams in the MCE Level at all the storey levels except

topmost showing hinges in yielding stage.

• Time History Analysis• More number of hinges at yielding in beam ends model

compared to pushover analysis at both DBE and MCE levels.

• At MCE level middle columns in upper stories also yielded; but in the pushover analysis not showing hinges in any column.

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Plastic Hinge Pattern at DBE Level

(a) Pushover Analysis (b) Time History Analysis

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Plastic Hinge Pattern at MCE Level

(a) Pushover Analysis (b) Time History Analysis

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Plastic Hinge Pattern• Pushover analysis

At final step (frame roof pushed up to 4% of height of frame) - hinge formation started with yielding in outer columns at all stories

and yielding of few beam ends in upper stories.

Middle columns in the upper stories start yielding with simultaneous yielding of base columns.

Beams experienced less number of hinges than columns but shows significant damage or failure stage.

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Conclusions• Base shear from time history analysis are 23% and 32% higher

than pushover analysis at DBE and MCE levels.

• Roof displacement at DBE and MCE levels indicates that frame satisfies the requirement for Life Safety performance at DBE level and not satisfies the requirement for Collapse Prevention performance at MCE level.

• From analyses the middle storey experience the maximum interstorey drift ratio at both levels.

• Pushover analysis over estimate the interstorey drift ratio compared with time history analysis

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• No significant difference of plastic hinge pattern at DBE and MCE levels from both analyses

• Time-history analysis shows more number of beam hinges at both levels.

• From time history analysis at MCE level, middle column shows yielding but not in pushover analysis.

• The behaviour of frame designed for gravity load shows column side sway mechanism.

Conclusions

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EXAMPLE-2

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Description of StructureA regular four storeyed (G+3), five storeyed (G+4), six storeyed (G+5) and a seven storeyed (G+6) building were considered in the present study. All the buildings are rectangular in plan with same plan dimensions and storey height. The plan view and sectional elevation of a G+3 building is shown in Figure.

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Figure: Comparison of Variation of Fundamental Time Period using Time History

Analysis

Figure :Comparison of Variation of Roof Displacement using Time History Analysis

Results

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• Analysis results shows that, hinges will be formed earlier in frames of structures without strut action than frames of structures with strut action

• It is observed that, in all the cases, the fundamental time period of the structure with strut action is considerably less than the structures without strut action.

• Figure, compares the roof displacement of G+3, G+4, G+5 and G+6 frames with and without strut action.

• The graph shows that roof displacement get considerably (50%) reduced with strut action.

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CONCLUSIONS From the pushover and time-history analyses of 2D RC frames with infill, the following conclusions are drawn:

• It is found that the fundamental time period of the structure get considerably reduced due to strut action. This will alter the response of the structure to lateral loads.

• In addition strut action will considerably reduce the roof displacement. This will increase the safety level of the structure.

• Hence it is recommended to model infill stiffness using equivalent diagonal struts for any lateral load analysis.

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References1. Ali M. Memari, Shahriar Rafiee, Alireza Y. Motlagh and

Andrew Scanlon (2001), “ComparativeEvaluation of Seismic Assessment Methodologies Applied to a 32-Story Reinforced Concrete Office Building”, Journal of Seismology and Earthquake Engineering, Vol. 3 ,No.1, 31-44.

2. Andreas J. Kappos, Alireza Manafpour (2001), “Seismic design of R/C buildings with the aid of advanced analytical techniques”, Engineering Structures, 23, 319–332

3. Chung C. Fu and Hamed AlAyed, “Seismic Analysis of Bridges Using Displacement-BasedApproach”, 1-20.

4. Federal Emergency Management Agency, Prestandard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 356), Washington D.C. November 2000.

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Contd…5. IS 456-2000, Indian Standard Plain and Reinforced Concrete - code

of practice, Bureau of Indian Standards.6. IS 1893 (Part 1) – 2002, Indian Standard Criteria for Earthquake

Resistant Design of Structures, Bureau of Indian Standards. 7. Mehmet Inel, Hayri Baytan Ozmen, (2006) “Effects of plastic hinge

properties in nonlinear analysis of reinforced concrete buildings”, Engineering Structures, 28, 1494–1502.

8. SAP2000. Linear and nonlinear static and dynamic analysis and design of structures. Ver.10.0. Berkeley (CA, USA): Computers and Structures, Inc.

9. Sashi K. Kunnath and Erol Kalkan (2004), “Evaluation of Seismic Deformation Demands using Nonlinear Procedures in Multistory Steel and Concrete Moment Frames”, ISET Journal of Earthquake Technology, Paper No. 445, Vol. 41, No. 1, March 2004, pp. 159-181

10. ATC 40 (1996), “Seismic Evaluation and Retrofit of Concrete Buildings”, Applied Technology Council, USA, Vol.1.

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Moment curvature relationship for singly

reinforced sections

57

Finding Mcr & cr Values

bc

crcr

bt

tstt

ckcr

crcr

yEf

yyD

ydmADybDbDI

ff

yIfM

22

3

2

7.0

58

Finding M- values

• Assume ec

• Find k1& k2 for corresponding ec

• Assume initially a value for kd , now

• Compare the assumed kd & the calculated kd. If matching take that value , otherwise try with new kd.

sstck

sss

cs

fAbkdfkk

Ef

kdkdd

31

59

Finding M- values (cont…)

kdkdbkdfkkM ck 231

kdc

c < o < u o < c < u

c o o c

k1 - 2/3 - /3

k

60

Stress block

0.002 0.0035

kd

fc

k2kd

T

C=C3fckbkdC1

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Stress block parameters

002.00002.0002.0

2446.02

c

ccckc ff

0035.0002.01002.0

25.01446.02

c

cckc ff

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Section considered for calculating M-relationship

Assumed 25 mm clear cover

All dimensions in mm

63

c M

start 0 0

cracked 8033504.196 9.74069E-07

0.0005 8283594.419 4.05201E-06

0.001 15378489.83 7.84424E-06

0.0015 21200915.35 1.13588E-05

0.002 25649262.16 1.45742E-05

0.0025 27587840.7 1.85134E-05

0.003 28996952.56 2.22161E-05

0.0035 29959200.87 2.59188E-05

M-values for the section considered

M in Nmm & in rad/mm

M-Phi

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

0 0.000005 0.00001 0.000015 0.00002 0.000025 0.00003

Phi

M

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Comparison of M- values for different pt values.

M in Nmm & in rad/mm

M-Phi

0

5000000

10000000

15000000

20000000

25000000

30000000

35000000

0 5E-06 0.00001 1.5E-05 0.00002 2.5E-05 0.00003 3.5E-05 0.00004 4.5E-05

Phi

M0.25% 0.50%

0.75% 0.96%