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DEPARTMENT OF CIVIL ENGINEERING
MANIPAL INSTITUTE OF TECHNOLOGY
Deepak S Bashetty
Reg.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. Introduction
2. Methods of analysis
3. Modeling Approach
4. Details of Analysis
5. Result and Discussion
6. Conclusion
7. 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 Objectives
Fully Operational,
Operational
Immediate-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’s
Beer!Beer!
Food!Food!
Beer!Beer!
Food!
Joe’s
Immediate
Occupancy
Immediate Occupancy – building is safe to occupy but
possibly not useful until cleanup and repair has occurred
Beer!Beer!
Food!Food!
Joe’s
Beer!Beer!
Food!Food!
Beer!Beer!
Food!
Life
Safety
Life Safe – building is safe during event but possibly not
afterward
Collapse
Prevention
CollapsePrevention–building is onvergeof
collapse, probabletotal loss

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Performance based design
Performance Levels
Building Damage States
Immediate
occupancy
Life
safety
Collapse
prevention
Displacement
parameter
Force
parameter
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 analysis
Generally for analyzing the structure the following analysis
methods are used depending upon the requirements.
1) Linear static procedure
2) Linear dynamic procedure
3) Nonlinear static procedure
1. Pushover analysis
2. Capacity spectrum method
4) Nonlinear dynamic procedure
1. 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 properties
Beams – M3, V2
Columns –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 point
Base shear Vs Roof Displacement
Sequential Hinge Formation

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Performance Analysis
Create Model as Designed
Define Time History Function
Define Linear Time History cases
Analyze
Check
Member 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
YESYES
NoNo
 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 hinge
Axial-moment and shear hinge
L = Critical distance from critical section of
plastic hinge to point of contra flexure
fye = yield strength of transverse reinforcement
dbl= 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 infill
Concrete 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 300 804
Acol
= 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
Magnit
ude
PGA
in g
EQ. Scale Factor
DBE 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 system
C1 = Modification factor to relate expected maximum inelastic displacements to
displacements calculated for linear elastic response
C2 = Modification factor to represent the effect of pinched hysteretic shape,
stiffness degradation and strength deterioration on maximum displacement
response
C3 = Modification factor to represent increased displacements due to dynamic
P- ∆ effects
Te = Effective fundamental period of building, sec
Sa = Response Spectrum Acceleration at effective fundamental period and
damping ratio of building
g
4
T
SCCCC 2
2
e
a3210t
π
=δ

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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 Spectrum
Capacity 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
htStoreyHeig
ntfloorsntofadjaceDisplaceme
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 %
StoreyLevel
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 %
StoreyLevel
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 %
StoreyLevel
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 %
StoreyLevel
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 Structure
A 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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References
1. 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.

55.
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56
Moment curvature
relationship for singly
reinforced sections

57.
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Finding Mcr & Φcr Values
( )
bc
cr
cr
bt
tstt
ckcr
cr
cr
yE
f
yyD
ydmA
D
ybDbDI
ff
y
If
M
=
+=
−+





−+=
=
=
φ
2
2
3
2
7.0

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Finding M-Φ 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
kd
kdd
=
=
−
=
31
ε
εε

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Finding M-Φ values (cont…)
( )kdkdbkdfkkM ck 231 −=
kd
cε
φ=
εc <
εo <
εu
εo <
εc <
εu
η εc
/εo
εo
/εc
k1 η - η2
/3 1 - η/3
k2
(1/3 −η/12)/(1−η/3) (6−4η + η2
)/(12 − 4 η)

60.
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Stress block
0.002 0.0035
kd
fc
k2kd
T
C=C3fckbkdC1

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Stress block parameters
002.00
002.0002.0
2446.0
2
≤<














−





= c
cc
ckc ff ε
εε

0035.0002.01
002.0
25.01446.0
2
≤<














−−= c
c
ckc ff ε
ε


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62
Section considered for calculating M-
Φ relationship
Assumed 25 mm clear cover
All dimensions in mm

63.
63
εc M Φ
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-Φ values for the section considered
M in Nmm & Φ 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-Φ values for different pt
values.
M in Nmm & Φ 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
M
0.25% 0.50%
0.75% 0.96%