1) The document discusses various methods of pushover analysis for seismic assessment of bridges, including standard pushover analysis, capacity spectrum method, and modal pushover analysis. 2) It provides examples of previous research applying these methods and identifies some limitations of standard pushover analysis, including that it only considers the fundamental mode and is an approximate method. 3) The document outlines the steps involved in different pushover analysis methods and compares results from these methods to results from time history analysis, which provides the closest estimate of earthquake response.

1. Presented By
APURWA D. YAWALE

2.  From last few decades structural engineers have been doing
research on the characterization and evaluation of structural
damage. Over the past decades it has been recognized that damage
control must become a more explicit design consideration which can
be achieved only by introducing some kind of nonlinear analysis
into the seismic design methodology.
Seismic
assessment and
design of
structures
Occurrence of
earthquakes
Differential
movements of
the earth’s crust

3. • Attention to the seismic vulnerability assessment of
existing buildings.
•
•
Importance of bridge.
An Important component of the road
transportation net work.
Provides a vital link to earthquake ravaged
areas
The Need of attention for existing bridges.
No detailed seismic design provision.
A large number of bridges were designed and constructed at a
time when bridge codes had no seismic design provisions

4. Bridges Total Affected
Number
Cost of Repair
/Rehabilitation /Item
Reconstruction
(Approx.)
Culverts 164
4030 million Rs.
Minor bridges (of length
less than 60m)
98
Major bridges (of length
more than 60m)
38

5. Longitudinal Displacement of
bridge during bhuj Earthquake
Failure of in-span hinge and
traffic railings at Old
Surajbadi Highway Bridge.

6. Failure of super and substructure of a bridge; rural area
between the towns of Gandhidham and Bhachau.

7. Cannot predict
the failure
mechanisms
Also the redistribution of
forces that follow plastic
hinge development during
strong ground shaking
Limitations
of Linear
Analysis
Provide an insight into the
structural aspects, which
control performance
during severe earthquakes
Provides data on the
strength and ductility of
the structure, which
cannot be obtained by
elastic analysis
Non Linear
Static
Analysis

8. To study and understand standard pushover analysis and
advanced pushover analysis procedure with their limitations and
superiority.
To employ design & analysis software Sap 2000 Vs 14 and to
study pushover analysis of bridge under consideration by
Standard pushover analysis, capacity spectrum analysis, Modal
pushover analysis and Time history analysis.
To investigate the effects of pushover direction on bridge
assessment.
To compare various seismic assessment parameters such as
capacity curve, displacement demand of different pushover
analysis methods.
To quantify the relative accuracy of the static analysis methods
with the dynamic analysis method i.e. Time History Analysis.

9. Taking into consideration the need of dissertation and its
objectives, an existing bridge located on Badnera Highway is
evaluated by using SAP 2000 vs. 14 computer program. The Bridge
is evaluated using pushover analysis. Standard pushover analysis,
Capacity spectrum method and Modal pushover analysis are
performed. Considering the short comings of standard pushover
analysis method results are obtained considering various parameters
such as base shear, displacement, plastic rotation. It is well known
that Dynamic analysis is most accurate evaluation method, hence
here in this dissertation Time history analysis is also performed on
the bridge under consideration and the results are compared with the
pushover analysis methods.

11. PUSHOVER ANALYSIS
• Came in to practice in 1970’s.
• Used to estimate the strength and drift capacity of
existing structure and the seismic demand for this
structure.
• Several seismic guidelines (ATC 40 and FEMA 356).

12. Response characteristics that can be obtained from the pushover
analysis are summarized as follows:
a) Estimates of force and displacement capacities of the
structure. Sequence of the member yielding and the progress of
the overall capacity curve.
b) Estimates of force (axial, shear and moment) demands on
potentially brittle elements and deformation demands on ductile
elements.
c) Estimates of global displacement demand, corresponding
inter-storey drifts and damages on structural and non-structural
elements expected under the earthquake ground motion
considered.
d) Sequences of the failure of elements and the consequent
effect on the overall structural stability.

13. • Advanced nonlinear analysis methods with
classical engineering principles
• To obtain an estimate of the single maximum
value of a response quantity, response-
spectrum analysis (RSA) was used.
Dameron’s
paper in
1997.
• Transverse and longitudinal pushover analyses
• Eighty-seven of the 90 bridge models were
subjected to both of these pushover analyses.
Three of the models were only subjected to a
longitudinal pushover analysis
Bignell’s
paper in
2005
• Fundamental mode-based (‘standard’)
pushover analysis was first performed
• standard Eigen value analysis.
KAPPOS
paper in
2006

14. • Software tools for seismic analysis of highway bridges
• A preliminary seismic response analysis of a two
spanhighway bridge was performed using linear
dynamic analysis procedures to identify the potential
for inelastic response.
Shatarat’s
paper in
2008.
• The seismic evaluation of the bridge was
performed using the FHWA
• Linear elastic force based method of evaluation
& non-linear static pushover analysis
Shattarat’s
paper in
2009.
• Critical issues in the application of inelastic
static (pushover) analysis are discussed
• New developments towards a fully adaptive
pushover method .
Elnashai
(2001)
paper

15. • Experimentally tested on three parallel shake
tables
• The intensity as well as the direction of the
deck rotations was significantly varying
depending on the seismic intensity.
Isaković
(2008)
paper
• The structural seismic analyses are carried out considering
either fiber-based or plastic hinge structural models.
• A parametric study is conducted on different bridge
configurations, comparing pushover curves as well as NSP
results which make use of those pushover curves
Monteiro
(2008)
• Typical short and medium span bridges structure like
a mono-pier, bent beam-pier frame (typical flyover)
with and without elastic-foundation in the urban area
• The response parameters like base shear and roof (top)
displacement for each case are studied.
Godse’s
(2013)

16. FAJFAR : Compared the capacity of a structure with the demands of
earthquake ground motion by capacity spectrum method. In the present
version of the method, highly damped elastic spectra have been used to
determine seismic demand. A more straightforward approach for the
determination of seismic demand is based on the use of the inelastic strength
and displacement spectra which can be obtained directly by time-history
analyses of inelastic SDOF systems, or indirectly from elastic spectra.
Spyrakos : investigated the effects of the soil-abutment interaction on
seismic analysis and design of integral bridges. Past experience and recent
research indicated that soil-structure interaction plays a very important role
on seismic response of bridge structures. Abutments attract a large portion of
seismic forces, particularly in the longitudinal direction. Therefore, he
considered participation of backfill soil at the abutments.
Benjamin: demonstrated significant improvement over the pushover
analysis procedure currently used in structural engineering practices due to its
ability to predict the higher mode effect.

17. Goel: Rooted in structural dynamics theory, three approximate procedures
for estimating seismic demands for bridges crossing fault-rupture zones and
deforming into their inelastic range are presented: modal pushover analysis
MPA, linear dynamic analysis, and linear static analysis.
Nicknam studied an urban steel bridge in metropolitan Tehran which
is accounted for as an important structure in the city transportation is
studied using nonlinear static procedure at two hazard levels. The hazard
levels were obtained by the use of probabilistic seismic hazard analysis
(PSHA).

18. SYSTEM DEVELOPEMENT

19. Methods of
Pushover Analysis.
Standard
Pushover
Capacity
Spectrum
Modal
Pushover
Analysis
Non-Linear
Time History
Analysis

20. Standard
Pushover Analysis
Lateral Load
Pattern
Estimate Target
Displacement

22. Estimation of Target Displacement
Estimate effective elastic stiffness, Ke
Estimate post yield stiffness, Ks
Estimate effective fundamental period, Te
Calculate target roof displacement as
2
2
3
2
1
0 4
/ 
 e
aT
S
C
C
C
C


24. SHORT COMINGS OF STANDARD
PUSHOVER ANALYSIS
• It is an approximate method.
• FEMA 356 guideline for load pattern does not cover all
possible cases.
• It is applicable only to those cases where the
fundamental mode is predominant.
• Do not consider the higher mode participation.
• Only horizontal earthquake load is considered in the
current procedure.
• Structural capacity and seismic demand are considered
independent in the current method.

25. Capacity Spectrum
Method
Estimate
Equivalent
Damping
Determine
Demand
Spectrum
Determine
Performance
Point
Construct Capacity
Spectrum

26. Constructing Capacity Spectrum
MDOF Equivalent SDOF
The displaced shape at any
point on the pushover curve is
used to obtain an equivalent
SDOF system.
α is the mass participation and
relates the base shears
PF is the participation factor
and relates the roof
displacement to the SDOF
displacement

27. Spectral
Acceleration
Spectral Displacement
 
 
roof
roof
d
a
PF
S
W
V
S
,
1
1
1
*
/
/
/






29. Response Spectrum (5% damping)
Spectral
Acceleration
Time Period
2.5CA
CV/T

30. Response Spectrum (5% damping)
CA and CV depend on:
- Seismic zone (0.075 to 0.4)
- Nearness to fault and source type (1 to 2)
- Soil Type (1 to 2.5)
- Level of Earthquake (0.5 to 1.5)

31. Spectral
Acceleration
Time Period
2.5CA/Bs
CV/(T BL)
Reduced Spectrum (Effective
damping)

34. The expected behavior of the
structure in the design
earthquake in terms of
limiting levels of damage to
the structural and
nonstructural components

35. 3) Modal pushover analysis of bridges by Chopra and
Goel
An extension of the ‘standard’ pushover analysis.
Modal pushover curves are then plotted and can be converted to SDF
capacity diagrams using modal conversion parameters based on the same
shapes.
Compute the natural periods, Tn and modes, n φ , for linearly elastic
vibration of the structure.
 Carry out separate pushover analyses for force distribution, * sn =mφn ,
where m is the mass matrix of the structure, for each significant mode of
the bridge and construct the base shear vs. displacement of the monitoring
point (Vbn- urn) pushover curve for each mode.

36. Idealized pushover curve of the nth mode of the MDOF
system, and corresponding capacity curve for the nth mode
of the equivalent inelastic SDOF system.

37. Time History Analysis
Actual earthquake response is hard to predict anyways.
- Closest estimate can be found using inelastic time-history
analysis.
The strong motion duration of an earthquake time history is
the time interval during which most of the energy of that time
history contained.
Peak ground acceleration (PGA) has frequently been used
as a parameter to characterize ground motion. Other parameters
included Arias intensity, ratio of PGA to PGV.

38. 1 N.E. INDIA 06-May-95 Khliehriat 0.22 0.01 0.001 3.72
2 CHAMBOLI 29-Mar-99 Himalaya 0.45 0.03 0.01 6.56
3 N.E. INDIA 08-May-97 Shilling 0.71 0.04 0.00 14.14
4 BHUJ 26-Jan-01 Ahmedabad 1.03 0.11 0.09 46.94
5 H.P.
EARTHQUAKE
26-Apr-86 Dharmsala 1.72 0.07 0.01 2.20
6 UTTARKASHI 20-Oct-91 Uttarkashi 2.37 0.17 0.02 6.22
7 IMPERICAL
VALLEY
19-May-40 El-Centro 0.31 0.033 0.01 40
8 KOBE 16-Jan-95 Takatori 0.68 0.12 0.012 48

39. Material properties:
M-25 grade of concrete and Fe-415 grade of reinforcing
steel are used for all members of the bridge. Elastic
material properties of these materials are taken as per
Indian Standard IS 456 (2000). The short-term modulus
of elasticity (Ec) of concrete is taken as:
Ec = 5000 fck MPa
where fck ≡ characteristic compressive strength of
concrete cube in MPa at 28-day .For the steel rebar, yield
stress (fy) and modulus of elasticity (Es) is taken as per IS
456 (2000)

40. Moment-Rotation Parameters
( )
B
A
dx
 
 
 
P u y P
L
  
 
2
y y
l
 

 
1
2
u y u y P
L
   
  
The rotation between A and B is given by
Plastic
rotation,
Yield rotation.
The ultimate rotation
is given by,
The rotation between A and
B is given by

41. A good estimate of the effective plastic hinge length may be obtained
from the following equation
Lp =0.08l + 0.022db fy

42.  The point ‘A’ corresponds to the unloaded condition.
 The point ‘B’ corresponds to the nominal yield strength and
yield rotation θ y
 The point ‘C’ corresponds to the ultimate strength and ultimate
rotation θu , following which failure takes place.
 The point ‘D’ corresponds to the residual strength, if any, in the
member. It is usually limited to 20% of the yield strength, and
ultimate rotation, θ u can be taken with that.
 The point ‘E’ defines the maximum deformation capacity and
is taken as 15 θy or θu , s whichever is greater.

43. In the present study, a point-plasticity approach is considered for modeling
nonlinearity, wherein the plastic hinge is assumed to be concentrated at a specific
point in the frame member under consideration. Beam and column elements in
this study were modeled with flexure hinges at possible plastic regions under
lateral load
Flexural Plastic Hinges
The flexural hinges in beams and column are modeled
with uncoupled moment (M3) hinges whereas for column
elements the flexural hinges are modeled with uncoupled M2-M3
properties.

44. BRIDGE
GEOMENTRY
DIMENSIONS
Length-312m
No. of span-13
Span length-24m
Width-17.2m
Cap Beam- 1m thk
Column-2.6m dia.
8 PSC girder at a
dist 2.23m
LOCATION
Bandera
Highway

48. • Case of Bridge I (Godse Parimal A. ( 2013) [22])
Typical short span bridge having four spans with precast
I-girders
Bent beam: 2m x 1.5m rectangular RCC beam
Concrete M25 grade and Steel Fe415 grade
Pier: 1.3 m diameter circular RCC section
Concrete M45 grade and Steel FE 415 grade.
Longitudinal reinforcement: 25 nos. of 25mm diameter bar.
Transverse reinforcement: 12mm diameter spiral at 115mm c/c spacing.
Superstructure details: Precast I-Girder section, there are 27 no. of
girders each having cross sectional area of 0.6 m2. Deck slab is 150mm
thick.
Dead weight from crash barrier, median and wearing course also
considered. Live load of 70 R 2-lane is taken.

50. Comparison of Results of SAP and Referred Paper
Location Performance Point Performance point
V, D 1180KN 0.110m 1260 KN 0.114m
Sa, Sd 0.127g 0.101m 0.135g 0.106m
Teff, Beff 1.676 0.202 1.777 0.202

51. Case of Bridge II

52. SPA 0.22m 0.24m
MPA 0.24m 0.28m
Comparison of Centre Pier Displacement Results of SAP and
Referred Paper.
The Krystallopigi bridge was selected in the referred paper, a
twelve span structure of 638m total length that crosses a valley in
northern Greece. The curvature in plan (radius equal to 488m) of the
bridge adds to the expected complexity of its dynamic behavior. The
deck consists of a 13m wide prestressed concrete box girder section.

53. 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0 1 2 3 4 5 6 7 8 9 10 11 12 13
U
r
,
m
Pier No.
SPA
MPA
NL-THA
Pier Top Displacements by SPA, MPA and
NL-THA. (Reference Paper [11])
Pier Top Displacements by SPA, MPA
and NL-THA. (Present Study)

54. Computational Analysis

55. Results of Standard Pushover Analysis:
0
50
100
150
200
250
0 0.05 0.1 0.15 0.2 0.25 0.3
Base
shear
Displacement
Transverse
Capacity curve in transverse
direction
Target Displacement:
245mm

56. 0
10
20
30
40
50
60
0 0.5 1 1.5 2
Base
Shear
Displacement
Longitudenal
Target Displacement:
390mm
Capacity curve in longitudinal
direction

57. Result of Capacity Spectrum analysis
141.34,0.234.
0.068g,
0.232m
3.546, 0.235.

58.  Target Displacement:
Performance
level
IO LS CP
Displacement 156mm 401mm 454mm

59. Bent demand/capacity ratios
Span Name Station
(m)
Direction Demand
(m)
Capacity
(m)
DCRatio
Span To span1 24.000000 TRANS 0.133817 0.535267 0.250000
Span To span1 24.000000 LONG 0.013172 0.052689 0.250000
Span To span2 48.000000 TRANS 0.139735 0.558941 0.250000
Span To span2 48.000000 LONG 0.013762 0.055048 0.250000
Span To span3 72.000000 TRANS 0.138361 0.553442 0.250000
Span To span3 72.000000 LONG 0.013647 0.054588 0.250000
Span To span4 96.000000 TRANS 0.138733 0.554931 0.250000
It is found that all values are less than 1 hence it indicates that
adequate capacity exist for all bents in all direction.

60. Mode 4:
T=1.742s
Deformed shape of Mode 4

61. Mode 18:
T=0.3498s
Deformed shape of Mode 18

62. Mode 19:
T=0.2248s
Deformed shape of Mode 19

63. Mode 31:
T=0.1523s
Deformed shape of Mode 31

64. • Hinge Formation

65. 0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0 0.1 0.2 0.3 0.4 0.5 0.6
Sa
(g)
Sd (m)
Mode 31
Mode 18
Mode 19
Mode 4
Capacity curves derived with respect to deck
displacement.

66. Evaluation of different procedure
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Displacement
(m)
Pier Location
Modal Deck displacement of Bridge
SPA
MPA
NL-THA

67. Diff
P1 0.121 0.016 -87 0.053527 -56
P2 0.268 0.052 -71 0.243 -9
P3 0.464 0.22 -50 0.45 -3
P4 0.65 0.432 -33 0.648 0
P5 0.842 0.645 -15 0.768 -9
P6 0.896 0.734 -12 0.844 -6
P7 1.54 1.17 -19 1.457 -5
P8 0.954 0.832 -8 0.91 -5
P9 0.768 0.642 -13 0.742 -3
P10 0.732 0.693 -2 0.704 -4
P11 0.589 0.564 -8 0.609 3
P12 0.444 0.164 -65 0.452 2
P13 0.321 0.132 -69 0.354 10
P14 0.129 0.014 -87 0.126 -2

68. Th
Th
po
Diff


 

(%)
Table lists the deck displacement of bridge calculated using different
pushover analyses as well as the NL-THA as the benchmark to
compare with others cases. As shown in the table, MPA procedure
provided the best estimate of deck displacement. The difference
between the maximum displacement calculated using the MPA (at
pier no. 7) and that of the NL-THA is 5% and the MPA displacement
profile is closely matching that profile derived from NL-THA with
differences ranging from 3% at pier no. 11 to 9% at pier no.5.

69. 0
0.002
0.004
0.006
0.008
0.01
0.012
1 2 3 4 5 6 7 8 9 10 11 12
Plastic
Rotation
Pier No.
SPA
MPA
NL-THA

70. 19514 14212 -27 15432 -21
P1 0.000927 0 - 0 -
P2 0.001837 0 - 0.001817 -1
P3 0.004641 0 - 0.004541 -2
P4 0.006218 0.005041 -19 0.006118 -2
P5 0.006428 0.005643 -12 0.006245 -3
P6 0.008176 0.007541 -8 0.007676 -6
P7 0.009938 0.009378 -6 0.009738 -2
P8 0.009086 0.008118 -11 0.008486 -7
P9 0.008176 0.007541 -8 0.007676 s-6
P10 0.007941 0.006431 -19 0.006941 -13
P11 0.005578 0 - 0.005378 -4
P12 0.002945 0 - 0.002745 -7
P13 0.000927 0 - 0.00003 -14

71. CONCLUSION
• In transverse direction, the Bridge behaved linearly elastic up to a base
shear value of around 221 KN. Above the value of base-shear 221KN, it
depicted non-linearity in its behavior.
• In longitudinal direction, the Bridge behaved linearly elastic up to a base
shear value of around 55 KN. Above the value of base-shear 55 KN, it
depicted non-linearity in its behavior.
• According to capacity spectrum method, Performance point is obtained
with displacement 234mm and all bents are found within the adequate
capacity.
• On the basis of the results obtained, MPA seems to be a promising
approach that yields more accurate results compared to the standard
pushover, without requiring the higher modeling effort and computational
cost, as well as the other complications involved in NL-THA.
• SPA underestimates the base shear by about 27% while MPA gives a
better results and underestimates the base shear by only 21%.
• The difference between the maximum displacement calculated using the
MPA (at pier no. 7) and that of the NL-THA is 5% and the MPA
displacement profile is closely matching that profile derived from NL-
THA with differences ranging from 3% at pier no. 11 to 9% at pier no.5.

72. • The MPA procedure introduced is found to yield better results
when the level of earthquake excitation is increased and more
inelastically developed in the structure.
• All the four methods yielded similar values of maximum inelastic
deck displacement ; however the variation of displacement along
the bridge are rather different. The SPA method predicts well the
displacement only in the central, first mode dominated, area of
the bridge. On the contrary MPA provided a significantly
improved estimate with respect to maximum displacement pattern
reasonably matching the more refined NL-THA method, even for
increasing level of earthquake loading that triggers increased
contribution of higher modes.
• Here the performance of the bridge, according to Capacity
spectrum method and Modal pushover analysis method is within
the life safety level.

73. Future Scope
•More work is clearly required to further investigate the effectiveness of MPA
by applying it to bridge structures with different configuration and study the
effect of superstructure-pier stiffness ratio on the behavior of bridges since
MPA is expected to be even more valuable for the assessment of the actual
inelastic response of bridges with significant higher modes.
•More work can be done with these methods with different parameters such
as bridge skew angle , wall pier pile foundation and degree of irregularity.
Applications
•To suggest retrofitting of existing bridge.
•For vulnerability assessment of RCC structure.
•The assessment of seismic performance of bridge under future earthquakes.
•Even if the results are not immediately reusable for other structures,
discussion of the principles and the main assumptions at the base of these
nonlinear analysis techniques may be of some help in future practical
applications.

74. REFERENCES
• apurwaReferences.docx

75. PUBLICATIONS
• Lande, P.S. and Yawale, A.D., “Review paper: Seismic
Vulnerability assessment of bridge using pushover
analysis” International journal of research & technology,
Vol. 3, Issue 2, Feb 2014.
• Lande, P.S. and Yawale, A.D., “Seismic performance
study of bridge using pushover analysis”, International
conference on “Innovative Trends in Science,
Engineering and Technology” organized by IRAJ, at
pune, on may 18, 2014.