EVALUATION OF NONLINEAR STATIC PROCEDURES IN THE SEISMIC DESIGN OF REINFORCED CONCRETE BUILDINGS

http://www.iaeme.com/IJCIET/index.asp 61 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 6, Issue 8, Aug 2015, pp. 61-99, Article ID: IJCIET_06_08_007
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JTypeIJCIET&VType=6&IType=8
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
___________________________________________________________________________
EVALUATION OF NONLINEAR STATIC
PROCEDURES IN THE SEISMIC DESIGN
OF REINFORCED CONCRETE BUILDINGS
Dr. B. Damodhara Reddy
Professor, Department of Civil Engineering, Sri Venkateswara College of
Engineering and Technology, Chittoor, Andhra Pradesh, India
Th. Jagat Singh
Associate Professor, Department of Civil Engineering, Sri Venkateswara College of
Engineering and Technology, Chittoor, Andhra Pradesh, India
ABSTRACT
Application of performance based engineering concepts in seismic design
is achieved only by introducing nonlinear analysis into seismic design
methodology. Furthermore, the identification of sources of inelastic energy
dissipation and quantification of the energy absorption capacity to reduce the
elastic forces for seismic design call for nonlinear analysis. The nonlinear
analysis can be done either by Nonlinear Static Procedure (NSP) or by
Nonlinear Dynamic Procedure (NDP). The NDP requires considerable
judgement and experience to perform whereas, the NSP, also called
“Pushover Analysis,” uses simplified nonlinear techniques to estimate seismic
structural deformations. Performance points and target displacements from
the NSP were compared with the maximum roof displacements of NDA for the
various ground motions intensities of probabilities of exceedance of 2% in 50
years and 10% in 50 years at Los Angeles and Seattle. The comparison is also
made for the seismic zones IV and V of IS: 1893-2002 by considering the
Indian Standard Response Spectrum compatible ground motion. The study
confirms the finding of the other researchers that pushover analysis is suitable
for structures where higher mode effects are insignificant. This is more
prominent for ground motions of higher intensity. It is also concluded that
NSP cannot completely replace NDP, as it fails to reflect completely the
behavior of the structures under dynamic loads and it should be supplemented
by the dynamic analysis of selected ground motions. For the Indian
conditions, seismic hazard mapping is essential for proper and meaningful
seismic evaluation by adopting NSP.
Key words: Performance based engineering, Nonlinear Static Procedure
(NSP) and Nonlinear Dynamic Procedure (NDP)

Dr. B. Damodhara Reddy and Th. Jagat Singh
Cite this Article: Dr. Damodhara Reddy, B. and Jagat Singh, T. Evaluation of
Nonlinear Static Procedures in the Seismic Design of Reinforced Concrete
Buildings. International Journal of Civil Engineering and Technology, 6(8),
2015, pp. 61-99.
http://www.iaeme.com/IJCIET/issues.asp?JTypeIJCIET&VType=6&IType=8
_____________________________________________________________________
1. INTRODUCTION
The seismic assessment and design of structures is required because of the occurrence
of earthquakes. The differential movements of the earth’s crust cause Earthquakes.
These movements result the ground shaking leading to significant damage in the form
of collapse of buildings and infrastructure systems. It can also cause landslides, when
soil slopes lose their cohesion, liquefaction in sand and destructive waves or
‘tsunamis’ in the maritime environments. The aforementioned actions have called for
the development of design and evaluation procedures in order to quantify the damage
to both structural elements and the entire structure, and also to reduce any loss of life.
Seismic evaluation is also important for designing retrofit schemes for the
strengthening and repair of existing structures.
2. NONLINEAR DYNAMIC PROCEDURE
The Nonlinear Dynamic Procedure, also commonly known as nonlinear time history
analysis is the best way to assess the performance of structure subjected to earthquake
action. Nonlinear dynamic procedure utilizes the combination of ground motion
records with a detailed structural model and is the most rigorous method. The
complications and requirements for decisions in dynamic analysis are an order of
magnitude higher than for static analysis. Besides, a mathematical tool able to handle
all the necessary dynamic analyses often exceeds the capabilities of a design office
working under tight time constraints.
3. NONLINEAR STATIC PROCEDURE OR PUSHOVER
ANALYSIS
The Nonlinear Static Procedure also called ‘Pushover Analysis,’ on the other hand,
uses simplified nonlinear techniques to estimate seismic structural deformations. The
genesis of Pushover Analysis can be traced back to the 70’s decade. However, the
emergence of performance-based design has brought the nonlinear static procedure to
the forefront. In last two decades, the majority of researches had taken up study on
pushover analysis focussing on the range of applicability and merit and demerits of
the method. Consistent efforts have been made so far to improve the method after
finding the various deficiencies and limitations.
4. OBJECTIVE
The objective of this study is to evaluate the applicability of the nonlinear static procedures
to predict the performance of the reinforced concrete framed buildings in different seismic
zones and seismic hazards to meet the various performance requirements.

Evaluation of Nonlinear Static Procedures in the Seismic Design of Reinforced Concrete
Buildings
5. SCOPE
The buildings used in the analysis are restricted to reinforced concrete moment
resisting frames. In order to achieve the objective, the following tasks were
undertaken.
1. A study on the pushover analysis with special emphasis on performance based
engineering was undertaken. Also the procedure of the analysis in SAP 2000 was
studied thoroughly.
2. A study on material nonlinearity with emphasis on the stress strain relationship of
confined concrete, moment curvature relationship and formation of plastic hinges was
undertaken.
3. A study on the Seismic Hazard Analysis was undertaken to identify the various
ground motions with different hazard levels.
4. A study on the nonlinear dynamic analysis was undertaken to perform nonlinear
dynamic analysis.
5. Four reinforced concrete framed structures, namely (i) three bay four-storied plane
frame, (ii) three bay six-storied plane frame, (iii) three bay ten-storied plane frame
and (iv) five-storied three dimensional frame were designed for seismic forces as per
the provisions of IS 1893(part 1): 2002 by equivalent static lateral force method.
These structures were then subjected to pushover analysis with (i) pattern load (ii)
acceleration load and (iii) load proportional to the first mode using SAP 2000 and
displacements of roofs were recorded. The Pattern Load for the ten-storied frame was
calculated using the provisions of FEMA 356. For other frames, design lateral forces
of different stories from the equivalent lateral force method were adopted as the
pattern load.
6. The same framed structures were subjected to nonlinear dynamic analysis under
various ground motions of various seismic hazards using SAP 2000 and the roof
displacements were recorded. The roof displacements of the two analyses were
compared to assess the applicability of nonlinear static procedures or pushover
analysis for seismic design of reinforced concrete framed buildings.
7. The storey drifts of the frames corresponding to the time of maximum displacement
when subjected to selected ground motions are found out and compared with the
storey drifts of the pushover analysis at the performance points for the corresponding
frames. The absolute values of the drifts as well as the shapes are studied to assess the
applicability of nonlinear static procedures.
6. SEISMIC HAZARD ANALYSIS
Ground motions are mainly characterized by, the intensity, the frequency content and
the duration of the ground motion. Factors that are equally as important include the
energy release mechanisms in the vicinity of the hypocenter and along the fault
interfaces, the geology and any variations in geology along the energy transmission
paths, the epicentre distance, the focal depth, the magnitude and the local soil
conditions at the recording station.
7. US SEISMIC HAZARD MAPS
The U. S. Geological Survey (USGS) National Seismic Hazard Maps display
earthquake ground motions for various probability levels across the United States and
are applied in seismic provisions of building codes. National probabilistic maps are
developed for ground motions with a 10% chance of exceedance in 50 years, a 10%
chance of exceedance in 100 years (which can also be expressed as a 5% chance of
exceedance in 50 years) and a 10% chance of exceedance in 250 years (which also

can be expressed as a 2% chance of exceedance in 50 years). These probabilities
correspond to motions that are expected to occur, on average, about once every 500,
1,000, and 2,500 years. In addition, local ground motions in regions with well-defined
earthquake sources, known as deterministic motions, were used to develop Maximum
Considered Earthquake (MCE) maps.
7.1. Maximum Considered Earthquake (MCE) Ground Motion Maps
The ground motion maps of MCE in ASCE 7-05 can be described as applications of
its site-specific ground motion hazard analysis procedure. This is achieved using
values of ground motion computed by the USGS National Seismic Hazard Mapping
Project for a grid of locations and/or polygons that covers the US. The lesser of a
probabilistic and a deterministic ground motion is calculated as the MCE ground
motion. Thus both types of ground motions are computed by the USGS, whereas
otherwise it would have only computed probabilistic ground motions. The USGS
combines research on potential sources of earthquakes (e.g., faults and locations of
past earthquakes), the potential magnitudes of earthquakes from these sources and
their frequencies of occurrence, and the potential ground motions generated by these
earthquakes. Uncertainty and randomness in each of these components is accounted
for in the computation via contemporary Probabilistic Seismic Hazard Analysis
(PSHA). Hazard curves are the primary output of PSHA computations for locations
on a grid covering the US in the case of the USGS computation.
7.2. Basic Safety Earthquakes (BSE)
According to the provisions of FEMA 273, two levels of earthquake shaking hazard are
used to satisfy the Basic Safety Objectives (BSO). These are termed Basic Safety
Earthquake 1 (BSE-1) and Basic Safety Earthquake 2 (BSE-2). BSE-2 earthquake
ground shaking, also termed Maximum Considered Earthquake (MCE) ground shaking
is similar to that defined for the MCE in the 1997 NEHRP Recommended Provisions
(BSSC, 1997). In most areas of the United States, BSE-2 earthquake ground motion has
a 2% probability of exceedance in 50 years (2%/50 year). In regions close to known
faults with significant slip rates and characteristic earthquakes with magnitudes in
excess of about 6.0, the BSE-2 ground shaking is limited by a conservative estimate
(150% of the median attenuation) of the shaking likely to be experienced as a result of
such a characteristic event. Ground shaking levels determined in this manner will
typically correspond to a probability of exceedance that is greater than 2% in 50 years.
The BSE-1 earthquake is defined as that ground shaking having a 10% probability of
exceedance in 50 years (10%/50 year). The motions need not exceed those used for new
buildings, defined as 2/3 of the BSE-2 motion.
Figure 1 Ground motion parameters for Los Angeles for site class B as per 2003 NEHRP

Buildings
Figure 2 Ground motion parameters for Seattle for site class B as per 2003 NEHRP design
code Design code
8. SELECTED GROUND MOTIONS FOR ANALYSIS
SAC Steel Project funded by FEMA with the formation of SAC joint venture by the
Structural Engineers Association of California (SEAOC), the Applied Technology
Council (ATC) and Consortium of Universities for Research in Earthquake
Engineering (CUREE) have developed earthquake ground motions in US through its
report submitted in 2000. In its draft report submitted in 1997, several suites of time
histories of probabilities of occurrence2% in 50 years, 10% in 50 years and 50 % in
50 years are given for the locations of Los Angeles, Seattle and Boston corresponding
to seismic zones of 2, 3 and 4 respectively. For this study, ground motion estimates
provided in two locations of Seattle and Los Angeles respectively are identified.
Suites of time histories at two probabilities of occurrence, 2% in 50 years and 10% in
50 years, in each of the two locations for rocky soil conditions are selected. Seven
suites are chosen from each of the probabilities. The IS 1893(Part 1): 2002 response
spectrum compatible time history is also used.
8.1. Los Angeles Ground Motions
Table 1 Details of Los Angeles ground motions of probability 2% in 50 years

Figure 3a Scaled time history of Kobe earthquake (1995) with probability of 2% in 50 years
Figure 3b Scaled time history of Loma Priesta earthquake (1989) with probability of
exceedence 2% in 50 years
Figure 4 Scaled time history of Northridge -I earthquake (1995) with probability of
exceedence of 2% in 50 years
Figure 5 Scaled time history of Northridge -II earthquake (1995) with probability of

Buildings
Figure 6 Scaled time history of Tabas earthquake (1974) with probability of exceedence of
2% in 50 years
Figure 7 Scaled time history of Elysian Park, (simulated) with probability of exceedence of
2% in 50 years
Figure 8 Scaled time history of Palos Verdes, (simulated) with probability of exceedence of
2% in 50 years
Table 2a Details of Los Angeles ground motions of probability 10% in 50 years

Figure 9 Scaled time history of Imperial Valley, 1940, El Centro with probability of
Figure 10 Scaled time history of Imperial Valley, 1979, Array #05 with probability of
Figure 11 Scaled time history of Imperial Valley, 1979, Array #06 with probability of
Figure 12 Scaled time history of Landers, 1992, Yermo with probability of exceedence of
10% in 50 years

Buildings
Figure 13 Scaled time history of Loma Priesta, 1989, Gilroy with probability of exceedence
of 10% in 50 years
Figure 14 Scaled time history of Northridge, 1994, Newhall with probability of exceedence
of 10% in 50 years
Figure 15 Scaled time history of North Palm Springs, 1986 with probability of exceedence of
10% in 50 years
8.2. Seattle Ground Motions
Figure 16 Scaled time history of Mendocino, 1992, with probability of exceedence of 2% in
50 years

Table 2b Details of Seattle ground motions of probability 2% in 50 years
Figure17 Scaled time history of Erzincan, 1992, with probability of exceedence of 2% in 50
years
Figure 18 Scaled time history of Olympia, 1949, with probability of exceedence of 2% in 50
years.
Figure 19 Scaled time history of Seattle, 1965, with probability of exceedence of 2% in 50
years

Buildings
Figure 20 Scaled time history of Valpariso, 1985, with probability of exceedence of 2% in 50
years
Figure 21 Scaled time history of Deep Interplate (simulation), with probability of exceedence
of 2% in 50 years
Figure 22 Scaled time history of Miyagi-oki, 1978, with probability of exceedence of 2% in
50 years
Table 3 Details of Seattle ground motions of probability 10% in 50 year

Figure 23: Scaled time history of Long Beach, Vernon CMD bldg.,probability of exceedence
of 10% in 50 years
Figure 24 Scaled time history of Morgan Hill, 1984, Gilroy, with probability of exceedence
of 10% in 50 years
Figure 25 Scaled time history of West Washington, Olympia, 1949, with probability of

Buildings
Figure 26 Scaled time history of West Washington, Seattle Army B., 1949, with probability
of exceedence of 10% in 50 years
Figure 27 Scaled time history of North Palm Springs, 1986, with probability of exceedence
of 10% in 50 years
Figure 28 Scaled time history of Puget Sound, Wa., Olympia, 1949, with probability of
Figure 29 Scaled time history of Llolleo, Chile 1985, with probability of exceedence of 10%
in 50 years

8.3. IS-1893 Response Spectrum Compatible Ground Motion
Figure 30 IS 1893(Part 1): 2002 Response Spectrum Compatible Time History (Courtesy to
Prof. Manish Shrikhnade, Department of Earthquake Engineering, I. I. T, Roorkee,)
9. NONLINEAR STATIC AND DYNAMICS ANALYSESUSING
SAP 2000
Nonlinear Static Analysis or Pushover Analysis could be performed directly by a
computer program which can model nonlinear behaviour of lateral load resisting
members of a structure. However, the computational scheme and the assumptions
involved in modelling nonlinear member behaviour could be different that there may
be variations in the pushover results obtained from different software. Therefore, the
underlying principles of any software utilized for pushover analysis should be well
understood to interpret the results of pushover analysis.
In this study, pushover analyses were performed on reinforced concrete moment
resisting building frames by SAP 2000 using various lateral load patterns. Nonlinear
dynamic analyses were also performed on these structures. The roof displacements
from these two methods were compared to evaluate the pushover analysis.
10. NONLINEAR STATIC PROCEDURE
Nonlinear Static Analysis or Pushover analysis can be performed as either force-
controlled or displacement controlled depending on the physical nature of the load and
the behaviour expected from the structure. Force-controlled option is useful when the
load is known (such as gravity loading) and the structure is expected to be able to support
the load. Displacement controlled procedure should be used when specified drifts are
sought (such as in seismic loading), where the magnitude of the applied load is not known
in advance, or when the structure can be expected to lose strength or become unstable.
A displacement-controlled pushover analysis is basically composed of the
following steps:
1. A two or three dimensional model that represents the overall structural behaviour is
created.
2. Bilinear or trilinear load-deformation diagrams of all important members that affect
lateral response are defined.
3. Gravity loads composed of dead loads and a specified portion of live loads are
applied to the structural model initially.
4. A predefined lateral load pattern which is distributed along the building height is then
applied.
5. Lateral loads are increased until some member(s) yield under the combined effects of
gravity and lateral loads.
6. Base shear and roof displacement are recorded at first yielding.

Buildings
7. The structural model is modified to account for the reduced stiffness of yielded
member(s).
8. Gravity loads are removed and a new lateral load increment is applied to the modified
structural model such that additional member(s) yield. Analysis with zero initial
conditions is performed on modified structural model under each incremental lateral
load. Thus, member forces at the end of an incremental lateral load analysis are
obtained by adding the forces from the current analysis to the sum of those from the
previous increments. In other words, the results of each incremental lateral load
analysis are superimposed.
9. Similarly, the lateral load increment and the roof displacement increment are added to
the corresponding previous total values to obtain the accumulated values of the base
shear and the roof displacement.
10. Steps 7, 8 and 9 are repeated until the roof displacement reaches a certain level of
deformation or the structure becomes unstable.
11. The roof displacement is plotted with the base shear to get the global capacity
(pushover) curve of the structure.
10.1. Nonlinear Static Analysis in Sap 2000
Nonlinear static analysis capabilities are provided in SAP2000. The nonlinear
behaviour occurs in discrete user-defined hinges. Currently, hinges can be introduced
into frame objects only and assigned at any location along the frame object.
Uncoupled moment, torsion, axial force and shear hinges are available. There is also a
coupled P-M2-M3 hinge that yields based on the interaction of axial force and
bending moments at the hinge location. More than one type of hinge can exist at the
same location; for example, both an M3 (moment) and a V2 (shear) hinge may be
assigned to the same end of a frame object.
A pushover analysis can consist of more than one pushover load case. Each
pushover load case can have a different distribution of load on the structure. For
example, a typical pushover analysis might consist of three pushover load cases. The
first would apply gravity load to the structure, the second would apply one distribution
of lateral load over the height of the structure, and the third would apply another
distribution of lateral load over the height of the structure. There are four different
methods of describing the distribution of load on the structure for a pushover load case:
1. A uniform acceleration can be automatically applied. In that case, the lateral force
automatically applied at each node is proportional to the mass tributary to that node.
2. A lateral force that is proportional to the product of a specified mode shape times its
circular frequency squared (w2
) times the mass tributary to a node can be
automatically applied at each node. The user may specify the mode shape to be used
in that instance.
3. An arbitrary static load pattern may be defined.
4. Any of the methods described in 1, 2 and 3 can be combined.
Several types of output can be obtained from the nonlinear static pushover analysis:
1. Base shear versus displacement at a specified control joint can be plotted.
2. Base shear versus displacement at a specified control joint can be plotted in the
ADRS format where the vertical axis is spectral acceleration and the horizontal axis is
spectral displacement. The demand spectra can be superimposed on that plot.
3. The sequence of hinge formation and the colour-coded state of each hinge can be
viewed graphically, on a step-by-step basis, for each step of the pushover.

4. The member forces can be viewed graphically, on a step-by-step basis, for each step
of the analysis.
5. Tabulated values of base shear versus displacement at each point along the pushover
curve, along with tabulations of the number of hinges beyond certain control points
on their hinge property force-displacement curve can be viewed on the screen,
printed, or saved to a file.
6. Tabulated values of the capacity spectrum (ADRS capacity and demand curves), the
effective period and the effective damping can be viewed on the screen, printed, or
saved to a file.
The following general sequence of steps is involved in a nonlinear static pushover
analysis:
1. Create a model.
2. Define arbitrary static load cases, if needed, for use in the pushover analysis. Note
that the program also has built-in capability to define the distribution of lateral load
over the height of the structure based on both uniform acceleration and mode shapes.
3. Define the pushover load cases.
4. Define hinge properties.
Figure 31 Nonlinear static analysis formAssign hinge properties to frame elements.
1. Run the pushover analysis by selecting a static nonlinear load case on the Set Load
Cases to Run form. The load case will be available only if there is at least one frame
object with a hinge property assigned to it, and there is at least one pushover load
case defined. If frame objects are specified to be designed by the program, this design
automatically will be performed before the pushover analysis routine begins.
2. Review the pushover results.
3. If necessary, revise the model and repeat steps 2 through 7.
11. NONLINEAR DYNAMIC PROCEDURE
Nonlinear Dynamic Procedure (NDP), also known as Nonlinear Time-History Analysis
provides for nonlinear evaluation of dynamic structural response under loading which
may vary according to the specified time function. Dynamic equilibrium equations are
solved using either modal or direct-integration methods. It utilizes the combination of
ground motion records with a detailed structural model. An important aspect of
nonlinear dynamic analysis is the selection of time step size. The size of the time step
has great effect on accuracy, stability and rate of convergence of the solution algorithm.
Three dimensional models are the best solutions for the accurate description of the
nonlinear dynamic response of the RC framed structures.

Buildings
11.1. Nonlinear Dynamic Analysis in SAP 2000
For running dynamic analysis using the nonlinear time-history option in SAP2000 requires
the users to define several dynamic and nonlinear parameters including time step, damping
ratio, and plastic hinges. The steps required in performing the analysis are given below:
1. Build a 2-D or 3-D model in the SAP2000 computer program.
2. Use the default hinge properties for concrete structures provided in the SAP2000
program, which corresponds to the hinge definitions in FEMA 356 (FEMA-356,
2000).
3. Define a damping ratio. A damping ratio of 5% has been selected.
4. Define an appropriate time step in the time history function definition. An output time
step size of 0.01 was selected in this research. The numbers of output time steps up
are assigned differently according to the nature ground motion used.
5. Set “Load Case Type” to be “Time History”, “Analysis Type” to be “Nonlinear”, and
“Time History Type” to be “Direct Integration.
6. Apply Acceleration load corresponding to the selected ground motion. Suitable scale
factors are used corresponding to the unit used and unit of acceleration in the time
history of the ground motion.
7. Define the initial conditions.
8. Run dynamic analysis.
Figure 32 Nonlinear direct integration time history form
12. STRUCTURAL MODELS OF BUILDINGS FOR ANALYSIS
12.1. Four-Storied Building 2D Frame
Figure 33 General layout of the four-storied building

General Features:
1. Type of structure: Multi-storeyed rigid jointed frame.
2. Number of stories: Four (G+3)
3. Ground storey height: 4.0 m
4. Floor-to-floor height: 3.35 m
5. External walls: 250 mm thick including plaster
6. Internal walls: 150 mm thick including plaster
7. Live load: 3.5 kN/m2
8. Materials: M 25 and Fe 415
9. Size of Column: 300 x 530 mm
10. Size of the interior column: 300 x 300 mm
11. Size of beams in longitudinal And
transverse direction:
300 x 450 mm
12. Total depth of slab: 120 mm
12.1.1. Six-Storied Building 2D Frame:
General Features:
2. Number of stories: Six (G+5)
5. External walls: 230 mm thick only at periphery
at typical floor and 1.5
kN/m2
at terrace
7. Floor Finish: 1.0 kN/m2
8. Water Flooring : 2.0 kN/m2
9. Terrace Finish: 1.0 kN/m2
11. Size of Columns
(a) Foundation top to GF 650 mm x 650 mm
(b) Ground to G+2 600 mm x 600 mm
(c) G+2 to Roof 550 mm x 550 mm
12. Size of beams in longitudinal
direction
300 mm x 600 mm
13. Size of beams in transverse direction Same as in longitudinal direction
14. Size of the secondary beams 200 mm x 500 mm

Buildings
(a)
(b) (c)
Figure 34: General layout of the six-storied building (a) Typical Floor Plan (b) Part section –
AA (c) Part frame section
12.1.2. Ten-Storied Building 2D Frame:
The same general features as the six-storied frame with the addition of four more
stories is taken for analysis and comparison of results.
General Features:
2. Number of stories: Ten (G+9)
5. External walls: 230 mm thick only at periphery
at typical floor and 1.5
kN/m2
at terrace
7. Floor Finish: 1.0 kN/m2
8. Water Flooring : 2.0 kN/m2

9. Terrace Finish: 1.0 kN/m2
10. Size of columns:
(a) Foundation top to GF 800 mm x 800 mm
(b) Ground to Fourth Floor 750 mm x 750 mm
(c) Fourth to Roof 650 mm x 650 mm
11. Size of beams in longitudinal direction
(a) Plinth Beam 400 mm x 750 mm
(b) First to Sixth Floor 300 mm x 600 mm
12. Size of Beams in the transverse direction: Same as in longitudinal direction
13. Size of Secondary Beams 200 mm x 500 mm
14. Materials:
(i) Columns:
(a) 800 mm x 800 mm M 30 and Fe 415
(b) 750 mm x 750 mm M 30 and Fe 415
(c) 650 mm x 650 mm M 30 and Fe 415
(d) Others M 25 and Fe 415
(ii) Beams
(a) 400 mm x 750 mm M 30 and Fe 415
(b) Others M 25 and Fe 415
12.1.3. Five-storied building 3D frame:
General Features:
Figure 35 General Layout of the Five-storied Building
2. Number of stories: Five (G+4)
5. External walls: 250 mm thick including plaster
6. Internal walls: 150 mm thick including plaster
8. Floor Finish Load: 1 kN/m2
9. Terrace Floor Finish: 2.0 kN/m2
11. Size of column:
(a) Foundation top to G+2 500 mm x 500 mm
(b) G+3 and G+4 450 mm x 450 mm

Buildings
12. Size of beams in longitudinal and transverse
direction:
300 x 450 mm
13. PUSHOVER ANALYSIS PARAMETER VALUES
1. Location: Los Angeles
Site Class B; Seismic Zone = 4
a) Maximum Considered Earthquake (MCE) parameters corresponding for
probability of excedence of 2% in 50 Years
Acceleration for short period = ;
Acceleration for one secondperiod = ;
b) Design Basis Earthquake (DBE) parameters corresponding to
;
Acceleration for one second period = ;
2. Location: Seattle
Site Class B; Seismic Zone: 3
a) Maximum Considered Earthquake (MCE) parameters corresponding to
;
b) Design Basis Earthquake (DBE) parameters corresponding to
;

3. Location: India
Table 4 Seismic demand spectrum of IS 1893: 2002 for different seismic zones
Acceleration for short period, = for Seismic Zone V
= 0.6 for Seismic Zone IV
Acceleration for one second period, = for Seismic Zone V
= for Seismic Zone IV
These parameters are for the Maximum Considered Earthquake (MCE) and for the
Design Basis Earthquake (DBE) the values will be multiplied by 0.50.
14. DYNAMIC CHARACTERISTICS OF THE BUILDINGS
Table 5 Dynamic characteristics of the buildings
15. LATERAL LOAD PATTERN
The vertical distribution of lateral load pattern for the four-storied 2D frame, six
storied 2D frame and five-storied 3D frame for the the pushover analysis is taken as

Buildings
the storey shears from the equivalent lateral seismic load analysis of the buildings as
per IS: 1893-2002. The lateral load pattern for the ten storey building is calculated as
per the provisions of FEMA as reproduced in equation 6.17 in Chapter six and
tabulated in Table 6.
Table 6 Vertical distribution of lateral load for the ten storey building
16. RESULTS AND DISCUSSIONS
16.1. Results:
The results obtained from the nonlinear static and dynamic analyses of the (i) four-
storied 2D building frame, (ii) six-storied 2D building frame, (iii) ten-storied 2D
building frame and (iv) five-storied building 3D-frame using SAP 2000 is tabulated
below. The results of pushover analysis are shown in Tables. The nonlinear dynamic
analysis results for the various ground motions of proximities 2% in 50 years and 10%
in 50 years are shown in Tables.
Table 7 Performance point/target displacement for pushover analysis for ground motions of
2% in 50 years in Los Angeles

Table 8 Performance point/target displacement for pushover analysis for ground motions of
2% in 50 years in Seattle
Table 9 Performance point/target displacement for pushover analysis ground motions of 10%
in 50 years at Los Angeles
Table 10 Performance point/target displacement for pushover analysis ground motions of
10% in 50 years at Seattle

Buildings
Table 11 Performance point/target displacement for pushover analysis for IS-1893
compatible ground motions for zone V
Table 12 Performance point/target displacement for pushover analysis for IS-1893
compatible ground motions for zone IV
Table 13 Maximum roof displacement under scaled ground motions of 2% in 50 at Los
Angeles

Table 14 Maximum roof displacement under scaled ground motions of 2% in 50 years at
Seattle
Los Angeles
Seattle

Buildings
Table 17 Maximum roof displacement under IS-1893 compatible time history
16.2. Performance Point and Roof Displacement Comparision
From the tables, graphs comparing the maximum roof displacement of dynamic
analysis and the performance pint/ target displacements are drawn for the various
types of buildings and various intensities of ground motion. The graphs are shown
from figure
16.2.1. Five-storied 3D building frame:-
Figure 36 Comparisons of displacements for ground motion of 2% in 50 years at Los Angeles
six-storied 2D building frame
Figure 37 Comparison of displacements for ground motion of 2% in 50 years at Seattle for
five-storied building 3D frame

Figure 38 Comparison of displacements for ground motion of 10% in 50 years at Los
Angeles for five-storied building 3D frame
Figure 39 Comparisons of displacements for ground motion of 10% in 50 years at Seattle for
five-storied building 3D frame
Discussion: Figure 38 to 39 shows that the performance points of the five
storied building from pushover analysis for the pattern load tend to be conservative
whereas the acceleration load tends to be non-conservative. The modal load performs
better when compared with the average maximum roof displacements under dynamic
loads for MCE as well as DBE at the two given locations.
Figure 40 Comparisons of displacements for IS: 1893 compatible time history for seismic
Zone V for five-storied building 3D frame

Buildings
Zone IV for five-storied building 3D frame
Figure 40 and 41 shows that pushover analysis performance points are much more
than the average roof displacements from dynamic analysis using IS-1893 response
spectrum compatible time history. The result is to be considered with caution as only
one group motion (artificial) has been considered.
16.2.2. Six-storied building frame:-
for six-storied building 2D frame
six-storied building 2D frame

Figure 44 Comparisons of displacements for ground motion of 10% in 50 years at Los
Angeles for six-storied building 2D frame
six-storied building 2D frame
Discussion: Figure 42 to 45 pushover analysis results cannot predict the roof
displacements and results of dynamic analysis exceeds the performance points of the
pushover analysis for ground motions of higher intensity (MCE). However for lower
intensity ground motions, (DBE), pushover analysis can predict the maximum roof
displacements reasonably well. Also the modal load again performs best.
zone V for six-storied building 2D frame

Buildings
zone IV for six-storied building 2D frame
Discussion: From Figure 46 and 47, it is evident that the dynamic analysis results
are very less compared to the pushover analysis. This has to be seen from the results
of pushover analysis are less compared to the respective results of Los Angeles and
Seattle for the corresponding intensities of earthquakes.
16.2.3. Four-storied building frame:-
for four-storied building 2D frame
four-storied building 2D frame

Figure 50 Comparisons of displacements for ground motions of 10% in 50 years at Los
Angeles for four-storied building 2D frame
four-storied building 2D frame
Discussion: Figure 48 to 51 shows that pushover analysis can fairly reflect the
performance of the structure under dynamic loads except for the ground motions at
Seattle of 2% in 50 years probabilities. Again the modal loads performs better in the
prediction of the dynamic performance.
zone V for four-storied building 2D frame
zone IV for four-storied building 2D frame

Buildings
Discussion: Figures 52 & 53 shows that dynamic analysis results are much less
than the pushover analysis results. This will most probably due to the insufficiency of
the IS-1893 compatible time history not being able to simulate the actual ground
motions of higher intensity.
16.2.4. Ten-storied building frame:-
for ten-storied building 2D frame
Figure 55 Comparisons of displacements for ground motion of 2% in 50 Years at Seattle for
ten-storied building 2D frame
Figure 56 Comparisons of displacements for ground motion of 10% in 50 Years at Los
Angeles for ten-storied building 2D frame
Figure 57 Comparisons of displacements for ground motion of 10% in 50 Years at Seattle for
ten-storied building 2D frame

Discussion: Figure 54 to 57 shows that pushover analysis cannot reflect the
performance of the structure under dynamic loads especially for ground motions of
higher intensity (MCE). For ground motions of lower intensity, pushover analysis
results give lower values than average dynamic results.
zone V for ten-storied 2D frame
zone IV for ten-storied 2D frame
Discussion: Figure 58 and 59 shows that the results remain the same as far as the
IS compatible time history is concerned. Pushover analysis results give performance
points much more than the dynamic analysis maximum roof displacements.
16.2.5. Storey Drift Comparison
The storey drifts are found out from the deformed shape of the structure at the time of
occurrence maximum displacement for dynamic analysis and from the deformed
shapes of pushover analysis pushed to the respective performance points. Results are
shown in Figuresbelow
Figure 60 Comparisons of storey drifts of pushover analysis and Kobe ground motion for ten-
storied 2D Frame

Buildings
Figure 61 Comparisons of storey drifts of pushover analysis and Tabas ground motion for
ten-storied 2D Frame
Figure 62 Comparisons of storey drifts of pushover analysis and Northridge-I ground motion
for ten-storied 2D Frame
Figure 63 Comparisons of storey drifts of pushover analysis and Seattle ground motion for
Figure 64 Comparisons of storey drifts of pushover analysis and ElCentro ground motion for

Figure 65 Comparisons of storey drifts of pushover analysis and Loma Priesta ground motion
for Six-storied 2D Frame
Figure 66 Comparisons of storey drifts of pushover analysis and Kobe ground motion for
Six-storied 2D Frame
Figure 67 Comparisons of storey drifts of pushover analysis and Northridge-II ground motion
for Six-storied 2D Frame
Figure 68 Comparisons of storey drifts of pushover analysis and ElCentro ground motion for
Six-storied 2D Frame

Buildings
Figure 69 Comparisons of storey drifts of pushover analysis and Landers, Yermo ground
motion for Six-storied 2D Frame
Figure 70 Comparisons of storey drifts of pushover analysis and Northridge-II ground motion
for five-storied 3D Frame
Figure 71 Comparisons of storey drifts of pushover analysis and Northridge-I ground motion
for four-storied 3D Frame
Discussion: Figures 60 to 71 clearly shows that pushover analysis cannot predict
the storey drifts as the values as well as patterns of the curves are different even for
four storied building.
17. CONCLUSIONS
The study subjected plane frames of a four storey, a five storey and a ten storey as
well as a three-dimensional frame of a five storey reinforced concrete buildings to
pushover analysis with (i) pattern load (ii) acceleration load and (iii) modal load and
compared the results with nonlinear dynamic analysis using ground motions of
various intensities. The following are the conclusions made from this study:-

1. The pushover analysis is a relatively simple way to explore the nonlinear behaviour
of buildings under seismic loading and consumes very less time compared to the
nonlinear dynamic analysis which consumes more time. The results obtained in terms
of demand, capacity and plastic hinges give an insight into the real behaviour of
structures enabling the modification of the structure for better performance of the
structure as reported by Freeman et al. (1975), Kunnath et al. (1996) and Faella
(1996).
2. The responses of the frames are sensitive to the shape of the lateral load pattern as
reported by Krawinkler (1996), Mwafy et al. (2001) and Goel (2010).
3. The results agree with the established findings that Pushover analysis is suitable for
structures where higher mode effects are insignificant as concluded by Fajfar et al.
(1988), Gaspersic et al (1992), Bracci et al. (1997), Kim et al. (2000) and
Kunnath(2004)
4. Pushover analysis is not suitable for prediction of storey drifts and thus will not
reflect the true behavior of a structure during a ground motion as reported by Gupta et
al. (2000), Kunnath et al. (2000) and Khoshnoud et al. (2012). As such, nonlinear
static procedures cannot completely replace the nonlinear dynamic procedures and
needs to be supplemented by dynamic analysis.
5. The discrepancy of the results between the pushover analysis and nonlinear dynamic
analysis is more prominent for ground motions of higher intensity.
6. For the Indian condition, the IS -1893 response spectrum compatible time history is
not able to represent the dynamic motions associated with the Seismic zones V and
IV.
REFERENCES
[1] Antoniou, S. and Pinho R. Development and Verification of a Displacement-
Based Adaptive Pushover Procedure. Journal of Earthquake Engineering, 8(5),
2004, pp. 643–661
[2] Applied Technology Council (ATC). Improvement of Nonlinear Static Seismic
Analysis Procedures. Report ATC-55, Redwood City, California, 2005.
[3] EC8. Eurocode 8: Design of Structures for Earthquake Resistance, General Rules,
Seismic Actions and Rules for Buildings. EN1998-1:2003, British Standards
Institution, London, 2003.
[4] Fajfar, P. and Gaspersic, P. The N2 method for the seismic damage analysis for
RC buildings. Earthquake Engineering Structural Dynamics, 25(1), 1996, pp.
23–67.
[5] FEMA. NEHRP Guidelines for the Seismic Rehabilitation of Buildings.
Developed by the Building Seismic Safety Council for the Federal Emergency
Management Agency, Report FEMA 273, Washington, D. C., 1997.
[6] FEMA. Prestandard and Commentary for the Seismic Rehabilitation of
Buildings. Prepared by American Society of Civil Engineers, Reston, Virginia for
the Federal Emergency Management Agency, Report FEMA 356, Washington,
D. C., 2000.
[7] Nautiyal, P., Singh, S. and Batham, G. A Comparative Study of the Effect of
Infill Walls On Seismic Performance of Reinforced Concrete Buildings.
International Journal of Civil Engineering & Technology (IJCIET), 4(4), 2013,
pp. 2935.
[8] FEMA. Improvement of Nonlinear Static Seismic Analysis Procedures. Prepared
by Applied Technology Council, Redwood City, California (ATC-55 project) for
the Federal Emergency Management Agency, Report FEMA 440, Washington,
D. C., 2005.

Buildings
[9] FEMA. 2009 NEHRP Recommended Seismic Provisions: Training and
Instruction Materials. Prepared by National Institute of Building Sciences and
Building Seismic Safety Council for the Federal Emergency Management
Agency, Report FEMA P-752, Washington, D. C., 2013.
[10] Goel, R. K. and Chopra, A. K. Role of Higher-‘Mode’ Pushover Analyses in
Seismic Analysis of Buildings. Earthquake Spectra, 21(4), 2005, pp. 1027–1041.
[11] Dr. Muthupriya, P. An Experimental Investigation on Effect of GGBS and Glass
Fibre In High Perfomance Concrete. International Journal of Civil Engineering
& Technology (IJCIET), 4(4), 2013, pp. 2935.
[12] Krawinkler, H. and Seneviratna, G. Pros and Cons of a Pushover Analysis for
Seismic Performance Evaluation. Engineering Structures, 20, 1998, pp. 452–464.
[13] Mander, J. B., Priestley, M. J. N. and Park, R. Theoretical Stress-Strain Model of
Confined Concrete. Journal of Struct. Eng., 114(8), 1988b, pp. 1804–1826.
[14] NDMA Development of Probabilistic Seismic Hazard Map of India. Technical
Report of The Working Committee Of Experts (WCE) Constituted By The
National Disaster Management Authority Govt. of India, New Delhi, 2011.

EVALUATION OF NONLINEAR STATIC PROCEDURES IN THE SEISMIC DESIGN OF REINFORCED CONCRETE BUILDINGS

Empfohlen

Empfohlen

Weitere ähnliche Inhalte

Was ist angesagt?

Was ist angesagt? (20)

Andere mochten auch

Andere mochten auch (11)

Ähnlich wie EVALUATION OF NONLINEAR STATIC PROCEDURES IN THE SEISMIC DESIGN OF REINFORCED CONCRETE BUILDINGS

Ähnlich wie EVALUATION OF NONLINEAR STATIC PROCEDURES IN THE SEISMIC DESIGN OF REINFORCED CONCRETE BUILDINGS (20)

Mehr von IAEME Publication

Mehr von IAEME Publication (20)

Kürzlich hochgeladen

Kürzlich hochgeladen (20)

EVALUATION OF NONLINEAR STATIC PROCEDURES IN THE SEISMIC DESIGN OF REINFORCED CONCRETE BUILDINGS