EVALUATION OF NONLINEAR STATIC PROCEDURES · PDF fileNSP cannot completely replace NDP, ... pushover analysis focussing on the range of applicability and merit and demerits of the

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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.

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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

6. Live load: 4.0 kN/m2 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

6. Live load: 4.0 kN/m2 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

7. Live load: 3.0 kN/m2

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. 2935.

[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. 2935.

[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.

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