42

CHAPTER 3

MODELING OF THE EXISTING RCC STRUCTURES

3.1 INTRODUCTION

In Coimbatore city many existing buildings which had been built

prior to 2002 are seismically deficient due to the fact that the seismic design

code IS 1893: 2002 (Part-I) requirements have been upgraded. Furthermore,

some of the Coimbatore buildings built over the past few years even after

2002 are seismically deficient because of lack of awareness of the builders

regarding the seismic behavior of structures. Most of the existing buildings in

this city are designed for gravity loads only. A large number of existing

buildings in Coimbatore need seismic evaluation due to various reasons such

as noncompliance with the codal requirements, updating of code, poor design

and construction practice and change in the use of the building. However, the

existing deficient structures in Coimbatore falling in Zone-III can be

upgraded to improve and sustain the expected performance level. Before

rehabilitation work, it is necessary to understand the capacity of the existing

building and to check if it meets the intended performance level.

The Nonlinear Finite Element Analysis software SAP2000

version 11 is utilized to create a three dimensional model and static pushover

43

analysis was studied. The software is able to predict the geometric nonlinear

behavior of space frames under static or dynamic loadings, taking into

account both geometric nonlinearity and material inelasticity. The software

accepts static loads (either forces or displacements) as well as dynamic

(accelerations) actions and has the ability to perform eigen values, nonlinear

static pushover and nonlinear dynamic analyses.

3.2 RESEARCH METHODOLOGY

The research work had been carried out in three phases. In the First

phase of the study is the creation and analysis of the model has to evaluate the

performance of a typical selected deficient existing building having different

types of lateral load resisting systems such as R.C. frame and Infilled frame

behavior with respect to seismic vulnerability. For this evaluation, a pushover

analysis had been performed. The analysis result showed the performance

levels, behavior of the components and failure mechanism of the building.

It also provided the sequence of hinge formation. Based on the analysis

the elements which needed retrofitting were identified. The process of the

Phase –I is shown in Figure 3.1.

The Second phase of the study involved the seismic strengthening

of the existing bare frame structure based on the SAP 2000 analysis results.

For strengthening of the existing building Glass Fiber Reinforced Polymer

Composite (GFRP) was used extensively to address the strength requirements

related to flexure and shear in the structural system. This phase highlighted

the behavior and performance of composite beams by the moment – rotation

relation and the ductility of the tested beams. The test result showed that the

44

beams strengthened with GFRP wrapped exhibited better performance. The

process of the Phase –II is shown in Figure 3.2.

The Third phase of the study involved the analysis of bare frame

with strengthened beams. After seismic strengthening of the existing hostel

building, its behavior during the earthquake was studied based on the

wrapped GFRP beams. The improved performance of the existing RCC

structure was studied in detail with reference to pushover curves, hinges

formation, moment-rotation, capacity spectrum and performance level of the

building by using SAP 2000.

Finally the GFRP composite retrofitting techniques are

suggested so that the strength and performance level of the structure could be

enhanced during the earthquake. The process of the Phase –III is shown in

Figure 3.3.

45

Figure 3.1 Analysis of the Existing RCC Building

46

Figure 3.2 Investigation of Seismic Strengthening of the Existing RCC

Bare Frame Building

47

Figure 3.3 Analysis of Bare Frame with Strengthened Beams

48

3.3 EVALUATION OF SEISMIC PERFORMANCE

To select an appropriate retrofitting method, an accurate evaluation

of the seismic performance and the condition of an existing structure is

necessary. Based on this evaluation, engineers can choose the most effective

retrofit technique among the various intervention techniques and optimize the

improvement in seismic performance for an existing structure. Seismic

deficiencies should first be identified through a seismic evaluation of the

structure. The selection of an appropriate intervention technique based on the

structural type and its deficiencies is the most important step in retrofitting.

Seismic evaluation consists of gathering as-built information and obtaining

the results of a structural analysis based on collected data. The Prestandard

and Commentary for the Seismic Rehabilitation of Buildings – FEMA 356

(2000) provides guidance for evaluating the seismic performance of existing

structures and determining the necessary retrofitting methods to achieve the

performance objectives ASCE (2000).

3.3.1 As-Built Information

Generally, in order to obtain a reliable result from a structural

analysis of an existing structure, sufficient as-built information is required.

As-built information refers to the configuration of the structural system, as

well as the type, detailing, material strength and condition of the structural

elements. Data are available from detailed drawings, construction documents,

and previously conducted seismic evaluations of the building. The reason is

for gathering this information, so that engineers can arrive at accurate results

from their analyses and compare those results with current requirements in

order to determine the deficiencies of a building. To obtain realistic as built

information, FEMA 356 (2000) suggests that a minimum of one site visit

should be made to observe exposed conditions of building configuration,

49

building components, site and foundation conditions and adjacent structures.

This information is to be used to verify that as-built information obtained

from other sources is representative of the existing conditions.

3.3.2 Evaluation Procedures

Based on as-built information, an evaluation of the seismic

performance of an existing structure can be conducted. FEMA 356 (2000)

outlines four different procedures for analysis of the seismic evaluation of a

structure: the linear static procedure, the linear dynamic procedure, the

nonlinear static procedure (push-over analysis) and the nonlinear dynamic

procedure. Using one of these procedures, the seismic performance of a

structure can be evaluated and the deficiencies or vulnerable elements can be

found. Therefore, the results of these analyses provide key information for

selecting proper retrofitting techniques.

3.3.2.1 Linear Procedures

The linear analysis procedures provided in FEMA 356 (2000)

consist of linear static and linear dynamic analysis. When the linear static or

dynamic procedures are used for seismic evaluation, the design seismic

forces, the distribution of applied loads over the height of the buildings and

the corresponding displacements are determined using a linearly elastic

analysis. It is difficult to obtain accurate results for structures that undergo

nonlinear response through linear procedures. Therefore, linear procedures

may not be used for irregular structures, according to the FEMA 356 (2000)

guidelines.

50

3.3.2.2 Nonlinear Procedures

Nonlinear procedures consist of nonlinear static and nonlinear

dynamic analysis. A nonlinear static analysis, also known as a push-over

analysis, consists of laterally pushing the structure in one direction with a

certain lateral force or displacement distribution until either a specified drift is

attained or a numerical instability has occurred (signaling a collapse).

Because linear procedures have limitations and nonlinear dynamic procedures

are complicated, nonlinear static analysis is commonly used by structural

design engineers. The nonlinear dynamic procedure (dynamic time-history

analysis) provides a more accurate estimate of the dynamic response of the

structure. However, because the results computed by the nonlinear dynamic

procedure can be highly sensitive to characteristics of individual ground

motions, the analysis should be carried out with more than one ground motion

record. This is also true for the linear dynamic analysis. FEMA 356 (2000)

provides guidelines regarding the required number of ground motions that

should be used for dynamic analysis.

3.3.3 Rapid Visual Screening, Data Collection and Preliminary

Evaluation

The Rapid visual screening involved a quick assessment of a

building based on visual inspection alone. It is a kind of guideline to the

inspectors to identify and to have inventory of the vulnerable buildings.

In order to facilitate seismic evaluation, it is necessary to collect

relevant data of a building as much as possible through drawings, enquiry,

design calculation, soil report, inspection reports of previous investigation,

previous repair work, any complaints by the occupants etc.

51

The purpose of preliminary evaluation is to identify the areas of

seismic deficiencies in an engineered building before detailed evolutions are

undertaken. The code compliance for seismic design and detail evaluation

need to be studied thoroughly.

3.3.4 Overview of the Existing Structures

Coimbatore is a fast growing city in India which is located in

seismic Zone-III. Many of the reinforced concrete frame buildings in

Coimbatore were designed and built prior to the year 2002. The Indian

seismic code IS 1893 was revised in 2002. Hence, buildings built prior to

2002 do not comply with the codal requirement. Diptesh Das and Murty

(2004) states that, most of the buildings with infilled walls have not

considered infills in their design. This chapter aims to evaluate the

performance of a typical selected building having different types of lateral

load resisting systems such as R.C. frame and infilled frame behavior with

respect to seismic vulnerability. In order to evaluate the Seismic behavior of

existing building with rigid floor diaphragms an existing hostel building was

selected in Coimbatore zone. For this evaluation, a Pushover analysis had

been performed. The analysis showed the behavior levels of various

components of building for different specified performance objective as per

ATC 40 (1996). Based on this evaluation, it is concluded that the building

needed retrofitting to enhance its performance to the required level.

The objective of the present analysis is to choose a typical building

in the Coimbatore (Zone III) region for evaluating the performance of the

building and identify the type of deficiency.

52

The above objective was achieved by following steps

1. Chosen a typical existing building designed prior to 2002

whose structural data was available.

2. Making a three dimensional model of the building using the

available data but ignoring partitions.

3. Making a three dimensional model of the building

considering effect of partitions as infills.

4. Conducted a pushover analysis of the models referred in steps

2 and 3.

5. Identified the hinge formation, base shear capacity and

performance with respect to immediate occupancy, life safety

and collapse prevention as per ATC 40 (1996) for the models

in steps 2 and 3.

3.4 DESCRIPTION OF THE FRAMED STRUCTURES

The present study was to evaluate the behavior of G+2 reinforced

concrete bare frame and infill frame building subjected to zone III level

earthquake forces. The three dimensional reinforced concrete structures were

analyzed by nonlinear static analysis (Pushover Analysis) using SAP2000

software. The analysis results showed the performance levels, behavior of the

components and failure mechanism of the building. It also showed the

sequence of hinge formation. Based on the analysis, the elements which need

retrofitting were identified.

53

The three dimensional frame of the selected building having

different types of lateral load resisting systems such as R.C. bare frame and

Infilled frame were considered in this study. Figure 3.4 shows the plan of the

building representing the X and Y direction used for analysis. Figure 3.5

shows a three dimensional line sketch of the frame in the X, Y and Z

direction. Figure 3.6 shows a typical longitudinal bare frame (in the X

direction in XZ plane). Figure 3.7 shows a configuration model of braces

representing infills. Figure 3.8 shows an elevation of the existing study hostel

building. The building exists in Coimbatore and is a typical example of many

such buildings in this region. It was built with M15 grade of concrete and

Fe415 grade of steel, Figure 3.9 shows the elevation of buildings similar to

the one examined in this region.

Figure 3.4 Plan of the Existing Hostel Building

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Figure 3.5 Three Dimensional View of the Bare Frame

Figure 3.6 Bare Frame

55

Figure 3.7 Three Dimensional view of the representing Infills Frame

with Braces

Figure 3.8 Elevation of the Existing Study Hostel Building

56

Figure 3.9 Examples of Existing Buildings

IS 456:2000 demands M20 to be the concrete grade for structural

applications. However, many buildings in Coimbatore region were built with

only M15 grade concrete. In order to check the vulnerability of such

buildings, the strength of concrete and grade of steel based on test results was

used in the pushover analysis.

For the selected building the strength of concrete was assessed as

16.5 N/mm2 using rebound hammer test and strength of steel was assessed as

Fe420 based on tensile strength test .These values were used in the pushover

analysis.

The chosen G+ 2 existing study hostel building has total height of

the building is 8.79 m. The building is 25.41 m in length and 11.95 m in

width. Typical floor to floor height is 2.93 m and slab thickness is 140 mm.

57

The dimensions of the beams and columns of the R.C. frames are shown in

Table 3.1.

Table 3.1 Dimension of the Beams and Columns (As per Structural

Designer Drawing)

S.NoStructural member

NotationsSizes (mm)

Length of the

member (mm)

Area of the steel (mm2 )

Percentage of the steel

(%)

1 Beam B1 273x412 3500 653 0.58

2 Beam B1a 273x312 2450 854 1.00

3 Beam B2 280x600 4750 1859 1.10

4 Beam B2a 280x701 4550 1859 0.94

5 Beam B3 280x600 4750 2173 0.08

6 Beam B4 200x500 3630 1206 1.20

7 Interior column

C1 400x2282930

1030 1.12

8 Exterior column

C2 460x2282930

1319 1.25

3.4.1 Analysis of Bare Frame

In Coimbatore region, most of the existing buildings designed and

constructed with masonry infill as a non-structural element and the analysis as

well as design were carried out by considering the mass but neglecting the

strength and stiffness contribution of infill. Thus, the structure was modeled

as bare frame and usually considered fixed at base. This is the commonly

accepted model for structural analysis and design for the buildings. The only

contribution of masonry infill is adding to the mass of the building acting as a

58

non-structural element. Consequently, analysis of the structure is based on the

bare frame. Since infills are not considered for load resistance, their

contributions to the lateral stiffness and strength may invalidate the analysis

and the proportioning of structural members for seismic resistance on the

basis of its results. However, this method is still being widely used by

designers even in the earthquake prone areas and has considered for

comparison in the present study.

With reference to, Mohamed Nour El-Din Abd-Alla (2007) beam

and column members had been defined as frame elements with the

appropriate dimensions and reinforcements. Slabs were defined as an area

element having the properties of shell elements with required thickness. Slabs

had been modeled as rigid diaphragms based on Sundar and Elangovan

(2000). Soil structure interaction was not considered and columns were

restrained with respect to all six degrees of freedom at the base. The building

was constructed in the medium soil site conditions on a firm ground with

underlying soil that has a value of bearing capacity which is equal to

200 kN/m2. In SAP2000 the behavior of the concrete is considered as non-

linear.

3.4.1.1 Assigning Loads

After having modeled the structural components, all possible load

cases are considered and they are listed below:

3.4.1.1.1 Gravity Loads

With reference to, Ishan Jyoti Sharma (2005) gravity loads on the

structure include the self weight of beams, columns and slabs other permanent

members. The self weight of beams, columns (Frame members) and slabs

59

(Area section) were automatically considered by the program itself. Infill

weight has been calculated and added.

3.4.1.1.2 Seismic Weight of the Building

With a reference to Pankaj Agarwal and Manish Shrikhande

(2008), the Seismic Weight of the whole building was the sum of the seismic

weights of all the floors. The seismic weight of each floor was its full dead

load plus appropriate amount of imposed load. While computing the seismic

weight of each floor, the weight of columns in any storey was equally

distributed to the floors above and below the storey.

The live load was considered for seismic weight calculation as per

Table – 8, IS 1893 (Part-1) 2002. Percentage of Imposed load to be

considered in Seismic weight calculation, since the live load class is up to 3

kN/m2, 25% of the imposed load was considered on floor. The imposed load

on roof was taken as zero.

3.4.1.1.3 Base Shear Calculations

The live load was assigned as uniform area loads on the slab

elements as per IS 1893 (part-1) 2002. Live load on floor = 2.0 kN/m2. In this

case 25% of the imposed load was considered on floor as seismic weight. The

live load on roof was taken as zero.

The design seismic base shear (Vb) was calculated using procedure

given in IS 1893(part 1)-2002 as follows.

Vb = Ah W (3.1)

Where Ah is the design horizontal seismic coefficient and is given by

60

Ah = ZI {Sa/g} / 2R (3.2)

Where Z - Zone factor given in table 2 of IS 1893-2002

I - Importance factor given in table 6 of IS 1893-2002 (Part-I)

R - Response reduction factor given in table 7 of IS 1893-2002

Sa/g - Average response acceleration coefficient.

Calculation

The approximate fundamental natural period of vibration (Ta), in

seconds, of a moment-resisting frame building without brick infill panels was

estimated by the empirical expression:

Ta = 0.075h0.75 (IS 1893-2002, Part-I) (3.3)

Where h = height of the building in m

= 0.075(8.79)0.75= 0.382 sec

From the response spectrum graph (Figure -2 of IS 1893-2002),

Average response acceleration coefficient (Sa/g) is found to be 2.5

Ah = 0.16x1{2.5}/ (2 x 3) = 0.067

Here

Z = 0.16- considering zone factor -III

I = 1.0 considering residential building.

R = 3.0 considering ordinary moment resisting frame (OMRF)

S a /g = 2.5

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Table 3.2 Seismic weight of the building for Bare Frame (W)

Floor No

Floor height from ground level (m)

Seismic weight ( kN)

1 2.93 4463.474

2 5.86 4463.474

3 8.79 1039.470

Total seismic weight of the building (W) 9966.418

The design base shear is calculated using =Vb =Ah W

W = Total seismic weight of the building, Refer Table 3.2.

Hence, Vb = 0.067 x 9966.418 = 667 kN

In the proposed model the reduction of the design base shear is

allowed based on the remaining useful life of the building reported by

Durgesh C. Rai (2005). The modification factor for the reduction of base

shear is given as follows,

0.5

rem

des

TU 0.7T

(3.4)

Here,

Trem- remaining useful life of the building, 38 years

Tdes- design useful life of the building, 50 years

Modification factor U= 0.871

The reduced base shear = 667x0.871= 580 kN.

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3.4.2 Analysis of Infill Frame

One of the main reasons in using masonry infill is being

economical and ease of construction, because it uses locally available

material and labor skill. Moreover, it has a better acoustics and heat insulation

and waterproofing properties, resulting in greater comfort for the occupants.

In Coimbatore many of the existing buildings were with masonry

infills as nonstructural element. The analyses as well as design of the frames

in these existing building were carried out by considering the mass but

neglecting the strength and stiffness contribution of the infill. Therefore, the

entire lateral load is assumed to be resisted by the frame only. One of the

disadvantages of neglecting the effect of infill is that, the building can

have both horizontal as well as vertical irregularities due to uncertain

positioning of infill and openings in them. Also, the infill walls are sometimes

rearranged to suit the changing functional needs of the occupants. The

changes are carried out without considering their effects on the overall

structural behavior.

The conventional finite element modeling of RC structures without

considering the effect of infill in the analytical model renders the structures

more flexible than they actually are. For this reason building codes imposes

an upper limit to the natural period of a structure by way of empirical

relations. Binay Charan Shrestha (2008) states that, since the infills are not

considered in conventional modeling in seismic design, their contributions to

the lateral stiffness and strength may invalidate the analysis and proportioning

of structural members for seismic resistance on the basis of its results. In

reality, the additional stiffness contributed by these secondary components

increases the overall stiffness of the buildings, which eventually leads to

63

shorter time periods, as they are observed during earthquakes; and hence

attracts larger seismic force to the structure.

Since early 50’s there have been numerous experimental as well as

analytical researches to understand the influence of infill on the lateral

strength and stiffness of the framed structures. Past earthquakes have shown

that buildings with regular masonry infill have a better response than with the

irregular ones. Also, masonry infills have a very high initial stiffness and low

deformability (Moghaddam and Dowling 1987) thus, making infill wall a

constituent part of a structural system. This changes the lateral load transfer

mechanism of the framed structure form predominant frame action to

predominant truss action (Murthy and Jain 2000), which is responsible for

reduction in bending moments and increase in axial forces in the frame

members. The presence of infill also increases damping of the structures due

to the propagation of cracks with increasing lateral drift. However, behavior

of masonry infill is difficult to predict because of significant variations in

material properties and failure modes that are brittle in nature. If not

judiciously placed, during seismic excitation, the infills also have some

adverse effects. One of the major ill effects is the soft storey effect. This is

due to absence of infill wall in a particular storey. The absence of infill in

some portion of a building plan will induce torsional moment. Also, the

partially infilled wall, if not properly placed may induce short column effect

thus creating localized stress concentration.

In Coimbatore, during the past days the designers used to ignore

the stiffness and strength of infill in the design process and treated the infill as

non-structural elements. This is mainly due to lack of awareness generally

accepted seismic design methodology in the present Indian Code that

incorporates structural effects of infill. Hence, there is a clear need to develop

64

a design methodology for seismic design of masonry infill Reinforced

Concrete structure.

Alternatively, a macro-model replacing the entire infill panel as a

single equivalent-strut has become the most popular approach for analyzing

infilled frame systems as shown in Figure 3.10 and it was proposed by Pauley

and Priestley (1992) and Holmes (1961). In this method, the brick infill was

idealized as a pin jointed diagonal strut and the RC beams and columns were

modeled as three-dimensional beam elements having six degree of freedoms

at each node. The idealization was based on the assumption that there was no

bond between frame and infill. The brick masonry infill was modeled as a

diagonal strut member whose thickness was same as that of the masonry and

the length was equal to the diagonal length between compression corners of

the frame. The effective width of the diagonal strut depends on various

factors like; contact length, aspect ratio of the infill and the relative stiffness

of frame and the infill. The brick-infill wall was simulated by the

compression-strut model suggested by the FEMA 356 (2000). In FEMA 356

(2000), the strut model is suggested based on the seismic behavior of RC

frames with brick infill.

Figure 3.10 Idealization of Brick Infill Panel as Equivalent Diagonal Strut

65

3.4.2.1 Calculation of Strut Area

The strut area is given by the following expressions,

Ae= wet (3.5)

we = 0.175( h)-0.4 w’ (3.6)

i4

c c

E tsin 24E I hi

Where, Ei - The modulus of elasticity of the infill material, N/mm2

Ei - 550fm -As recommended by FEMA 356 (2000)

fm - Compressive strength of hand molded burnt clay brick

Ef - The modulus of elasticity of the frame material, N/mm2

Ic - The moment of inertia of column section, mm4

t - The thickness of infill, mm

we - Equivalent strut width

h - The centre line height of the frame

hi - The height of infill

w' - The diagonal length of infill panel

- The slope of infill diagonal to the horizontal.

The brick masonry infill thickness is 230 mm and 115 mm for outer

and inner walls respectively. Based on the above equation (3.5) the strut areas

are calculated as 454 mm x 230 mm (Exterior wall) and 367 mm x 115 mm

(Interior wall).

66

3.4.2.2 Base Shear Calculations

The approximate fundamental natural period of vibration (Ta), in

seconds, of a moment-resisting frame building with brick infill panels may be

estimated by the empirical expression: Ta = 0.009h/ d with infill stiffness

considered given in IS 1893 (part-1) 2002, where h - is the height of the

building in m, d - is the base dimensions of the building in the direction of the

vibration in m.

Ta = 0.009h/ d = 0.009x8.79 25.41 = 0.398 sec in X- direction (3.7)

Ta = 0.009h/ d = 0.009x8.79 11.95 = 0.273 sec in Y- direction (3.8)

The spectral acceleration coefficient (Sa/g) values are calculated as follows.

For medium soil sites,

(3.9)

From the response spectrum graph (Figure -2) IS 1893-2002,

Average response acceleration coefficient (Sa/g) is found to be 2.5

The design horizontal seismic coefficient (Ah) = 0.16x1{2.5}/ (2 x 3) = 0.067

Ah= 0.16x1{2.5}/ (2 x 3) = 0.067

Here

Z = 0.16- considering zone factor -III

I = 1.0 considering residential building.

R = 3.0 considering ordinary moment resisting frame (OMRF)

S a /g = 2.5

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Table 3.3 Seismic weight of the building for Infill Frame (W)

Floor No

Floor height from ground level (m)

Seismic weight (kN)

1 2.93 4463.474

2 5.86 4463.474

3 8.79 1039.470

Total seismic weight of the building (W) 9966.418

The design base shear is calculated using =Vb =Ah W (3.10)

Hence, Vb = 0.067 x 9966.418= 667 kN

The reduction base shear = 667x0.871= 580 kN.

Though Fundamental natural period of vibration (Ta), is different

for frame with and without infill, since Sa/g is 2.5, there is no difference in

base shear (Vb) in both cases.

3.5 PUSHOVER ANALYSIS

Nonlinear static analysis or pushover analysis has been developed

over the past twenty years and has become the preferred analysis for

design and seismic performance evaluation purposes since the procedure is

relatively simple and considers post elastic behavior. However, the procedure

involves certain approximations and simplifications that some amount of

variation is always expected to exist in seismic demand prediction of

pushover analysis.

The non-linear static procedure or simply push over analysis is a

simple option for estimating the strength capacity in the post-elastic range.

68

This procedure involves applying a predefined lateral load pattern which is

distributed along the building height. The lateral forces are then

monotonically increased in constant proportion with a displacement control

mode of the building until a certain level of deformation is reached. The

applied base shear and the associated lateral displacement at each load

increment are plotted. Based on the capacity curve, a target displacement

which is an estimate of the displacement that the design earthquake will

produce on the building is determined. The extent of damage experienced by

the building at this target displacement is considered as representative of the

damage experienced by the building when subjected to design level ground

shaking.

The most frequently used terms in pushover analysis as given in

ATC-40 (1996) are:

3.5.1 Demand

It is a representation of the earthquake ground motion or shaking

that the building is subjected to. In nonlinear static analysis procedures,

demand is represented by an estimation of the displacements or deformations

that the structure is expected to undergo. This is in contrast to conventional,

linear elastic analysis procedures in which demand is represented by

prescribed lateral forces applied to the structure.

3.5.2 The Capacity Spectrum and Demand Spectrum

The Capacity Spectrum Method (CSM) is a method which allows

for a graphical comparison between the structure capacity and the earthquake

demand. The lateral resisting capacity of the structure is represented by a

force-displacement curve obtained from the pushover analysis. The demand

of the earthquake is represented by its response spectrum curve.

69

Simultaneously, the acceleration and displacement spectral values are

calculated from the corresponding response spectrum for a certain damping

(say 5% initially), are plotted as the ordinate and abscissa respectively. The

presentation of the two curves in one graph is termed as the Acceleration

versus Displacement Response Spectrum (ADRS) format as shown in

Figure 3.11. With increasing nonlinear deformation of the components, the

equivalent damping and the natural period increase. The spectral values of the

acceleration and displacement can be modified from the 5 percent damping

curve by multiplying a factor corresponding to the effective damping

(Table 3, IS 1893:2002). Thus, the instantaneous spectral acceleration and

displacement point (demand point) shifts to a different response spectrum for

higher damping. The locus of the demand points in the ADRS plot is referred

to as demand spectrum.

Figure 3.11 Demand and Capacity Spectra Mehar Prasad (2008)

70

3.5.3 Displacement-Based Analysis

It refers to analysis procedures, such as the nonlinear static analysis

procedures, whose basis lies in estimating the realistic, and generally

inelastic, lateral displacements or deformations expected due to actual

earthquake ground motion. Component forces are then determined based on

the deformations.

3.5.4 Elastic Response Spectrum

It is the 5% damped response spectrum for the (each) seismic

hazard level of interest, representing the maximum response of the structure,

in terms of spectral acceleration Sa, at any time during an earthquake as a

function of period of vibration T.

3.5.5 Performance Level and Performance Point

A limiting damage state or condition described by the physical

damage within the building, the threat to life safety of the building’s

occupants due to the damage, and the post earthquake serviceability of the

building. A building performance level is that combination of a structural

performance level and a nonstructural performance level.

The performance point is the point where the capacity spectrum

crosses the demand spectrum, as shown in Figure 3.11. If the performance

point exists and the damage state at this point is acceptable, then the building

is considered to be adequate for the design of earthquake forces. To have

desired performance, every structure has to be designed for this level of

forces.

71

3.5.6 Yield Point

The point along the capacity spectrum where the ultimate capacity

is reached and the initial linear elastic force-deformation relationship ends

and effective stiffness begins to decrease.

3.5.7 Building Performance Levels

A performance level describes a limiting damage condition which

may be considered satisfactory for a given building and a given ground

motion. The limiting condition is described by the physical damage within the

building, the threat to life safety of the building’s occupants created by the

damage, and the post-earthquake serviceability of the building.

3.5.7.1 Immediate Occupancy

The earthquake damage state in which only very limited structural

damage has occurred, the basic vertical and lateral forces resisting the

systems of the building retain nearly all of their pre-earthquake characteristics

and capacities. The risk of life threatening injury from structural failure is

negligible.

3.5.7.2 Life Safety

The post-earthquake damage state in which significant damage to

the structure might have occurred but in which some margin against either

total or partial collapse remains. Major structural components have not

become dislodged and fallen, threatening life safety either within or outside

the building. While injuries during the earthquake may occur, the risk of life

threatening injury from structural damage is very low. It should be expected

that extensive structural repairs will likely be necessary prior to reoccupation

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of the building, although the damage may not always be economically

repairable.

3.5.7.3 Collapse Prevention Level

This building performance level consists of the structural collapse

prevention level with no consideration of nonstructural vulnerabilities, except

that parapets and heavy appendages are rehabilitated.

3.5.7.3.1 Primary Elements and Secondary Elements

These are the primary elements that are required to resist lateral

loads after several cycles of inelastic response to the earthquake ground

motion.

The secondary elements may be required to support vertical gravity

loads and may resist some lateral loads.

3.5.8 Nonlinear Plastic Hinge Properties

This requires the development of the force - deformation curve for

the critical sections of beams, columns and brick masonry by using the

guidelines FEMA 356 (2000). The force deformation curves in flexure are

obtained from the reinforcement details and assigned for all the beams and

columns. The Nonlinear properties of beams and columns have been

evaluated using the section designer and have been assigned to the computer

model in SAP2000. The flexural default hinges (M3) and shear hinges (V2)

were assigned to the beams at two ends. The interacting (P-M2-M3) hinges

assigned for all the columns at upper and lower ends. The axial hinges (P)

were assigned to the brick masonry strut element.

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Figure 3.12 the plot of the lateral force on a structure against the

lateral deformation of the roof of the structure. This is often referred to as the

‘push over’ curve. Performance point and location of hinges in various stages

can be obtained from pushover curve as shown in the Figure 3.12. Five points

labeled A, B, C, D and E are used to define the force deflection behavior of

the hinge. The points labeled A to B – Elastic state, B to IO- below immediate

occupancy, IO to LS – between immediate occupancy and life safety, LS to

CP- between life safety to collapse prevention, CP to C – between collapse

prevention and ultimate capacity, C to D- between ultimate capacity and

residual strength, D to E- between residual strength and collapse and greater

than E – collapse.

Figure 3.12 Different Stages of Plastic Hinge ATC 40 (1996)

3.5.9 Pushover Cases

The pushover hinges were assigned for beams and columns and the

lateral forces were applied at each floor level. Pushover analysis was

performed separately for the two orthogonal directions in order to study the

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performance of the buildings in these two directions independently. Therefore

there are three cases for the evaluation of the buildings.

Three pushover cases for the evaluation of buildings are follows.

Gravity push, which is used to apply gravity load,

(D.L. + 0.25 LL)

Push 1- is the lateral push in the X direction, starting at the

end of gravity push

Push2- is the lateral push in the Y direction starting at the end

of gravity push

In general, the gravity load push is force controlled while lateral

push is deformation controlled. The displacements are monitored at the roof

level. The pushover analysis is performed in the frame considering the

P- effect. The pushover analysis involves the application of monotonically

increasing lateral deformation and monitoring the inelastic behavior of the

structure. The relationship of base shear and roof displacement (capacity

curve) and 5 % damped elastic design response spectrum (demand curve) of

the two models were established. The capacity and demand curves were

converted into a spectral displacement and the spectral acceleration format to

obtain the performance point. The performance point is the intersection point

of the capacity and demand curves.

The output of the capacity curve gives the co-ordinates of each step

of the pushover curve and summarizes the number of hinges in each state.

The coordinates of capacity curve and demand curve were transformed into

spectral acceleration versus spectral displacement coordinates. The curves

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plotted in this format are called as capacity spectrum and demand spectrum

respectively. The number of hinges formed in the beams and columns at the

performance point and their performance levels are used to study the local

vulnerability of the structure and global behavior of the building.

3.5.10 Pushover Analysis in SAP2000

1. The basic computer model (without the pushover data) in the usual

manner was created. The graphical interface of SAP2000 makes

this a quick and easy task.

Figure 3.13 Modeling of the Frame

2. The properties and acceptance criteria for the pushover hinges were

defined.

3. The program includes several built-in default hinge properties that

are based on average values from ATC-40 (1996) for concrete

members and average values from FEMA-273 (1997) for steel

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members. These built in properties were used for preliminary

analyses but user-defined properties were used for final analyses.

Figure 3.14 Default Hinge Properties of the Frame

4. The pushover hinges on the model were located by selecting the

frame members and assigning them one or more hinge properties at

hinge locations.

5. The pushover load cases were defined in SAP2000, where more

than one pushover load case could be run in the same analysis. Also

a pushover load case could be started from the final conditions of

another pushover load case that was previously run in the same

analysis. Typically the first pushover load case is used to apply

gravity load and then subsequent lateral pushover load cases are

specified to start from the final conditions of the gravity pushover.

Pushover load cases can be force controlled, that is, pushed to a

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certain defined force level, or they can be displacement controlled,

that is, pushed to a specified displacement.

Typically a gravity load pushover is force controlled and

lateral pushovers are displacement controlled. SAP2000

allows the distribution of lateral force used in the pushover to

be based on a uniform acceleration in a specified direction, a

specified mode shape, or a user-defined static load case.

6. Initially the basic static analysis was made to run in SAP 2000 and

then the static nonlinear pushover analysis.

Figure 3.15 Analysis Cases of the Frame

7. The pushover curve was displayed in the system as shown in

Figure 3.16. A table which gives the coordination of each step of

the pushover curve and summarizes the number of hinges in each

state as defined in Figure 3.9 (for example, between IO and LS or

between D and E).

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Figure 3.16 Pushover Curve of the Frame

8. Next the capacity spectrum curve was displayed. The performance

point for a given set of values is defined by the intersection of the

capacity curve (green) and the single demand spectrum curve (red).

Figure 3.17 Capacity Spectrum of the Frame

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9. The pushover displaced shape and sequence of hinge formation were reviewed on a step-by-step basis. Hinges appear when they yield and they are color coded based on their state.

Figure 3.18 Sequence of Hinge Formation of the Frame

10. Output for the pushover analysis can be printed in a tabular form for the entire model or for selected elements of the model. The types of output available in this form include joint displacements at each step of the pushover, frame member forces at each step of the pushover and the hinge force, displacement and state at each step of the pushover.

Figure 3.19 Output of the Pushover Analysis

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3.5.11 Use of Pushover Analysis

Pushover analysis is the preferred method for seismic performance

evaluation of structures by the major rehabilitation guidelines and codes

because it is conceptually and computationally simple. Pushover analysis

allows tracing the sequence of yielding and failure on member and structural

level as well as the progress of overall capacity curve of the structure.

The expectation from pushover analysis is to estimate critical

response parameters imposed on structural system and its components as

close as possible to those predicted by nonlinear dynamic analysis. Pushover

analysis provides information on many response characteristics that cannot be

obtained from an elastic static or elastic dynamic analysis. The following are

the response characteristics of the pushover analysis:

The realistic force demands on potentially brittle elements,

such as axial force demands on columns, force demands on

brace connections, moment demands on beam to column

connections, shear force demands in deep reinforced concrete

spandrel beams, shear force demands in unreinforced

masonry wall piers, etc.

Estimation of the deformations demands for elements that

have to form inelastically in order to dissipate the energy

imparted to the structure.

Consequences of the strength detoriation of the individual

elements on the behavior of the structural system.

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Identification of the critical regions in which the deformation

demands are expected to be high and that have to become the

focus through detailing.

Identification of the strength discontinuities in plan elevation

that will lead to changes in the dynamic characteristics in

elastic range.

Estimates of the interstory drifts that account for strength or

stiffness discontinuities and that may be used to control the

damages and to evaluate P-Delta effects.

Verification of the completeness and adequacy of load path,

considering all the elements of the structural system, all the

connections, the stiff nonstructural elements of significant

strength, and the foundation system.

3.6 CONCLUSIONS

In this chapter, Seismic evaluation procedure, modeling of the

existing RCC building with and without infill, pushover analysis, hinge

properties, procedure of pushover analysis using SAP2000 and use of

pushover analysis were discussed and presented.