seismic analysis of symmetric rc frame

International Journal Of Scientific Research And Education ||Volume||2||Issue|| 3||Pages 483-499 |||2014|| ISSN (e): 2321-7545

Website: http://ijsae.in

Harshitha. R et al. IJSRE Volume 2 Issue 3 March 2014 Page 483

SEISMIC ANALYSIS OF SYMMETRIC RC FRAME USING RESPONSE

SPECTRUM METHOD AND TIME HISTORY METHOD

1Harshitha. R,

2A.Soundarya,

3Krishnareddygari Prathima,

4Y.Guruprasad

1,2,3,4Assistant Professor, Department of Civil Engineering, Sri Venkateswara College of Engineering and

Technology, Chittoor 517127, Andhra Pradesh, India.

ABSTRACT

In the History of Civil Engineering, the structures were usually designed considering only Static load

factor. Later due to research in the civil engineering field it was explored that the structures are also acted

upon by several other loads which included Seismic loads, Wind loads, Snow loads, etc, depending upon the

dimensions of the structure, location of the structure, type of the ground profile, etc. Hence this brought in

the process of analyzing a structure for different types of loads and designing the structure for the critical

load case of which Dynamic load is considered as one of the important load for which the structure should

be analyzed and designed. In the present work an attempt has been made to study the dynamic behavior of

multistoried building frame (Symmetric) using IS1893-2002 code recommended response spectrum method

and time history method. The time history analysis, two earthquake data such as from previous earthquakes

corresponding to Bhuj (2001) and Spitak (1988). Study focuses to evaluate the Base shear, Response

Spectra at different storey levels, Bending Moment Diagram and Shear Force Diagram variations in the

buildings. Analysis has been carried out using the STAAD software based on the Matrix Analysis. Based on

the result it is found that the base shear obtained from Time history analysis is slightly higher compared to

Response Spectrum analysis. This may be due to the variation in amplitude and frequency content of the

ground motions.

INTRODUCTION

The tremendous pace of urbanization of rural areas and ever increasing population in urban areas has

necessitated the increase in the construction of multi-storeyed buildings in order to optimize accommodation

in vertical direction and there by minimize the space in horizontal direction. Added to this, introduction of

high strength materials, new design concepts, new structural systems and modern construction methods have


made possible to construct sky scrapers by reinforced concrete frames with infill panels.Reinforced concrete

(RC) frames consist of horizontal elements (beams) and vertical elements (columns) connected by rigid

joints. These structures are cast monolithically that is, beams and columns are cast in a single operation in

order to act in unison. RC frames provide resistance to both gravity and lateral loads through bending in

beams and columns.

Earthquake

Earthquake is a natural phenomenon, which is generated in earths crust. Earthquake is a sudden shock on

the Earth's surface. It is shaking and vibration at the surface of the earth resulting from underground

movement along a fault plane of or from volcanic activity. Earthquakes are among the powerful events on

the earth, and their results can be terrifying. Some of them are as follows:

1. A severe earthquake may release energy 10,000 times as great as that of the first atomic bomb.

2. Rock movements during an earthquake can make rivers change their course.

3. Earthquakes can trigger landslides that cause great damage and loss of life.

4. Even large earthquakes beneath the ocean can create a series of huge waves called tsunamis that flood

coasts.

The consequences of earthquake events are well known to the public: thousands of persons are killed or

injured each year, thousands are homeless, heavy damage to the building stock, complete disruption of the

infrastructure, irreversible damage to the cultural heritage, very large indirect costs resulting from business

interruption, loss of revenues, and interruption of industrial production. Recent Earthquakes have clearly

demonstrated that the houses, bridges, public buildings constructed in many third world countries are not

engineered to resist even moderate earthquakes. Recently in India, earthquakes caused huge economic losses

and death toll, however not much attention is given in preventing such structural damages caused by

earthquakes.

Prediction of time of occurrence, location and intensity of future earthquakes are unfortunately not yet

possible. Recent earthquakes have shown that effective prevention has to be based mainly on adequate

design, construction and maintenance of new civil engineering structures, and retrofitting of existing

structures and monuments lacking appropriate seismic resistance characteristics.

The assessment of the seismic vulnerability of structures is a very complex issue due to the non-

deterministic characteristics of the seismic action and the need for an accurate prediction of the seismic

responses for levels beyond conventional linear behavior. The major developments in earthquake

engineering have occurred in last four decades. This has been possible as a result of combination of factors

such as installation of strong motion instruments world over in active seismic areas, as a result sizeable


amount of ground motion data is available, development of basic principles of seismic design, design for

strength and ductility, and basic concepts of design response spectrum, developments in mathematical

modeling and dynamic analysis-linear and non linear, shake table testing, quasi-static and pseudo dynamic

testing, response control, seismic isolation and energy dissipating devices. The availability of high-speed

digital computers has played a vital role in these developments. Besides, study of behavior of structures and

their performance in past earthquakes have provided a wealth of information on earthquake protection and

safety.

SEISMIC ANALYSIS

It is part of the process of structural design, earthquake engineering or structural assessment and retrofit (see

structural engineering) in regions where earthquakes are prevalent. Seismic Analysis is a subset of structural

analysis and is the calculation of the response of a building (or non-building) structure to earthquakes. A

building has the potential to wave back and forth during an earthquake (or even a severe wind storm). This

is called the fundamental mode, and is the lowest frequency of building response. Most buildings,

however, have higher modes of response, which are uniquely activated during earthquakes. The figure just

shows the second mode, but there are higher shimmy (abnormal vibration) modes. Nevertheless, the first

and second modes tend to cause the most damage in most cases. All real physical structures behave

dynamically when subjected to loads or displacements. The additional inertia forces, from Newtons second

law, are equal to the mass times the acceleration. If the loads or displacements are applied very slowly, the

inertia forces can be neglected and a static load analysis can be justified. Hence, dynamic analysis is a

simple extension of static analysis .In addition, all real structures potentially have an infinite number of

displacements. Therefore, the most critical phase of a structural analysis is to create a computer model with

a finite number of mass less members and a finite number of node (joint) displacements that will simulate

the behavior of the real structure. The mass of a structural system, which can be accurately estimated, is

lumped at the nodes. Also, for linear elastic structures, the stiffness properties of the members can be

approximated with a high degree of confidence with the aid of experimental data. However, the dynamic

loading, energy dissipation properties and boundary (foundation) conditions for many structures are difficult

analyses using different computer models, loading and boundary conditions. It is not unrealistic to conduct

20 or more computer runs to design a new structure or to investigate retrofit options for an existing structure.

Because of the large number of computer runs required for a typical dynamic analysis, it is very important

that accurate and numerically efficient methods be used within computer programs.

TYPES OF SESIMIC ANALYSIS:

Code based Procedure for Seismic Analysis (IS 1893:2002)

Equivalent Lateral Force


Seismic analysis of most of the structures is still carried out on the basis of lateral force assumed to be

equivalent to the actual loading. The base shear which is the total horizontal force on the structure is

calculated on the basis of structure mass and fundamental period of vibration and corresponding mode

shape. The base shear is distributed along the height of structures in terms of lateral force according to code

formula. This method is conservative for low to medium height buildings with regular conformation.

Response Spectrum Analysis

This method is applicable for those structures where modes other than the fundamental one affect

significantly the response of the structure. In this method the response of Multi-Degree-of-Freedom

(MDOF) system is expressed as the superposition of modal response, each modal response being determined

from the spectral analysis of single -degree-of-freedom (SDOF) system, which is then combined to compute

total response. Modal analysis leads to the response history of the structure to a specified ground motion;

however, the method is usually used in conjunction with a response spectrum. A response spectrum is

simply a plot of the peak or steady-state response (displacement, velocity or acceleration) of a series of

oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock. The

resulting plot can then be used to pick off the response of any linear system, given its natural frequency of

oscillation. One such use is in assessing the peak response of buildings to earthquakes. The science of strong

ground motion may use some values from the ground response spectrum (calculated from recordings of

surface ground motion from seismographs) for correlation with seismic damage. If the input used in

calculating a response spectrum is steady-state periodic, then the steady-state result is recorded. Damping

must be present, or else the response will be infinite. For transient input (such as seismic ground motion),

the peak response is reported. Some level of damping is generally assumed, but a value will be obtained

even with no damping.Response spectra can also be used in assessing the response of linear systems with

multiple modes of oscillation (multi-degree of freedom systems), although they are only accurate for low

levels of damping. Modal analysis is performed to identify the modes, and the response in that mode can be

picked from the response spectrum. This peak response is then combined to estimate a total response. A

typical combination method is the square root of the sum of the squares (SRSS) if the modal frequencies are

not close. The result is typically different from that which would be calculated directly from an input, since

phase information is lost in the process of generating the response spectrum.The main limitation of response

spectra is that they are only universally applicable for linear systems. Response spectra can be generated for

non-linear systems, but are only applicable to systems with the same non-linearity, although attempts have

been made to develop non-linear seismic design spectra with wider structural application. The results of this

cannot be directly combined for multi-mode response.


Time History Analysis

A linear time history analysis overcomes all the disadvantages of modal response spectrum analysis,

provided non-linear behavior is not involved. This method requires greater computational efforts for

calculating the response at discreet times .One interesting advantage of such procedure is that the relative

signs of response quantities are preserved in the response histories. This is important when interaction

effects are considered in design among stress resultants. Although this is too simplistic to apply to a real

structure, the Heaviside Step Function is a reasonable model for the application of many real loads, such as

the sudden addition of a piece of furniture, or the removal of a prop to a newly cast concrete floor. However,

in reality loads are never applied instantaneously - they build up over a period of time (this may be very

short indeed). This time is called the rise time.As the number of degrees of freedom of a structure increases

it very quickly becomes too difficult to calculate the time history manually - real structures are analyzed

using non-linear finite element analysis software.Time-history analysis is increasingly used in design of new

structures and evaluation of existing ones .In the case of time-history analysis, seismic action is described by

a suite of ground acceleration records.

SCOPE, OBJECTIVE AND METHODOLOGY

SCOPE OF THE STUDY

(i) The present study on Dynamic analysis reveals an attempt to determine the fundamental natural

frequency of different buildings using Matrix method based software, STAAD.

(ii)The building adopted consists of reinforced concrete frames which are fixed at the base. These frames are

analyzed for different earthquake data.

Parameters Considered:

1) Buildings

a) Symmetric Buildings.

b) Asymmetric Buildings.

2) Earthquakes

a) Spitak Earthquake

b) Bhuj Earthquake.

OBJECTIVE OF THE STUDY

To evaluate the displacements in structure at various levels, relative to ground displacements in

horizontal direction.

Response acceleration at different floors to estimate the lateral forces including shear.


Response of 3-D bare frame under dynamic loading.

To aim at the determination of fundamental natural frequency for the different building models.

To find the base shear value for different structures.

METHODOLOGY

1. Collection of data regarding earthquake ground motion.

2. Selection of different types of building models.

3. Assigning material properties to the frame section.

4. Assigning the boundary to the structure.

5. Analysis of different buildings and storey height by Response Spectra and Time History methods.

6. Interpretation of Results.

RESULTS OF ANALYSIS

DYNAMIC RESPONSE ANALYSIS RESPONSE SPECTRUM METHOD

ANALYSIS FOR RC BUILDING FRAME 1

PROPERTIES OF BARE FRAME 1

Number of Storey = 10

Height of each Storey = 3.5m

Span width in X Direction = 5m (1-Bay)

Span width in Z Direction = 5m (1-Bay)

MEMBER PROPERTIES

Column Size = 0.6 m X 0.23 m

Beam Size = 0.5m X 0.23 m

Thickness of Slab = 150mm

Grade of Concrete = M 25

LOAD CASE DETAILS

Self weight in X, Y and Z direction

Dead load in X,Y and Z direction = 14kN/m

Floor load in X,Y and Z direction = 5kN/m^2

Response spectrum for hard soil is considered with a scale factor of 0.245


Zone factor = 0.10 (As per IS1893-2002)

Importance factor = 1.5 (for Important buildings).

Reduction factor = 3 (for Ordinary moment resisting frame).

RESULTS

MODE SHAPES

There many number of Modes shapes depending upon the type and directions of the forces acting on it. The

STAAD software shows the various mode shapes with respect to the cut off modes mentioned in the input.

The first three are mentioned below along with their figures.

1. Mode Shape 1 - In X Direction.

2. Mode Shape 2 - In Z Direction.

3. Mode Shape 3 - Torsional Moment

FIG 3.1.1(a) FIG 3.1.1(b)


(1) (2) (3)

Fig 3.1.2.a (1 to 3) Mode Shapes

Fig 3.1.2 (b) Frequency variation with Mode number.

The above fig 3.1.2 (b) shows the variation of frequency with respect to modes. With the increase of modes

frequency also increases gradually. Table 3.1.2 (b) gives the values of frequency at each mode. Various

mode shapes can be observed in Fig 3.1.2 at (1 to 6 ) Mode 1 is always more effective than any other mode.

BASE SHEAR AT EACH STOREY

0

0.5

1

1.5

0 1 2 3 4 5 6 7

Fre

qu

en

cy(H

z)

Mode Number


Fig 3.1.2 (c)

In response spectrum method base shear is the most important result to be extracted. Base shear will me

maximum at the base and decreases as the height of the frame increases.

DYNAMIC RESPONSE BY TIME HISTORY ANALYSIS FOR SPITAK EARTHQUAKE DATA

EARTQUAKE DETAILS

Acceleration = 0.1 g

Frequency = 4.8 Hz

PROPERTIES OF BARE FRAME 1

Number of Storey = 10

Height of each Storey = 3.5m

Span width in X Direction = 5m (1-Bay)

1

3

5

7

9

1 2 3 4 5 6 7 8 9 10

443.81 431.62

402.12 364.16

330.25 305.25

282.96 247.22

187.68 102.05

BASE SHEAR CHART

Frame 1 Base Shear (kN) Storey Number

-0.1

-0.05

0

0.05

0.1

0.15

0 2 4 6 8 10 12 14 16 18 20 Acc

ele

rati

on

(g)

Time Period (Sec)

Acceleration Graph


Span width in Z Direction = 5m (1-Bay)

MEMBER PROPERTIES

Column Size = 0.6 m X 0.23 m

Beam Size = 0.5m X 0.23 m

Thickness of Slab = 150mm

Grade of Concrete = M 25

LOAD CASE DETAILS

DEAD LOAD

Self Weight in Y Direction

Wall load = 14 kN/m

Floor Load = 5 kN/m2

Super Dead Load = 1.5 kN/m2

LIVE LOAD

Floor Load = 2.5 kN/m2

DYNAMIC LOAD

Self Weight in ( X Y Z ) direction

Joint Load in X direction ( Fx ) = 154 kN

Member loads on Beams = 14 kN/m (Along X,Y,Z direction)

Floor Load = 5 kN/m2 (Along X,Y,Z direction)

RESULTS OF FRAME-1 FOR SPITAK EARTHQUAKE

BASE SHEAR VALUE = 595.13 kN.

MODE NUMBER VS FREQUENCY

The table shown below represents values of frequencies for their respective modes that are obtained by

the Analysis of the structure considering the Dynamic Load case.

The graph shown represents the variations of Frequencies that are obtained for different types of

modes.

It is observed that frequency increases with the mode number and there is sudden increase from 3rd

mode to 4th

mode.


Fig 3.2.1.1 (a) Graph Representing Mode Number Vs Frequency

STOREY NUMBER vs. DISPLACEMENT

Fig 3.2.1.1 (b) Graph Representing Variation of Displacement with Storey

The values in the displacement vary according to their Storey height. The following table represents the

displacement values for the respective Storey and the graph below shows the linear increase in displacement

values with the increasing Storey height.

STOREY NUMBER VS ACCELERATION

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0 1 2 3 4 5 6

Fre

qu

en

cy(h

z)

Mode number

0

2

4

6

8

10

12

0 50 100 150 200 250

Sto

rey

Nu

mb

er

Displacement (mm)


3.2.1.1 (c) Shows variation in Acceleration values.

The graph above shows the variation of values of frequencies with increase of storey numbers

from ground to top.

The acceleration values vary in X-pattern showing sudden increase and decrease in the values

with the increasing storey height.

The frequency values of every storey shown in the table shown below.

RESPONSE SPECTRUM GRAPH

The Response Spectrum graph shown below represents the variations of the Spectral

Acceleration in (g) of every Storey with the increasing time period.

The graph indicates that for the same Earthquake data the response of each storey of the structure

shows non-linear variations.

As observed in graph the maximum spectral acceleration values for each storey records around at

0.2 to 0.5 seconds.

0 1 2 3 4 5 6 7 8 9

10 11

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Sto

rey

Nu

mb

er

Acceleration (g)


Fig 3.2.1.1 (d) Graph of Spectral acceleration along the Time period for Each Storey.

TIME HISTORY ANALYSIS FOR BHUJ EARTHQUAKE DATA

EARTQUAKE DETAILS

Acceleration = 0.1 g

Frequency = 1.1 Hz

Fig (3.2): Bhuj Earthquake data in terms of g.

The bare frame is analyzed using STAAD software for the given Time History data obtained by plotting the

vales of Acceleration data in terms of (g) in Y-axis against the Time period in X-axis of Bhuj earthquake

data that was recorded. The ground motion was recorded for almost 134 seconds with a strong ground

motion being recorded between 30 to 55 seconds.

RESULTS OF FRAME-1 FOR BHUJ EARTHQUAKE

BASE SHEAR VALUE = 552.01 kN

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Spe

ctra

l acc

ele

rati

on

(g)

Time period(sec)

RESPONSE SPECTRUM

-2

-1

0

1

0 20 40 60 80 100 120 140 160

Spe

ctra

l Acc

ele

rati

on

(g)

Time Period (sec)

Acceleration graph


MODE NUMBER VS FREQUENCY

The table shown below represents values of frequencies for their respective modes that are obtained by the

Analysis of the structure considering the Dynamic Load case.The graph shown represents the variations of

Frequencies that are obtained for different types of modes.

It is observed that frequency increases with the mode number and there is sudden increase from 3rd

mode to

4th

mode

Fig 3.3.1.1(b) Graph Representing Mode Number Vs Frequency

STOREY NUMBER VS DISPLACEMENT

The values in the displacement vary according to their storey height. The following table represents the

displacement values for the respective storey numbers and the graph below shows the linear variation of

displacement values with the increasing storey height.

Fig 3.3.1.1 (c) Graph Representing Variation of Displacement with Storey

STOREY NUMBER VS SPECTRAL ACCELERATION

Every structure has its own frequency values so the spectral acceleration values depend on the buildings

natural frequency, hence each storey would have different variations. The graph below shows the variation

of values of frequencies with increase in storey number.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6

FREQ

UEN

CY

(Hz)

MODE NUMBER

0

2

4

6

8

10

12

0 50 100 150 200 250 300

STO

REY

NU

MB

ER

DISPLACEMENT(mm)


Fig 3.3.1.1(d) Graph representing spectral - acceleration against storey-number

RESPONSE SPECTRUM GRAPH

Fig 3.3.1.1(e) spectral acceleration along the time period for each storey

The Response Spectrum graph shown below represents the variations of the Spectral Acceleration in (g) of

every Storey with the increasing time period.the graph indicates that for the same Earthquake data the

response of each storey of the structure shows non-linear variations.

COMPARISION OF DISPLACEMENTS VALUES OBTAINED FROM SPITAK AND BHUJ

EARTHQUAKE

BUILDING FRAME 1

The horizontal displacement of the frame is slightly increased by 2.1% due to Bhuj earthquake data. This

may be due to the decrement of frequency in Bhuj earthquake data(1.1Hz) and that of Spitak is 4.8 Hz.

0

2

4

6

8

10

12

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

STO

REY

NU

MB

ER

SPECTRAL ACCELERATION(g)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

SPEC

TRA

L A

CC

ELER

ATI

ON

(g)

TIME PERIOD (SECS)

Response Spectrum


Fig3.3.1 (a) the variation of displacement

COMPARISION OF BASE SHEAR

RC Building Frame 1

Base shear is comparatively greater for Time History analysis than Response Spectrum

analysis. This can be clearly observed in following Fig

Fig 3.3.2.1(a)

CONCLUSIONS

Dynamic Response analysis is necessary for the design of any structure.

Time History analysis has wide application over Response Spectrum method as any type of structure

can be analyzed by this method and Response Spectrum analysis is restricted to code book.

Time History analysis can be used in the analysis of any kind of structure.

The bending moment, shear force and displacement values are greater in time history compared to

response spectrum analysis.

The displacement values will depend upon frequency of earthquake and natural frequency of the

structure.

0

100

200

300

0 1 2 3 4 5 6 7 8 9 10 11

Dis

pla

cem

en

t (m

m)

Storey Number

Comparision Of Displacement values

Displacement due to Spitak Earthquake (mm)

Displacement due to Bhuj Earthquake (mm)

Response spectrum

Time History (Spitak)

Time History (Bhuj)

443.81

595.13

522.02

Comparision Of Base Shear For Frame 1

Base shear (kN)


The base shear values obtained in case of Time History analysis are more compared to response

Spectrum analysis as it depends on the frequency content of the Earthquake data.

seismic analysis of symmetric rc frame

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