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Certificate
This is to certify that Miss. Megha Gupta, Civil OCES -2011, BARC Training School, Mumbai
has completed her Project Work on Response of RC buildings considering soil structure
interaction under seismic loads under my guidance.
Signature _____________________________
Name & Designation_____________________
Division/Unit_________________________________
2
Acknowledgements
I would like to express my sincere gratitude to my guide Dr. V.S. Phanikanth, A&CED for
giving me the opportunity to work with him and also providing excellent guidance and
continuous assistance throughout the project work. His constant advice, assertions, appreciation
were very vital, giving me the motivation without which it wouldnt have been possible to finish
the project. I am thankful to him for his encouragement throughout the project.
I wish to express my gratitude to the Division Head, Mr.K.Srinivas for giving me an opportunity
to work on this project.
I am also thankful to all the staff members of Architectural and Civil Engineering Division
(A&CED) for their continuous support.
Finally I would like to thank my parents and all my friends who stood beside me from the
beginning to the end of this project work.
3
Table of Contents
Certificate 1
Acknowledgements 2
Table of contents 3
List of Tables 4
List of figures 5
Abstract 6
Chapter 1 Introduction 7
Chapter 2 Dynamic analysis of RC structures
2.1 Dynamic analysis of RC structures 9
2.2 Description of Structural system 13
2.3 Seismic Analysis of 3-D frame in ETABS 18
Chapter 3 Soil Structure Interaction modeling-Impedance approach
3.1 Soil Properties and Foundation Modeling 24
3.2 Soil Structure analysis in ETABS 26
Chapter 4 Conclusions 30
References 31
4
List of Tables
Table No. Description of the Table Page No.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Spring Constants for a rectangular mat foundation.
RC Frame Description
Material Description
Parameters for calculation of Seismic loads
Response Spectrum parameters
Total Dead Load
Design Seismic Base Shear
Load combinations as per IS 1893:2002 (Part 1)
Comparison of time periods
Comparison of Base Shear and VB for the three RC frames
Mass participation ratio for RC frame 1(single storey)
Mass participation ratio for RC frame 2 (3-storey)
Mass participation ratio for RC frame 3 (5-storey)
Soil Properties
Column Foundation Dimensions
Equivalent Spring Stiffness for Single Storey Frame
Equivalent Spring Stiffness for Three Storey Frame
Equivalent Spring Stiffness for Five Storey Frame
Variation of Time period with VS for Frame 1 (single storey)
Variation of Time period with VS for Frame 2 (Three storey)
Variation of Time period with VS for Frame 3 (Five storey)
Variation of Response Spectrum acceleration with Vs for Frame
1(single storey)
Variation of Response Spectrum acceleration with Vs for Frame
2(Three storey)
Variation of Response Spectrum acceleration with Vs for Frame
3(Five storey)
8
14
15
15
15
17
18
18
19
19
21
21
22
24
24
25
25
25
26
26
27
28
28
29
5
List of Figures
Figure No. Description of figure Page No.
1
2
3
4
5
6
7
8
9
10
11
12
13
Response spectra for rock and soil sites for 5% damping.
Plan and 3-D view of Frame 1
Plan and 3-D view of Frame 2
Plan and 3-D view of Frame 3
Showing application of Wall load for single storey
Showing waterproofing load
Showing Live Load
Variation of scale factor with height
Significant Mode shapes for single storey
Significant Mode shapes for Three storey
Significant Mode shapes for Five storey
Variation of Time period with VS
Variation of Response Spectrum acceleration with Shear
velocity
12
13
13
14
16
16
17
20
22
23
23
27
28
6
ABSTRACT
The structural design of R.C. buildings under seismic loading in majority of the cases is based on
fixed base analysis assumption. In general this assumption leads to simplified analysis of
structural response under dynamic loads. Whereas the aim is justifiable by avoiding the complex
modeling of soil structure aspects there by using simplified assumptions, the same cannot be
ignored in the design of industrial and safety related structures, which may result in under design
of the structural system.
In this study an attempt has been made to investigate the influence of soil structure interaction in
the dynamic behavior of R.C. structures using the impedance approach as suggested by
TECDOC 1347/ASCE 4-98.The detailed dynamic analysis is evaluated with the help of
commercial Finite element software ETABS using beam elements. As brick in-fill panel effects
are not modeled, the amplification in the base shear as per IS1893-2002 is also investigated for
different storeys considered. The influence of soil-structure interaction in the analysis and
design of a single, 3 storey and 5 storey reinforced concrete frame building is also investigated.
Finite element models simulating two different conditions: namely soil-structure interaction and
fixed-base behavior are considered. The results show an increase in the vibration period in
comparison with the fixed-base model, which does not consider the supporting soil. This shows
that the aspects may be ignored for flexible structures whereas the same cannot be applicable for
rigid structures like nuclear power plants where the increase in time period may result in
amplification of dynamic forces.
7
1. Introduction
The analysis of R.C. structures require consideration of various loads such as dead loads, live
loads, superimposed loads if any, wind loads or earthquake loads etc. The analysis of structures
to earthquake forces in turn may be based on seismic coefficient method for conventional
structures and may need detailed dynamic analysis using response spectrum method as suggested
by the code or site specific spectrum as applicable. Usually the designers carry out fixed base
analysis due to simplicity. However the soil effects are ignored in this assumption.
The effect of Soil structure interaction (SSI) on the response of buildings has been focus of
attention for more than 30 years. It is also well recognized that SSI could play a significant role
on structural response particularly for rigid structures on soft soil. Soil structure interaction is a
coupled phenomena in the response of structures caused by the flexibility of the foundation soils,
as well as in the response of soil region caused by the presence of structures.
Past earthquakes indicated that the bedrock movements could be intensified by the dynamic
effects of site and due to these effects of SSI changes in structural response is required to be
evaluated. The consideration of the influence of foundation flexibility is essential for accurate
representation of soil structure system. Soil structure interaction is an important issue, especially
for stiff and massive structures constructed on the relatively soft ground, which may alter the
dynamic characteristics of the structural response significantly. The dynamic response of
structures depend on the soil properties beneath the foundation, so the representation of soil
properties along with the structure in the FE model gives realistic estimation of dynamic
response. Some of the important parameters that change the dynamic response of the structure
are shear modulus, Poissons ratio etc. As discussed above, assessment of seismic behavior of
structure by neglecting soil structure interaction effects may lead to un-conservative results. In
recent years several researches carried out comprehensive studies on effects of SSI to improve
the accuracy of analysis. In order to evaluate SSI phenomenon for earthquake loading, elastic
half space approach is to be carried out. However this procedure is quite complex due to
modeling inherent non-linearity in the soil, alternative simplified approach using Impedance
method, is usually carried out by the designers due to the simplicity. These procedures are
8
recommended by ASCE4-98/TECDOC1347-2003.The impedance approach involved replacing
the soil stiffness by equivalent soil springs (frequency independent) in all rotational and
translational directions and the expressions for evaluating the spring stiffness and damping
values have been suggested for rigid circular/rectangular foundations in ASCE4-98.
Table 1: Spring Constants for a rectangular mat foundation. (TECDOC1347-2002/ASCE4-98)
Movement Foundation Stiffness
Horizontal sliding
Vertical
Rocking
Here,
= Poissons ratio of soil medium
G = Shear modulus of soil medium
B = width of the foundation perpendicular to the direction of horizontal excitation
L = length of the foundation in the direction of horizontal excitation
9
2. Dynamic analysis of RC structures
Dynamic analysis is related to the inertia forces developed by a structure when it is excited by
means of dynamic loads applied suddenly (e.g., wind blasts, explosion, and earthquake).
Dynamic analysis for simple structures can be carried out manually, but for complex structures
finite element analysis can be used. In a 3-D structure there are three dynamic degrees of
freedom (DDOF) for every unrestrained node with non-zero mass and there is potentially a
natural vibration mode for each DDOF. Thus, there may be hundreds of potential vibration
modes in a typical structure, but usually, it is only a small number of vibration modes with the
lowest frequencies that are of interest. In a multi-storey building, for example, it might be only a
few in each of two horizontal directions, plus one or two torsional modes that have to be
considered. The natural frequency of a system is dependent only on the stiffness of the structure
and the mass which participates with the structure (including self-weight). It is not dependent on
the load function.
A modal analysis calculates the frequency modes or natural frequencies of a given system. The
vibration mode shapes are normalized. This means that the largest value in each tabulated mode
shape is +1.0. Modal analysis of a structure comprises of following steps:
1. Find the natural modes (the shape adopted by a structure) and natural frequencies
2. Calculate the response of each mode
3. Optionally superpose the response of each mode to find the full modal response to a
given loading.
Determining the natural mode shapes and frequencies does not provide any quantitative
information about the response of the structure to excitation, but in some cases it may be
sufficient to know what the natural frequencies are so they can be avoided.
2.1 Seismic Evaluation Methods
Equivalent Static Method
Response Spectrum Method
10
2.1.1 Response Spectrum Method
Response spectrum analysis is a procedure for computing the statistical maximum response of a
structure to a base excitation. Each of the vibration modes that are considered may be assumed to
respond independently as a single-degree-of-freedom system. Design codes specify response
spectra which determine the base acceleration applied to each mode according to its period (the
number of seconds required for a cycle of vibration).Having determined the response of each
vibration mode to the excitation, it is necessary to obtain the response of the structure by
combining the effects of each vibration mode because the maximum response of each mode will
not necessarily occur at the same instant, the statistical maximum response, where damping is
zero, is taken as the square root of the sum of the squares (SRSS) of the individual responses.
Response spectrum analysis produces a set of results for each earthquake load case which is
really in the nature of an envelope. It is apparent from the calculation, that all results will be
absolute values - they are all positive. Each value represents the maximum absolute value of
displacement, moment, shear, etc. that is likely to occur during the event which corresponds to
the input response spectrum.
2.1.2 Equivalent Static Method
The equivalent static method is the simplest method of analysis because the forces depend on the
code based fundamental period of structures with some empirical modifiers. The design base
shear is to be computed as whole, then it is distributed along the height of the building based on
some simple formulae appropriate for buildings with regular distribution of mass and stiffness.
The design lateral force obtained at each floor shall then be distributed to individual lateral load
resisting elements depending upon the floor diaphragm action.
Following are the major steps in determining the seismic forces:
Determination of Base shear:
The total design lateral force or design base shear along any principal direction shall be
determined by this expression:
(1)
11
Where,
Ah = design horizontal seismic coefficient for a structure
W= seismic weight of building.
The design horizontal seismic coefficient for a structure Ah is given by:
(
) (
) (
) for Design Basis Earthquake (DBE) (2)
Z is the zone factor given in Table 2 of IS 1893:2002 (part 1) for the maximum considered
earthquake (MCE) and service life of a structure in a zone. The factor 2 is to reduce the MCE to
the factor for design base earthquake (DBE).
I is the importance factor, depending upon the functional use of the structure, characterized by
hazardous consequences of its failure, post-earthquake functional needs, historical or economic
importance. The minimum values of importance factor are given in Table 6 of IS 1893:2002
R is the response reduction factor, depending on the perceived seismic damage performance of
the structure, characterized by ductile or brittle deformations. The need for introducing R in base
shear formula is an attempt to consider the structures inelastic characteristics in linear analysis
as it is undesirable as well as uneconomical to design a structure on the basis that it will remain
in elastic range for all major earthquakes. Note: IS code recommends that the value of I/R should
not exceed 1.0 the values of R are given in Table 7 of IS 1893:2002 (part 1).
Sa/g is the average response acceleration coefficient for rock and soil sites as given in figure 2 of
IS 1893:2002 (part 1). The values are given for 5 % of damping of the structure.
12
Figure 1: Response spectra for rock and soil sites for 5% damping.
T, the fundamental natural period for buildings are calculated as per Clause 7.6 of IS 1893:2002
(part 1).
for moment resisting frame without brick infill panels. (3)
for resisting steel frame building without brick infill panels. (4)
for all other buildings including moment resisting RC frames. (5)
h is the height of the building in m and d is the base dimension of building at plinth level in m
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
IS1893,Hard rock
S DJ /g
Time(sec)
Normalised spectra of TECDOC and IS1893-2002
13
2.2 Description of Structural system
Three RC frames are modeled as single storey, 3 storey and 5 storey in ETABS. Appropriate
beam and column dimensions are chosen and secondary beams are provided to reduce the span
of the slab. The following section shows an overview of the model showing the plan and 3-D
view of the model.
2.2.1 Model Overview
Frame 1 Single Storey
Figure 2: Plan and 3-D view of Frame 1
Frame 2 Three storey
Figure 3 : Plan and 3-D view of Frame 2
14
Frame 3 Five storey
Figure 4 : Plan and 3-D view of Frame 3
2.2.2 Description of model geometry and material properties
The RC frames are modeled considering the dimensions as shown in Table 1. Secondary beams
are provided so as to reduce the span of the slab and thus ensure two way action of the slab.
Table 2: RC Frame Description
Frame 1 Frame2 Frame 3
Number of stories 1 3 5
Plan Dimensions 6mx6m 6mx6m 6mx6m
Plinth Depth 3.0m 3.0m 3.0m
Storey Height 3.5m 3.5m 3.5m
Total Height from the
base 6.5m 13.5m 20.5m
Beam Dimensions
(mm) 300x600 300x600 300x600
Column Dimensions
(mm) 300x500 300x500 300x500
Slab Depth (mm) 120 120 120
15
Table 3 gives a brief description of the materials for the beams and columns. The concrete used
is of M30 grade and steel of Fe 415 grade is used.
Table 3: Material Description
Concrete Steel
Grade 30 Fe 415
Unit Weight (kN/m3) 25 77
Modulus of Elasticity (kN/m2) 27.386X10
3 2x10
8
Poisson Ratio, 0.2 0.3
2.2.3 Seismic evaluation parameters
The parameters considered for the calculation of seismic loads are listed in Table 4. The structure
is considered to be in Zone III and an Importance factor of 1.5 is assigned to the structure.
Table 4: Parameters for calculation of Seismic loads
Zone III
Zone Factor 0.16
Importance Factor,I 1.5
Response reduction Factor,R 3
Spectrum IS-1893:2002
The response spectrum corresponding to 5% damping value is chosen and is applied in all three
directions, i.e. x, y, and z directions. For the directional combination of the responses SRSS
method is applied and the responses from the various modes are combined through CQC
combination. Table 5 gives a brief description of the various response spectrum parameters
applied to the model.
Table 5: Response Spectrum parameters
Directional Combination SRSS
Modal Combination CQC
Spectrum type Acceleration
Direction X, Y, Z
Damping 5%
16
2.2.4 Loading on the structure
Dead Load
Includes self-weight of all members + Brick Load + Water Proofing load from the
slab.Self weight of members include the weight of columns, beams and that of the
slabs.Wall load due to 3.5 m high wall and of thickness 230mm and of 20 kN/m3 density,
WL= 20x.23x3.5=16kN/m.
Figure 5: Showing application of Wall load for single storey
Waterproofing Load considering average waterproofing thickness of 100mm and density of
24kN/m3= 24x0.1=2.4 kN/m
2.
Figure 6: Showing waterproofing load
17
The values of Self weight of members, wall load and waterproofing load calculated for the RC
frames are shown in Table 6.
Table 6: Total Dead Load
Frame 1 Frame 2 Frame 3
Self weight of members (kN) 434.1 1010.70 1587.3
Wall load (kN) 384.0 1152.0 1920.0
Waterproofing load (kN) 86.4 86.4 86.4
Total Dead load (kN) 904.5 2249.1 3593.7
Live Load
Live load is taken as 1.5 kN/m2 with a live load reduction factor of 25%.
Figure 7: Showing Live Load
Seismic Load
The design seismic base shear was calculated as per IS 1893:2002 (Part 1) for equivalent
static procedure. The values of base shear calculated are tabulated below for the RC
18
frames. The design shear is calculated for both cases of with infill walls and without infill
walls based on Equations 3 and 4.
Table 7: Design Seismic Base Shear (VB)
Frame 1 Frame2 Frame 3
Time Period (sec) 0.3053 0.5282 0.7226
Ah 0.1 0.0750 0.0554
Seismic Weight (KN) 918 2289.6 3661.2
VB (kN)(without
infills) 91.8 171.72 202.83
VB (kN)(without
infills) 91.8 184.63 194.48
2.2.5 Load Combinations applied
Table 8 shows the load combinations applied to the model.
Table 8: Load combinations as per IS 1893:2002 (Part 1)
1.5(DL + LL)
1.2(DL + LL EL)
1.5(DL EL)
0.9DL 1.5EL
2.3 Seismic Analysis of 3-D Frame in ETABS
After the loading on the structure is complete, fixed base and SSI analysis is done for the
structure.
2.3.1 Comparison of Fundamental Time periods obtained through ETABS with that of IS-
1893:2002
Time Period calculated by the Equivalent Static Method as prescribed by the code is compared
with the fundamental time period calculated by ETABS for the three RC frames.
The comparison shown in Table 9 indicates that ETABS predict a higher value of the time
periods than given by the code.The value of time period given by the code takes in account only
19
the height and plan dimensions (in case of infills) of the structure. There is no provision to
capture the mass or stiffness of the structure. Therefore, a detailed dynamic analysis of the
structure will provide more accurate results.
Table 9: Comparison of time periods
ETABS IS-1893:2002
Frame 1 0.3615 0.3053
Frame 2 0.8812 0.5282
Frame 3 1.4094 0.7226
2.3.2 Comparison of Seismic Base shear as computed by IS-1893:2002(Part-1) with ETABS.
Design seismic base shears ( ) were calculated using IS 1893:2002 in the X and Y directions
(EQx and EQy). Base shear from response spectrum analysis (VB) was calculated from the modal
combination of the first twelve modes (EQ). VXand VYare the components in X- and Y- directions,
respectively. As VBwas lessthan , the seismic force demands in the frame elements from
response spectrum analysis were scaledup by a factor equal to the ratio of the two base shears
( . In case of without infills the base shear needs to be amplified by 16%, 36.5% and
60.5% in X- direction and an amplification of 19.3%, 73.8% and 99% is required in Y- direction.
Table 10: Comparison of Base Shear and VB for the three RC frames.
Frame 1 Frame 2 Frame 3
Vx (kN) Vy(kN) Vx (kN) Vy(kN) Vx (kN) Vy(kN)
Equivalent Static ( )(without infills) EQx 91.80 91.80 171.72 171.72 202.83 202.83
Equivalent Static ( ) (with infills) EQx 91.80 91.80 184.63 184.63 194.48 194.48
Response Spectra (VB)
EQ 79.13 76.95 120.12 94.34 120.64 97.30
(without
infills)
1.160 1.193 1.365 1.738 1.605 1.990
(with infills)
1.160 1.193 1.467 1.869 1.539 1.908
20
From the analysis, the scale factor is found to be increasing with height of the structure.
Figure 8: Variation of scale factor with height ( without infills).
2.3.3 Comparison of Mass participation ratios for the three frames.
The mass participation ratios (%) for the first twelve modes are tabulated in Table 11,12 and 13
for the three RC frames. The significant modes for single storey frames are mode 1 (Y-direction)
and mode 3 (X-direction) while that for 3 and 5 storey frame are mode 1 (Y- direction) and mode
2 (X-direction). Rest all modes are insignificant as their mass participation is less than 20%. For
simplicity the mass participation in Z direction has been ignored in this analysis, otherwise, it has
to be considered.
0
0.5
1
1.5
2
2.5
1 storey 3 storey 5 storey
Scal
e F
acto
r
X-dir
Y-dir
21
Table 11: Mass participation ratio for RC frame 1(single storey).
Mode
no.
X-Trans
(%mass)
Y-Trans
(%mass)
Z-Trans
(%mass)
Sum
X(%mass)
Sum
Y(%mass)
Sum
Z(%mass)
1 0.00 87.32 0.00 0.00 87.32 0.00
2 0.00 0.00 0.00 0.00 87.32 0.00
3 84.39 0.00 0.00 84.39 87.32 0.00
4 0.00 12.68 0.00 84.39 100.00 0.00
5 0.00 0.00 0.00 84.39 100.00 0.00
6 0.00 0.00 0.00 84.39 100.00 0.00
7 15.61 0.00 0.00 100.00 100.00 0.00
8 0.00 0.00 0.00 100.00 100.00 0.00
9 0.00 0.00 0.00 100.00 100.00 0.00
10 0.00 0.00 0.00 100.00 100.00 0.00
11 0.00 0.00 0.00 100.00 100.00 0.00
12 0.00 0.00 0.00 100.00 100.00 0.00
Table 12: Mass participation ratio for RC frame 2 (3-storey).
Mode
no.
X-Trans
(%mass)
Y-Trans
(%mass)
Z-Trans
(%mass)
Sum
X(%mass)
Sum
Y(%mass)
Sum
Z(%mass)
1 0.00 85.64 0.00 0.00 85.64 0.00
2 83.97 0.00 0.00 83.97 85.64 0.00
3 0.00 0.00 0.00 83.97 85.64 0.00
4 0.00 8.19 0.00 83.97 93.83 0.00
5 0.00 0.00 0.00 83.97 93.83 0.00
6 9.07 0.00 0.00 93.04 93.83 0.00
7 0.00 2.40 0.00 93.04 96.24 0.00
8 0.00 0.00 0.00 93.04 96.24 0.00
9 0.00 3.76 0.00 93.04 100.00 0.00
10 0.00 0.00 0.00 93.04 100.00 0.00
11 3.00 0.00 0.00 96.04 100.00 0.00
12 0.00 0.00 0.00 96.04 100.00 0.00
22
Table 13: Mass participation ratio for RC frame 3 (5-storey).
Mode
no.
X-Trans
(%mass)
Y-Trans
(%mass)
Z-Trans
(%mass)
Sum
X(%mass)
Sum
Y(%mass)
Sum
Z(%mass)
1 0.00 84.06 0.00 0.00 84.06 0.00
2 82.53 0.00 0.00 82.53 84.06 0.00
3 0.00 0.00 0.00 82.53 84.06 0.00
4 0.00 9.07 0.00 82.53 93.13 0.00
5 9.79 0.00 0.00 92.32 93.13 0.00
6 0.00 0.00 0.00 92.32 93.13 0.00
7 0.00 2.75 0.00 92.32 95.88 0.00
8 0.00 0.00 0.00 92.32 95.88 0.00
9 0.00 1.28 0.00 92.32 97.17 0.00
10 3.09 0.00 0.00 95.41 97.17 0.00
11 0.00 0.59 0.00 95.41 97.75 0.00
12 0.00 0.00 0.00 95.41 97.75 0.00
Significant Mode Shapes:
Single Storey:
Figure 9: Significant Mode shapes for single storey.
23
Three Storey:
Figure 10: Significant Mode shapes for Three storey.
Five Storey:
Figure 11: Significant Mode shapes for 5 storey.
24
Chapter 3 Soil Structure Modeling- Impedance approach.
Soil Structure Interaction plays a significant role in case of rigid structures and hence needs to be
modeled with the structure for accurate results. Impedance approach for soil structure interaction models
the soil in the form of equivalent springs. Soil stiffness is considered by providing springs in horizontal
and vertical direction for translation and for rotational and torsional degrees of freedom.
3.1 Soil Properties and Foundation Modeling
The properties of soil considered for calculation of soil spring stiffness are as given in Table 14.
Table 14: Soil Properties
Unit Weight (kN/m3) 18
Poisson Ratio, 0.3
Safe Bearing Capacity
@3m below G.L.(kN/m2)
200
Assuming the aspect ratio of the column foundation to be same as that of column i.e. 5:3, the
dimensions of foundation are calculated as given in Table 15.For Kx and KRy, the ratio is
used in the calculation of X and and for Ky andKRx , ratio of is used.
Table 15: Column Foundation Dimensions.
Frame 1 Frame 2 Frame3
Length,L(m) 1.8 3.1 3.8
Breadth,B(m) 1.1 1.8 2.3
Table 16, 17 and 18 shows the values of the Equivalent Spring Stiffness for the three frames
calculated using the equations as per Table 1 and foundations dimensions as per Table 5. The
soil properties considered are given in Table 14.
25
Table 16: Equivalent Spring Stiffness for Single Storey Frame
Soil
name
Vs
(m/s)
Soil
type
Kx x 106
(kN/m)
Ky x
106
(kN/m)
Kz x
106
(kN/m)
KRx x 106
(kNm/rad)
KRy x 106
(kNm/rad)
KT x10-5
(kNm/rad)
A 1100 7.797 8.122 4.284 6.630 11.303 1.000 B 1000 II 6.444 6.712 3.541 5.479 9.341 1.000
C 800 II 4.124 4.296 2.266 3.507 5.979 1.000
D 600 II 2.320 2.416 1.275 1.973 3.363 1.000
E 400 II 1.031 1.074 0.566 0.877 1.495 1.000
F 200 III 0.258 0.268 0.142 0.219 0.374 1.000
Table 17: Equivalent Spring Stiffness for Three Storey Frame
Soil
name
Vs
(m/s)
Soil
type
Kx x 106
(kN/m)
Ky x
106
(kN/m)
Kz x
106
(kN/m)
KRx x 106
(kNm/rad)
KRy x 106
(kNm/rad)
KT x10-5
(kNm/rad)
A 1100 I 12.953 13.635 7.117 30.261 54.86 1.000
B 1000 II 10.705 11.268 5.882 25.009 45.338 1.000
C 800 II 6.851 7.212 3.764 16.006 29.016 1.000
D 600 II 3.854 4.057 2.117 9.003 16.322 1.000
E 400 II 1.711 1.801 0.940 3.997 7.247 1.000
F 200 III 0.428 0.460 0.235 0.999 1.812 1.000
Table 18: Equivalent Spring Stiffness for Five Storey Frame
Soil
name
Vs
(m/s)
Soil
type
Kx x 106
(kN/m)
Ky x
106
(kN/m)
Kz x
106
(kN/m)
KRx x 106
(kNm/rad)
KRy x 106
(kNm/rad)
KT x10-5
(kNm/rad)
A 1100 I 16.200 17.064 8.907 60.564 105.329 1.000
B 1000 II 13.388 14.102 7.361 50.050 87.044 1.000
C 800 II 8.568 9.025 4.711 32.032 55.708 1.000
D 600 II 4.819 5.076 2.650 18.018 31.336 1.000
E 400 II 2.142 2.254 1.177 8.000 13.913 1.000
F 200 III 0.535 0.564 0.294 2.000 3.478 1.000
26
3.2 Soil Structure analysis in ETABS.
3.2.1 Variation of Time period with shear velocity (VS) for the significant modes.
The variation of time period of the structure with the shear velocity for the significant modes is
shown in Figure 12. It is indicated that the time period decreases with increase in shear wave
velocity,i.e. as the soil stiffness increases, frequency increases, hence time period decreases.
Table 19, 20 and 21 show the time period values corresponding to different soil types for the
three RC frames.
Table 19: Variation of Time period with VS for Frame 1 (single storey).
VS
(m/s)
Mode 1
(Y-dir) (sec)
Mode 3
(X-dir) (sec)
200 0.3882 0.2930
400 0.3684 0.2719
600 0.3646 0.2676
800 0.3633 0.2660
1000 0.3627 0.2653
1100 0.3625 0.2651
Table 20: Variation of Time period with VS for Frame 2 (Three storey).
VS
(m/s)
Mode 1
(Y-dir) (sec)
Mode 2
(X-dir) (sec)
200 0.9187 0.7186
400 0.8907 0.6857
600 0.8855 0.6795
800 0.8836 0.6772
1000 0.8828 0.6762
1100 0.8825 0.6759
27
Table 21: Variation of Time period with VS for Frame 3 (Five storey).
VS
(m/s)
Mode 1
(Y-dir) (sec)
Mode 2
(X-dir) (sec)
200 1.4761 1.1842
400 1.4263 1.1253
600 1.4169 1.1140
800 1.4136 1.1100
1000 1.4121 1.1081
1100 1.4116 1.1076
Figure 12: Variation of Time period with VS
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
1.4000
1.6000
200 400 600 800 1000 1100
Tim
e P
eri
od
(se
c) Mode 1 (Y-dir) Frame 1
Mode 3(X-dir) Frame 1
Mode1 (Y-dir) Frame 2
Mode 3 (X-dir) Frame 2
Mode 1 (Y-dir) Frame 3
Mode 2 (X-dir) Frame 3
Shear velocity (m/s)
28
3.2.2 Variation of Response Spectrum accelerations with shear velocity (VS) for the significant
modes.
Table 22, 23 and 24 show the variation of Response spectrum acceleration with shear velocity.
There is no variation in response spectrum accelerations for single storey frame as the time
period values for the different shear wave velocities fall in the range corresponding to the
maximum value of spectral acceleration.
Table 22: Variation of Response Spectrum acceleration with Vs for Frame 1(single storey).
Vs (m/s)
Mode 1(Y-dir)
(m/s2)
Mode 3 (X-dir)
(m/s2)
200 1.1692 1.1368
400 1.1692 1.1368
600 1.1692 1.1368
800 1.1692 1.1368
1000 1.1692 1.1368
1100 1.1692 1.1368
In case of 3 and 5 storey frames, for Vs values between 400 m/s to 1000 m/sthe response
spectrum accelerations are found to increase with the shear velocity which can be explained by
the corresponding decrease in the time period.
Table 23: Variation of Response Spectrum acceleration with Vs for Frame 2(Three storey).
Vs (m/s)
Mode 1(Y-dir)
(m/s2)
Mode 2 (X-dir)
(m/s2)
200 1.2534 1.2567
400 1.0531 1.1052
600 1.0592 1.1160
800 1.0609 1.1198
1000 1.0623 1.1215
1100 0.7814 0.8071
29
Table 24: Variation of Response Spectrum acceleration (Sa) with Vs for Frame 3(Five storey).
Vs (m/s)
Mode 1(Y-dir)
(m/s2)
Mode 2 (X-dir)
(m/s2)
200 0.8862 0.8893
400 0.7452 0.7663
600 0.7497 0.7743
800 0.7513 0.7772
1000 0.7520 0.7785
1100 0.5531 0.5727
Figure 13: Variation of Response Spectrum acceleration with Shear velocity
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
1.2000
1.4000
200 400 600 800 1000 1100
Re
spo
nse
sp
ect
rum
acc
ele
rati
on
(m
/s2 )
Mode 1(Y-dir)-Frame 1Mode 3 (X-dir)Frame 1Mode 1(Y-dir) Frame2Mode 2 (X-dir)Frame 2Mode 1(Y-dir) Frame3Mode 2 (X-dir)Frame 3
Shear Velocity (m/s)
30
Chapter 4 Conclusions
An attempt has been made to incorporate the soil stiffness in the finite element model of the
structure by introducing equivalent soil springs. In general, the effect of soil structure interaction
increases the time period of the structure. This effect of soil structure interaction is found to be
insignificant for flexible structures and significant for the rigid structures. Detailed comparison
of time period for fixed base is performed in ETABS.A comparative study of response spectrum
acceleration and Time period variation with shear velocity is also performed.
31
REFERENCES
1. ASCE4-98/TECDOC1347-2003.
2. IS 1893 (Part 1):2002, Criteria for Earthquake Resistant Design of Structures.
3. ETABS, Commercial package Finite Element Software.
4. Tavakoli ,H.R. ,Naeej, M. , Salari.A ,(2011), Response of RC structures subjected to near fault
and far fault earthquake motions considering Soil structure Interaction.