Ijciet 08 01_073

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 8, Issue 1, January 2017, pp. 628–638 Article ID: IJCIET_08_01_073
Available online at http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication Scopus Indexed
SEISMIC RESPONSE OF PLANE FRAMES WITH
EFFECT OF BAY SPACING AND NUMBER OF
STORIES CONSIDERING SOIL-STRUCTURE
INTERACTION
Y. Naga Satyesh
PG Student, Civil Engineering Department,
K L University, Vaddeswaram, A.P, India
K. Shyam Chamberlin
Assistant Professor, Civil Engineering Department,
K L University Vaddeswaram, A.P, India
ABSTRACT
Objective: The primary object of the work is to study the response of plane frames with
isolated footings for medium soil. Method: Destruction of structure initiates with the occurrence
of earthquakes, as most of the designers do not consider the soil structure interaction in analysis
and design of RCC frames which was having much influence in it. So single bay frames were
used for the analysis. The plane frames are having an increase in a number of stories (9m, 15m,
21m, 27m, 33m) are considered with varying in bay lengths (2m, 4m, 6m, 8m, 10m). Frames are
modeled by using STAAD PRO software under two base conditions (i) fixed base
condition(without soil structure interaction) (ii) flexible base condition (soil structure
interaction). The effect of soil flexibility is to be accounted through the consideration of springs
of specified stiffness. Dynamic analysis is carried out for frames using the equivalent static
method given by IS: 1893-2002, using STAAD PRO software. FINDINGS: The influence of soil
structure interaction on various soil parameters such as bending moment of column and beam,
lateral displacement and axial force are presented in this paper. IMPROVEMENTS: Reducing
the complexity of practical purpose, by employing Winkler hypothesis, to consider SSI instead
of fixed base. This SSI concept accepts the strong column week beam theory from the results.
Key words: Soil Structure Interaction, Medium Soil, Frames, Fixed and Flexible Foundation,
Response Spectrum Method, Bending Moment, Axial Force, Lateral Displacement
Cite this Article: Y. Naga Satyesh and K. Shyam Chamberlin, Seismic Response of Plane
Frames with Effect of Bay Spacing and Number of Stories Considering Soil-Structure
Interaction. International Journal of Civil Engineering and Technology, 8(1), 2017, pp. 628–
638.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=1

Seismic Response of Plane Frames with Effect of Bay Spacing and Number of Stories Considering Soil-Structure
Interaction
1. NTRODUCTION
In the regard of the rapid increase in population and constructions, one is compelled to construct the
structures in medium soil and soft soil instead of hard soil which was having less resistance to earthquake
forces. Construction of structure in the medium and soft soil leads to consideration of stiffness properties
and relative mass of soil. Thus the physical property of the foundation medium is an important factor in
the earthquake response of structures supported on it. Also, structures need to overcome the forces
occurs at the foundation level. This will call the attention of designers to understand the dynamic
behavior of such kind of structures considering SSI. Many researchers have proposed different methods
to evaluate the effect of soil structure interaction from time to time. The soil medium as a system of
identical but mutually independent, closely spaced, discrete, linearly elastic springs. The complete set
of algebraic formulas and dimensionless charts for readily computing the dynamic stiffness (K) and
damping coefficient (c) of foundation harmonically oscillating in a homogenous half space1
. The
response spectrum of multi-storied building frames such as lateral deflection, storey drift, base shear
and moment values were compared for buildings with flexible and fixed base. It is observed that values
are higher for buildings with flexible base and higher for rigid base2
.With the adjustment in soil property
from hard to medium and from hard to delicate the parallel avoidance has expanded by 53.33 and 60.25%
separately for adaptable base3
. Soil-structure Interaction was considered on three types of soils for
various structural parameters i.e. natural time period, base shear, roof displacement, beam moment and
column moment. The study shows that Finite Element Method has proved to be an effective method for
consideration of elastic continuum below foundation4
.The structures with adaptable bases have
demonstrated an extensive expand that range from 10% to around 230% contrasted with the settled base
case for structures found between hard soil and soft Soil . This would thusly expand the sidelong
avoidance of the entire building. Subsequently, SSI can detrimentally affect the execution of buildings
5
. Diminish in bending moment is watched for end ranges for edges both in longitudinal and transverse
beams utilizing Winkler approach 6
.
2. METHODOLOGY
Frames with fixed and flexible base conditions subjected to seismic forces were analyzed under medium
soil condition. The Elastic constant of the soil is considered as per Bowel’s E = 30000 for medium soil.
The plane frames are having an increase in a number of stories (9m, 15m, 21m, 27m, 33m) are
considered with varying in bay lengths (2m, 4m, 6m, 8m, 10m).The frames were analyzed using an
equivalent static method using software STAAD Pro. The seismic analysis was carried out by following
IS1893:2002 and considering zone as 3, Response reduction factor is 3, importance factor is 1, the
damping ratio of 5%.The details of frames, loads on frame and soil mass considered for the study are
given in Table 1.
Table 1. Geometric and material properties of frame, loads on frame, soil mass
Component Description Data
Frames
Size of Beam 0.3x0.4
Size of column 0.4x0.45
Thickness of Slab 0.115
Frame height 9m, 15m, 21m, 27m, 33m
Bay width variation 2m, 4m, 6m, 8m, 10m
Each storey height 3m
Loads on frame
Self weight -
Slab load 3 KN/m
Brick wall load 14 KN/m
Parapet wall load 2.5 KN/m
Floor finish 1 KN/m
Live load 2 KN/m
Soil (Medium soil)
Modulus Elasticity of soil 35000 KN/m2
Poisson's ratio of Soil 0.4

Y. Naga Satyesh and K. Shyam Chamberlin
3. MODELING OF FRAMES
3.1. Modeling of frames with fixed base condition in STAAD PRO
Modeling of frames with fixed base condition was done in STAAD PRO. Figure 1 shows a variation of
increment in a number of stories for 2m span, likewise for the bay length of (2m, 4m, 6m, 8m, 10m)
modeling was done with Increment in a number of stories (15m, 21m, 27m, 33m).
Figure 1. Increment in number of stories for 2m span
3.2. Idealization of discrete support
Effect of soil flexibility is incorporated by considering equivalent springs with 6 DOF as shown in Figure
2.
Figure 2. Equivalent soil spring stiffness along 6degrees of freedom

Interaction
Kx, Ky, Kz = Stiffness of equivalent soil springs along the translational DOF along X, Y and Z axis.
Krx, Kry, Krz = Stiffness of equivalent rotational soil springs along the rotational DOF along X, Y and
Z axis.
The stiffness along these 6 degrees of freedom is determined as per Gazetas and is shown in Table 2.
Table 2. Spring Stiffness Equations
Degrees of Freedom Stiffness of equivalent soil spring
Vertical [2GL/(1-ν)](0.73+1.54χ0.75
) with χ =Ab/4L2
Horizontal
(lateral direction)
[2GL/(2-ν)](2+2.50χ0.85
) with χ = Ab/4L2
Horizontal
(longitudinal direction)
[2GL/(2-ν)](2+2.50χ0.85
)-[0.2/(0.75-ν)]GL[1-(B/L)] with χ =
Ab /4 L2
Rocking
(about longitudinal)
[G/(1-ν)]Ibx
0.75
(L/B)0.25
[2.4+0.5(B/L)]
Rocking
(about lateral)
[G/(1-ν)]Iby
0.75
(L/B)0.15
Torsion 3.5G Ibz
0.75
(B/L)0.4
(Ibz/B4
)0.2
Ab= Area of the foundation considered;
B and L=Half-width and half-length of a rectangular foundation, respectively;
Ibx, Iby, and Ibz = Moment of inertia of the foundation area with respect to longitudinal, lateral and length.
The values of stiffness for medium soil is calculated for vertical, horizontal (longitudinal direction),
rocking (about lateral) as per the equations are given in table 2,as the frame considered for analysis is
two-dimensional frame and are presented in Table 3, Table 4, Table 5, Table 6, Table 7.
Table 3. Spring Stiffness for 9m (G+2) frame
Bay Length Horizontal(KN/m) Vertical(KN/m) Rocking about
longitudinal axis
(KN/m)
2m 28828.13 38779.16 4979.96
4m 33750.00 45399.99 8290.57
6m 39375.00 52966.66 12815.62
8m 44296.88 59587.49 18302.09
10m 48867.19 65735.41 25166.06
longitudinal axis
(KN/m)
2m 37968.75 51074.99 11804.35
4m 47812.50 64316.66 22546.82
6m 54140.63 72829.16 34224.18
8m 59765.63 80395.83 44432.28
10m 66093.75 88908.33 61276.74

Bay Length Horizontal(KN/m) Vertical(KN/m) Rocking about longitudinal axis (KN/m)
2m 45703.13 61479.16 20587.37
4m 56953.13 76612.50 39106.46
6m 66093.75 88908.33 61276.74
8m 73828.13 99312.50 85547.97
10m 80859.38 108770.83 114012.99
longitudinal axis
(KN/m)
2m 527434.37 70937.49 30997.71
4m 66445.31 89381.25 63263.94
6m 75234.38 101204.16 91835.83
8m 84375.00 113499.99 129540.20
10m 92812.50 124849.99 170466.13
longitudinal axis
(KN/m)
2m 58359.38 78504.16 42864.24
4m 72421.88 97420.83 81916.71
6m 84023.44 113027.08 127927.69
8m 90000.00 121066.66 155378.67
10m 99140.63 133362.50 210144.57
The spring stiffness obtained in the above tables are used for flexible base condition (soil structure
interaction) to the frames in STAAD. Pro software, in which Horizontal (about longitudinal) as KFX,
Vertical as KFY and Rocking (about longitudinal) as KMX.
3.3. Modeling of frames with flexible base condition in STAAD PRO
Modeling of frames with the flexible base condition was done in STAAD PRO. Figure 3 shows a
variation of increment in a number of stories for 2m span, likewise for the bay length of (2m, 4m, 6m,
8m, 10m) modeling was done with Increment in a number of stories (15m, 21m, 27m, 33m).

Interaction
Figure 3. Increment in number of stories for 2m span
4.RESULTS AND DISCUSSIONS
The plane frames are having an increase in a number of stories (9m, 15m, 21m, 27m, 33m) are
considered with varying in bay lengths (2m, 4m, 6m, 8m, 10m).The frames were analyzed using an
equivalent static method using software STAAD Pro. The results shown in the graph are percentage
variation for fixed and flexible base condition. The percentage variation of beam moment, column
moment, lateral deflection and axial force for fixed and flexible base condition of frames are noted. It is
observed that many variations in a moment of beams and columns occur in the ground storey when
support changes from fixed to flexible and there is less variation in a moment of beams and columns is
occurred in the ground storey when support changes from fixed to flexible.
4.1. Beam moment
The percentage variation in beam moment of frames of fixed base condition and flexible base condition
with an increase in a number of stories with variation in bay length is presented in Figure 4 and 5.

Figure 4. Beam Moments of flexible base frames compared with fixed frames in percentage variation
Figure 5. Beam Moments of flexible base frames compared with fixed frames in percentage variation
When support changed from fixed to spring, for the frame, beam moments are observed to be
decreased. This says that there is the effect of soil on the frame. In figure 4, a number of stories was
shown on X- axis, beam moment decrement is shown on Y-axis and each line in the graph specify the
bay length (2m, 4m, 6m, 8m, 10m). From figure 4 it was observed that for a particular bay length, the
decrement of beam moment is increasing with increase in storey height. Decrement of beam moment of
2m bay length increases from 15.91% to 43.39%, 4m bay length increases from 3.2% to 7.01%, 6m bay
length increases from 1.41% to 2.15%, 8m bay length increases from 0.61% to 1.01%, 10m bay length
increases from 0.405 to 0.72% with increase in storey height. In figure 5, bay length was shown on X-
axis, beam moment decrement is shown on Y-axis and each line specify storey height (9m, 15m, 21m,
27m, 33m). From Figure 5 it was observed that for a particular storey height, the decrement of beam
moment is decreasing with increase in bay length. Decrement of beam moment of 9mstorey height

Interaction
decreases from 15.91% to 0.40%, 15m storey height decreases from 27.02% to 0.407%, 21m storey
height decreases from 33.18% to 0.45%, 27m storey height decreases from 38.23% to 0.63%, 33m storey
height decreases from 43.39% to 0.72% with increase in bay length.
4.2. Column Moment
The percentage variation in column moment of frames of fixed base condition and flexible base
condition with an increase in a number of stories with variation in bay length is presented in Figure 6
and 7. When support changed from fixed to spring, for the frame, column moments are observed to be
increased for bay lengths 2m and 4m and decreased for bay lengths 6m, 8m, 10m for given storey height
. This says that there is the effect of soil on the frame. In Figure 6., a number of stories was shown on
X- axis, column moment is shown on Y-axis and each line specify the bay length (2m, 4m, 6m, 8m,
10m). From figure 6, it was observed that for bay lengths of 2m and 4m increment of column moment
is increasing with increase in storey height and for bay lengths of 6m, 8m and 10m decrement of column
moment is decreasing with increase in storey height.
Figure 6. Column Moments of flexible base frames compared with fixed frames in percentage variation
In Figure 7, bay length was shown on X- axis, column moment is shown on Y-axis and each line
specify storey height (9m, 15m, 21m, 27m, 33m). From Figure 7 it was observed that increment of
column moment decreases from 2m to 4m bay lengths for any storey height. For given storey height,
the decrement of column moment increases from 6m to 10m bay lengths.

Figure 7. Column Moments of flexible base frames compared with fixed frames in percentage variation
4.3. Lateral Displacement
The percentage variation in Lateral displacement values of frames of fixed base condition and flexible
base condition for an increase in a number of stories with variation in bay length are presented in Figure
8 and 9.
When support changed from fixed to spring, for the frame lateral deflection are observed to be
increased. This says that there is the effect of soil on the frame. In Figure 8, a number of stories was
shown on X- axis, lateral displacement increment is shown on Y-axis and each line specify the bay
length (2m, 4m, 6m, 8m, 10m). From the figure it was observed that for a particular bay length, the
increment of lateral displacement is increasing with increase in storey height. Increment of lateral
displacement of 2m bay length increases from 60.4% to 73.5%, 4m bay length increases from 29.14%
to 45.42%, 6m bay length increases from 9.95% to 14.85%, 8m bay length increases from 4.68% to
6.45%, 10m bay length increases from 2.06 to 3.18% with increase in storey height.
Figure 8. Lateral Displacement of flexible base frames compared with fixed frames in percentage variation

Interaction
Figure 9. Lateral Displacement of flexible base frames compared with fixed frames in percentage variation
In Figure 9, bay length was shown on X- axis, lateral displacement increment is shown on Y-axis
and each line specify storey height (9m, 15m, 21m, 27m, 33m). From the figure it was observed that for
a particular storey height increment of lateral displacement is decreasing with increase in bay length.
Increment of lateral displacement of 9m storey height decreases from 60.4% to 2.06%, 15m storey height
decreases from 189.1% to 2.52%, 21m storey height decreases from 186.6% to 2.58%, 27m storey height
decreases from 189.8% to 2.82%, 33m storey height decreases from 195.75% to 3.18% with increase in
bay length.
CONCLUSIONS
The review of current state of the art of modeling of the frame structures supported on fixed base
condition and flexible base condition leads to following conclusions. Maximum variation in a moment
of beams and columns occurs in ground storey when support changes from fixed to flexible. For a given
bay length and given the number of stories, beam moment is observed to be decreasing when the base
condition of frame changes from fixed to the flexible base condition. For a given bay length, with an
increase in a number of stories from 2 to 10, the decrement of beam moment increases. For a given
number of stories, with an increase in bay length from 2m to 10m, the decrement of beam moment
decreases. For bay lengths of 2m and 4m, the increment of column moment is increasing with increase
in storey height and for bay lengths of 6m, 8m and 10m decrement of column moment is decreasing
with increase in storey height. The increment of column moment decreases from 2m to 4m bay lengths
and decrement of column increases from 6m to 10m bay lengths, for any storey height. For a given bay
length and given the number of stories, lateral deflection is observed to be increasing when the base
condition of frame changes from fixed to the flexible base condition. For a given bay length, with an
increase in a number of stories from 2 to 10, increment of lateral deflection increases. For a given number
of stories, with an increase in bay length from 2m to 10m, the increment of lateral deflection decreases.
The variation in axial forces of columns of frames is negligible when comparing frames of flexible base
condition with fixed base condition.

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