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Vol 66, No.12;Dec 2016
Jokull Journal83
COMPARISON BETWEEN FLAT SLAB AND SOLID SLAB SYSTEMS
IN STRESSES DISTRIBUTION UNDER THE FOUNDATION USING
FINITE ELEMENT ANALYSIS
M. E. EL KILANY1, T. A. EL-SAYED2*, N. R. EL-SAKHAWY3, A. I.
EL-DOSOKY4
1Associate Professor, Civil Str. Eng. Dep., Faculty of Eng.,
Zagazig University, Egypt 2Assistant Professor, Civil Str.Eng.
Dep., Shoubra Faculty of Eng., Benha University, Egypt
3Professor, Civil Str. Eng. Dep., Faculty of Eng., Zagazig
University, Egypt 4M.Sc Degree, Civil Str. Eng. Dep., Faculty of
Eng., Zagazig University, Egypt
* Corresponding author. Tel.: +20 1008444985, Fax: +202
22911118
E-mail address: [email protected] (T. A EL-SAYED*)
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84 Jokull Journal
Vol 66, No.12;Dec 2016
COMPARISON BETWEEN FLAT SLAB AND SOLID SLAB SYSTEMS
IN STRESSES DISTRIBUTION UNDER THE FOUNDATION USING
FINITE ELEMENT ANALYSIS
M. E. EL KILANY1, T. A. EL-SAYED2*, N. R. EL-SAKHAWY3, A. I.
EL-DOSOKY4
1Associate Professor, Civil Str. Eng. Dep., Faculty of Eng.,
Zagazig University, Egypt 2Assistant Professor, Civil Str.Eng.
Dep., Shoubra Faculty of Eng., Benha University, Egypt
3Professor, Civil Str. Eng. Dep., Faculty of Eng., Zagazig
University, Egypt 4M.Sc Candidate, Civil Str. Eng. Dep., Faculty of
Eng., Zagazig University, Egypt
ABSTRACT
Soil structure interaction is interdisciplinary field which
includes auxiliary and
geotechnical engineering. In the ordinary non- interaction
examination of building frame
structural designer assumed that columns are resting on
unyielding support. So also, in
foundation design, foundation settlements are calculated without
considering the impact of
the structural stiffness. The sub-grade reaction modulus "Ks"
can be considered as a
fitting interface between the geotechnical and structural
architects. The present research
studies the effect of statical systems of slabs (flat slab &
solid slab) on the columns loads
distribution to achieve uniform stresses distribution under the
foundation using finite
element analysis program sap 2000.
KEYWORDS
Soil structure interaction, Stresses distribution, modulus of
sub grade reaction "Ks", structural analysis, SAP2000, static
loading.
1. INTRODUCTION
A few studies have been made on the impact of soil-structure
cooperation issues to get
more reasonable examination. They have evaluated the impact of
connection conduct and
built up that there is redistribution of strengths in the
structure and soil mass.
Consequently, structures and their supporting soils ought to be
considered as a solitary
perfect unit. The connection impacts are discovered very
noteworthy, especially for the
structures laying on exceptionally compressible soils. The
adaptability of soil mass causes
the differential settlement and turn of footings under the use
of burden.
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The interaction behavior of plane frames with an elastic
foundation of the Winkler’s type,
having normal and shear moduli of sub-grade reactions is studied
by Aljanabi et al. [1].
An exact stiffness matrix for a beam element on an elastic
foundation having just a normal
modulus of sub-grade reaction was changed to include the shear
modulus of sub-grade
reaction of the foundation and additionally the axial force in
the beam. The outcomes
showed that bowing minutes may be significantly influenced by
kind of edge and
stacking.
The proficiency of the coupled finite-infinite elements
formulation regarding
computational exertion, information arrangement and the far
field representation of the
unbounded area is explored by Noorzaei [2]. Al-Shamrani and
Al-Mashary [3] displayed a
streamlined strategy for the investigation of soil-structure
interaction behavior of two-
dimensional skeletal steel or reinforced concrete frame
structures laying on isolated
footings that are supported by various sorts of soil. The
principle program was made of
two noteworthy modules; one for soil settlement computations and
another for the
investigation of structure. They assessed the impact of
interaction on the predicted
settlements, footing loads, and internal bending moments of the
structural members. Roy
et al. [4] performed an examination on an admired model
comprising of multi-storey 3-D
frame structure with grid foundation. The grid foundation is
assumed to lay on springs,
which romanticize the soil behavior.
The impact of soil-structure interaction on a space frame laying
on a pile group installed in
the cohesive soil (clay) with flexible cap is analyzed by Chore
et al. [5]. They assessed the
impacts of pile spacing, pile configuration, and pile diameter
of the pile group on the
reaction of superstructure. The impact of soil structure
interaction is observed to be very
huge.
The impact of contact between strap beam and bearing stratum is
examined by Guzman
[6]. The outcomes demonstrate that when a strap footing is
utilized as major of a
foundation system, a point of interest that take into
consideration pressure to be alleviated
from the strap beam is vital on construction documents. Without
it, an impressive
unanticipated load path made that may bring about the result in
the failure of strap beam
followed by overstress of the soil under the eccentric
footing.
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The interaction and non-interaction examinations for the space
frame-raft foundation-soil
system utilizing ANSYS finite element code is compared by
Thangaraj and Ilamparuthi
[7]. The soil was dealt with as an isotropic, homogenous and
elastic half space medium. A
gritty parametric study was directed by shifting the soil and
raft stiffness for a constant
building stiffness. The interaction examination demonstrated
less total and differential
settlements than the non-interaction analysis and relative
stiffness of soil plays significant
role in the execution of the raft. The stress and settlement
distribution of a tank foundation
by using the finite element analysis software (ANSYS) is
considered by Xiujuan et al. [8].
2. NUMERICAL STUDIES
2.1 Computer Analysis for Mat Foundation [9, 10]
Computer analysis for mat foundation is usually based on an
approximation where the mat
is divided into a number of discrete finite elements using grid
lines. There are three
general discrete element formulations which may be used:
1- Finite Difference (FD).
2- Finite Grid Method (FGM).
3- Finite Element Method (FEM).
All three of these methods use the modulus of sub grade reaction
k, as the soil contribution
to the structural model. Computers and available software make
the use of any of the
discrete element methods economical and rapid.
2.2 Finite Element Analysis (Sap 2000) [9, 10]
2.2.1 Shell Element
The six faces of a shell element are defined as the positive 1
face, negative 1 face, positive
2 face, negative 2 face, positive 3 face and negative 3 face as
shown in Fig. 2.1. In this
definition the numbers 1, 2 and 3 correspond to the local axes
of the shell element. [9, 10]
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Note that the positive 3 face is sometimes called the top of the
shell element in SAP2000
and the negative 3 face is called the bottom of the shell
element.
2.2.2 Frame Element Internal Forces and Moments [9, 10] The
frame element internal forces and moments are present at every
cross-section along
the length of the frame. For each load pattern and load
combination the frame internal
forces and moments are computed and reported at each frame
output station as following:
1- P, the axial force
2- V2, the shear force in the 1-2 plane
3- V3, the shear force in the 1-3 plane
4- T, the axial torque (about the 1-axis)
5- M2, the bending moment in the 1-3 plane (about the
2-axis)
6- M3, the bending moment in the 1-2 plane (about the
3-axis).
3. VARIABLES OF THE STUDY Table 1 summarizes the variable
studied in this research. 3.1 Models Geometries and Statical
Systems Figure 1 to Figure 3 show models geometries and dimensions.
Models consist of two
equal spans in the both directions 10 m x 10 m, supported by 9
columns with dimensions
40 cm × 40 cm. There are two statical systems employed in this
research: the first one is
flat slab with variable slab thickness, the second system is
solid slab with constant slab
thickness 20 cm and each bay is surrounded by beams with width
30 cm and variable
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depth. Both systems are constructed on a square mat foundation
with dimensions 10 m x
10 m with variable thickness. The mat will be founded at 1.5 m
below the original ground
level.
3.2 Number of Stories This research includes two types of models
with constant story height 3.0 m and different
number of stories as fellows: 1- Five stories model with solid
slab system.
2- Five stories model with flat slab system.
3- Ten stories model with solid slab system.
4- Ten stories model with flat slab system.
3.3 Structure Elements Dimensions 3.3.1 Raft Thickness 1- In
models consist of five stories, raft thickness is variable from (40
cm = span/12.5) to
(100 cm = span/5).
2- In models consist of ten stories, raft thickness is variable
from (80 cm = span/8.33) to
(140 cm = span/3.57).
3.3.2 Columns Dimensions In all models, columns dimensions are
constant and equal 40 cm x 40 cm
(span/12.5 in the both direction).
3.3.3 Slab Thickness 1- In models with flat slab system, slab
thickness is variable from (18 cm = span/27.78) to
(30 cm = span/16.67).
2- In models with solid slab system, slab thickness is constant
and equal 20 cm (span/25).
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3.3.4 Beams Depth 1- In models with flat slab system, there are
no beams.
2- In models with solid slab system, beams depths is variable
from (40 cm = span/12.5) to
(100 cm = span/5).
3.4 Applied Loads and Load Combinations In this research, Loads
are uniform and constant in all stories for all models. Own
weight
is taken into consideration, covering load is 3.0 KN/m2 and live
load is 2.0 KN/m2.
Columns reactions are computed by combination: (1.0 own weight +
1.0 covering load +
1.0 live load).
3.5 Springs Constant
The modulus of sub grade reaction "Ks" is used to compute node
springs based on the
contributing plan area of an element to any node.
Where: (Joint spring = Modulus of sub grade reaction x area) As
follows:
1- Interior node springs = Ks x (0.50x0.50).
2- Edge node springs = Ks x 0.50 x (0.50x0.50).
3- Corner node springs = Ks x 0.25 x (0.50x0.50).
3.6 Soil Types One type of soil is employed in this research.
The description and properties of the soil are
summarized in Table 2. "Vesic" relation is the governing
relation for estimating "Ks" in
our study [11]. Substituting υs (poisson,s ratio) = 0.3, B
(footing width) = 10 m, EcIc
(flexural rigidity of the raft) =2.50×1010 kN.m2 [12] and Es
(soil modulus of elasticity) =
300578 KPa [13].
…………….equation (1) [11]
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4. RESULTS AND ANALYSIS Columns loads (corner, edge, internal
column) are computed and compared in all models
as variation in column load can be consider as an indication to
the same variation in
stresses under this column because raft dimensions and meshing
are constant and equal
for all models. ℴ (stresses) = P (column load) /A (area), i.e
(ℴα P).
Tables and charts give the relation between relative columns
loads (computed sap
column load / column load computed by area method) and relative
element dimensions
(maximum span / element dimension) in order to make general
relation related to
maximum span in the building and try to achieve the same column
load computed by area
method and getting uniform stresses under the foundation.
4.1 Models Consist of 5 Stories with Solid Slab System
Figures from 4 to 6 show the effect of increase the raft
thickness from 40 cm to 100 cm
and increase the beams depth from 40 cm to 100 cm on the columns
loads in models of
five stories with solid slab system.
Figure 4 indicate that corner column load decrease by 9% when
beams depth increase
from 40 cm to 100 cm in models with raft thickness 40 cm and
decrease by 12% in
models with raft thickness 60 cm and decrease by 9% in models
with raft thickness 80 cm
and decrease by 7% in models with raft thickness 100 cm. Corner
column load increase
by 10% at beams depth 40 cm when raft thickness increase from 40
cm to 100 cm and
increase by 12% at beams depth 100 cm.
Figure 5 indicate that there is an insignificant difference in
edge column load when
beams depth increase from 40 cm to 100 cm in all models. Edge
column load increase by
1% at beams depth 40 cm when raft thickness increase from 40 cm
to 100 cm and
increase by 5% at beams depth 100 cm.
Figure 6 indicate that there is no difference in internal column
load when beams depth
increase from 40 cm to 100 cm in models with raft thickness 100
cm. They also clears
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that internal column load increase by 12% when beams depth
increase from 40 cm to 100
cm in models with raft thickness 40 cm and increase by 8% in
models with raft thickness
60 cm and increase by 4% in models with raft thickness 80 cm.
Internal column load
decrease by 15% at beams depth 40 cm when raft thickness
increase from 40 cm to 100
cm and decrease by 27% at beams depth 100 cm.
Figures from 7 to 10 show the effect of increase the raft
thickness from 40 cm to 100 cm
on the stresses distribution under the foundation in models
consist of five stories with
solid slab system at beams depths equal 40 cm. Figure 7 and
Figure 10 indicate that soil
stresses changed from (from 52 KN/m2 to 138 KN/m2) in model with
raft thickness 40 cm
to (from 80 KN/m2 to 99 KN/m2) in model with raft thickness 100
cm which mean that
maximum soil stress decrease by 28.26 %.
Figures from 11 to 14 show the effect of increase the raft
thickness from 40 cm to 100 cm
on the stresses distribution under the foundation in models
consist of five stories with
solid slab system when beams depths equal 100 cm. Figure 11 and
Figure 14 indicate that
soil stresses changed from (from 63 KN/m2 to 152 KN/m2) in model
with raft thickness 40
cm to (from 92 KN/m2 to 115 KN/m2) in model with raft thickness
100 cm which mean
that maximum soil stress decrease by 24.34%.
4.2 Models Consist of 10 Stories with Solid Slab System
Figures from 15 to 17 show the effect of increase the raft
thickness from 80 cm to 140 cm
and increase the beams depth from 40 cm to 100 cm on the columns
loads in models of ten
stories with solid slab system.
Figure 15 indicate that corner column load decrease by 7% when
beams depth increase
from 40 cm to 100 cm in models with raft thickness 80 cm and
decrease by 3% in models
with raft thickness 100 cm and increase by 4% in models with
raft thickness 140 cm. They
also clears that there is an insignificant difference in corner
column load when beams
depth increase from 40 cm to 100 cm in models with raft
thickness 120 cm. Corner
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column load increase by 13% at beams depth 40 cm when raft
thickness increase from 80
cm to 140 cm and increase by 24% at beams depth 100 cm.
Figure 16 indicate that there is an insignificant difference in
edge column load when
beams depth increase from 40 cm to 100 cm in all models. Edge
column load decrease by
2% at beams depth 40 cm when raft thickness increase from 80 cm
to 140 cm and
decrease by 5% at beams depth 100 cm.
Figure 17 indicate that there is an insignificant difference in
internal column load when
beams depth increase from 40 cm to 100 cm in models with raft
thickness 80 cm and 100
cm. They also clears that internal column load decrease by 5%
when beams depth increase
from 40 cm to 100 cm in models with raft thickness 120 cm and
decrease by 7% in models
with raft thickness 140 cm. Internal column load decrease by 11%
at beams depth 40 cm
when raft thickness increase from 80 cm to 140 cm and decrease
by 20% at beams depth
100 cm.
Figures from 18 to 21 show the effect of increase the raft
thickness from 80 cm to 140 cm
on the stresses distribution under the foundation in models
consist of ten stories with solid
slab system when beams depths equal 40 cm. Figure 18 and Figure
21 indicate that soil
stresses changed from (from 123 KN/m2 to 195 KN/m2) in model
with raft thickness 80
cm to (from 151 KN/m2 to 175 KN/m2) in model with raft thickness
140 cm which mean
that maximum soil stress decrease by 10.25%.
Figures from 22 to 25 show the effect of increase the raft
thickness from 80 cm to 140 cm
on the stresses distribution under the foundation in models
consist of ten stories with solid
slab system when beams depths equal 100 cm. Figure 22 and Figure
25 indicate that soil
stresses changed from (from 145 KN/m2 to 229 KN/m2) in model
with raft thickness 80
cm to (from 174 KN/m2 to 207 KN/m2) in model with raft thickness
140 cm which mean
that maximum soil stress decrease by 9.6%.
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4.3 Models Consist of 5 Stories with Flat Slab System
Figures from 26 to 28 show the effect of increase the raft
thickness from 40 cm to 100 cm
and increase the slab thickness from 18 cm to 30 cm on the
columns loads in models of
five stories with flat slab system.
Figure 26 indicate that there is an insignificant difference in
corner column load when slab
thickness increase from 18 cm to 30 cm in all models. Corner
column load increase by 2%
at slab thickness 18 cm when raft thickness increase from 40 cm
to 100 cm and increase
by 4% at slab thickness 30 cm.
Figure 27 indicate that there is an insignificant difference in
edge column load when slab
thickness increase from 18 cm to 30 cm in all models. Edge
column load increase by 2%
at slab thickness 18 cm when raft thickness increase from 40 cm
to 100 cm and increase
by 4% at slab thickness 30 cm.
Figure 28 indicate that there is no difference in internal
column load when slab thickness
increase from 18 cm to 30 cm in models with raft thickness 40
cm. They also clears that
internal column load decrease by 3% when slab thickness increase
from 18 cm to 30 cm in
models with raft thickness 60 cm and decrease by 6% in models
with raft thickness 80 cm
and decrease by 9% in models with raft thickness 100 cm.
Internal column load decrease
by 5% at slab thickness 18 cm when raft thickness increase from
40 cm to 100 cm and
decrease by 14% at slab thickness 30 cm.
Figures from 29 to 32 show the effect of increase the raft
thickness from 40 cm to 100 cm
on the stresses distribution under the foundation in models
consist of five stories with flat
slab system when slab thickness equal 18 cm. Figure 29 and
Figure 32 indicate that soil
stresses changed from (from 45 KN/m2 to 110 KN/m2) in model with
raft thickness 40 cm
to (from 72 KN/m2 to 83 KN/m2) in model with raft thickness 100
cm which mean that
maximum soil stress decrease by 24.54%.
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Figure 33 and Figure 36 show the effect of increase the raft
thickness from 40 cm to 100
cm on the stresses distribution under the foundation in models
consist of five stories with
flat slab system when slab thickness equal 30 cm. Figure 33 and
Figure 36 indicate that
soil stresses changed from (from 56 KN/m2 from 133 KN/m2) in
model with raft thickness
40 cm to (from 85 KN/m2 from 100 KN/m2) in model with raft
thickness 100 cm which
mean that maximum soil stress decrease by 24.81%.
4.4 Models Consist of 10 Stories with Flat Slab System Figures
from 37 to 39 show the effect of increase the raft thickness from
80 cm to 140 cm
and increase the slab thickness from 18 cm to 30 cm on the
columns loads in models of
ten stories with flat slab system.
Figure 37 indicate that corner column load increase by 6% when
slab thickness increase
from 18 cm to 30 cm in models with raft thickness 80 cm and
increase by 10% in models
with raft thickness 100 cm and increase by 12% in models with
raft thickness 120 cm and
increase by 14% in models with raft thickness 140 cm. Corner
column load increase by
2% at slab thickness 18 cm when raft thickness increase from 80
cm to 140 cm and
increase by 10% at slab thickness 30 cm.
Figure 38 indicate that there is an insignificant difference in
edge column load when slab
thickness increase from 18 cm to 30 cm in all models. They also
clears that there is no
difference in edge column load when raft thickness increase from
80 cm to 140 cm in all
models.
Figure 39 indicate that internal column load decrease by 11%
when slab thickness increase
from 18 cm to 30 cm in models with raft thickness 80 cm and
decrease by 14% in models
with raft thickness 100 cm and decrease by 17% in models with
raft thickness 120 cm and
decrease by 18% in models with raft thickness 140 cm. Internal
column load decrease by
4% at slab thickness 18 cm when raft thickness increase from 80
cm to 140 cm and
decrease by 11% at slab thickness 30 cm.
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Figures from 40 to 43 show the effect of increase the raft
thickness from 80 cm to 140 cm
on the stresses distribution under the foundation in models
consist of ten stories with flat
slab system. Figure 40 and Figure 43 indicate that soil stresses
changed from (from 110
KN/m2 to 154 KN/m2) in model with raft thickness 80 cm to (from
132 KN/m2 to 145
KN/m2) in model with raft thickness 140 cm which mean that
maximum soil stress
decrease by 5.84 %.
Figures from 44 to 47 show the effect of increase the raft
thickness from 80 cm to 140 cm
on the stresses distribution under the foundation in models
consist of ten stories with flat
slab system when slab thickness equal 30 cm. Figure 44 and
Figure 47 indicate that soil
stresses changed from (from 132 KN/m2 to 198 KN/m2) in model
with raft thickness 80
cm to (from 158 KN/m2 to 180 KN/m2) in model with raft thickness
140 cm which mean
that maximum soil stress decrease by 9.09 %.
4.5 Comparison between Models Consist of 5 Stories and Models
Consist
of 10 Stories with Solid Slab System
Figures from 48 to 50 show the comparison between columns loads
in models consist of
five stories and models consist of ten stories with solid slab
system at raft thickness 80 cm
and 100 cm and beam depth increase from 40 cm to 100 cm. Figure
48 indicate that corner column load increase by 7% with raft
thickness 80 cm at
beam thickness 40 cm and increase by 9% at beam thickness 100 cm
and increase by 9%
in models with raft thickness 100 cm at beam thickness 40 cm and
increase by 13% at
beam thickness 100 cm.
Figure 49 indicate that there is an insignificant difference in
edge column load when
number of stories increase from 5 stories to 10 stories in
models with raft thickness 80 cm
and 100 cm when beam thickness increase from 40 cm to 100
cm.
Figure 50 indicate that internal column load decrease by 11%
with raft thickness 80 cm at
beam thickness 40 cm and decrease by 13% at beam thickness 100
cm and decrease by
13% in models with raft thickness 100 cm at beam thickness 40 cm
and decrease by 15%
at beam thickness 100 cm.
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4.6 Comparison between Models Consist of 5 stories and Models
Consist
of 10 Stories with Flat Slab System
Figures from 51 to 53 show the compare between columns loads in
models consist of five
stories and models consist of ten stories with flat slab system
at raft thickness 80 cm and
100 cm and slab thickness increase from 18 cm to 30 cm. Figure
51 indicate that corner column load increase by 3% with raft
thickness 80 cm at
slab thickness 18 cm and increase by 9% at slab thickness 30 cm
and increase by 3% in
models with raft thickness 100 cm at slab thickness 18 cm and
increase by 12% at slab
thickness 30 cm.
Figure 52 indicate that edge column load increase by 3% with
raft thickness 80 cm at slab
thickness 18 cm and increase by 2% at slab thickness 30 cm and
increase by 3% in models
with raft thickness 100 cm at slab thickness 18 cm and increase
by 2% at slab thickness 30
cm.
Figure 53 indicate that internal column load decrease by 10%
with raft thickness 80 cm at
slab thickness 18 cm and decrease by 15% at slab thickness 30 cm
and decrease by 11% in
models with raft thickness 100 cm at slab thickness 18 cm and
decrease by 16% at slab
thickness 30 cm.
5. CONCLUSION
1- In case of building consists of stories five stories and
solid slab system:
a) Increasing beams depths from 40 cm to 100 cm leads to
decrease in corner columns
loads by (7%: 12%) and increase in internal column load by (0%:
12%) but it have no
effect on edge columns loads.
b) Increasing raft thickness from 40 cm to 100 cm leads to
increase in corner columns loads
by (10%: 12%), increase in edge columns loads by (1%: 5%) and
decrease in internal
column load by (15%: 27%).
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c) Increasing raft thickness from 40 cm to 100 cm leads to
decrease the maximum soil
stress under the foundation by (24.4 %: 28.3%).
d) Beams depths must be small as it can be and according to
structure requirements.
e) Raft thickness must be at least equal (span/6) and it is
prefer to increase raft thickness to
get uniform stresses distribution under the foundation.
2- In case of building consists of stories ten stories and solid
slab system:
a) Increasing beams depths from 40 cm to 100 cm leads to change
in corner columns loads
from decrease by 7% to increase by 4% and decrease in internal
column load by (1%:
7%) but it have no effect on edge columns loads.
b) Increasing raft thickness from 80 cm to 140 cm leads to
increase in corner columns loads
by (13%: 24%), decrease in edge columns loads by (2%: 5%) and
decrease in internal
column load by (11%: 20%).
c) Increasing raft thickness from 80 cm to 140 cm leads to
decrease the maximum soil
stress under the foundation by (9.6 %: 10.3%).
d) Beams depths must be small as it can be and according to
structure requirements when
raft thickness less than (span/5) but when raft thickness is
bigger than that it is prefer to
increase beams depths to get uniform stresses distribution under
the foundation.
e) Raft thickness must be at least equal (span/4) and it is
prefer to increase raft thickness to
get uniform stresses distribution under the foundation.
3- In case of building consists of stories five stories and flat
slab system:
a) Increasing slab thickness from 18 cm to 30 cm leads to
decrease in internal columns
loads by (0%: 9%) but it have no effect on corner and edge
columns loads.
b) Increasing raft thickness from 40 cm to 100 cm leads to
increase in corner and edge
columns loads by (2%: 4%) and decrease in internal column load
by (5%: 14%).
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c) Increasing raft thickness from 40 cm to 100 cm leads to
decrease the maximum soil
stress under the foundation by (24.8 %: 24.6%).
4- In case of building consists of stories ten stories and flat
slab system:
a) Increasing slab thickness from 18 cm to 30 cm leads to
increase in corner columns loads
by (6%: 14%) and decrease in internal columns loads by (11%:
18%) but it have no
effect on edge columns loads.
b) Increasing raft thickness from 80 cm to 140 cm leads to
increase in corner columns loads
by (2%: 10%) and decrease in internal column load by (4%: 11%)
but it have no effect
on edge columns loads.
c) Increasing raft thickness from 80 cm to 140 cm leads to
decrease the maximum soil
stress under the foundation by (9.1 %: 5.9%).
5- Effect of increase the raft thickness on stresses
distribution under the foundation is bigger
on buildings with average number of stories five stories than
buildings with average number
of stories ten stories.
6- Increase beams depths have an insignificant effect on
stresses distribution under the
foundation in case of buildings with solid slab system.
7- Effect of increase slab thickness on stresses distribution
under the foundation in case of
buildings with flat slab system is bigger on buildings with
average number of stories ten
stories than buildings with average number of stories five
stories.
6. REFERENCES
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Interaction of plane frames with
elastic foundation having normal and shear moduli of subgrade
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2- J. Noorzaei, Concepts and application of three dimensional
infinite elements to soil-
structure-interaction problems, Int. J. Eng., 9(3), 1996,
131-142.
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3- M.A. Al-Shamrani, and F.A. Al-Mashary, A simplified
computation of the interactive
behavior between soils and framed structures, Eng. Sci., 16(1),
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4- R. Roy, K. Bhattacharya, and S.C. Dutta, Behaviour of grid
foundation under static
gravity loading, J. Inst. Eng. (India), 85, 2005, 261-268.
5- H.S. Chore, R.K. Ingle, and V.A. Sawant, Building frame -
pile foundation - soil
interaction analysis: a parametric study, J. Interact.
Multiscale Mech., 3(1), 2010, 55-79.
6- T. Guzman, Heavily loaded strap footing-design, detailing and
behavior, Structure
Magazine, 2010, 12-15.
7- D. Thangaraj and K. Ilamparuthi, Parametric study on the
performance of raft foundation
with interaction of frame, Electron. J. Geotech. Eng., 15, 2010,
861-878.
8- Y. Xiujuan, X. Zongxiang, Z. Lisong, and Y. Xiangzhen, 3D
simulation of weak
foundation for good-sized oil storage tank, Proc. of
International Conference on
Mechanic Automation and Control Engineering, China, 2010,
1345-1348.
9- Sap-2000 (V.16) User's Manual, Computers and Structures,
Inc.1995 University Avenue,
Berkeley, California 94704, USA.
10- T. A. El-sayed, m. E. El kilany, n. R. El-sakhawy and a. I.
El-dosoky , 2016. Methods for
achievement uniform stresses distribution under the foundation,
international journal of
civil engineering & technology (ijciet).volume:7, issue: 2,
pages: 45-66.
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Determination of
Coefficient of Subgrade Reaction, electronic journal of
geotechnical engineering. Volume
14- Bundle E.
12- Egyptian code for Reinforced concrete (ECCS – 203 - 2001)
REV.02 – chapter 06 –
Foundation design - Egypt.
13- Bowles (1997) "Foundation Analysis and Design" Text book -
International Edition -
McGraw-Hill Book Co. - Singapore.
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100 Jokull Journal
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Table 1: Research Variables
Table 2: Soil properties and descriptions
Soil Type Soil description Es
(KPa)
Bearing capacity
B/C (KN/ m2)
Modulus of Sub
grade Reaction
Ks (KPa)
Type (1) Medium Dense Sand 300578 220 18000
Soil Type Type (1) Slab System Flat Slab Solid Slab
Slabs Thicknesses 18 : 30 cm 20 cm Beams Depths ——— 40 : 100
cm
Number of Stories 10-Stories 5-Stories 10-Stories 5-Stories Raft
Thickness 80 : 140 cm 40 : 100 cm 80 : 140 cm 40 : 100 cm
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Figure 1: Flat slab system
Figure 2: Solid slab system
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Vol 66, No.12;Dec 2016
Figure 3: Raft system and dimensions
Figure 4: Corner column load in models consist of 5 stories with
solid slab system
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Figure 5: Edge column load in models consist of 5 stories with
solid slab system
Figure 6: Internal column load in models consist of 5 stories
with solid slab system
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Vol 66, No.12;Dec 2016
Figure 7: Soil stresses distribution in model with beam Figure
8: Soil stresses distribution in model with beam depth 40 cm &
raft thickness 40 cm & solid slab & 5 stories depth 40 cm
& raft thickness 60 cm & solid slab & 5 stories
Figure 9: Soil stresses distribution in model with beam Figure
10: Soil stresses distribution in model with beam depth 40 cm &
raft thickness 80 cm & solid slab & 5 stories depth 40 cm
& raft thickness 100 cm & solid slab & 5 stories
Figure 11: Soil stresses distribution in model with beam Figure
12: Soil stresses distribution in model with beam Depth 100 cm
& raft thickness 40 cm & solid slab & 5 stories depth
100 cm & raft thickness 60 cm & solid slab & 5
stories
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Figure 13: Soil stresses distribution in model with beam Figure
14: Soil stresses distribution in model with beam depth 100 cm
& raft thickness 80 cm & solid slab & 5 stories depth
100 cm & raft thickness 100 cm & solid slab & 5
stories
Figure 15: Corner column load in models consist of 10 stories
with solid slab system
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Figure 16: Edge column load in models consist of 10 stories with
solid slab system
Figure 17: Internal column load in models consist of 10 stories
with solid slab system
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Vol 66, No.12;Dec 2016
Figure 18: Soil stresses distribution in model with beam Figure
19: Soil stresses distribution in model with beam depth 40 cm &
raft thickness 80 cm & solid slab & 10 stories depth 40 cm
& raft thickness 100 cm & solid slab & 10 stories
Figure 20: Soil stresses distribution in model with beam Figure
21: Soil stresses distribution in model with beam depth 40 cm &
raft thickness 120 cm & solid slab & 10 stories depth 40 cm
& raft thickness 140 cm & solid slab & 10 stories
Figure 22: Soil stresses distribution in model with beam Figure
23: Soil stresses distribution in model with beam depth 100 cm
& raft thickness 80 cm & solid slab & 10 stories depth
100 cm & raft thickness 100 cm & solid slab & 10
stories
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Vol 66, No.12;Dec 2016
Figure 24: Soil stresses distribution in model with beam Figure
25: Soil stresses distribution in model with beam depth 100 cm
& raft thickness 120 cm & solid slab & 10 stories depth
100 cm & raft thickness 140 cm & solid slab & 10
stories
Figure 26: Corner column load in models consist of 5 stories
with flat slab system
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Figure 27: Edge column load in models consist of 5 stories with
flat slab system
Figure 28: Internal column load in models consist of 5 stories
with flat slab system
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Vol 66, No.12;Dec 2016
Figure 29: Soil stresses distribution in model with slab Figure
30: Soil stresses distribution in model with slab thickness 18 cm
& raft thickness 40 cm & flat slab & 5 stories
thickness 18 cm & raft thickness 60 cm & flat slab & 5
stories
Figure 31: Soil stresses distribution in model with slab Figure
32: Soil stresses distribution in model with slab thickness 18 cm
& raft thickness 80 cm & flat slab & 5 stories
thickness 18 cm & raft thickness 100 cm & flat slab & 5
stories
Figure 33: Soil stresses distribution in model with slab Figure
34: Soil stresses distribution in model with slab thickness 30 cm
& raft thickness 40 cm & flat slab & 5 stories
thickness 30 cm & raft thickness 60 cm & flat slab & 5
stories
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Vol 66, No.12;Dec 2016
Figure 35: Soil stresses distribution in model with slab Figure
36: Soil stresses distribution in model with slab thickness 30 cm
& raft thickness 80 cm & flat slab & 5 stories
thickness 30 cm & raft thickness 100 cm & flat slab & 5
stories
Figure 37: Corner column load in models consist of 10 stories
with flat slab system
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Vol 66, No.12;Dec 2016
Figure 38: Edge column load in models consist of 10 stories with
flat slab system
Figure 39: Internal column load in models consist of 10 stories
with flat slab system
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Vol 66, No.12;Dec 2016
Figure 40: Soil stresses distribution in model with slab Figure
41: Soil stresses distribution in model with slab thickness 18 cm
& raft thickness 80 cm & flat slab &10 stories
thickness 18 cm & raft thickness 100 cm& flat slab &10
stories
Figure 42: Soil stresses distribution in model with slab Figure
43: Soil stresses distribution in model with slab thickness 18 cm
& raft thickness 120 cm & flat slab&10 stories
thickness 18 cm&raft thickness 140 cm&flat slab & 10
stories
Figure 44: Soil stresses distribution in model with slab Figure
45: Soil stresses distribution in model with slab thickness 30 cm
& raft thickness 80 cm & flat slab &10 stories
thickness 30 cm & raft thickness 100 cm&flat slab & 10
stories
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Vol 66, No.12;Dec 2016
Figure 46: Soil stresses distribution in model with slab Figure
47: Soil stresses distribution in model with slab thickness 30 cm
& raft thickness 120cm&flat slab&10 stories thickness
30 cm & raft thickness 140 cm & flat slab & 10
stories
Figure 48: Comparison between corner column load in models
consist of 5 stories and models consist of 10 stories with solid
slab system
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Vol 66, No.12;Dec 2016
Figure 49: Comparison between edge column load in models consist
of 5 stories and models consist of 10 stories with solid slab
system
Figure 50: Comparison between internal column load in models
consist of 5 stories and models consist of 10 stories with solid
slab system
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Vol 66, No.12;Dec 2016
Figure 51: Comparison between corner column load in models
consist of 5 stories and models consist of 10 stories with flat
slab
Figure 52: Comparison between edge column load in models consist
of 5 stories and models consist of 10 stories with flat slab
system
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Figure 53: Comparison between internal column load in models
consist of 5 stories
and models consist of 10 stories with flat slab system