Effect of Tie Beam Length and Depth of Isolated Footings ... · Effect of Tie Beam Length and Depth of Isolated Footings on ... studied the behavior of eccentric footings connected

Advances in Environmental Biology, 10(1) January 2016, Pages: 122-143

AENSI Journals

Advances in Environmental Biology

ISSN-1995-0756 EISSN-1998-1066

Journal home page: http://www.aensiweb.com/AEB/

Copyright © 2016 by authors and Copyright , American-Eurasian Network for Scientific Informatio n (AENSI Publication).

Effect of Tie Beam Length and Depth of Isolated

Footings on Settlement of Granular Soils

Abd EL Samee W. Nashaat Civil Engineering Department, Faculty of Engineering, Beni- Suief University, P.O. 62512Beni- Suief, Egypt Address For Correspondence:

Abd EL Samee W. Nashaat Civil Engineering Department, Faculty of Engineering Beni- Suief University P.O. 62512 Beni-Suief, Egypt.

E-mail: [email protected]

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Received 28 December 2015; Accepted 28 January 2016; Available online 24 February 2016

ABSTRACT The determination of settlement of shallow foundations on cohesionless soil is an important task in geotechnical engineering. This research investigates the cooperation between tie beams and footings depth. Filed tests have been conducted by using the plate load test. In the present study two steel rigid plates (one is square and one is circular) were used. The plates have a finished thickness of 32 mm. The effect of footings size with dimensions 1.0 * 1.0 * 0.5 m, 2.0 * 2.0 * 0.5 m, and 3.0 * 3.0 * 0.5 m has been investigated. The settlement has been calculated from the actual settlement of plate 0.3 * 0.3 m measured at field. A finite element package of the PLAXIS version 7.2 (a finite element code for soil and rock analyses) has been used for proposal of a two-dimensional finite element model in order to simulate theoretically tie beam and foundations. Settlement was found to be sensitive to the tie beam length connected footings. It was also found that the settlement under footings connected with tie beam decreases with decreasing tie beam length. However, footings connected with short tie beams are found to work as combined footings.

KEYWORDS: Tie beam – settlement-Granular soil – finite element -footing

INTRODUCTION

Shallow foundations are generally designed to satisfy bearing capacity and settlement criteria. Settlement criteria are to ensure that the settlement is within tolerable limits. It is commonly believed that the settlement criteria are more critical than the bearing capacity one in the designs of shallow foundations. The study of settlement of footing subjected to static loads is an essential and introductory step toward understanding the problem of settlement of structures. The differential settlement of isolated footings should be limited. In order to minimize the differential settlement between isolated footings, it is recommended to connect them by tie beams. In addition, tie beams are also used to carry ground floor walls and partitions [1]. The present study gives a spot of light on the field settlement of cohesionless soil (sandy soil) under footings connected with tie beams that are subjected to static loads. Cooperation between footings and tie beams to transfer the vertical loads of column to supporting soil has been investigated. The effect of tie beam length and depth of footings on settlement of soil are the different investigated parameters. The numerical models allow variable factors to affect the tie beam length and surcharge on settlement of soil.

Fraser, R.A. and Wardle, L.J. [2] studied the behavior of uniformly loaded rectangular rafts of any rigidity resting on a homogeneous elastic layer underlain by a rough rigid base. The vertical displacement at the center, mid-edges and corner of the raft in addition of the maximum bending moment in the raft were determined. The solution has been obtained by the finite element method with the interaction between raft and finite soil layer being incorporated through the use of surface elements. Variations in raft rigidity, aspect ratio, soil layer depth and Poisson's ratio can markedly affect both displacements and bending moments in raft foundations.

123 Abd EL Samee W. Nashaat, 2016 Advances in Environmental Biology, 10(1) January 2016, Pages: 122-143

Fellenius, B. H. and Altaee, A., [3] compared the magnitude of the settlement of a footing in sand to the settlement of a different size footing in the same sand, is considered to be a non-linear function of the footing width. Further, the settlement is considered to be proportional to the density of the sand. Results of finite element analysis of settlement for footings of three sizes placed in two different sand types show that the settlement in sand is a direct function of neither footing size nor soil density. Instead, the settlement should be related to the steady state line of the sand and to the upsilon distance of the sand, that is, the initial void ratio distance to the steady state line at equal mean stress and at homologous points.

El-Kasaby, E.A.A. [4] studied the behavior of eccentric footings connected with strap beams resting on soil. The effect of soil flexibility and beam stiffness on contact pressure, settlement and bending moment of strap foundation were presented. The finite difference technique has been used to solve the beam-footings system. The Winkler foundation model has been used to represent the soil behavior.

Awad Mohammed A. and El-Mezaini Nasreddin S. [5] presented an experimental study of a uniform sand layer loaded up to failure with two plates of different sizes and equal pressure. The effect of internal distance between the two plates on the settlement and on the bearing capacity is investigated. It is found that when the internal distance between two adjacent footings is less than the width of the smaller footing, the two footings act as one. Bearing capacity and settlement are found to be sensitive to the distance between the footings. It is also found that larger footing exhibits more settlement at the elastic stage. While at failure, the smaller footing exhibits more settlement.

Elsamny M.Kassem, Almasmoum ali. A, and Mahdy. M.M. [6,7] measured the settlement of footing in sandy soil at field by using plate load tests with different sizes of rigid plates (Diameter B = 300mm, B =455mm and B = 610mm). The settlement has been measured at ground surface and at different depths, (B/4, B/2, and B).The measurements were underneath the center of the plate as well as the sides. The shape of settlement (called settlement isobars) has been determined under different applied stresses.

Junhwan, Lee and Rodrigo Salgado [8] analyzed the load-settlement response of vertically loaded footings placed in sands using both the finite element method with a nonlinear stress-strain model and the conventional elastic approach. Calculations are made for both normally consolidated and heavily over consolidated sands with various relative densities.

Elsamny, M. K., Ibrahim, M. A.-R., El-Saadany, M., Kotb, M. and Ezz- Eldeen, H.A. [9] investigated cooperation between footings and tie beams to transfer the vertical loads of column to supporting soil. The tie beam dimensions (depth and length), vertical position of tie beam (in footings level or above footings surface) and the footing depth as well as soil type with or without upper tie beam are the different investigated parameters for centric and eccentric footings. The finite element technique is used to perform the analysis for the problem. Commercial package "COSMOS/M version 2.6" is used. Footings, beams, upper tie beams and columns are modeled using three-dimensional eight–node solid concrete elements. Soil is modeled using one dimensional two nodes linear spring elements.

Al-Omari, R. R. and Al-Ebadi, L. H. [10] investigated the effect of tie beams on settlement, moments and shear developed in the foundation. A case study is selected; it is the case of grid foundation composed of nine footings. Three dimensional non linear finite element analyses have been conducted. The soil has been assumed to follow the Drucker-Prager rate independent plasticity criterion. The parametric study conducted involved the effects of tie beams proportion, tie beams soil contact and an induced soil weakness beneath parts of the total foundation area. The detailed results indicated that the tie beams reduce the total and differential settlements of footings but this restriction is often on the expense of increasing the shear and moment particularly in the central footing. However, the settlement reduction may be considered invaluable in view of avoiding the excessive stresses in beams and slabs of the superstructure.

El-Samny M.K., Abd Elsamee W.N. and Elsedeek M. B.(2010) [11] presented the effect of footing shape and size on wedge angle. The wedge angle of cohesionless soil at surface with and without surcharge has been determined in field for graded sand samples. The tests have been conducted in field by using the plate load test. In the present study nine steel rigid plates were used in testing. The settlement has been measured under different stress levels at the surface along the center line of the plate as well as the edge of the plate. The displacement field has been plotted at the ultimate bearing capacity for each case. Also, the obtained relationships between the wedge angle and the angle of internal friction have been obtained. An empirical formula to determine the wedge angle for circular, square and rectangular plates at different depths has been presented. The relationship between the wedge angle and the ratio (D/B) of footing depth and width has been also obtained.

El-Samny, M.K., Abd Elsamee, W.N. and Elsedeek, M.B. [12] determined the ultimate bearing capacity of footings on cohesionless soil at surface with and without surcharge in field for graded sand samples. The tests have been conducted in field by using the plate load test. The settlement has been measured under different stress levels at the surface along the center line of the plate as well as the edge of the plate. Also, the settlement has been measured under different applied stresses. The effect of plate shape and size on the ultimate bearing capacity of cohesionless soil has been determined for different relative densities of the tested soil.


El-Samny, M.K., Elsedeek, M. B., Abd Elsamee, W.N. [13] determined the Young's modulus "Es" of footings on cohesionless soil at surface with and without surcharge in field for graded sand samples. The tests have been conducted in field by using plate load test. Two steel rigid plates were used in testing. A circular plate with diameter 305 mm and a square plate with dimension 305* 305 mm. The settlement has been measured under different stress levels .The settlement has been measured under different stress levels at the surface along the center line of the plate as well as the edge of the plate. Also, the settlement has been measured under different applied stresses.

Elsamny, M.K., Ibrahim, M.A., Radwan, A., Mashhour, M.A. and Mahdy, M.M. [14] investigated a new test setup is used to measure the settlement and the shape of displacement of soil under two different types of rigid plates connected with tie. One square plate with dimensions (305 x 305) mm is connected to a rectangular plate with dimensions (305 x 610) mm, by a tie .The tie has a width of 60mm with different lengths (305,610 and 915 mm). Graded sand is used all through the tests. The settlement of cohesionless soil has been measured for different relative densities under different stresses at surface as well as different depths.

Elsamny, M. K., Abd Elsamee, W.N., Ezz-Eldeen, H.A. and Abo Al Anwar, M. [15] investigated the effect of tie beam length and surcharge on settlement of soil is the different parameters. A theoretical formulii has been presented to calculate the settlement for the square and the rectangular footings with tie beam including surcharge effect.

Experimental Study:

The plate load tests were carried out and the settlement of sand was measured under different stress levels at surface of plate. The plates are manufactured from steel machined on both faces. The plates have concentric markings on one face and are plated against corrosion.

2-1 Field Samples:

In the present study for determining the effect of footings connected with tie beam length on settlement of cohesionless soil, graded sand sample has been used. Each sample has been compacted in layers and the relative density for each layer has been determined.

2-2 Loading:

The loads were applied by using steel frame fixed in the ground as shown in Fig (1). The applied load has been measured by using pressure gauge connected to a hydraulic jack which gives the applied load

Fig. 1: Loading frame

2-3 Used Plates:

In the present study two plates were used in testing (square 300 * 300 mm and circular D=305 mm). The plates have a finished thickness of 32 mm and are according to ASTM D1194 and D1196. As shown in Fig (2).


Fig. 2: The two rigid plates

2-4 Measuring of Settlement:

Measured of settlement has been done as follows: a- The soil has been placed in a square open box. b- The box was filled with different soil layers compacted to different densities which has been

determined by sand cone test. c- The settlement has been measured by using dial gauges of sensitivity 0.01mm placed on the edge

of the steel plates. d- The settlement has been measured at the surface of the plates as shown in Fig (3).

Fig. 3: Initial settlement readings were recorded using dial gauges before applying loads

2-5 Test Procedure:

The test procedure was as follows:- a- The square box was filled in compacted sand layers. b- The sand cone method has been carried out in field for each layer after compaction to determine

the field density. c- The surface of the tested soil was prepared for plate test using fine sand at the surface. d- The steel plate was placed on the prepared surface. e- The hydraulic jack was placed on the steel plate. f- Four dial gauges has been placed on the plate surface. g- The readings were recorded of all dial gauges before applying loads (initial readings). h- The load was applied in increment by using steel frame. Each load increment was maintained

constant until the settlement rate reaches 0.02 mm/min but not less than one hour in any case.


Experimental Results: The settlement in field was recorded for cohesionless soil for different shapes and sizes (square and

circular) of plate along the edge of plates under different stresses ranging between 58.9 kN/m2 and 530.1 kN/m2.

Scale Effect By -Terzaghi And Peck(1948): One of the early developments in estimating settlement of footings was by Terzaghi and Peck (1948) that

used the modulus of subgrade reaction as defined by settlement to pressure ratio. In that approach, the modulus of subgrade reaction as determined from plate load tests in a 0.3 m x 0.3 m wide plate according to Eq. (1). In order to estimate the settlement, S of a wider footing, the settlement , S1 corresponds to that using the 0.3 m wide plate is multiplied by extrapolation factor as follows .

2

1 3.0

2

+=

B

BSS

(1) Where: s = the settlement of footing.

1S = the settlement of the 0.3m wide plate (cm) B = the width of the footing in meter The settlement of footings with dimensions 1.0 * 1.0 * 0.5 m, 2.0 * 2.0 * 0.5 m, and 3.0 * 3.0 * 0.5 m has

been calculated using the above equation from the actual settlement of plate (0.3 * 0.3 m) measured at field.

Theoretical Analysis: A finite element package of the PLAXIS version 7.2 (a finite element code for soil and rock analyses) has

been used for proposal of a two-dimensional finite element model in order to simulate theoretically tie beam and foundations depth settlement. The elements for soil are chosen to be 15-node triangular elements as shown in Fig. (4). The5-node beam elements are used together with the 15-node soil elements as shown in Fig. (5). the chosen model to present soil in PLAXIS version 7.2 known as Mohr-Coulomb model (perfect-plasticity). The material properties for soil, tie beams and foundations which have been used in the finite element model.

Fig. 4: Nodes and stress points of elements for 15-node triangular elements

Fig. 5: Position of nodes and stress points in a 3-node and a 5-node beam element

The material properties for the used sand were chosen as follows: i. Dry soil weight (γdry) = 18.5 kN/m3. ii. Friction angles (Ø) for soil = (30o , 35o , 40o and45 o) iii. Young's modulus for soil = (40000, 50000, 60000 and 70000) kN/m2. iv. Cohesion (c) = 0.0 kN/m2. v. Poisson's ratio (ν) = 0.30. Theoretical analysis has been done for the two square footings connected with different tie beam lengths at

different depths of footings. The details and variation of the selected parameters used in the analysis are listed in the following table.


Problem No. B (meter) Ltie (meter) Df (meter) 1

1.0 1.0 0

2 1.5 0.5 3 2.0 1.0 4

2.0 1.0 0

5 1.5 0.5 6 2.0 1.0 7

3.0 1.0 0

8 1.5 0.5 9 2.0 1.0

Where : B : Footing width Ltie : Tie beam length Df : Depth of footing The followingsjn concrete properties are used:

i. Footing thickness (d) = 0.5 m. ii. Normal stiffness (EA) = 2.10 x 107 kN/m iii. Flexural rigidity (EI) = 1.75 x 104 kN.m2/m.

Results:

From the present study, the following relationships are obtained:- i.Figs (6), (7) and (8) show the deformed mesh of soil and total the displacement in soil as vectors and as

contour lines for footings B=1.0 m and tie beam length=1.0 m. From these figures it can be shown that the two footings act as combined one.

ii.Figs (9), (10) and (11) show the deformed mesh of soil and total displacements in soil as vectors and as contour lines for footings B=1.0 m and tie beam length= 2.0 m.

From these figures it can be shown that the two footings act as separated footings. It can be also shown that the settlement is sensitive to the tie beam length.

iii.Figs (12) to (23) show the relationships between (D/B) ratio (effect of footings depth) and the settlement of square footings having dimensions 1.0 * 1.0 * 0.5 m, 2.0 * 2.0 * 0.5 m, and 3.0 * 3.0 * 0.5 m connected with different tie beam lengths for angle of internal frictions (30o , 35o , 40o and45 o). However, square and circular footings without tie beam shown in figures have been calculated from Terzaghi equation (1).

These figures show that the settlement under square footings without tie beam is smaller than that under circular footings. In addition, using tie beam between footings decreases settlement. However, short tie beam decreases the settlement under footings.

iv.Figs (24) to (35) show the effect of footing size on settlement of square footings having dimensions 1.0 * 1.0 * 0.5 m, 2.0 * 2.0 * 0.5 m, and 3.0 * 3.0 * 0.5 m for different angle of internal friction.

These figures show that the settlement decreases with increasing footing size. Figs (36- 38) show the effect of internal friction angle on settlement of square footings Connected with tie beam. These figures revealed that the settlement decreases with increasing the angle of internal friction.

AA BB

Fig. 6: Deformed mesh of soil for (B=1.0 m, Ltie = 1.0 m)


AA BB

A A*

B B*

C C*

D D*

Fig. 7: Total displacements in soil as vectors for (B=1.0 m, Ltie = 1.0 m)

AA BB

C

D

EF

GH

I

J

K

L

M

N

O

[*10-3 m]

A : -0.400

B : -0.000

C : 0.400

D : 0.800

E : 1.200

F : 1.600

G : 2.000

H : 2.400

I : 2.800

J : 3.200

K : 3.600

L : 4.000

M : 4.400

N : 4.800

O : 5.200

P : 5.600

Fig. 8: Total displacements in soil as contour lines for (B=1.0 m, Ltie = 1.0 m)

A A A A

Fig. 9: Deformed mesh of soil for (B=1.0 m, Ltie = 2.0 m)


A A A A

Fig. 10: Total displacements in soil as vectors for (B=1.0 m, Ltie = 2.0 m)

Fig. 11: Total displacements in soil as contour lines for (B=1.0 m, Ltie = 2.0 m)

RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)

(square footing with No tie beam)

(circular footing with No tie beam)

ANGLE OF INTERNAL FRICTION 300

Fig. 12: The relationship between (D/B) ratio and settlement for square footings (1*1*0.5) m connected with

different tie beam lengths- At applied stress 294.7 kN/m2


RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)





different tie beam lengths - Applied stress 353.7kN/m2

RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)







RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)





different tie beam lengths At applied stress 294.7 kN/m2

RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)







RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)






RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)







RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)




Fig. 19: The relationship between (D/B) ratio and settlement for square footings (2*2*0.5) m connected with different tie beam lengths - Applied stress 353.7kN/m2

RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)







RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)






RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)







RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)

( Tie beam1.0m)

( Tie beam1.5m)

( Tie beam2.0m)






RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LE

ME

NT

(m

m)

( square footing (3 * 3 * 0.6))m


( square footing (1 *1 * 0.6))m


Fig. 24: Effect of footing size on settlement for square footings connected with same tie beam lengthen=1.0 m

For Ø=300


RATIO (D/B)

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)






For Ø=350

RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)






For Ø=400


RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)






For Ø=450

RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)






For Ø=300


RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TL

EM

EN

T (

mm

)






For Ø=350

RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LE

ME

NT

(m

m)






For Ø=400


RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)






For Ø=450

RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)






For Ø=300


RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)






For Ø=350

RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)






For Ø=400


RATIO (D/B)

0

2

4

6

8

10

12

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)






For Ø=450

RATIO (D/B)

0

2

4

6

8

10

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)

( Fiction angle (30)




Fig. 36: Effect of internal friction angle on settlement of square footings (1.0 * 1.0 * 0.5) connected with same

tie beam lengths=1.0 m


RATIO (D/B)

0

2

4

6

8

10

0 0.25 0.5 0.75 1 1.25 1.5S

ET

TLE

ME

NT

(m

m)







RATIO (D/B)

0

2

4

6

8

10

0 0.25 0.5 0.75 1 1.25 1.5

SE

TT

LEM

EN

T (

mm

)







Conclusions: From the present study the followings are concluded:-

i. Settlement under square footings without tie beam is less than that under circular footings. ii. The settlement under square footings connected with tie beam decreases with decreasing tie beam length. iii. The settlement under square footings connected with tie beam decreasing with increasing footing size. iv. The settlement under square footings connected with tie beam decreasing with increasing depth of

foundations. v. The settlement under square footings connected with tie beam decreases with increasing internal friction

angle.


vi. Footings connected with short tie beams are found to work as combined footings. However, footings act as separated one with longer tie beams.

REFERENCES

1. Egyptian Code, 2001. “Soil Mechanics and Foundation ". 2. Fraser, R.A. and L.J. Wardle, 1976. "Numerical Analysis of Rectangular Rafts On Layered Foundations", J.

Of Geotechnique, 26(4): 613-630. 3. Fellenius, B.H. And A. Altaee, 1994. “Stress and settlement of footings in sand”, Proceedings of the

American Society of Civil Engineers, ASCE, Conference on Vertical and Horizontal Deformations for Foundations and Embankments, Geotechnical Special Publication, GSP, 40(2): 1760-1773.

4. El-Kasaby, E.A.A., 1993. "Behavior Of Strap Footings With Tie-Beam Resting On Soil", Civil Engineering Research Magazine, Faculty Of Engineering Al-Azhar University Cairo Egypt, 15(6): 47-59.

5. Awad, A.A. And B. Muniram, 2001. "An Experimental Study On Bearing capacity of Shallow footing" Fourth international conference in Geotechnical Enrineering San Diego, California.

6. Elsamny, M.K., A.A. Almasmoum and M.M. Mahdy, 2002. "compressibility of cohessionless soil under spread footings", paper no. ST -105, Annual conference of the Canadian society for civil engineering.

7. Elsamny, M.K., A.A. Almasmoum and M.M. Mahdy, 2002. "Settlement domain under footings on cohesionless soil", paper no. ST -106, Annual conference of the Canadian society for civil engineering.

8. Junhwan, L., S. Rodrigo, And K. Sooil, 2005 "Bearing capacity of circular footings under surcharge using state-dependent finite element analysis" Computers and Geotechnics, 32: 445-457.

9. Elsamny, M.K., M.A.-R. Ibrahim, M. El-Saadany, M. Kotb And H.A. Ezz- Eldeen, 2006. "Soil Structure Interaction for Foundations Connected With Beam", M.Sc. Thesis, Faculty of Engineering, Al-Azhar University Cairo Egypt.

10. Al-Omari, R.R. And L.H. Al-Ebadi, 2008. “Effect Of Tie Beams On Settlements And Moments Of Footings” The 12th International Conference Of International Association For Computer Methods And Advances In Geomechanics (IACMAG) October, Goa, India, pp: 3216-3223.

11. Elsamny, M.K., Abd W.N. Elsamee and M.B. Elsedeek, 2010. “Effect Of Footings shape and size on ultimate bearing capacity of cohesionless soil” civil engineering research magazine, Al-Azhar University.

12. Elsamny, M.K., W.N. Abd Elsamee and M.B. Elsedeek, 2010, “Effect Of Depth Of Foundation On Modulus Of Elasticity “ES” For cohesionless Soil” civil engineering research magazine, Al-Azhar University.

13. Elsamny, M.K., W.N. Abd Elsamee and M.B. Elsedeek, 2010, “Effect Of Footings shape and size on wedge angle of cohesionless soil” civil engineering research magazine, Al-Azhar University.

14. Elsamny, M.K., M.A. Ibrahim, A. Radwan, M.A. Mashhour and M.M. Mahdy, 2011. “Effect Of Tie Beam Length On Foundations Settlement”, J. Of CERM, Al Azhar University, Faculty of Engineering, Cairo, Egypt, 33(4).

15. Elsamny, M.K., W.N. Abd Elsamee, H.A. Ezz-Eldeen and M. Abo Al Anwar, 2012. “Tie Beam Length and Foundation Settlement” , J. Of CERM, Al Azhar University, Faculty of Engineering, Cairo, Egypt, 34(2).

Documents

Effect of Tie Beam Length and Depth of Isolated Footings ... · Effect of Tie Beam Length and Depth of Isolated Footings on ... studied the behavior of eccentric footings connected