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 Total Downloads : 582
 Authors : Nashwa M. Yossef
 Paper ID : IJERTV4IS070521
 Volume & Issue : Volume 04, Issue 07 (July 2015)
 Published (First Online): 20072015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Effect of Reducing Deflection of Steel IBeams Strengthened While Loading
Dr. N. M. Yossef
Structural Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt.
Abstract Extensive parametric study of the behavior of steel beam strengthened while under load, the steel cover plate is welded after the deflection of the beam was reduced. The finite element model was verified using test results presented by the author in part I, the verified model was applied to investigate the effect of several influential parameters. The parameters studied include: 1) cover plate length, 2) strengthening pattern,

span to depth ratio of the strengthened beam, 4) magnitude of reduced deflection, 5) lateral restraint and initial lateral displacement, and 6) steel grade of the Isection and back plates. The numerical results were used to deduce the technical recommendations needed for enhancing the behavior of strengthening steel beams under study.
Keywords Strengthening; Steel Beams; Cover Plate; F. E. Model; Numerical Analysis; Influential Parameters.

INTRODUCTION
Using traditional way to strengthening steel beams, Newman [1] presented a web seminar discussing many issues concerning strengthening structural steel beams. Newman discussed code provisions for the renovation of steel structures, investigating existing conditions and strengthening methods. Newman showed many strengthening methods like replacement, passive vs. active methods, shortening span, adding members, external prestressing and enlarging section. He states that strengthening steel beams by welding (enlarging section) may need special procedures, and strengthening rafter by laying welds or weld a plate at flange help with torsion and flexure performance.
A review of previous researches [220] on strengthening existing structural systems has been provided in part one of the paper with title strengthening steel Ibeams by welding steel plates before or while loading. The experimental study of Liu [2] showed that welding cover steel plate to the steel beam while under load causes an increment in deflection during strengthening. At our researches, the author produces a reduction in deflection while the beam is strengthened. Part of this target is achieved through experimental study, which described in part one of this research. Numerical modeling will be used to extend the experimental study. Results from the numerical modeling and testing are expected to provide an understanding of the behavior of these beams in general; load deflection behavior and ultimate loadcarrying capacity are considered in the investigation beside the effects of reducing deflection before strengthening on the ultimate strength.
This paper describes a modeling technique using ANSYSTM software [21]. Subsequently, the finite element model is validated with test results. It is shown that the FE (Finite Element) model is able to simulate the test results with considerable accuracy. The validation model is then used in the subsequent parametric study to further influential parameters. These parameters have been identified through the experimental study, like the effect of strengthening pattern, span to depth ratio of the strengthened beam, Magnitude of reduced deflection, lateral restraint, initial lateral displacement and steel grade of the Isection and cover plates. Technical recommendations, based on the finite element study are presented.

FINITE ELEMENT MODELING

Model description
All specimens are discretized using the commercial software ANSYSTM. The beam flanges, web, stiffeners, cover plate and welds are modeled using four node structural shell element 181. SHELL181 is suitable for analyzing thin to moderatelythick shell structures[2]. The four stiffeners are fully connected at the load points. Contact element 174 and target 170 are used to model surface between the cover plate and specimens flange. All nodes of the strengthened flange and cover plate are coupled at a distance equal to the average of their thickness. The thickness of weld elements is varied to maintain a crosssectional equal to that of the 6 mm fillet weld.

Model setup
Rotations are permitted at one support, while rotations and axial translation are permitted at the other support. An initial imperfection with maximum deflection of L/500 at the mid length is implemented. This maximum imperfection is greater than L/1000 (the maximum allowable out of straightness). The imperfection is to indirectly account for residual stresses, which are not included in the simulation. Fig. 1 shows an example of the proposed model with imposed boundary conditions.
A displacement controlled load is used to determine the capacity of the strengthened beams; the displacement controlled load is applied at the rate of 0.5 mm/time, 0.167 mm/time in vertical and lateral direction respectively. The loading rate is selected through a trial and error process as a compromise to reduce computational run time while minimizing the difference between experimental and F.E analysis.
Weld
Cover plate
Cross section
hinged support (rotations are permitted)
Stiffeners

Mesh sensitivity
A mesh sensitivity study is first performed to ensure that the mesh being used leads to reasonable results. The mesh used by Lui et al. (2009b) was initially considered, Lui used the maximum width of element 20 mm. The final mesh seen in Fig. 1 is selected because there are insignificant changes in the results upon furthering mesh refinement. Elements with maximum width 50 mm and aspect ratio 0.5 are used herein.

Verification of model
Roller support (rotation & axial displacement are permitted)
The finite element model is verified using the results of the experimental tests described in Part I. The experimental ultimate loads of the specimens (Pexp) are compared with the corresponding finite element model ultimate loads (PF.E.) as shown in table 1. The comparison shows that, the difference between the experimental and F.E. results is within reasonable
Fig. 1 Finite element model for strengthening beam
The displacement controlled load is applied at loading point till failure. For beam strengthened while under load shown in Fig. 2, loading process need five steps: 1) modeling of beam section, cover plate and welds are created, and initial imperfection is incorporated into the model. 2) All elements of the cover plate and welds are deactivated using element birth and death feature, then 3) the nonlinear analysis is performed in the model using the displacement controlled load till preloaded level. 4) At preloaded level, deflection of the nodes of lower flange (at mid panel) is controlled. 5) All deactivate elements are then reactivated and the loading process is resumed till failure.
limit, the difference between ultimate loads are maximum 2.3%. Deformations of experimental specimens together with finite element results are shown in Fig.s 3 – 4 in case of BL 9050 and BL65 respectively. The experimental and numerical curves appear to match, and the deformations presented by the numerical model are a reasonable approximation of the test results as shown in Fig. 5. A comparison between the experimental and numerical results highlights the good accuracy of the model.
TABLE 1 COMPARISON OF EXPERIMENTAL AND F.E. RESULTS
Tested beams
Experimental ultimate load Pexp (kN)
F.E. ultimate load PF.E. (kN)
Pexp/ PF.E.
Perent of Increase in load capacity
*%
BC
218.15
215.15
1.01
1.3
BL65
220.62
219.54
1.00
0.5
BL90
229.17
231.06
0.99
0.8
BLU45
226.02
222.68
1.01
1.5
BL9025
235.76
232.23
1.02
1.5
BL9050
242.34
236.78
1.02
2.3
Test specimen before loading
Deflected shape at preload ratio
Step 1: loading till preload ratio
Test specimen before loading
w
Deflected shape at preload ratio
Step 2: reducing deflection during welding
Deflected shape at preload ratio
Welding plate
Step 3: welding plate
Fig. 2 Strengthening technique during loading
*Percentage of the Increase in ultimate load capacity equal .. %


PARAMETRIC STUDY
Testing of full scale beams is the most direct and reliable approach to examine the strength and behavior of the strengthened steel beams. However, because of the lake of the test results presented in Part I, the finite element model used to expand the limited database of test results.

Selection of parameters
Extensive simulations were conducted to explore the effect of various influential parameters on the strengthened beam response. Many parameters are expected to influence the strength and the behavior of the strengthened steel beam using the mentioned techniques. The parameters considered include:
1) cover plate length, 2) Strengthened pattern, 3) span to depth ratio of the strengthened beam, 4) Magnitude of reduced deflection, 5) lateral restraint and initial lateral displacement and 6) Steel grade of the Isection and cover plates.
One hundred fifty eight steel beams were analyzed numerically to fully investigate the effect of these variables. Table 2 shows a list of the selected variables.
300
250
Load (kN)
200
150
100
50
F.E. Model
Experiment al BL90 50
300
250
200
Load
150
100
50
0
Experiment al BL9050

Model
0
0 20 40
Deflection
0 5 10
Lateral displacment

Load deflection curve (b) Load lateral displacement curve Fig. 3 Comparison of experimental and F.E. deflection and lateral displacement of BL9050

250
200
F.E. Model
250
200
F.E Model
Load (kN)
150
100
50
0
Experiment al BL65
0 20 40 60
Deflection (mm)
150
Load (kN)
100
50
0
Experimental BL65
0 5 10 15
Lateral displacment
(a) Load deflection curve (b) Load lateral displacement curve Fig. 4 Comparison of experimental and F.E. deflection and lateral displacement of BL65.
TABLE 2 LIST OF THE SELECTED VARIABLES AND THEIR RANGES FOR THE PARAMETRIC STUDY
No. of analyzed beams
Strengthen pattern
Span/depth ratio
Span (mm)
(wi)
(vi)
Lateral restraint
Pstr./ Punstr
(w)
fy (MPa)
beam
Plate
25
A, B, C &D
9
1800
L/500
zero
Partial (w/v = 3)
Unstrengthed,0, 0.25, 0.41, 0.57,
0.73, 0.84
w0*
275
275
25
13.5
2700
Unstrengthed, 0,
0.26, 0.42, 0.59,
0.76, 0.85
25
18
3600
Unstrengthed, 0,
0.26, 0.42, 0.60,
0.76, 0.87
60
A, B, C & D
18
3600
7.2
mm
zero
Partial (w/v = 3)
0.26, 0.6 and 0.87
0, w0,
(0.3 wmax),
(0.6 wmax), wmax
275
275
15
C
18
3600
7.2
mm
zero, 1,
3, 5 and
8 mm –
No lateral
restraint
0.6
w0*
275
275
Partial
(w/v = 3)
Full restraint
8
A, B, C & D
18
3600
7.2
mm
zero
Partial (w/v = 3)
0.6
w0*
235
235
235
275
Total:158
*w0 = deflection at mid span wmax deflection at loading point wLoad (as shown in figure 2)
Fig. 5 Experimental and numerical deformation of BL90



NUMERICAL RESULTS
A. Effect of cover plate length and area
The experimental results with the data in Liu et al. [2, 3] showed that: 1) Increase welded cover plate length causes an increase in the ultimate capacity Pu, for analyzing beam BL with beam length 180 cm the ultimate capacity increase by 1.1
%, 5 % and 23 % when the plate length increase from 60 cm, 90 cm and 170 cm respectively. 2) The effect of the cover plate length decreases when the area of the cover plate is smaller than the flange area. These points suggest that, for the
Examination of table 5 reveals that the change of preloaded ratio has minor effect on the increment of ultimate load (the amount of incremental in ultimate capacity as a percentage ranging from 1.96 % to 0.79 %). Even so, the increase in the preloaded ratio near the end of the elastic zone reduces the increment of ultimate load for strengthening pattern A.
TABLE 3 STRENGTHENING PATTERNS
Patterns*
A
B
C
D
Cross section
Calculated
moment of inertia about major axis
2665.5 cm4
2836.2 cm4
2433.06 cm4
3467.32 cm4
Description/Name
Strengthening lower flange / BL
Strengthening lower &
upper flange / BLU
Strengthening upper flange
/BU
Strengthening lower flange vertically
/BLV
* For all strengthening pattern: area of cover plate = area of flange plate, & Length of cover plate = span of beam
160
next analyzed beam, the welded cover plate length and area are adapted in this work to be equal to strengthened beam span
140
Load (kN)
120
Pattern B Pattern D
and flange area respectively.

Effect of strengtheningpattern with different preload ratio
IBeam can be strengthened with steel plate welded to upper flange or lower flange with different orientations. Table
100
80
60
40
20
0
Pattern A
Control
Pattern C
3 indicates the strengthening patterns suggested in this study, the suggested patterns based on practicing the same area of cover plate with different orientations to enhance beam behavior.
Fig. 6 represents the load deflection curves for different patterns of the strengthening beams with two spans / depth ratio. The strengthening of steel beams under load increases the capacity of the control beam for all strengthening patterns. It can be noted that pattern B is the most effective pattern, although pattern B is less inertia than pattern D. The strengthening of upper and lower flange for pattern B enhances the behavior of the beam, moreover pattern D has difficulties with welding technique, as the initial deflect of cover plate about its major axis (to take the deflected shape of the strengthening beam under load) causes additional stress in the plate.
Another important effect of strengthening pattern is related to yield deflection wy. The deflection of the midspan point at yield for two different spans was listed in table 4. At a certain preload ratio, strengthening pattern A and D reduce the yield deflection of control beam, a slight reduction in deflection of nearly 3% and 8% for pattern A and D respectively was observed. On the contrary, an incremental in yield deflection of nearly 5% and 15% for pattern C and B respectively was observed.
0 20 40 60
Deflection
Fig. 6 Effect of strengthening pattern on the ultimate capacity of Strengthened beam (L = 3600mm, Lpl = 3500mm &
preload ratio = 0.60)
TABLE 4 EFFECT OF STRENGTHENING PATTERN ON THE YIELD DEFLECTION OF STRENGTHENING BEAMS
Strengthening pattern
Span length = 360 cm
Span length = 270 cm
wy yield deflection (mm)
Incremental*
%
wy yield deflection
(mm)
Incremental*
%
Control (BC)
12.6
–
22
–
A
12.2
3.2
21.2
3.6
B
14.5
15.1
24.86
13.0
C
12
4.8
20.19
8.2
D
11.7
7.1
20.22
8.1
*Incremental of ultimate yield deflection at midpoint = ( )
Span/depth ratio
Preload ratio
Pattern
Ultimate load increment
%
Pattern
Ultimate load increment
%
Pattern
Ultimate load increment
%
Pattern
Ultimate load increment
%
9
0
23.12
46.13
39.11
36.30
13.5
22.25
47.28
38.55
38.61
18
22.32
49.09
36.85
36.71
9
0.41:
0.42
23.34
46.38
39.59
36.19
13.5
A
23.21
B
47.93
C
38.95
D
37.66
18
21.79
48.67
37.15
35.01
9
0.73:
0.76
23.02
46.70
40.41
36.10
13.5
21.77
48.06
39.39
36.35
18
21.95
49.13
39.05
32.34
( )
different preload ratios as shown in Fig. 7. Especially for pattern B, at a higher preloaded ratio (Pstr/Punstr = 0.87), the general trend of the ultimate capacity versus the amount of reduced deflection remains the same. For pattern D, the finite element results show that the reduced deflection is not a desirable technique for strengthening that type of beam. Since, it is difficult to weld the plate to the lower flange with the increase of deflection, moreover, to take the deflected shape of the beam.
TABLE 6 ULTIMATE LOAD INCREMENT OF BEAMS WITH DIFFERENT SPAN/DEPTH RATIO
100%
TABLE 5 ULTIMATE LOADS FOR BEAM WITH DIFFERENT PRELOAD RATIO AND FOUR PATTERNS
L
(beam
span in mm)
Preload ratio
Strengthen
pattern A
Strengthen
pattern B
Strengthen
pattern C
Strengthen
pattern D
Pu (kN)
Incr.(2)%
Pu (kN)
Incr.(2)%
Pu (kN)
Incr.
(2)%
Pu (kN)
Incr
.(2)%
2700(1)
0.00
162.41
0.00
195.66
0
184.07
0
183.75
0
0.26
163.60
0.73
196.50
0.43
184.47
0.22
183.14
0.33
0.42
163.69
0.79
196.53
0.44
184.60
0.29
182.48
0.69
0.59
162.46
0.03
196.60
0.48
184.98
0.49
181.58
1.18
0.76
161.77
0.39
196.70
0.53
185.18
0.60
180.74
1.64
0.85
161.41
0.62
196.81
0.59
185.43
0.74
180.20
1.93
(1) Ultimate load for unstrengthen beam BC260 = 132.85 kN (2) Incremental of ultimate load ( =0) 100%
( =0)

Effect of span to depth ratio
In order to study the effect of span to depth ratio on steel beams strengthened while under load, short, intermediate and long beams were analyzed. The span to depth ratio 9, 13.5 and 18 of the strengthening beams are investigated. A set of runs were conducted for the three different ratios with different pattern and preloaded ratio, the results were listed in table 6.
It is commonly understood that span/depth ratio effect on failure mode of the studied beams, it resulted in different ultimate capacity. Table 6 shows that, the effect of the span / depth ratio is negligible. The change of the ultimate load increment is about 1% to 3% with the change o span / depth ratio. That can be explained, since the lateral displacement is
120
Load (kN)
118
116
114
112
110
145
143
Load
141
139
Preload ratio = 0.26 Preload ratio = 0.60 Preload ratio = 0.87
0 5 10 15
Reduced deflection (mm)
Pattern A
Preload ratio = 0.26 Preload ratio = 0.60
controlled and the failure was due to excessive yield in the
middle of the beam, the ratio between deflection and lateral
137
135
Preload ratio = 0.87
displacement at loading points w/v = 3.
D. Effect of the reduced deflection w
The effect of reduced deflection w (imposed to studied beams before the welding of cover plate) is studied for 60 analyzed beams. All studied beams have a span / depth ratio equal to 18 with three preloaded ratios 0.26, 0.60 and 0.87 as listed in table 2.
The results presented in Fig. 7 show that increasing the amount of reduced deflection increase the ultimate capacity of strengthening beam. For pattern A, the ultimate capacity of beam BL35087 increase from 112.23 kN (w = 0) to be
117.12 kN (w = 12.58 mm) with an incremental ratio equal
4.3 %. For pattern B and C, the reduced deflection has minor effect on the ultimate capacity of the strengthened beam at
140
138
Load
136
134
132
130
0 5 10 15 20
Reduced deflection (mm)
Pattern B
Preload ratio = 0.26 Preload ratio = 0.60 Preload ratio = 0.87
0 5 10 15 20
Reduced deflection (mm)
Pattern C
130
Load (kN)
128
126
124
122
120
Preload ratio = 0.26 Preload ratio = 0.60 Preload ratio = 0.87
0 1 2 3 4
Reduced deflection (mm)
Pattern D
Finite element results for beam BU35060 with different lateral restraint imposed at load points presented in Fig.s 8 – 9. The results show that partial lateral restraint imposed at load points causes higher lateral displacement at the beginning of loading if compared with free lateral restrain case. In particular, there is a high incremental in lateral displacement at the step of reducing deflection, while the lateral displacement still under control even on failure. Moreover, the lateral displacement incremental of the unrestraint beam is uncontrolled within yield of the compression flange causing extensive increase in lateral displacement and failure.
Fig. 7 Relationships between ultimate load and the amount of
recovered deflection at different preload ratio

Effect of lateral restraint and initial lateral displacement
The response of the studied beam to lateral buckling is of interest to determine its ultimate capacity, lateral buckling is affected by the beam lateral restraint of compression flange. To study the effect of lateral restraint, three cases of lateral restraint for the compression flange were considered: 1) partial restraint with ratio (w/v = 3), 2) full lateral restraint, and 3) no lateral restraint.
From the experimental study presented by the author in the accompanying paper, the effect of loading mechanism can be simulated by introducing controlled vertical displacement w and horizontal displacement v that simulate the partial restraint at loading points of the compression flange.
In case of free lateral restraint, the initial lateral displacement must be introduced to the perfect geometry to analyze the post buckling behavior, where initial lateral displacement (vi) is the lateral displacement at mid length. Table 7 shows that initial lateral displacement has a significant effect on ultimate capacity of the free lateral restraint beams, since 1 mm, 3 mm, 5 mm and 8 mm initial lateral displacement imposed to mid length cause reduction about 3.85, 5.53, 6.74 and 8.31% of the ultimate capacity of the free lateral restraint beam with prefect geometry (no initial deformation) respectively.
In cases of partial and full restraint, shown in table 7, the initial lateral displacement has negligible effect on the ultimate capacity of the studied beams, since the maximum reduction of the ultimate load of beam with partial restraint was 0.9% due to initial lateral displacement (vi) equal 8 mm.
TABLE 7 ULTIMATE LOADS OF BU3500.6 WITH DIFFERENT INITIAL
LATERAL DISPLACEMENT
L (mm)
Preload
ratio
* (vi) in mm
No lateral restraint
With partial lateral
restraint w/v = 3
With lateral
restraint
Pu (kN)
Reduction
**
Pu (kN)
Reduction*
*
Pu (kN)
Reduction*
*
3600
0.6
0
137.60
–
131.54
–
137.62
–
1
132.50
3.71%
131.45
0.07%
137.59
0.02%
3
129.99
5.53%
131.15
0.30%
137.49
0.09%
5
128.33
6.74%
130.86
0.52%
137.36
0.19%
8
126.16
8.31%
130.36
0.90%
137.30
0.23%
*Maximum imposed lateral displacement at mid length before loading
**Reduction of ultimate load ( =0) 100%
( =0)
Lateral restraint at load points
Plan of upper flange

Beam with lateral restraint
Partial restraint
(w/v = 3)
Plan of upper flange

Beam with partial restraint
Fig. 9 Relationship between load and lateral displacement () at midpoint of the upper flange for beams with different lateral restraint (Pattern C, L
=3600 mm, Pstr./ Punstr =0.60 and vi = 5mm)


Effect of steel grade
For older structures, beams may be of steel grade with low nominal yield strength if compared with modern structures that would be used for strengthen plates. So strengthen beams may be composed of different two grades. Beams with two different combinations of steel grades were investigated: 1) beams strengthened with the same steel grade for the plate and the rolled section (fy = 235 MPa or fy = 275 MPa), 2) strengthens beams with fy = 235 MPa for the section and fy = 275 MPa for the plates, as shown in table 2
Table 8 and Fig. 10 indicate that, when the grade of strengthen steel plate increased from fy =235 MPa to fy =275 MPa, the steel grades neither significantly affect the strength of the strengthened beam, max increment was about 5.05% of the ultimate capacity for BUL35060 with span length 360, nor reduce the deflection as shown in Fig. 10.
TABLE 8 ULTIMATE LOADS FOR BEAM WITH DIFFERENT STEEL GRADE AND FOUR PATTERNS
L
(mm)
fy for beam (MPa)
fy for Pl (MPa)
Strengthen
pattern A
Strengthen
pattern B
Strengthen
pattern C
Strengthen
pattern D
Pu
(kN)
Incr.%
Pu
(kN)
Incr.%
Pu
(kN)
Incr.%
Pu
(kN)
Incr.%
3600
235
235
100.92
0.5
123.73
5.05
115.75
2.68
112.01
1.97
235
275
101.43
129.99
118.85
114.22
140
120
Load (kN)
100
80
60
40 fy (Plate) = 275 kN
20 fy (Plate) = 235 kN 0
0 10 20 30 40 50
Deflection (mm)
Fig. 10 Loaddeflection relationship for BLU35060 with change of steel grades of cover plate (Pattern B, L =3600 mm, Pstr. / Punstr =0.60 and vi =
5mm fy for beam section = 235 kN)


CONCLUSIONS AND RECOMMENDATIONS

A study of steel beams strengthened by welding steel plates with reducing of deflection while under load has been presented in this research.
The finite element models were developed and their results were compared to data from detailed experimental tests. A maximum error of 2.3% between the experimental and the finite element model was obtained, indicating that the finite element model provides a reasonable approximation of the behavior of beams studied.
Numerous parameters may affect the strength of rolled I section strengthened were studied numerically. A total of 158 finite element models of steel I beams strengthened after reducing deflection while under load were developed.
From the results of the parametric study the following technical notes were presented:

The cover plate length and crosssection area is the most important parameter affecting strength of strengthened beam, ultimate capacity increase by 1.1
%, 5 % and 23 % when the plate length increased to 0.33, 0.5 and 0.95 of the span respectively. So using a cover plate with full span length and has an area equal or greater than the area of the flange is recommended.

The welding pattern affects the behavior and strength of the strengthened beam. So strengthening of upper and lower flanges (Pattern B) is recommended if possible, since the ultimate capacity and yield deflection of the control beam BC270 were increased by 47% and 14% respectively. Contrariwise, strengthening lower flange vertically (Pattern D) is not recommended.

Strengthening steel beams while under loading shows that the preloaded ratio has minor effect on the ultimate strength of the strengthened beam (the amount of incremental in ultimate capacity as a percentage ranging from 1.96 % to 0.79 %), even so the welding of the steel plate prior to yield enhances the beam behavior put the increment of the ultimate capacity decreases.

Reducing beam deflection before welding has minor effect on the beam strength (the ultimate capacity of beam BL35087 increase from 112.23 kN at w = 0 to be 117.12 kN at w = 12.58 mm with an incremental ratio equal 4.3 %). But, its recommended since it overcomes the increase of deflection causes by welding.

The initial lateral displacement must be limited. 1 mm to 8 mm initial lateral displacement imposed to mid length cause reduction about 3.85 to 8.31% of the ultimate capacity of the free lateral restraint, furthermore partial and full restraint have negligible effect on the ultimate capacity of the studied beams.

The use of different grades in strengthening beams was found to have a minor effect on the strength of the strengthened beam.
ACKNOWLEDGMENT
The author wants to thank Prof. Mohamed Ahmed Daboan for and Prof. Osman Ramadan for their support and valuable comments during editing of this research.
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