Influence of double idealized shear flow zones on the torsional resistance in fibrous normal strength concrete beams

Influence of double idealized shear flow zones on the

torsional resistance in fibrous normal strength concrete

beams

Karim, F.R.

,

Abu Bakar, B.H.

,

KokKeong, Choong

,

Aziz, O.Q.

*

PhD Candidate, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia **

Professor, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia ***Associated Professor, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia ****Professor, Civil Engineering Department, College of Engineering, Salahaddin University, Erbil, Iraq

Abstract- This investigation highlights the influence of double idealized shear flow zones on the torsional resistance for under-reinforced fibrous normal strength concrete beams subjected to pure torsion. The beam sections were double under-reinforced by transverse and longitudinal reinforcements, once was located in the idealized shear flow zone and the other one was located in the idealized tension zone. To study the influence of double idealized shear flow zones on the torsional resistance of under-reinforced fibrous normal strength concrete beams, four fibrous concrete beams were cast and tested under pure torsion. The under-reinforced beams designed based on ACI 318-14. The main transverse and longitudinal reinforcements in the shear low zone are kept constant in the beams while the transverse reinforcement in the idealized tension zone was covered different percentage of this zone. The test results were confirmed that the torsional resistance at peak loads was improved up to 23.7% while the area enclosed by stirrup in core zone has extended to 46.2%. In addition, the twisting angle at peak loads was enhanced up to 60.9%and the shear strain in concrete and the strain in longitudinal reinforcement were enhanced whereas the strain in transverse reinforcement was decreased. The spacing between spiral cracks and the inclination angle of crack at failure were increased with inclusion of reinforcement in core zone. The space truss model was modified to cover the influence of double shear flow zones. The proposed modification model was showed that it has a good agreement with test results.

Index Terms- Double shear flow zone, Fibrous normal strength concrete, Pure torsion, andSpace truss analogy,.

I. INTRODUCTION

he idealized core zone in space truss model has been ignored even though this model was modified for fibrous normal strength concrete beams.[1, 2] However, the fibrous concrete has a higher tensile strength than what the non-fibrous concrete has[3]. In addition, although the compressive strength of fibrous concrete has been improved, the effective thickness of shear flow zone is still the same for fibrous and non-fibrous concrete beams[4]. Moreover, the compressive strain in the concrete surface has found to be maximum and zero at the end distance of effective depth of inclined compression strut[4] whereas it was ignored the influence of concrete cover thickness[5].

Based on the space truss analogy, the torsional strength of reinforced concrete has been provided by reinforcement and the concrete that surrounds the steel[6]. However, the activating of idealized core zone comes from the absence of tension element. Therefore, the completed elements included tension and compression could be the unique way to make the majority of this area effective to resist torsion at failure.

II. RESEARCHSEGNIFICANCE

This paper highlights the influence of reinforcement in the idealized core zone on torsional resistance at peak load. Even though, the idealized core zone in space truss model is employed up to 40% of the solid section, this area is ignored to resist torsion. However, the fibrous concrete has a tensile strength more than that has non-fibrous one and inclusion full reinforcements in this zone is produced the elements for new space truss inside of main space truss. Therefore, the section separated in to two idealized shear flow zones for resisting torsion and the majority of the solid section is contributed to resist torsion.

III. EXPERIMENTAL WORKS

The under-reinforced concrete (B-1-N) beam is a control beam and the other beams (B-2-N, B-3-N and B-4-N) included the full reinforcement in the idealized tension zone, the reinforcement was covered the varying area of the core zone .The covered area by reinforcements in the core zone was between 0 and 0.462 at post-cracking stage. The span to depth ratio and the aspect ratio of the beam section are kept as 5.75 and 1.22, respectively. The twisting moment was conducted on the beams from two point loads act on the loading arms which are converted to pure torsion on the tested beam.

2.1 MATERIALS, MIX PROPORTIONS AND SPECIMEN PREPARATION 2.1.1 MATERIALS AND MIX PROPORTION

The fibrous normal strength concrete beams were cast for cylinder compressive strength of 25 MPa. An ordinary Portland cement (Tasik cement) was used. Crushed stone with 10 mm maximum size of aggregate, silica sand, silica fume, tap water, HRWR super-plasticizer Sika VC2199, retard-admixture (Plastiment-R) with two size of copper coated micro steel fibre were used. The mix proportion of the materials used for producing this concrete is shown in Table 1.

Table 1:Mix proportion of fibrous normal strength concrete

Materials Quality,

kg/m3

Cement (Type I) 275

Silica sand 926.7

Crushed stone 763.8

Silica fume 13.75

Water 200.7

Super-plasticizer VC2199 5.5

Retarder-admixture (Plastiment R) 1.375

Micro steel fibre A (21mm X 0.35 mmΦ) 18.055

Micro steel fibre B (12 mm X 0.2 mmΦ) 72.22

Slump, mm 90

Φ: diameter of fibre, mm

2.1.2 PREPARATION OF BEAM SPECIMEN

The longitudinal reinforcement contained 4-12 mm diameter bars, two of them at the bottom and the rest at the top. Transverse

reinforcement was provided in the form of two –legs rectangular stirrup with 135˚ standard hooks. The 6mm diameter bars were made

stirrups with dimension 166 mm wide and 216 mm depth and the spacing between stirrups was 95 mm as shown in Figure 1. While the details of the reinforcements in the idealized core zone wereshown in Figure 2.The beam dimensions are tabulated in Table 2.

Table 2:Measured dimensions of the fibrous concrete beams

Beam denotation

Concrete cover,

mm

Width, mm

Height, mm

Span length, mm

B-1-N 29 230 280 1587

B-2-N 25 222 272 1569

B-3-N 26 224 274 1570

B-4-N 25 222 272 1569

2.1.3 FIBRICATION OF SPECIMENS

The fibrous normal strength concrete was blended in the two pan mixer with 0.05 m3which obeyed the following sequence for mixing

2.1.4 TESTING OF BEAMS

Under-reinforced fibrous normal strength concrete beams were tested under pure torsional moment. The Universal Testing Machine of 500 kN capacity in the Structural Laboratory in the School of Civil Engineering was used for the test.The specimens were tested in pure test arrangement as shown in Figure 3 and 4. The twisting angle was measured during loading of the beam by using U shape steel frame and two LVDTs on the ends of arms of U shape as shown in Figure 5.The shear strain in concrete and axial strain in reinforcements were measured by LVDTs and electrical strain gauges. The load was applied manually until the fibrous concrete beam was failed under torsion.

Figure 1: Detail of reinforcements in the fibrous concrete beam B-1-N

Figure 3: Schematic Test set-up

Figure 5: Schematic measuring of twisting angle

IV. RESULTS AND DISCUSSIONS

The properties of fibrous normal strength concrete for each beam were measured and tabulated in Table 3.The torsional resistance and twisting angles were measured during the loading of the beam. Besides, the inclusion angle of crack was measuredat failure as shown in Table 4.

Table 3: Measured properties of fibrous normal strength concrete beams

Beam denotation fc’,

MPa

fsp,

MPa fr, MPa

Bond strength, MPa

fbt fbL

B-1-N 29.50 4.473 7.571 1.314 6.644

B-2-N 29.70 4.268 6.016 1.613 7.896

B-3-N 28.20 4.709 5.929 3.913 8.906

B-4-N 27.44 3.362 4.690 3.171 7.926

Table 4: Results of pure torsion test in fibrous normal strength concrete beams

Beam denotation Tcr,

kN.m

Фcr,

rad/m Tu,

kN.m

Фu,

rad/m

θ, degree

B-1-N 12.147 0.619 17.846 15.165 45

B-2-N 13.454 0.300 22.074 24.409 45

B-3-N 12.601 0.691 21.897 18.139 46

B-4-N 11.173 0.802 18.104 22.459 50

3.1 CRACKING TORSIONAL MOMENT

Figure 6: Torsional moment at crack load versus the percentage of idealized tension zone covered by the reinforcement

3.2 TORSIONAL RESISTANCE PROVIDED BY REINFORCEMENT AND FIBRE

The torsional resistance provided by reinforcements and fibre was improved up to 23.7% due to reduction of idealize tension zone area which produced another shear flow zone inside of idealized tension zone area as shown in Figure 7.

Figure 7: Torsional moment at peak load versus the percentage of idealized tension zone covered by the reinforcement 29.5 27.44 28.2 29.7 26 26.5 27 27.5 28 28.5 29 29.5 30 0 5 10 15 20 25 30 35

0 0.44 0.614 0.84

C o m p re ss ive s tr engt h, M P a T o rs io n al m o m en t at cr ack in g l o ad , k N .m

Ratio of area covered the idealize tension zone

covered area in idealize tension zone compressive strength

0 5 10 15 20 25

0 0.242 0.335 0.462

T o rs io n al m o m en t at u ltim ate lo ad , k N .m

3.3TWISTING ANGLE

The inclusion of reinforcements in the idealize tension zone area was improved the contribution of reinforcement for resisting torsion and increased the flexibility of the beam. In addition, the twisting angle was improved at crack and peak loads up to 29.5% and 60.9%, respectively as shown in Figure 8.

Figure 8: Torsional moment versus twisting angle

3.4 SHEAR STRAIN IN CONCRETE

The amount of shear strain in concrete during torsion test was influenced by reduction of idealized tension zone area as shown in Figure 9. The value of shear strain was reached to 0.03370. Therefore, the contribution of fibrous concrete was increased to resist torsion at crack load.

3.5 STRAINS IN LONGITUDINAL AND TRANSVERSE REINFORCEMENTS

The strain in longitudinal reinforcements are increased up to 26.4% whereas the strain in stirrups are decreased in the range of 24.5%. Therefore, the activating idealized tension zone area by inclusion reinforcements in this zone increases the contribution of longitudinal reinforcement for resisting torsion as shown in Figure 10-13.

3.6 CRACKING PATTERNS

The activating idealized tension zone area is influenced on the detail of spiral cracks. For instance, number and spacing between cracks as well as inclination angle of crack at failure as tabulated in Table 5. The pattern of cracks of the tested beams which were tested and failed under pure torsional moment as shown in Figures 14-17.

0 5 10 15 20 25

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

T

o

rs

io

na

l m

o

m

ent

,

kN

.m

Twisting angle , rad/m

Figure 9: Torsional moment versus shear strain in concrete

Figure 10: Torsional moment versus strain in main stirrups 0

5 10 15 20 25

0 5 10 15 20 25 30 35

T

o

rs

io

na

l m

o

m

ent

,

kN

.m

shear strain in concrete, mm/mm X 10-3

B-1-N B-2-N B-3-N B-4-N

0 5 10 15 20 25

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0

T

o

rs

io

na

l m

o

m

ent

,

kN

.m

Strain in stirrups, mm/mm X 10-3

Figure 11: Torsional moment versus strain in stirrup located in idealized tension zone

Figure 12: Torsional moment versus strain in main longitudinal reinforcement

0

5

10

15

20

25

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

T

o

rs

io

na

l m

o

m

ent

,

kN

.m

Strain in stirrups, mm/mm X 10-3

B-2-N-SS

B-3-N-SS

B-4-N-SS

0 5 10 15 20 25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

T

o

rs

io

na

l m

o

m

ent

,

kN

.m

Strain in longitudinal reinforcement, mm/mm X10-3

Figure 13: Torsional moment versus strain in longitudinal reinforcement located in idealized tension zone

Table 5:Detail of spiral crack of fibrous normal strength concrete beams test under pure torsion

Beam denotation

No. of spiral cracks

Θ,

degree

Average spacing between spiral

cracks, mm

B-1-N 6 45 205

B-2-N 7 45 148

B-3-N 4 46 307

B-4-N 7 50 249

V. THEORETICAL ANALYSIS AND PROPOSEDEQUATION

The inclusion of reinforcement in the idealized core zone is produce another shear flow zone and it is reduced the idealize core zone to a minimum. The reinforcement in the new shear flow zone is contributed to improve ultimate torsional resistance. To prove this

improvement, it is considered the dimensions of transverse reinforcement in the main shear flow zone Xo1 , and Yo1while the

dimensions of transverse reinforcement in the secondary shear flow zone is Xo2, and Yo2 as shown in Figure (18).

0 5 10 15 20 25

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

T

o

rs

io

na

l m

o

m

ent

,

kN

.m

Strain in longitudinal reinforcement, mm/mm X10-3

Figure 14: Side view of beam B-1-N at failure

Figure 15: Side view of beam B-2-N at failure

Figure 16: Side view of beam B-3-N at failure

Figure 18: Dimensions of stirrups in shear flow zones

The shear stress in shear flow zones are resisting torsional moment as shown in Figure (19). The external torsional moment is resisted by torsional resistance from shear flow zone.

𝑇𝑇1=𝑉𝑉1.𝑌𝑌𝑜𝑜1₂(1)

𝑇𝑇2=𝑉𝑉2.𝑋𝑋₂𝑜𝑜1(2)

𝑇𝑇3=𝑉𝑉3.𝑌𝑌𝑜𝑜1₂(3)

𝑇𝑇4=𝑉𝑉4.𝑋𝑋₂𝑜𝑜1(4)

𝑇𝑇5=𝑉𝑉5.𝑌𝑌𝑜𝑜2₂(5)

𝑇𝑇6=𝑉𝑉6.𝑋𝑋₂𝑜𝑜2(6)

𝑇𝑇7=𝑉𝑉7.𝑌𝑌𝑜𝑜2₂ (7)

𝑇𝑇8=𝑉𝑉8.𝑋𝑋₂𝑜𝑜2(8)

After cracking, the two thin-walled tubes are produced and the transverse reinforcements in the centerline of shear flow zones in long sides of the section are resisting torsional moment as shown in Figure (20).

𝐹𝐹1=𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑡𝑡1(9)

𝐹𝐹2=𝐴𝐴𝑡𝑡2.𝑓𝑓𝑡𝑡𝑡𝑡2 (10)

Yo2 Yo1

Xo1

Figure 19: Shear force in shear flow zones

From the equilibrium of vertical forces in main shear flow zone

Σ𝐹𝐹𝑦𝑦↑+= 0(11)

𝑉𝑉4− 𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑦𝑦1.𝑛𝑛1= 0(12)

𝑉𝑉4=𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑦𝑦1.𝑛𝑛1but𝑛𝑛1=𝑌𝑌𝑜𝑜1_𝑆𝑆.𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₁

∴ 𝑉𝑉4=𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑦𝑦1.𝑌𝑌𝑜𝑜1._𝑆𝑆𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₁ (13)

Figure 20: Side view of longitudinal section of the beam after cracking

From the equilibrium of vertical forces in secondary shear flow zone

Σ𝐹𝐹𝑦𝑦↑+= 0 (14)

Shear force in main shear flow zone Yo1 Xo1

Y o2 X

o2

V5

V7 V6

V8

V1

V4

V3 V2

Shear force in secondary shear flow zone

F1 F₂

F₁

F₂

F₂ S₁

S₂

Y_{o2 Y}

o1

Z₂

Z₁ V₈ V₄

X Y

𝑉𝑉8− 𝐴𝐴𝑡𝑡2.𝑓𝑓𝑡𝑡𝑡𝑡2.𝑛𝑛2= 0(15)

But

𝑛𝑛2=𝑌𝑌𝑜𝑜2._𝑆𝑆𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶 2

∴ 𝑉𝑉8=𝐴𝐴𝑡𝑡2.𝑓𝑓𝑡𝑡𝑡𝑡2.𝑌𝑌𝑜𝑜2._𝑆𝑆𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₂ (16)

Substitute V4 and V8 in the Eq. (13 and 16), thus

𝑇𝑇4=𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑦𝑦1.𝑌𝑌𝑜𝑜1._𝑆𝑆𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₁ .𝑋𝑋𝑜𝑜1₂ (17)

𝑇𝑇8=𝐴𝐴𝑡𝑡2.𝑓𝑓𝑡𝑡𝑡𝑡2.𝑌𝑌𝑜𝑜2_𝑆𝑆.𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₂ .𝑋𝑋₂𝑜𝑜2 (18)

The total torsional resistance in one side is the summation of T4 and T8.Because of T4=T2 and T8=T6, The total torsional resistance in

two long sides Th.

𝑇𝑇ℎ = 2.𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑦𝑦1.𝑌𝑌𝑜𝑜1._𝑆𝑆𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₁ .𝑋𝑋₂𝑜𝑜1+ 2.𝐴𝐴𝑡𝑡2.𝑓𝑓𝑡𝑡𝑡𝑡2.𝑌𝑌𝑜𝑜2_𝑆𝑆.𝐶𝐶𝑜𝑜𝑡𝑡𝐶𝐶₂ .𝑋𝑋₂𝑜𝑜2 (19)

The total torsional resistance in short sides is Tw, which is

𝑇𝑇𝑤𝑤 =𝑇𝑇1+𝑇𝑇3+𝑇𝑇5+𝑇𝑇7 (20)

But, 𝑇𝑇₁=𝑇𝑇₃ and 𝑇𝑇₅=𝑇𝑇₇ Thus,

∴ 𝑇𝑇𝑤𝑤= 2.𝑇𝑇1+ 2.𝑇𝑇5 (21)

Where,

Th: torsional resistance provided by stirrups in shear flow zones in long side of the section, kN.m

Tw: torsional resistance provided by stirrups in shear flow zones in short side of the section, kN.m

After cracking, the torsional resistance in two short sides is coming from the shear forces in the centerline of shear flow zones as

shown in Figure (21). Similarly, the Tw=Th,Then, the total torsional resistance is equal to twice of Th and it can be expressed as

follows:

𝑇𝑇𝑡𝑡=𝑇𝑇ℎ+𝑇𝑇𝑤𝑤 = 2.𝑇𝑇ℎ (22)

𝑇𝑇𝑡𝑡= 2.𝐴𝐴𝑡𝑡1.𝑓𝑓𝑡𝑡𝑦𝑦1.𝑌𝑌𝑜𝑜1_𝑆𝑆.𝑋𝑋₁01𝑐𝑐𝑜𝑜𝑡𝑡𝐶𝐶+ 2.𝐴𝐴𝑡𝑡2.𝑓𝑓𝑡𝑡𝑡𝑡2.𝑌𝑌𝑜𝑜2_𝑆𝑆.₂𝑋𝑋02.𝑐𝑐𝑜𝑜𝑡𝑡𝐶𝐶 (23)

Figure 21: Top view of longitudinal section of the beam after cracking

Where,

Ts: torsional resistance provided by stirrups in shear flow zones, kN.m

At1: area of one leg of the stirrup in the main shear flow zone, mm

2

At2: area of one leg of the stirrup in the secondary shear flow zone, mm2

S₂

F1 F₂

F₁

F₂

F₂ S₁

X_{o2 X}

o1

Z₂

Z₁ V₅ V₁

X Z

S1: spacing between stirrup in the main shear flow zone, mm

S2: spacing between stirrup in the secondary shear flow zone, mm

Xo1: width of the stirrup in main shear flow zone, mm

Xo2: width of the stirrup in secondary shear flow zone, mm

Yo1: height of the stirrup in main shear flow zone, mm

Yo2: height of the stirrup in secondary shear flow zone, mm

ϴ: angle of inclination of spiral crack, degree

fty1: yield stress in the stirrup in main shear flow zone, N/mm2

fts2: stress in the stirrup in secondary shear flow zone, N/mm

2

and it can be predicted in the following equations based on the grade of concrete

𝑓𝑓𝑡𝑡𝑡𝑡2=�3.8012�𝑌𝑌_𝑌𝑌02₀₁� 2

−5.117𝑌𝑌02

𝑌𝑌01+ 2.2079� 𝑓𝑓𝑡𝑡𝑦𝑦1(24)

VI. CONCLUSIONS

Based on the test results and the modification of space truss model to include double idealized shear flow zones, the following conclusions could be carried out:

1. The torsional resistance of fibrous normal strength concrete beams is improved up to 23.7% and torsional resistance provided by reinforcements and fibre is improved up to 63.11% due to cover the idealized tension area in the range of 46.2%.

2. The value of twisting angle is improved up to 29.5% and 60.9% at crack and peak loads, respectively from the activating idealized tension zone.

3. The shear strain on concrete surface at ultimate moment is increased up to 0.03370 due to reduction of the idealized tension effective area.

4. The axial strain in the longitudinal reinforcement is increased up to 26.4% whereas the strain in transverse reinforcement is decreased up to 24.5%. Thus, the contribution of longitudinal reinforcement was increased to resist torsion in post cracking stage. 5. The proposed modified space truss model in Eq. 23 and 24 were found that it has a good agreement with test results.

ACKNOWLEDGMENT

This work was conducted as part of the doctoral studies of the first author. The PhD programme has been financially supported by Kurdistan Government Region-Iraq and UniversitiSains Malaysia, School of Civil Engineering which are gratefully acknowledged.

REFERENCES

[1] R. Narayanan and A. S. Kareem-Palanjian, "A space truss model for fibre-concrete beams in torsion," The Stucture Engineer, vol. 63B, pp. 14-19, 1985. [2] K. N. Rahal, "Torsional strength of reinforced concrete beams," Canadian Journal of Civil Engineering, vol. 27, pp. 445-453, 2000.

[3] F. R. Karim, B. H. Abu Bakar, and C. Kok keong, "Influence of fibre size on the compressive and split tensile strengths of fibrous normal strength concrete," presented at the 1st International conference on Engineering and Innovative Technology, Erbil, Kurdistan, Iraq, 2016.

[4] M. E. Kamara and B. G. Rabbat, "Torsion Design of Structural Concrete Based on ACI 318-05," 2007.

[5] F. R. Karim, B. H. Abu Bakar, C. Kok keong, and O. Q. Aziz, "Enhancement of torsional resistance in fibrous normal strength concrete beams,"

International Journal of Research in Engineering and Technology, vol. 5, 2016.

[6] C. Wang, C. G. Salmon, and J. A. Pincheira, Reinforced Concrete Design, 7 ed.: Jhon Wiley and Sons, Inc., 2007.

[7] ASTM, "Standard Test Method for Splitting Tensile Strength of Cylinderical Concrete Specimens," Annual book of ASTM standards C496/C496M,, vol. 4.02, pp. 299-303, 2006.

[8] ASTM, "Standard Test Method for Flexural Performance of Fibre-Reinforced Concrete (Using Beam With Three-point Loading," Annual book of ASTM standards C1609/C1609M,, vol. 4.02, pp. 846-854, 2010.

[9] B.EN., "Part3: Compressive strength of test specimens," BSI, vol. 12390, pp. 1-15, 2002.

[10] I. Standard, "Methods of testing bond in reinforced concrete Part 1: Pullout test," Bureau of Indian standard, vol. 2770, pp. 1-10, 2007.

AUTHORS

First Author – Karim, F.R., PhD Candidate, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia, email: f1974e1997m2004@yahoo.com.

Second Author – Abu Bakar, B.H., Professor, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia, email: cebad@usm.my.

Third Author – KokKeong, Choong, Associated Professor, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia,email: cekkc@usm.my.

Fourth Author – Aziz, O.Q., Professor, Civil Engineering Department, College of Engineering, Salahaddin University, Erbil, Iraqand email : omerqarani@gmail.com.