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

Transcription

1 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August 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 underreinforced fibrous normal strength concrete beams subjected to pure torsion. The beam sections were double 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 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 6.9%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 Taddition, 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[]. 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. RESEARCH SEGNIFICANCE 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 4% 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 and.462 at post-cracking stage. The span to depth ratio and the aspect ratio of the beam section are kept as.7 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 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August MATERIALS, MIX PROPORTIONS AND SPECIMEN PREPARATION MATERIALS AND MIX PROPORTION The fibrous normal strength concrete beams were cast for cylinder compressive strength of 2 MPa. An ordinary Portland cement (Tasik cement) was used. Crushed stone with mm maximum size of aggregate, silica sand, silica fume, tap water, HRWR superplasticizer 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 PREPARATION OF BEAM SPECIMEN Table 1:Mix proportion of fibrous normal strength concrete Materials Quality, kg/m 3 Cement (Type I) 27 Silica sand Crushed stone Silica fume 13.7 Water 2.7 Super-plasticizer VC2199. Retarder-admixture (Plastiment R) 1.37 Micro steel fibre A (21mm X.3 mmφ) 18. Micro steel fibre B (12 mm X.2 mmφ) Slump, mm 9 Φ: diameter of fibre, mm 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 13 standard hooks. The 6mm diameter bars were made stirrups with dimension 166 mm wide and 216 mm depth and the spacing between stirrups was 9 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 B-2-N B-3-N B-4-N FIBRICATION OF SPECIMENS The fibrous normal strength concrete was blended in the two pan mixer with. m 3 which obeyed the following sequence for mixing materials: granite crushed stone and silica sand were blended for 1. minutes. Then, the cement was added to the blended materials. Next, the entiremixing water and HRWR were added to the mix for another. minute. Afterwards, silica fume and retard-admixture were added to the mix for another. minutes. After that, copper coated micro steel fibre was added to the mixed materials, which was passed through the steel wire mesh during 3 minutes. The mixing process of materials was continued for an additional two minutes to confirm that the fibre was distributed uniformly in the concrete. Fibrous normal strength concrete was cast in the plywood mold with 4 layers and each layer was externally vibrated for 4 seconds in fourpoints in the length of the beam. The process of casting was associated with casting of three cubes, three cylinders, three prisms and six cubes for testing bond between reinforcement and fibrous concrete and they were vibrated for 4 seconds on vibrating table[7-]

3 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August TESTING OF BEAMS Under-reinforced fibrous normal strength concrete beams were tested under pure torsional moment. The Universal Testing Machine of 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.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 2: Detail of reinforcements in the idealized core zone

4 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August Figure 3: Schematic Test set-up Figure 4: Experimental set-up of the beams

5 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August Figure : 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 f sp, MPa f r, MPa Bond strength, MPa f bt f bl B-1-N B-2-N B-3-N B-4-N Table 4: Results of pure torsion test in fibrous normal strength concrete beams Beam denotation T cr, kn.m Ф cr, rad/m T u, kn.m Ф u, rad/m θ, degree 3.1 CRACKING TORSIONAL MOMENT B-1-N B-2-N B-3-N B-4-N The cracking torsional resistance was improved up to.76% due to additional reinforcement in idealized tension zone while the cylinder compressive strength of fibrous concrete beams were slightly changed as shown in Figure 6.

6 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August Torsional moment at cracking load, kn.m Compressive strength, MPa Ratio of area covered the idealize tension zone covered area in idealize tension zone compressive strength 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. 2 Torsional moment at ultimate load, kn.m Percentage of area covered by adding reinfocement in the idealized tension zone Figure 7: Torsional moment at peak load versus the percentage of idealized tension zone covered by the reinforcement

7 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August TWISTING 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.% and 6.9%, respectively as shown in Figure 8. 2 B-1-N B-2-N B-3-N B-4-N 2 Torsional moment, kn.m Twisting angle, rad/m 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.337. Therefore, the contribution of fibrous concrete was increased to resist torsion at crack load. 3. 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.%. 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 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. The pattern of cracks of the tested beams which were tested and failed under pure torsional moment as shown in Figures

8 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August B-1-N B-2-N B-3-N B-4-N Torsional moment, kn.m shear strain in concrete, mm/mm X -3 Figure 9: Torsional moment versus shear strain in concrete B-1-N-M.S B-2-N-MS B-3-N-MS B-4-N-MS 2 Torsional moment, kn.m Strain in stirrups, mm/mm X -3 Figure : Torsional moment versus strain in main stirrups

9 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August B-2-N-SS B-3-N-SS B-4-N-SS Torsional moment, kn.m Strain in stirrups, mm/mm X -3 Figure 11: Torsional moment versus strain in stirrup located in idealized tension zone 2 B-1-N-ML B-2-N-ML B-3-N-ML B-4-N-ML 2 Torsional moment, kn.m Strain in longitudinal reinforcement, mm/mm X -3 Figure 12: Torsional moment versus strain in main longitudinal reinforcement

10 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August B-2-N-SL B-3-N-SL B-4-N-SL 2 Torsional moment, kn.m Strain in longitudinal reinforcement, mm/mm X -3 Figure 13: Torsional moment versus strain in longitudinal reinforcement located in idealized tension zone Table :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 B-2-N B-3-N B-4-N 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 X o1, and Y o1 while the dimensions of transverse reinforcement in the secondary shear flow zone is X o2, and Y o2 as shown in Figure (18).

11 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August Figure 14: Side view of beam B-1-N at failure Figure 1: Side view of beam B-2-N at failure Figure 16: Side view of beam B-3-N at failure Figure 17: Side view of beam B-4-N at failure

12 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August Yo2 Yo1 Xo2 Xo1 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. TT 1 = VV 1. YY oo1 2 (1) TT 2 = VV 2. XX oo1 2 (2) TT 3 = VV 3. YY oo1 2 (3) TT 4 = VV 4. XX oo1 2 (4) TT = VV. YY oo2 2 () TT 6 = VV 6. XX oo2 2 (6) TT 7 = VV 7. YY oo2 2 (7) TT 8 = VV 8. XX oo2 2 (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 (2). FF 1 = AA tt1. ff tttt1 (9) FF 2 = AA tt2. ff tttt2 ()

13 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August X o1 X o2 V1 V6 V V2 Y o2 Y o1 V8 V4 V7 V3 Shear force in secondary shear flow zone Shear force in main shear flow zone From the equilibrium of vertical forces in main shear flow zone ΣFF yy + = (11) VV 4 AA tt1. ff tttt 1. nn 1 = (12) VV 4 = AA tt1. ff tttt 1. nn 1 butnn 1 = YY oo1.cccccccc SS 1 VV 4 = AA tt1. ff tttt 1. YY oo1.cccccccc SS 1 (13) Figure 19: Shear force in shear flow zones S 1 S 2 F 2 Y o2 Y o1 V 8 V 4 F 2 F 1 F 2 F 1 Y Z 2 X Z 1 Z Figure 2: Side view of longitudinal section of the beam after cracking From the equilibrium of vertical forces in secondary shear flow zone ΣFF yy + = (14)

14 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August VV 8 AA tt2. ff tttt2. nn 2 = (1) But VV 8 = AA tt2. ff tttt2. YY oo2.cccccccc SS 2 (16) Substitute V 4 and V 8 in the Eq. (13 and 16), thus TT 4 = AA tt1. ff tttt 1. YY oo1.cccccccc SS 1. XX oo1 2 (17) nn 2 = YY oo2. CCCCCCCC SS 2 TT 8 = AA tt2. ff tttt2. YY oo2.cccccccc. XX oo2 (18) SS 2 2 The total torsional resistance in one side is the summation of T 4 and T 8.Because of T 4 =T 2 and T 8 =T 6, The total torsional resistance in two long sides T h. TT h = 2. AA tt1. ff tttt 1. YY oo1.cccccccc SS 1. XX oo AA 2 tt2. ff tttt2. YY oo2.cccccccc. XX oo2 (19) SS 2 2 The total torsional resistance in short sides is T w, which is TT ww = TT 1 + TT 3 + TT + TT 7 (2) But, TT 1 = TT 3 and TT = TT 7 Thus, TT ww = 2. TT TT (21) Where, T h : torsional resistance provided by stirrups in shear flow zones in long side of the section, kn.m T w : 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 T w =T h,then, the total torsional resistance is equal to twice of Th and it can be expressed as follows: TT ss = TT h + TT ww = 2. TT h (22) TT ss = 2. AA tt1. ff tttt 1. YY oo1.xx 1 SS 1 cccccccc + 2. AA tt2. ff tttt2. YY oo2.xx 2 SS 2. cccccccc (23) S 1 S 2 F 2 X o2 X o1 V V 1 F 2 F 1 F 2 F 1 Z Z 2 X Z 1 Y Figure 21: Top view of longitudinal section of the beam after cracking Where, T s : torsional resistance provided by stirrups in shear flow zones, kn.m A t1 : area of one leg of the stirrup in the main shear flow zone, mm 2 A t2 : area of one leg of the stirrup in the secondary shear flow zone, mm 2

15 International Journal of Scientific and Research Publications, Volume 6, Issue 8, August S 1 : spacing between stirrup in the main shear flow zone, mm S 2 : spacing between stirrup in the secondary shear flow zone, mm X o1 : width of the stirrup in main shear flow zone, mm X o2 : width of the stirrup in secondary shear flow zone, mm Y o1 : height of the stirrup in main shear flow zone, mm Y o2 : height of the stirrup in secondary shear flow zone, mm ϴ: angle of inclination of spiral crack, degree f ty1 : yield stress in the stirrup in main shear flow zone, N/mm 2 f ts2 : 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 ff ssss2 = YY 2 YY YY 2 YY ff tttt 1 (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.% and 6.9% 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.337 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.%. Thus, the contribution of longitudinal reinforcement was increased to resist torsion in post cracking stage.. 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 , 198. [2] K. N. Rahal, "Torsional strength of reinforced concrete beams," Canadian Journal of Civil Engineering, vol. 27, pp , 2. [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, 216. [4] M. E. Kamara and B. G. Rabbat, "Torsion Design of Structural Concrete Based on ACI 318-," 27. [] 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., 216. [6] C. Wang, C. G. Salmon, and J. A. Pincheira, Reinforced Concrete Design, 7 ed.: Jhon Wiley and Sons, Inc., 27. [7] ASTM, "Standard Test Method for Splitting Tensile Strength of Cylinderical Concrete Specimens," Annual book of ASTM standards C496/C496M,, vol. 4.2, pp , 26. [8] ASTM, "Standard Test Method for Flexural Performance of Fibre-Reinforced Concrete (Using Beam With Three-point Loading," Annual book of ASTM standards C169/C169M,, vol. 4.2, pp , 2. [9] B.EN., "Part3: Compressive strength of test specimens," BSI, vol. 1239, pp. 1-1, 22. [] I. Standard, "Methods of testing bond in reinforced concrete Part 1: Pullout test," Bureau of Indian standard, vol. 277, pp. 1-, 27. AUTHORS First Author Karim, F.R., PhD Candidate, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia, f1974e1997m24@yahoo.com. Second Author Abu Bakar, B.H., Professor, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia, cebad@usm.my. Third Author KokKeong, Choong, Associated Professor, School of Civil Engineering, UniversitiSains Malaysia, Pulau Pinang, Malaysia, cekkc@usm.my. Fourth Author Aziz, O.Q., Professor, Civil Engineering Department, College of Engineering, Salahaddin University, Erbil, Iraqand omerqarani@gmail.com. Correspondence Author Karim, F.R., f1974e1997m24@yahoo.com, alternate f1974e1997m24@gmail.com,phone:+6-()