a study on the flexural behaviour of glass fiber ...

A National Conference on Innovative World of Concrete ICI-IWC 2013

A STUDY ON THE FLEXURAL BEHAVIOUR OF GLASS FIBER REINFORCED SELF COMPACTING CONCRETE Dr.M.L.V. Prasad 1, Dr. P. Rathish Kumar 2, M. Sri Rama Chand 3 1. 2. 3.

Assist. Executive Engineer, I& CAD Department, Irrigation Circle, Kurnool, A.P, India. Associate Professor, Department of Civil Engineering, NIT, Warangal, A.P, India. Master’s Student, Department of Civil Engineering, NIT, Warangal, A.P, India.

ABSTRACT This paper presents flexural behaviour of statically determinate Glass Fiber Reinforced Self Compacting Concrete (GFRSCC) beams, taking into consideration, the confinement offered by lateral ties to concrete in compression zone. A confinement model was developed based on the axial compressive strength studies on Tie Confined GFRSCC prisms. The confinement model thus developed from the investigation was used as a stress block for confined GFRSCC to generate the complete analytical Moment-Curvature behaviour. The Moment-Curvature behaviour obtained using the selected confinement model was compared with experimental results. It was observed that there was a considerable change in the values of moment curvature due to the addition of glass fiber. The benefit was clearer in case of glass fiber based SCC beams. The result obtained from the predicted model is close to the experimental values. Keywords: Self Compacting Concrete, Glass Fiber, Confinement, Stress Block Parameters and Moment – Curvature.

INTRODUCTION Self Compacting Concrete (SCC) is a special concrete aimed at improving the quality and efficiency of the building industry. SCC is a highly flowable, stable concrete which flows readily into place, filling formwork without any consolidation and without undergoing any significant segregation (1, 2). The presence of micro-cracks at the mortar aggregate interface is responsible for the inherent weakness of plain concrete and results in poor ductility. This weakness can be rectified by the inclusion of the fibers in the mix. The fibers help to transfer loads at the internal micro-cracks. Such concrete is popularly known as Fiber Reinforced Concrete (FRC). The construction of modern structures calls for the attention of the use of materials with improved properties in respect of strength, stiffness, toughness and durability (3). The fact that the inclusion of fibers is more beneficial in improving the crack resistance, flexural strength and energy absorption capacity of concrete, rather than other properties, is well established (4).

RESEARCH SIGNIFICANCE The most fundamental requirement in predicting the behaviour of Fiber Reinforced Self Compacting Concrete (FRSCC) is the knowledge of stress-strain behaviour of the constituent materials. As concrete is basically used to resist compression, the knowledge of its behaviour in compression is very important. If the behaviour of unconfined and confined concrete in uniaxial compression is known, its flexural behaviour can be predicted. The addition of fibers in the presence of lateral ties was found to improve the deformation characteristics and especially the integrity of concrete (4). Therefore, over the few decades, a considerable volume of research has been directed towards generating stress-strain relationships of compressed concrete both in confined and unconfined condition. In the present work the M – ø behaviour of GFRSCC is proposed based on the analytical model developed for the material in compression. The flexural behaviour of this material is then validated. This will help the designers to use the stress-strain behaviour and flexural behaviour of SCC with Glass Fiber inclusions. From the axial compressive studies on GFRSCC, the stress – block parameters for confined concrete without and with fiber were obtained and an analytical model suiting the behaviour is proposed. The validation of this analytical model was then done by casting and testing beams in flexure.

FIBER REINFORCED SELF COMPACTING CONCRETE


Fresh SCC must possess the key properties including filling ability, passing ability and resistance to segregation at required level. To satisfy these conditions EFNARC (5) has formulated certain test procedures. The slump flow equipment (Fig.1) is currently widely used in concrete practice, and the method is very simple and straightforward. Thus the slump flow combined with T50 was selected as the first priority test method for the filling ability of SCC. The V-funnel (Fig.2) or Orimet tests are recommended as second priority alternatives to the T50 measurement. The passing ability of fresh SCC can be tested by L-box (Fig.3).

Fig.1 H- Flow (Slump Cone)

Fig.2 V-Flow (V-Funnel)

Fig.3 Passing Ability (L-Box)

The characteristics and performance of Fiber Reinforced Concrete (FRC) change depending on the properties of concrete and the fibers. The properties of fibers that are usually of interest are fiber concentration, fiber geometry, fiber orientation, and fiber distribution. Glass and Glass fibers have various applications in concrete like crack control, prevent coalescence of cracks, and to change the behaviour of the material by bridging of fibers across the cracks. In other words, ductility is provided with fiber reinforced cementitious composites because fibers bridge crack surfaces and delay the onset of the extension of localized crack. FRSCC must possess the basic properties to satisfy the conditions as per EFNARC (5) specifications. The details of mix proportions adopted in the present study designed as per Nansu (6) method of mix design are shown in Table-2 and the fresh properties of SCC and GFRSCC are shown in Table 3. Companion cube specimens of standard dimensions 150mm x 150mm were also cast and tested for the strength. The results of the compressive strength are presented in Table 3. Table 2: Details of Mix Proportions for M40 grade concrete. Grade Fly– Glass Cement C.A F.A Water S.P VMA S.No Designaiton of Ash Fiber kg kg kg (lit) (lit) lit Concrete kg (kg) 1

SCC

M40

412

781

913

138

0.0

193

13.75

0.46

2

GFRSCC

M40

412

781

913

166

1.00

193

16.0

0.48

Table 3: Fresh and Hardened Properties of SCC with Glass Fiber. Slump Cone Test Sl. No.

Designaiton

HFlow (mm)

T50 (time in Sec)

V Funnel Test Time for complete discharge Sec

L Box Test

T5 min in Sec

Time for 0200 mm spread

Time for 0- 400 mm spread

H2/H1

Comp. Strength (Mpa)

1 SCC

710

4.12

6.79

9.00

2.56

5.00

0.91

52.90

2 GFRSCC

675

4.61

10.50

13.20

3.00

6.11

0.82

54.26

ANALYTICAL STRESS – STRAIN MODEL FOR CONFINED FIBER REINFORCED SELF COMPACTING CONCRETE


A structural reinforced concrete member can be theoretically analyzed if the stress-strain behaviour of its constituent materials i.e. steel and concrete is known. Stress strain relation of steel is not a big problem as there is very less material variation compared to that of concrete. Concrete being produced at site has very high uncertainty; moreover, there is significant variation in the behaviour of SCC. Also, there is much variation in behaviour of confined and unconfined concrete as well. The developed stress – strain relationship is adopted to predict the behaviour of Confined Fiber Reinforced Self Compacting Concrete (CFRSCC). The stress-strain model developed by M.L.V.Prasad & P.Rathish Kumar (7) was used here. The Confinement index (Ci), Fiber index (Fi) were taken as the parameters, which includes all factors affecting the behaviour of concrete confined with lateral ties and fibers. The factors considered were concrete strength, spacing, strength, percentage of fibers and arrangement of ties, limiting pitch of ties and the core area. The equation for stress-strain curve as per the existing model proposed by Saenz is given as: A  --------------------------------------- (1) f  2

1  B   C  

Where ,



f

= Stress in Fiber Reinforced Confined concrete, = Strain in Fiber Reinforced Confined concrete. 1

1

fu

A = A1 (  u ), B= B1 (  u ), C = C1 (  u ) , A1 = 2.866, B1= 0.866, C1= 1.0 (for Ascending Portion) and A1= 1.206, B1= -0.794, C1= 1.0 (for Descending Portion). 2

where,

fu

= peak stress of confined prism,

 u = strain at peak stress of confined prism.

The increase in strength and strain at peak stress is given by: fu u  (1  0.866 C i )(1  0.101 Fi )  (1  3.761Ci )(1  0.407 Fi ) f' ' here,

f ' = Strength of plain SCC prism (Unconfined),  ' = strain at peak stress of unconfined SCC prism Ci  ( Pb  Pbb )

Confinement Index

fv f c'

b -------------------------------------- (2) s

where, Pb = Ratio of the volume of the binder to the volume of the confined concrete based on the mean lateral dimension of the binder, Pbb =Ratio of the volume of the binder to the volume of the confined concrete, when the pitch of the binder is equal to 1.2 times the least lateral dimension of the specimen, b is the breadth of the prism and s is the spacing of ties. The stress in the steel binder is given by f v   v .E s and is always limited to maximum yield strength.  v and E s are the strains and modulus of elasticity of the binder steel. Here, binder refers to the lateral steel reinforcement. Fiber Index (Fi ) =

Weight fraction of fibre (Wf ) x Aspect ratio of fiber(l/d)

----------------(3)

From the stress- strain behaviour it was noted that a single equation cannot predict the complete behaviour of GFRSCC. Hence it is proposed to give two separate equations based on Saenz’s model for ascending and descending portion of the stress-strain curve separately. The same is shown in equations given below, where f is the Stress in Confined concrete.

f  fu

2.866 ( 

u ) 2

f  fu

1.206 ( 

----------- (4 & 5)

u ) 2

    ANALYTICAL 1  0.866 (  MOMENT )  1.0  CURVATURE (M 1  -) 0.794RELATIONSHIP (  )  1.0 

u

   u

u

   u


Based on the above developed analytical model for the behaviour of GFRSCC in compression, it is now proposed to predict the analytical M – ø behaviour of GFRSCC. In deriving the expressions of the moments and curvatures for concrete section confined with rectilinear ties, the assumptions followed for the normal vibrated concrete are followed here also. In addition to the three basic relationship viz., (i) Equilibrium of forces, (ii) compatibility of strains and (iii) Stress-strain relationship of the materials have to be satisfied.

Fig.4 Stress – Strain distribution of a member in flexure From the above diagram; b = width of the beam, d = effective depth of the tension steel,

nd = neutral axis depth, fc=stress in

extreme compression fiber, εc = extreme compression fiber strain, εs = steel strain and γ & α are reduction factors for distance between CG from neutral axis and area under stress-strain curve respectively. Compressive force (Cc)

CC 

b.nd

c





f d

-----------------------------(6)

o

and, moment of compressive force (Cc) about neutral axis (Mc)

MC

 nd  b    c

   

2C

 o

f . .d --------------------------(7)

Thus, if the area under concrete stress-strain curve and moment of area under the stress-strain curve is known the compressive force (Cc) and its moment about neutral axis (Mc) can be evaluated. For obtaining the complete moment–curvature relationship for any cross-section, discrete values of concrete strains ( εc) were selected such that even distributions of points on the plot, both before and after the maximum were obtained. The procedure used in computation is given below: 1. The extreme fiber concrete compressive strain ( εc) was assumed. In present study the values of εc was in the range of 0.0001 to the failure strain (ie 0.01). 2. The neutral axis depth, nd, was assumed initially as 0.5 times the effective depth (i.e. 0.5d) 3. For this value of neutral axis depth, the compressive force in the concrete, ‘Cc’ was calculated from the respective stress-strain model developed by the authors. 4. The strain in tension and compression steel was calculated, based on the strain compatibility. 5. Based on the strains in tension steels. The corresponding stresses were taken from stress- strain curve of steel. 6. The total tensile force (T) in tensile steel was calculated. 7. Same process was repeated for compressive steel to calculate the compressive force (Cs) in compression steel. 8. The total compressive force C acting in the section was calculated as C = Cc + Cs. 9. If C = T, then the assumed value of neutral axis depth (nd) was correct, and the moment (M) and the corresponding curvature (φ) was calculated. Otherwise, the neutral axis depth was modified until the condition C = T was achieved. Now, the total moment about the N.A. was given by; M = Mt (moment of force in tensile steel about the neutral axis) + Mc (moment of Compressive force in


Concrete about the neutral axis) + Mcs (moment of force in Compression steel about the neutral axis) + Mf (moment of force due to fibers). The corresponding curvature () was given by;



c

nd

------------------------------------- (8)

EXPERIMENTAL PROGRAMME An experimental program was designed to validate the above analytical procedure suggested for obtaining the Moments and corresponding Curvatures. The experimental programme consisted of casting four beams of M40 grade concrete strength, without and with fiber. For each grade, without fiber underreinforced beams (WFUR) and over reinforced (WFOR) beams were cast and tested. Similarly with fiber based under-reinforced beams (GFUR) and over reinforced (GFOR) beams were cast and tested. The details of the beams are given in Table 4. The balanced reinforcement required for a particular strength of concrete was arrived based on the stress–strain curve as suggested by IS 456: 2000(10), without considering the partial safety factors.

400

mm Fig.5: Schematic sketch of the test set up The size of the beam was 120mm × 200mm × 1800mm, with an effective span of 1600mm. 53 grade OPC cement conforming to IS 12269:1987(11), Zone II sand and 20 mm well graded coarse aggregate confirming to IS-383: 1970(12) was used in the study for casting all the beams. Potable water was used for mixing as well as curing of concrete. 8mm diameter steel was used for stirrups. The spacing of 75 mm, 50 mm was provided for M40 grade with and without fibrous concrete to prevent the shear failure of beams. The beams thus cast were tested under two-point symmetrical loading, with constant moment zone of 400 mm, in order to ensure the flexural failure. The schematic sketch of test setup is given in Fig.5. Table 4: Details of SCC and GFRSCC Beams Tested Designation

M40 grade without fiber M40 grade With Glass fiber

Beam

Top Bar

WFUR2

2-4 mm

WFOR2

2-4 mm

WGUR2

2-4 mm

WGOR2

2-4 mm

Bottom Bar 2-16 mm 2-16 mm 2-20 mm 2-16 mm 2-16 mm 2-20 mm

Required Steel (mm 2)

Provided Steel (mm2) 402

8 mm Stirrups Spacing 75 mm

757.00

1030

50 mm

402

75 mm

1030

50 mm

757.00


COMPARISON OF ANALYTICAL AND EXPERIMENTAL BEHAVIOUR The predicted moment curvature obtained using the proposed confinement model was compared with the experimental moment curvature data both graphically and numerically. Fig 7 and 8 shows graphical comparison of the moment curvature behaviour. For the numerical comparison three significant points were chosen namely; ultimate moment and corresponding curvature (Mu and φu ), moment and corresponding curvature at 85 % of the ultimate moment in ascending portion (M0.85a and φ0.85a ) and the moment and corresponding curvature at 85% of the ultimate moment in descending portion (M0.85d and φ0.85d ). The experimental strain in concrete ( εc ) and steel ( εs ) at the above mentioned points and their corresponding moment and curvature values were taken as the comparison criteria. Fig 6 & 7 show the M – ø relationship for the cases of without and with fiber respectively for under reinforced and over reinforced SCC beams. ANA-NBGUR

80

ANA-NBWUR

80

EXP-NBGUR

EXP-NBWUR 70

70

ANA-NBWOR

ANA-NBGOR EXP-NBGOR

60

60

50

50

Moment(kN-m)

Moment (kN-m)

EXP-NBWOR

40 30

40 30

20

20

10

10

0

0

0

25

50

75

100

125

150

175

Curvature x 10

200

225

250

275

300

0

25

50

75

100

-6

125

150

175

Curvature x 10

Fig6: M40 Grade without Fiber (UR & OR)

200

225

250

275

300

-6

Fig 7: M40 Grade with Glass Fiber (UR & OR)

Table 5: Comparison of Experimental and Analytical values of Moment and Curvature at ultimate of Simply Supported SCC Beams Experimental Analytical Values M ana  ana M Ø Єc Єs M Ø Єc Єs x x M exp exp Beam (kN-m) 10-6 x 10-6 x 10-6 (kN-m) 10-6 x 10-6 x 10-6 NBWUR 29.51 69.96 2791.27 5954.18 25.24 58.89 3300 5807.39 0.86 0.84 NBWOR 65.42 62.51 5752.18 1748.91 57.53 53.09 5700 1640.4 0.88 0.85 NBGUR 33.52 92.4 2926.00 8624.00 29.51 72.72 3700 8589.49 0.88 0.79 NBGOR 68.9 75.2 6008.00 3016.00 65.36 63.45 6000 3123.75 0.95 0.84 Average 0.89 0.830 % Mean error 10.75 16.95 Table 6: Comparison of Experimental and Analytical values of Moment and Curvature at 0.85 Ascending of Simply Supported SCC Beams Beam Experimental 0.85 ascending Analytical Values 0.85 ascending Єc

Єs

x 10-6

x 10-6

25.3

39.6

NBWOR

52.99

NBGUR

28.3

NBGOR

58.4

M (kNm) NBWUR

M ana M exp

 ana exp

3981.35

0.962

0.998

4800

1448.75

0.985

0.895

2000

2905.15

0.940

0.873

19000

1300.9

0.840

1.224

average % Mean error=

0.93

0.99 11.45

Ø x 10-6

Єc

Єs

x 10-6

M (kNm)

x 10-6

x 10-6

1104

3846

24.35

39.54

2700

41.92

4821.03

1087.37

52.18

37.53

33.27

1345.45

2813.64

26.61

29.03

28.8

1872

1584

49.03

35.24

Ø

6.83


Tables 5,6 and 7 show the experimental moments, corresponding curvatures, strains in steel and concrete at ultimate moment, 85 % of the ultimate moment in ascending portion and 85 % of the ultimate moment in descending portion. The experimental and analytical values thus obtained were used for the numerical comparison. The ratio of analytical/experimental values was calculated at all the significant points. The average of analytical to experimental ratios and mean error in prediction was taken for the comparison. Tables 5, 6 and 7 show a comparison of moment and corresponding curvature at the three significant points for the predicted model. The average and mean error in the prediction is also listed at the bottom of each table Table 7: Comparison of Experimental and Analytical values of Moment and Curvature at 0.85 Descending of Simply Supported SCC Beams Beam Experimental 0.85 descending Analytical Values 0.85 descending M Ø Єc Єs M Ø Єc Єs M ana  ana (kN(kN-6 -6 -6 -6 -6 -6 M exp exp m) x 10 x 10 x 10 m) x 10 x 10 x 10 NBWUR 25.10 155.53 3426.50 16014.36 25.48 133.21 6100 16412.6 1.02 0.86 NBWOR 55.54 164.90 12428.18 7360.91 59.51 126.47 12500 6871.22 1.07 0.77 NBGUR 28.30 163.24 6826.72 13577.82 30.83 135.68 5000 13842.91 1.09 0.83 NBGOR 58.88 147.02 13714.36 3927.82 65.80 122.31 13700 5294.35 1.12 0.83 Average 1.07 0.82 % Mean error= 7.33 17.84

DISCUSSION The analytical moments and curvatures corresponding to the experimental strains in concrete and steel were considered for comparison. In general, it was noticed that strain in steel was the governing criteria in under-reinforced self compacting concrete, while it was the concrete strain in over-reinforced self compacting concrete. Even in glass fiber reinforced concrete beams it was noticed that strain in steel was the governing criteria in under-reinforced self compacting concrete beams, while it was the concrete strain in over-reinforced self compacting concrete beam and the effect of fiber is more on curvature values when compared to non fibrous beams. A comparison of the analytical moment and curvature obtained using the predicted model with the experimental moment curvature is studied. To validate the analytical results quantitatively the analytical/experimental ratios were obtained for the proposed model regarding ultimate moment and corresponding curvature ( Mu and Øu), 85% of ultimate moment and corresponding curvature in ascending portion (M0.85a and Ø0.85a) and 85% of ultimate moment and corresponding curvature in descending portion(M0.85d and Ø0.85d). a) Ultimate Moment and Corresponding Curvature Table 5 shows the comparison of ultimate moment and corresponding curvature for the predicted analytical model under consideration. The average mean error value of peak moment predicted by proposed analytical model is close to 10.75% and while it is 16.95% in case of curvature. b) 85% of Ultimate Moment and Corresponding Curvature in ascending portion Table 6 shows the comparison of 85% of ultimate moment and corresponding curvature in ascending portion for the proposed analytical model under consideration. The average value of mean error at 85% of ultimate moment in ascending portion predicted by the proposed model was close to 6.83%. In general, proposed model underestimated the value of curvature corresponding to 85% of ultimate moment in ascending portion. The mean error prediction made by the proposed model for curvature corresponding to 85% of ultimate moment in ascending portion was 11.45%. c) 85% of Ultimate Moment and Corresponding Curvature in descending portion Table 7 shows the comparison of 85% ultimate moment and corresponding curvature in descending portion for the proposed model under consideration. The proposed model showed a mixed result while predicting the 85% of ultimate moment in descending portion. The prediction of 85% of ultimate moment in descending portion by the proposed model was with a mean error closer to 7.33%. The selected model underestimated the value of curvature corresponding to 85% of ultimate moment in the descending portion. The model underestimated the value of curvature corresponding to 85% of the ultimate moment in the descending portion and had a higher value of mean error of 17.84%.


CONCLUSIONS From the studies on the Glass Fiber Reinforced Self Compacting Concrete the following conclusions can be drawn. 1) The toughness and ductility of the glass fiber reinforced self compacting concrete beams increased with an increase in the fiber content. The ductility ratio is greater with optimum dosage of fiber in fiber-reinforced concrete beams compared to non fiber-reinforced beams. Addition of fiber increases both the ductility and energy absorption capacity. 2) The proposed analytical expressions using analytical model, for moment–curvature relationship, load–deflection response provided good comparison between the predicted and experimental results for self compacting concrete beams containing glass fiber. 3) An analytical model is proposed for predicting the moment - curvature behaviour for flexural beams. It can be observed that the model incorporates the method for evaluating the strain and the corresponding stress in transverse steel at peak confined concrete strength. This is more efficient in predicting the overall Moment-Curvature behaviour. 4) The average mean error value of peak moment predicted by the proposed model was close to 11% and curvature corresponding to the ultimate moment had a mean error of around 17%. 5) The average mean error value of 85% of ultimate moment in ascending portion predicted by the proposed model was close to 7% and curvature corresponding to the 85% of ultimate moment in ascending portion had a mean error of around 12%. 6) The average mean error value of 85% of ultimate moment in Descending portion predicted by the proposed model was close to 7% and curvature corresponding to the 85% of ultimate moment in descending portion had a mean error of around 18%.

REFERENCES 1) Okamura.H & Ozawa.K(1995), Mix design for Self-Compacting, concrete library of JSCE, pp107-120. 2) H.J.H.Brouwers and H.J. Radix (2005), Theoretical and experimental study of Self-Compacting Concrete, Cement & Concrete Research, 9, pp 2116–36. 3) Mustafa Sahmaran and I. Ozgur Yaman (2005), Hybrid fiber reinforced self-compacting concrete with a high-volume coarse fly ash, Elsevier Science Publishers, PP 109-126. 4) P.Rathish Kumar and M.L.V. Prasad (2007), Fresh and Hardened Properties of Glass and Polypropylene Fiber Reinforced Self Compacting Concrete, 2nd National Conference on Current Trends in Technology, Ahmedabad Nov 29th - Dec 1st. PP 210-215. 5) EFNARC (2002), Specifications and Guidelines for Self-Compacting Concrete, Association House, 99 West Street, Farnham, UK. 6) Nan Su, K.C.Hsu, H.W.Chai (2001), A Simple mix design methods for Self compacting concrete, Cement and Concrete Research 2001, PP 1799 – 1807. 7) M.L.V.Prasad and P.Rathish Kumar (2009), Development of analytical stress-strain model for glass fiber reinforced self compacting concrete, International Journal of Mechanics and Solids, Research India Publications. Vol 4, No.1, pp 25-37, ISSN 0973-1881. 8) P.Rathish Kumar and M.L.V.Prasad(2011), Structural Behaviour of a Tie Confined Self Consolidating Performance Concrete (SCPC) under Axial Compression, RILEM International Conference, Hong Kong University of Science & Technology, Hong Kong, September 5th – 7th . 9) M.L.V.Prasad and P.Rathish Kumar( 2012), A Study on Tie Confined Glass Fiber Reinforced Self Compacting Concrete (TCGFRSCC), International Conference on Recent Advances in Engineering, Technology and Management (SPICON2012), Mumbai ,India, May 31 to June 02. 10) IS: 456(2000), Code of practice for plain and reinforced concrete. Bureau of Indian Standards. 11) Indian Standard Code IS: 12269(1987), Specifications for 53 Grade Ordinary Portland cement. 12) Indian Standard Code IS: 383(1970), Specification for coarse and fine aggregates from natural sources for concrete.