shear resistance of high strength concrete beams without

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 1, No 1, 2010

© Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN 0976 – 4399

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Shear Resistance of High Strength Concrete Beams Without Shear Reinforcement

Sudheer Reddy.L 1 , Ramana Rao .N.V 2 , Gunneswara Rao T.D 3 1. Assistant Professor, Faculty of Civil Engineering, Kakatiya Institute of Technology and

Science, Warangal 2. Professor and Principal, Faculty of Civil Engineering, Jawaharlal Nehru Technological

University, Hyderabad 3. Assistant Professor, Faculty of Civil Engineering, National Institute of Technology (NITW),

Warangal [email protected]

ABSTRACT

The use of high strength concrete in major constructions has become obligatory, whose mechanical properties are still at a research phase. This paper deals with the review of available data base and shear models to predict the shear strength of reinforced concrete beams without web reinforcement. An attempt has been made to study shear strength of high strength concrete beams (70 Mpa) with different shear span to depth ratios (a/d = 1, 2, 3 & 4) without web reinforcement and compare the test results with the available shear models. Five shear models for comparison are considered namely, ACI 318, Canadian Standard, CEPFIP Model, Zsutty Equation and Bazant Equation. The results revealed that the most excellent fit for the test data is provided by Zsutty’s Equation and a simplified equation is proposed to predict the shear capacity high strength concrete beams without shear reinforcement.

Keywords: Highstrength Concrete, Shear, Shear span to Depth Ratio (a/d).

1. Introduction Use of high strength concrete in construction sector, has increased due to its improved mechanical properties compared to ordinary concrete. One such mechanical property, shear resistance of concrete beams is an intensive area of research. To Estimate the shear resistance of beams, standard codes and researchers all over world have specified different formulae considering different parameters into consideration. The parameters considered are varying for different codes and researchers leading to disagreement between researchers, making it difficult to choose an appropriate model or code for predicting shear resistance of reinforced concrete. Therefore an extensive research work on shear behavior of normal and high strength concrete is being carried out all over the world. The major researchers include Bazant Z.P. [1], Zsutty T.C, [2] Piotr Paczkowski [3], JinKeun Kim [4], and Imran A. Bukhari [5] and many more. Estimation of shear resistance of high strength concretes is still controversial therefore it’s a thrust area for research.

The shear failure of reinforced concrete beams without web reinforcement is a distinctive case of failure which depends on various parameters such as shear span to effective depth ratio (a/d), longitudinal tension steel ratio (ρ), aggregate type, strength of concrete, type of loading, and support conditions, etc. In this research, shear spantoeffective depth ratio is taken as main



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variable keeping all other parameters constant. Most of the researchers concluded that failure mode is strongly dependent on the shear

span to depth ratios (a/d). Berg [6], Ferguson [7], Taylor [8], Gunneswara Rao [9], found that shear capacity of reinforced concrete beams varied with a/d ratio.

2. Objectives • To study the shear response of concrete beams with out shear reinforcement varying

shear span to depth ratio (a/d) from 1 to 4 (1,2,3 & 4). • To compare the shear formulae formulated by eminent codes with the experimental test

data. • To propose a simplified formula to predict shear strength of HSC beams with out shear

reinforcement.

3. Research Significance This paper provides the test data related to behaviour of HSC beams in shear. The data is useful for developing constitutive models for shear response of structural elements where high strength concrete is used.

4. Experimental Programme Eight reinforced high strength concrete beams were cast and tested, under two point loading varying the shear span to effective depth ratio (a/d). The test specimens are divided into four series. Each series consisted of two high strength concrete beams with out shear reinforcement with a/d ratio 1, 2, 3 & 4. For all the series, the parameters viz., concrete proportions and percentage of longitudinal steel were kept constant. The details are listed in the Table 1 below:

Table 1: Reinforced beams without shear reinforcement

Serial No

Beam Designation

Length of beam (m)

a/d Ratio

No. of Beams

1 R01 0.7 1 2 2 R02 1.0 2 2 3 R03 1.3 3 2 4 R04 1.6 4 2

4.1 Test Materials

4.1.1 Cement Ordinary Portland cement whose 28 day compressive strength was 53Mpa was used.

4.1.2 Fine Aggregate Natural River sand confirming with specific gravity is 2.65 and fineness modulus 2.33 was used.



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4.1.3 Coarse Aggregate Crushed Coarse aggregate of 20mm and 10 mm procured from local crusher grading with specific gravity is 2.63 was used.

4.1.4 Water Portable water free from any harmful amounts of oils, alkalis, sugars, salts and organic materials was used for proportioning and curing of concrete.

4.1.5 Super plasticizer In the present experimental investigations naphthalene based superplasticizer conplast337 was used for enhancing workability.

4.1.6 Fly Ash: Class F fly ash was used acquired from KTPS, Kothagudam, Andhra Pradesh, India.

4.1.7 Ground Granulated Blast Furnace Slag The slag was procured from Vizag. The physical requirements were confirming to BS: 6699.

4.1.8 Tension Reinforcement 16 mm diameter bars were used as tension reinforcement whose yield strength was 475Mpa.

4.2 Mix Design The high strength concrete mix design was done using Erntroy and Shacklock method. By conducting trial mixes and with suitable laboratory adjustments for good slump and strength the following mix proportion was arrived as shown in Table 2

Table 2: Mix Proportion of Concrete

Cement (Kg)

Fine Aggregate (Kg)

Coarse Aggregate (Kg)

Water (lit)

Fly Ash (By Wt. of Cement)

GGBS (By Wt. of Cement)

Super Plasticizer (By wt. of Cement)

520 572 1144 130 5% 15% 1.5% . 4.3 Specimen details Tests were carried out on sixteen beams, simply supported under two point loading. All the beams had constant cross section of 100mm x 150mm illustrated in Fig 1. The length of beam was worked out to be 0.7m, 1.0m, 1.2m and 1.6m for corresponding a/d ratio = 1, 2 , 3 & 4 respectively. All the four series of beams were provided with 3 – 16 mm diameter HYSD bars as longitudinal reinforcement to avoid any possible failure by flexure and the grade of concrete was kept constant.

4.4 Test Procedure



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The beams were tested under two point loading on 100 Ton loading frame. The test specimen was simply supported on rigid supports. Two point loads were applied through a rigid spread beam. The specimen was loaded using a 100 ton jack which has a load cell to monitor the load. Based on the shear span to depth ratio, the support of the spread beam was adjusted. Two LVDT’s were provided, one at the centre of the span and other at the centre of the shear span to measure deflections

Figure 1: Details of test beams with arrangement of loads and supports

. The load and deflections were monitored for every 5 seconds. The load that produced the diagonal crack and the ultimate shear crack were recorded. Crack patterns were marked on the beam. The average response of two beams tested in a series, was taken as the representative response of the corresponding series. The test set up is presented in figure 2.

Figure 2: Beam and LVDT arrangement in 100 ton loading Frame

0.15m

Span of the beam (L) (0.7m, 1.0m, 1.3m, 1.6m)

0.1m

P

0.1 a 0.2 a 0.1



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5. Different Models to predict shear capacity Comparative analysis is made for well known shear models which are used to calculate shear resistance of beams without web reinforcement. The following equations are used:

• ACI code Equation. • Canadian Equation. • CEPFIP Model. • Zsutty Equation. • Bazant Equation.

5.1 Shear Design by ACI code Equation According to ACI Building Code 318 [9], the shear strength of concrete members without transverse reinforcement subjected to shear and flexure is given by following equation

……… (1)

……………… (1a)

Compressive strength of concrete at 28 days in MPa. bwd Width and depth of Effective cross section in mm. MuVu – Factored moment and Factored shear force at Cross section. ρ – Longitudinal Reinforcement Ratio.

Many researchers [10] have expressed certain imperfections in the Eq (1), as it underestimates the effect of shear span to depth ratio on shear resistance.

5.2 Shear Design by Canadian Equation According to Canadian Standard [11], the shear strength of concrete members is given by following equation

(N)………………………………………. (2) Compressive strength of concrete at 28 days in MPa.

bwd Width and depth of Effective cross section in mm.

The Canadian standard in Eq (2) has not considered the effect of shear span to depth ratio and longitudinal tension reinforcement effect on shear strength of concrete.

5.3 Shear Design by CEP – FIP Model According to CEP – FIP Model [12], the shear strength of concrete members is given by following equation



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(N)……… (3)

Compressive strength of concrete at 28 days in Mpa. bwd Width and depth of Effective cross section in mm. a/d – Shear span to Depth ratio. ρ – Longitudinal Reinforcement Ratio.

The CEP – FIP model as formulated in Eq (3) takes into formula, the size effect and longitudinal steel effect, but still underestimates shear strength of short beams.

5.4 Shear Design by Zsutty Equation Zsutty (1968) [2] has formulated the following equation for shear strength of concrete members

……….. (4)

……………….. (4a) Compressive strength of concrete at 28 days in MPa.

bwd Width and depth of Effective cross section in mm. a/d – Shear span to Depth ratio. ρ – Longitudinal Reinforcement Ratio.

Most of researchers suggested that Zsutty equation is more appropriate and simple to predict the shear strength of both shorter and long beams as it takes into account size effect and longitudinal steel effect.

5.5 Shear Design by Bazant Equation Bazant (1987) [1] has formulated the following equation for shear strength of concrete members

d (N)……. (6)

Compressive strength of concrete at 28 days in MPa. bwd Width and depth of Effective cross section in mm. a/d – Shear span to Depth ratio. ρ – Longitudinal Reinforcement Ratio.

The Eq (6) stated by Bazant (1987) to predict shear strength of concrete members looks complicated, but takes into account all the parameters involved in predicting the shear strength of concrete members.

6. Discussion on Test Results



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Comparison of the experimental results (Table 3 with ACI code [Eq 1] , Canadian Code[Eq 2], CEPFIP model[Eq 3], Zsutty Equation[Eq 4] and Bazant equation[Eq 5] ) reveals that a/d ratio significantly effects the shear capacity of the high strength concrete beams. Most of the equations are under estimating the shear capacity at lower a/d ratios. When the a/d ratio is less than 2.0, strut action prevails and the shear resistance is very high. For a/d ratios up to 2 the experimental values showed remarkable increase in shear strength compared to various design approaches. Only predicted shear capacity using Zsutty Equation for a/d ratio up to 2 were closer to experimental values. For a/d ratios 2 to 4 almost all the models predicted values of shear force were fair and were closer to experimental values where arch action prevails.

The results tabulated in Table 3 and comparison illustrated in Figure 3, the discussion may be concluded as follows:

• ACI code underestimates the shear capacity of high strength concrete beams without web reinforcement.

• Canadian code has not taken into account the effect of shear span to depth ratio. The shear resistance of HSC member predicted based on Canadian code, under estimates the actual shear capacity of member at all a/d ratios.

• Shear capacity of the HSC members predicted based on CEP FIP model, showed lower values at all a/d ratios.

• Shear resistance of HSC members using Zsutty Equation closely predict the shear capacity of high strength concrete beams without web reinforcement.

• The shear capacity calculated using Bazant equation indicate that the equation moderately under estimates the shear capacity of HSC beams.

Table 3: Predicted and Experimental Results Vpredicted (kN)

Beam ID MPa

a/d Vexp (kN)

ACI CODE

CAN CODE

CEP FIP

MODEL

ZSUTTY EQ

BAZANT EQ

R01 70 1 129 35.36 24.19 51.75 131.79 62.90 R02 70 2 78.5 27.36 24.19 41.08 52.31 32.51 R03 70 3 55.5 24.69 24.19 35.89 36.56 28.35 R04 70 4 42.5 23.35 24.19 32.61 33.22 27.14



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0

20

40

60

80

100

120

140

0.0 1.0 2.0 3.0 4.0 5.0

a/d Ratio

Shear F

orce (kN)

ACI CAND CEBFIP ZSUTTY BAZANT EXP VAL

Figure 3: Influence of a/d on shear resistance

The variation of deflection with load of HSC beams without shear reinforcement for a/d = 1, 2, 3, and 4 are shown in Fig 4, which indicate the increase in a/d ratio has shown reduction in shear capacity of the beam. At lower a/d ratios the ultimate load was observed to be more than twice at diagonal cracking. The deflections increased with a/d ratio, which signify that at lower a/d ratios i.e. up to 2 the strut behavior and above 2 the arch behaviour of the beams. At lower a/d ratios (up to 2), the failure was observed to be sudden compared to failure pattern observed for higher a/d ratio (a/d – 2 to 4).

0

50

100

150

200

250

300

0 5 10 15 20 25

Deflection (mm)

Load (kN)

R01 R02 R03 R04

R01 a/d=1

R02 a/d=2

R03 a/d=3 R04 a/d=4

Figure 4: Load Deflection illustration for R01 (a/d=1), R02 (a/d=2), R03 (a/d=3) & R04 (a/d=4)

The failure pattern of the beams shown in Fig. 5 clearly indicate that for a/d 1 and 2 crack initiated approximately at 45degrees to the longitudinal axis of the beam. A compression failure finally occurred adjacent to the load which may be designated as a shear compression



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failure. For a/d 3 and 4 the diagonal crack started from the last flexural crack and turned gradually into a crack more and more inclined under the shear loading. The crack did not proceed immediately to failure, the diagonal crack moved up into the zone of compression became flatter and crack extended gradually at a very flat slope until finally sudden failure occurred up to the load point. The failure may be designated as diagonal tension failure.

Figure 5: Crack patterns and load points of the failed specimens R01, R02, R03 and R04



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As the present research work focuses on enhancement of shear capacity of HSC beams without web reinforcement, the tensile strength of concrete plays a vital role. The shear equations proposed by different codes cited in shear resistance models clearly disclose that shear resistance is factor of tensile strength of concrete, shear span to depth ratio (a/d) and tensile reinforcement ratio. To estimate the shear capacity of HSC beams the parameters viz.., tensile strength of concrete, shear span to depth ratio (a/d) and tensile reinforcement ratio were taken into account in form of Shear Influencing Parameter (SIP).

( ) t f SIP a d

ρ =

………………… (7)

t f Tensile strength of concrete in Mpa. a/d – Shear Span to Depth Ratio. ρ – Tensile Reinforcement Ratio.

y = 31.988x 0.7962

R 2 = 0.9964

0

2

4

6

8

10

0.00 0.05 0.10 0.15 0.20 0.25 SIP

Shear Stress (M

Pa)

Figure 6: Variation of shear strength with Shear Influencing Parameter (SIP)

The influence of shear resistance, which is taken as average value of the two specimens tested with SIP’s calculated using Eq.7 is illustrated in Fig. 6. To estimate the shear resistance (Vc) a linear regression equation was set in power series.

( ) 0.8

32 t c w

f V b d a d

ρ =

(N) ………………. (8)

where bw and d Width and depth of Effective cross section in mm.



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The empirical shear stress values calculated from the Eq.8 and the shear stress values obtained by testing the beams for shear span to depth (a/d) ratio = 1, 2, 3 & 4 are listed in Table 6. The values clearly signify that the experimental and empirical values fall within +5% and 5% variation. Thus the proposed equation can fairly estimate the shear resistance of HSC beams without stirrup reinforcement, under shear loading.

Table 4: Experimental and Empirical shear stress

S. No a/d Ratio

Experimental Shear Stress

(MPa)

Empirical Shear Stress

(MPa) 1 1 8.60 8.68 2 2 5.23 5.01 3 3 3.70 3.62 4 4 2.83 2.88

7. Conclusions

With the discussion on shear models and the experimental studies conducted on HSC beams without shear reinforcement the following conclusions can be drawn:

• The prediction of shear capacity of High strength concrete beams without shear reinforcement using the shear equations (Eqs 1 to 6) listed in this paper with a/d ratio is less than 2.0, a separate equation has to be used as there is remarkable difference between experimental values and predicted values and for a/d ratio more than 2.0, the available equations satisfactorily predict the shear capacity of the beams.

• The equation (Eq. 8) stated above includes almost all the parameters required to predict the shear capacity beams without shear reinforcement. Therefore a single simplified equation can be used to predict the shear capacity of HSC beams with a/d = 1, 2, 3 & 4.

REFERENCES

1. Bazant, Z.P., and Kim, J. K., “ Size Effect in Shear Failure of Longitudinally reinforced beams”, ACI Journal Proceedings V. 83, No 2 Mar Apr. 1986, pp. 456468.

2. Zsutty, T. C., “Shear Strength Predictions for Separate Categories of Simple Beam Tests”, ACI Journal, Proceedings, 68(2) (1971), pp. 138–143.

3. Piotr Paczkowski and Andrezej, Nowak, S., “Shear Resistance of Reinforced Beams without Web Reinforcement.” Architecture Civil Engineering Environment Journal No. 1/2008. pp 99112.

4. JinKuen Kim and YonDong Park. “Prediction of Shear Strength of Reinforced Beams



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without Web Reinforcement.” ACI Materials Journal, V 93, No. 3, May Jun 1996. pp. 213221.

5. Imran A. Bukhari and Saeed Ahmed, “Evaluation of Shear Strength of High Strength Concrete Beams without Stirrups.” The Arabian Journal for Science and Engineering, Vol33, Number 2B, October 2008, pp.323335.

6. Berg, F. j., “Shear Strength of Reinforced Concrete Beams Without Web Reinforcement”, Journal of ACI, 59(11)(1962), pp. 1587–1599.

7. Ferguson. P.M.,”Some Implications of recent Diagonal Tension Tests”, Journal of ACI, 28(2), 1956, pp.157172.

8. Taylor, R., “Some Shear Tests on Reinforced Concrete Beams Without Shear Reinforcement”, Magazine of Concrete Research, 12(36)(1960), pp. 145–154.

9. Gunneswara Rao T.D et.al., (2006) “An Appraisal Of The Shear Resistance Of Ferrocement Elements” Asian Journal Of Civil Engineering (Building And Housing) Vol. 7, No. 6 (2006) Pages 591602.

10. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 31802) and Commentary (318R02). Farmington Hills, Mich.: American Concrete institute, 2002.

11. Karim S. Rebeiz, Javier Fente and Michael Frabizzio, “New Shear Strength Prediction Using Statistical and Interpolation Function Techniques”, 8 th ASCE Speciality Conference on Probabilistic Mechanics and Structural Reliability, PMC 2000, pp 279283

12. CSA Technical Committee on Reinforced Concrete Design, Design of Concrete Structures A23.394,. Rexdale, Ontario, 1994.

13. European CEBFIP Model Code. London: Thomas Telfair, Services, 1990

14. Ahmad, S.H., Khaloo, A.R., and Poveda, A. (1986), “Shear Capacity of Reinforced High Strength Concrete Beams,” ACI Journal, 83(2), 297305.

15. Batchelor, B., “Shear in R.C. Beams without Web Reinforcement”, Journal of Structural Division, 107(ST5) (1981), pp. 907–919.

16. Elahi, A., “Effect of Reinforcement Ratio and Shear Span on Shear Strength of High strength Concrete Beams”, MSc Thesis, Taxila University, 2003.



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17. Elzanaty, A.H., Nilson, A.H., and Slate. F.O., “Shear Capacity of Reinforced Concrete Beams Using Highstrength Concrete”, ACI Journal, Proceedings, 83(2)(1986), pp. 290–296.

18. Reineck, K. H., Kuchma, D., Kim, K.S., and Marx, S., “Shear Database for Reinforced Concrete Members Without Shear Reinforcement”, ACI Structural Journal, 100(2)(2003), pp. 240–249.

shear resistance of high strength concrete beams without

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