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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

101

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]

doi:10.6088/ijcser.00202010009

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, CEP-FIP 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: High-strength 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], Jin-Keun 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 span-to-effective depth ratio is taken as main





102

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.





103

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





104

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





105

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.

CEP-FIP 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)



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.


a/d – Shear span to Depth 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)





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)





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





107

Comparison of the experimental results (Table 3 with ACI code [Eq 1] , Canadian Code[Eq 2],

CEP-FIP 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

Beam

ID

MPa

a/d Vexp

(kN)

Vpredicted

(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





108

0

20

40

60

80

100

120

140

0.0 1.0 2.0 3.0 4.0 5.0

a/d Ratio

Sh

ear

Fo

rce (

kN

)

ACI CAND CEB-FIP 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)

Lo

ad

(k

N)

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





109

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





110

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).

tfSIPa

d

………………… (7)

tf - Tensile strength of concrete in Mpa.

a/d – Shear Span to Depth Ratio.

ρ – Tensile Reinforcement Ratio.

y = 31.988x0.7962

R2 = 0.9964

0

2

4

6

8

10

0.00 0.05 0.10 0.15 0.20 0.25

SIP

Sh

ear

Str

ess (

MP

a)

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 tc w

fV b d

ad

(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. 456-468.

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ACI Journal, Proceedings, 68(2) (1971), pp. 138–143.

3. Piotr Paczkowski and Andrezej, Nowak, S., “Shear Resistance of Reinforced Beams

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pp 99-112.

4. Jin-Kuen Kim and Yon-Dong Park. “Prediction of Shear Strength of Reinforced Beams





112

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13. European CEB-FIP Model Code. London: Thomas Telfair, Services, 1990

14. Ahmad, S.H., Khaloo, A.R., and Poveda, A. (1986), “Shear Capacity of Reinforced High

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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 High-strength Concrete”, ACI Journal, Proceedings, 83(2)(1986), pp. 290–296.

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Shear Resistance of High Strength Concrete Beams Without ... · PDF fileand support conditions, ... shear span-to-effective depth ratio is taken as main ... conducting trial mixes