**2.4 Beam specimens and testing procedure**

A total of six reinforced HSC beams divided into two series were cast:


*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.86499*

#### **Figure 4.**

*Stress-strain curve in compression of HSC.*


#### **Table 2.**

*Average mechanical properties of HSC.*

To find a precision in the experimental results, three beams were tested in each series.

The beams were tested under monotonic static loading using a 250 kN servocontrolled hydraulic jack (**Figure 8**). The details of the beams tested are presented in **Table 3**. It is noted that the value of shear-span/effective depth ratio (a/d) is within the a/d ranges leading to a dominant shear behaviour which results in a shear failure of the reinforced concrete beams [6, 12–16].

**Figure 5.** *Direct tensile test and measurement of the steel deformations by Gom-Aramis software (using DIC).*

tested under direct tension using a machine with capacity of 500 kN to determine the Young's modulus and the elastic limit. Measurement of the current deformations is carried out by Gom-Aramis software [11] using Digital Image Correlation (DIC) technique (**Figure 5**). The test results give a Young's modulus of 204 GPa and

A total of six reinforced HSC beams divided into two series were cast:

• The first series of beams without transverse reinforcement, noted 'Series A'.

• The second series of beams containing transverse reinforcement in the form of

an elastic limit of 500 MPa.

*Data acquisition system for the compression test.*

**Figure 3.**

**48**

**Figure 2.**

*Digital Imaging*

*Concrete cylinder compression test.*

stirrups, noted 'Series B'.

**2.4 Beam specimens and testing procedure**

### *Digital Imaging*

**Figures 6** and **7** illustrate the casting of the beams and the detail of reinforcement. A highly sensitive video camera was used to detect the development of cracks, monitor the evolution of the diagonal cracks as the load was gradually increased and measure their widths (**Figure 8**). The analysis of the DIC is

**Figure 6.**

*Formwork and manufacture of beams. (a) Beams with stirrups, (b) beams without stirrups, and (c) casting of beams.*

performed by Gom-Aramis software [11] (**Figure 9**) to obtain the deformation of concrete and to monitor the crack evolution in terms of width, spacing and length.

**Identification of beams b (mm) h (mm) d (mm) a/d** *ρ<sup>s</sup>* **(%)** *ρ<sup>w</sup>* **(%) fy (MPa)** Series A 100 150 135 2.2 1.16 0.00 500 Series B 100 150 129 2.3 1.16 0.56 500 *b = width of beam; h = height of beam; a/d = shear-span/effective depth; ρ<sup>s</sup> = longitudinal reinforcement ratio;*

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced…*

*ρ<sup>w</sup> = transverse reinforcement ratio; fy = yield strength of longitudinal reinforcement.*

*DOI: http://dx.doi.org/10.5772/intechopen.86499*

The vertical flexural cracks are the first type developed in the bottom zone of beam between the two point landings; this is the tension zone. The effect of stirrups is considered negligible before the formation of the diagonal cracking. From a loading rang of 60–70% of total ultimate load, the diagonal crackling is occurred from the flexural cracks (**Figure 11(b)**) within the shear zone between the support of the beam and the loading point (**Figure 10(b)**). In the Series A of the beams, the diagonal cracking formed independently of flexural cracks. When this cracking presents a sufficiently width, the failure was also by diagonal cracking as shown in

The addition of the transverse reinforcement in the Series B of the beams retards

the appearance of the diagonal cracking and limits their opening and therefore prevents the shear failure of the beam and changes the failure mode of the beam, from shear to flexure. When the diagonal cracking is sufficiently penetrated in the compression zone between the two loading points, the concrete is crushed as shown in **Figure 10(b)**. This mode of failure is designated by shear-compression. This series of beams showed no cracking along the longitudinal reinforcements and have developed many diagonal cracks. Generally, the diagonal cracking is inclined of about 45° with the longitudinal axis of the beam as shown in **Figures 10(a)** and **11(d)**.

**3.1 Development of cracks and failure modes of the beams**

**Figure 10(a)**. This mode of failure is designated by shear.

**3. Analysis of results**

*Image analysis by Gom-Aramis software.*

**Table 3.**

**Figure 9.**

**51**

*Details of the tested beams.*

**Figure 7.** *Reinforcement of the beam and the flexural devise.*

**Figure 8.** *Four-point bending test with the camera.*

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.86499*


*b = width of beam; h = height of beam; a/d = shear-span/effective depth; ρ<sup>s</sup> = longitudinal reinforcement ratio; ρ<sup>w</sup> = transverse reinforcement ratio; fy = yield strength of longitudinal reinforcement.*

#### **Table 3.**

**Figures 6** and **7** illustrate the casting of the beams and the detail of reinforcement. A highly sensitive video camera was used to detect the development of cracks, monitor the evolution of the diagonal cracks as the load was gradually increased and measure their widths (**Figure 8**). The analysis of the DIC is

*Formwork and manufacture of beams. (a) Beams with stirrups, (b) beams without stirrups, and (c) casting of*

**Figure 6.**

*Digital Imaging*

**Figure 7.**

**Figure 8.**

**50**

*Four-point bending test with the camera.*

*Reinforcement of the beam and the flexural devise.*

*beams.*

*Details of the tested beams.*

#### **Figure 9.**

*Image analysis by Gom-Aramis software.*

performed by Gom-Aramis software [11] (**Figure 9**) to obtain the deformation of concrete and to monitor the crack evolution in terms of width, spacing and length.

## **3. Analysis of results**

#### **3.1 Development of cracks and failure modes of the beams**

The vertical flexural cracks are the first type developed in the bottom zone of beam between the two point landings; this is the tension zone. The effect of stirrups is considered negligible before the formation of the diagonal cracking. From a loading rang of 60–70% of total ultimate load, the diagonal crackling is occurred from the flexural cracks (**Figure 11(b)**) within the shear zone between the support of the beam and the loading point (**Figure 10(b)**). In the Series A of the beams, the diagonal cracking formed independently of flexural cracks. When this cracking presents a sufficiently width, the failure was also by diagonal cracking as shown in **Figure 10(a)**. This mode of failure is designated by shear.

The addition of the transverse reinforcement in the Series B of the beams retards the appearance of the diagonal cracking and limits their opening and therefore prevents the shear failure of the beam and changes the failure mode of the beam, from shear to flexure. When the diagonal cracking is sufficiently penetrated in the compression zone between the two loading points, the concrete is crushed as shown in **Figure 10(b)**. This mode of failure is designated by shear-compression. This series of beams showed no cracking along the longitudinal reinforcements and have developed many diagonal cracks. Generally, the diagonal cracking is inclined of about 45° with the longitudinal axis of the beam as shown in **Figures 10(a)** and **11(d)**.

**Figure 10.**

*Cracks and failure patterns of beams. (a) Failure of Series A (HSC beams without transverse reinforcement) and (b) failure of Series B (HSC beams with transverse reinforcement).*

**Table 4** gives the average experimental results of the first crack loads (*Pcr*), the diagonal cracking loads (*Pd*) and the total ultimate loads (*Pu*) for all tested beams. The presence of the transverse reinforcements improves the resistance reserve of the beams beyond the diagonal cracking. An increase in the ultimate load varies of around 50% has been recorded for the Series B by comparison to Series A. Comparable results have been reported in the literature [12–15] on reinforced concrete beams made of different strength of concrete ranging from 20 to 68 MPa. This shows that the effect of the transverse reinforcement is practically the same in any type of concrete.

**Figure 11.**

**53**

*prior to failure—diagonal cracking (width = 0.16 mm).*

*A sequence of crack development within a shear zone in Series B (photos obtained by digitizing video Gom-Aramis). (a) At 24% of ultimate load—no cracking in the shear zone. (b) At 60% of ultimate load—inclined cracking (width = 0.01 mm). (c) At 70% of ultimate load—diagonal cracking (width = 0.04 mm). (d) Just*

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced…*

*DOI: http://dx.doi.org/10.5772/intechopen.86499*

A typical monitoring of a diagonal cracking using DIC is shown in **Figure 11**.

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.86499*

#### **Figure 11.**

*A sequence of crack development within a shear zone in Series B (photos obtained by digitizing video Gom-Aramis). (a) At 24% of ultimate load—no cracking in the shear zone. (b) At 60% of ultimate load—inclined cracking (width = 0.01 mm). (c) At 70% of ultimate load—diagonal cracking (width = 0.04 mm). (d) Just prior to failure—diagonal cracking (width = 0.16 mm).*

**Table 4** gives the average experimental results of the first crack loads (*Pcr*), the diagonal cracking loads (*Pd*) and the total ultimate loads (*Pu*) for all tested beams. The presence of the transverse reinforcements improves the resistance reserve of the beams beyond the diagonal cracking. An increase in the ultimate load varies of around 50% has been recorded for the Series B by comparison to Series A. Comparable results have been reported in the literature [12–15] on reinforced concrete beams made of different strength of concrete ranging from 20 to 68 MPa. This shows that the effect of the transverse reinforcement is practically the same in any

*Cracks and failure patterns of beams. (a) Failure of Series A (HSC beams without transverse reinforcement)*

*and (b) failure of Series B (HSC beams with transverse reinforcement).*

A typical monitoring of a diagonal cracking using DIC is shown in **Figure 11**.

type of concrete.

**52**

**Figure 10.**

*Digital Imaging*

## *Digital Imaging*


## **Table 4.**

*Diagonal cracking load and ultimate load of the tested beams.*

**Figure 12.** *Load-deflection curves for the HSC beams.*

#### **3.2 Load-deflection characteristics**

One LVDT was attached to the bottom surface of the beams at mid-span to measure the deflection. From the load-deflection curves (**Figure 12**), it can be seen that the behaviour of the beams with transverse reinforcement (Series B) shows three main phases:

• **Phase I:** presents a linear form where the deflection increases at the same time as the load; this is the elastic behaviour of the beams up to the appearance of the first flexural crack.

interlocking *Vay*, the contribution of the longitudinal reinforcement *Vd* and the contribution of the stirrups *Vs* as shown in Eq. (1) and **Figure 15**. This can be

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced…*

expresses the shear resistance of concrete *Vc*, and the Eq. (1) is

The three shear forces which present the contribution of the concrete to shear strength are evaluated by Taylor [17] and by Paulay and Fenwick [18] as follows:

*Vu* ¼ *Vcy* þ *Vay* þ *Vd* þ *Vs* (1)

*Vu* ¼ *Vc* þ *Vs* (2)

written as:

**Figure 14.**

**Figure 13.**

*Brittle shear failure (Series A).*

*DOI: http://dx.doi.org/10.5772/intechopen.86499*

*Vcy* þ *Vay* þ *Vd*

*Ductile behaviour (Series B).*

• *Vcy* = 20–40% of *Vu*

• *Vay* = 35–50% of *Vu*

• *Vd* = 15–25% of *Vu*

**55**

simplified as follows:


#### **3.3 Shear analysis of HSC beams**

#### *3.3.1 Theoretical analyses of the shear force*

The ultimate shear force *Vu* in 'kN' of reinforced concrete beam is determined by the contribution of the compression zone *Vcy*, the contribution of the aggregate *Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.86499*

**Figure 13.** *Brittle shear failure (Series A).*

**Figure 14.** *Ductile behaviour (Series B).*

**3.2 Load-deflection characteristics**

*Load-deflection curves for the HSC beams.*

*Diagonal cracking load and ultimate load of the tested beams.*

the first flexural crack.

**3.3 Shear analysis of HSC beams**

**54**

*3.3.1 Theoretical analyses of the shear force*

three main phases:

**Figure 12.**

**Table 4.**

*Digital Imaging*

One LVDT was attached to the bottom surface of the beams at mid-span to measure the deflection. From the load-deflection curves (**Figure 12**), it can be seen that the behaviour of the beams with transverse reinforcement (Series B) shows

**Identification of beams** *Pf* **(kN)** *Pd* **(kN)** *Pu* **(kN) Mode of failure** Series A 16.50 43.79 60.00 Shear

Series B 18.75 60.62 86.18 Flexion shear-compression

• **Phase I:** presents a linear form where the deflection increases at the same time as the load; this is the elastic behaviour of the beams up to the appearance of

• **Phase II:** a second phase of linear form after the occurrence of the first flexural crack. The deflection increases with the load but with relatively higher values. In this phase, the cracks are sufficiently developed in length and opening, the Series A of the beams (without transverse reinforcement) lose their rigidity and fail without undergoing further sufficient deflection (**Figure 13**) compared

• **Phase III:** corresponds to the plastic behaviour of the beams, where the deflection is not proportional to the load with higher deformation of concrete before the failure of the beams. This phase illustrates the ductile behaviour as shown in **Figure 14**.

The ultimate shear force *Vu* in 'kN' of reinforced concrete beam is determined by the contribution of the compression zone *Vcy*, the contribution of the aggregate

to those containing transverse reinforcement (Series B).

interlocking *Vay*, the contribution of the longitudinal reinforcement *Vd* and the contribution of the stirrups *Vs* as shown in Eq. (1) and **Figure 15**. This can be written as:

$$V\_u = V\_{cy} + V\_{ay} + V\_d + V\_s \tag{1}$$

*Vcy* þ *Vay* þ *Vd* expresses the shear resistance of concrete *Vc*, and the Eq. (1) is simplified as follows:

$$V\_u = V\_c + V\_s \tag{2}$$

The three shear forces which present the contribution of the concrete to shear strength are evaluated by Taylor [17] and by Paulay and Fenwick [18] as follows:


**Figure 15.** *Mechanism of shear forces in a beam with transverse reinforcement [15].*

**Figure 16.** *Distribution of shear force in a reinforced concrete beams [17].*

**Figure 16** shows the contribution of the different components of ultimate shear force (*Vu*) in a reinforced concrete beams as shown in **Figure 14** and given by Eq. (1).

**Table 5** presents the theoretical models to determine the ultimate shear strength of reinforced concrete beams, given by the different universal design codes.

of HSC material to the shear strength of reinforced concrete beams. An average around 40% of underestimating was recorded. Among the five models, The European Eurocode 2 gives the best predictions with underestimating of around 24% the shear strength of HSC beams. By comparison, the Indian Standard IS456 is the most conservative to predict the ultimate shear force of HSC beams with a prediction of around 65% below the experimental results. This requires more effort and research to extrapolate and to valid these models developed essentially for normal strength concrete to HSC and therefore faithfully reflect the contribution of this new

**Codes Model of the total ultimate shear force** *Vu* **(kN) Explanation**

*a*/*d* ≥ 2

for *a*/*d* < 2

*f c* <sup>p</sup> *bwd* <sup>þ</sup> *Av fsvd s*

<sup>6</sup>*:*89 100 ð Þ*<sup>ρ</sup>* >1

*bwd* <sup>þ</sup> <sup>0</sup>*:*<sup>87</sup> *Av fsvd*

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced…*

*<sup>s</sup>* for

*<sup>s</sup>* sin *α*

*bwd* <sup>þ</sup> <sup>0</sup>*:*<sup>87</sup> *Av fsvd s*

*s*

*<sup>s</sup> fc* = cylinder compressive strength

*k* ¼ 1 þ

ffiffiffiffiffiffi 200 *d* q

*z* = lever arm = 0.9*d*

, *d* (mm)

*fck* = characteristic compressive strength = *fc*/0.8 *d* = effective depth of beam *a* = shear span *bw* = width of beam *Av* = section of stirrup *fsv* = yield strength of stirrups *s* = stirrups spacing *ρ* = *As*/*bwd As* = section of longitudinal reinforcement *fcu* = cube compressive strength *γ<sup>m</sup>* = material partial safety factor for shear, taken as 1.25 *α* = inclination of stirrups (*α* = 90°) *θ* = angle between inclined concrete struts and the main tension chord (*θ* = 45°)

ACI 318 [5] *Vu* <sup>¼</sup> <sup>1</sup>

[19] *Vu* <sup>¼</sup> <sup>0</sup>*:*<sup>79</sup>

BS 8110

Eurocode 2 [20]

NZS 3101 [21]

Indian Standard IS456 [22]

**Table 5.**

**Figure 17.**

**57**

7 ffiffiffiffi *f c* <sup>p</sup> <sup>þ</sup> <sup>120</sup>*<sup>ρ</sup> <sup>d</sup> a* � �*bwd* <sup>þ</sup> *Av fsvd*

*γm* ð Þ <sup>100</sup>*<sup>ρ</sup>* <sup>1</sup> <sup>3</sup> 400 *d* � �<sup>1</sup> <sup>4</sup> *fcu* <sup>25</sup> � �<sup>1</sup> 3

*DOI: http://dx.doi.org/10.5772/intechopen.86499*

*Vu* ¼ 0*:*18 *k:* 100*:ρ:fc*

� �<sup>1</sup> 3 h i*bwd* <sup>þ</sup> *Av fsv <sup>z</sup>*ð Þ cot *<sup>θ</sup>*<sup>þ</sup> cot *<sup>α</sup>*

*Vu* <sup>¼</sup> ð Þ <sup>0</sup>*:*<sup>07</sup> <sup>þ</sup> <sup>10</sup>*<sup>ρ</sup>* ffiffiffiffi

*Theoretical models of the ultimate shear strength given by different codes.*

<sup>0</sup>*:*8*fck* <sup>p</sup> ffiffiffiffiffiffiffiffi <sup>1</sup>þ5*<sup>β</sup>* <sup>p</sup> �<sup>1</sup> � � <sup>6</sup>*<sup>β</sup> bwd* <sup>þ</sup> *Av fsvd*

where *<sup>β</sup>* <sup>¼</sup> <sup>0</sup>*:*8*<sup>f</sup> ck*

*Vu* <sup>¼</sup> <sup>0</sup>*:*<sup>85</sup> ffiffiffiffiffiffiffiffiffi

*Vu* <sup>¼</sup> <sup>2</sup> *<sup>d</sup> a* � � <sup>0</sup>*:*<sup>79</sup> *γm* ð Þ <sup>100</sup>*<sup>ρ</sup>* <sup>1</sup> <sup>3</sup> 400 *d* � �<sup>1</sup> <sup>4</sup> *fcu* <sup>25</sup> � �<sup>1</sup> 3

material to the shear strength of reinforced concrete beams.

*Experimental and predicted values of the shear strength of HSC beams.*

### *3.3.2 Comparison between test results and theoretical predictions of the shear strength*

**Figure 17** shows the experimental and the theoretical ultimate shear forces predicted by the five universal design codes presented in **Table 5** above, for two series of beams. The Series A is not transversely reinforced (*Vs* = 0) so the ultimate shear force of this series represents the contribution of concrete to the shear resistance (*Vc*). As shown in this figure, the five models underestimate the contribution *Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced… DOI: http://dx.doi.org/10.5772/intechopen.86499*


**Table 5.** *Theoretical models of the ultimate shear strength given by different codes.*

**Figure 17.**

**Figure 16** shows the contribution of the different components of ultimate shear

**Table 5** presents the theoretical models to determine the ultimate shear strength

force (*Vu*) in a reinforced concrete beams as shown in **Figure 14** and given by

of reinforced concrete beams, given by the different universal design codes.

*3.3.2 Comparison between test results and theoretical predictions of the shear strength*

**Figure 17** shows the experimental and the theoretical ultimate shear forces predicted by the five universal design codes presented in **Table 5** above, for two series of beams. The Series A is not transversely reinforced (*Vs* = 0) so the ultimate shear force of this series represents the contribution of concrete to the shear resistance (*Vc*). As shown in this figure, the five models underestimate the contribution

Eq. (1).

**56**

**Figure 16.**

**Figure 15.**

*Digital Imaging*

*Mechanism of shear forces in a beam with transverse reinforcement [15].*

*Distribution of shear force in a reinforced concrete beams [17].*

*Experimental and predicted values of the shear strength of HSC beams.*

of HSC material to the shear strength of reinforced concrete beams. An average around 40% of underestimating was recorded. Among the five models, The European Eurocode 2 gives the best predictions with underestimating of around 24% the shear strength of HSC beams. By comparison, the Indian Standard IS456 is the most conservative to predict the ultimate shear force of HSC beams with a prediction of around 65% below the experimental results. This requires more effort and research to extrapolate and to valid these models developed essentially for normal strength concrete to HSC and therefore faithfully reflect the contribution of this new material to the shear strength of reinforced concrete beams.

The Series B of the beams is transversely reinforced by stirrups, the ultimate shear force of this series represents the contribution of concrete (*Vc*) and the contribution of stirrups (*Vs*) to the shear strength of HSC beams. The ultimate shear strength of this series is also shown in **Figure 17**. The concrete contribution *Vc* represents 70% of the total shear force and the steel contribution *Vs* represents 30%. Therefore, the presence of the transverse reinforcement has improved the ultimate shear strength of HSC beams by around 30%. The five design codes greatly overestimate the contribution of the stirrups to the shear strength of HSC beams. An average overestimation is around 45% was recorded. This is due to the fact that the contribution of the stirrups to the shear strength developed in the five code models is based on the yielding of this reinforcement; this is the Ritter [23] and Mörsch [24] truss analogy. The analogy proposes that a reinforced concrete beam failing after yielding of the transverse reinforcement, and before the crushing of concrete. In all tested beams, the failure mode is characterized by crushing of concrete after the complete penetration of the diagonal cracking in the compression zone of the beam as shown in **Figure 10(b)**, and in the same time the transverse reinforcements have not yielding. The contradiction between the analogy of Ritter and Mörsch and the experimental observations led to a greatly overestimation of the transverse reinforcement contribution to the shear strength of reinforced concrete beams.

• The contribution of the HSC to the shear resistance of reinforced concrete beams was underestimated by the five universal design codes, and in the same time, the contribution of the stirrups was overestimated. These design codes need more refinement to reflect and to ascertain the improved shear strength

*Experimental and Theoretical Investigation on the Shear Behaviour of High Strength Reinforced…*

The experimental investigation presented in this chapter was sponsored by the Ministry of Higher Education and Scientific Research of Algeria. The tests were carried out at Laboratory of Engineering of the Materials of Bretagne (LIMATB) at the University of Bretagne Sud, Lorient, France. Also, Dr. Thibaut Lecompte is gratefully thanked for their willing discussion and active participation in the

of high strength reinforced concrete beams.

*DOI: http://dx.doi.org/10.5772/intechopen.86499*

**Acknowledgements**

project.

**Author details**

Touhami Tahenni<sup>1</sup>

**59**

\* and Thibaut Lecompte<sup>2</sup>

University of Khemis Miliana, Khemis Miliana, Algeria

\*Address all correspondence to: touhami\_tahenni@yahoo.fr

2 Université de Bretagne-Sud, Lorient, France

provided the original work is properly cited.

1 Department of Technology, Faculty of Sciences and Technology, Djilali Bounaama

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

On adding up the contribution of concrete and the contribution of the stirrups to the shear strength of HSC beams, Eurocode 2 seems to give the best predictions for the ultimate shear strength compared to other code models.

The five universal design codes require more refinement to reflect the real contributions of both materials; the HSC and the steel reinforcement, to the shear resistance of high strength reinforced concrete beams.
