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International Association of Scientific Innovation and Research (IASIR)
(An Association Unifying the Sciences, Engineering, and Applied Research)
International Journal of Engineering, Business and Enterprise
Applications (IJEBEA)
www.iasir.net
IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 101
ISSN (Print): 2279-0020
ISSN (Online): 2279-0039
Performance of Reinforced Concrete Beam under Line Impact Loading
I.K .Khan
Department of Civil Engineering
Aligarh Muslim University, Aligarh-2002002 (U.P.), INDIA
___________________________________________________________________________________________
Abstract: There has been a growing interest in the past few decades among the engineering community to
understand the response of reinforced concrete structures subjected to extreme loads due to blast and impact.
These severe transient dynamic loads are rare in occurrence but for most of the structures, their effect can
result in catastrophic and sudden structural failure. Even residential buildings and other dwelling units are very
commonly attacked for spreading panic by terrorists using explosive devices. Missiles and inert projectiles of
spherical or cylindrical shape, hitting the structures with high kinetic energy are potent threats to the survival of
structures. Thus as concrete is our main construction material it is necessary to know its behaviour under such
type impact load. Nowadays, with the rising concern for improved protective civilian structures, these design
methods are proving uneconomical and require development of the improved procedures and design tools for
impact and blast design of conventional structures. In the present research behaviour of conventionally
designed RC beam was studied under line impact using impact hammer testing machine.
Keywords: Reinforced concrete, impact load, Impact hammer, Grade of concrete, Shear reinforcement,
deflection Crack pattern and Strain energy.
_________________________________________________________________________________________
I. Introduction
Impact is a daily life phenomenon. It happens whenever two bodies collide. The study of projectile impact has
been an area of interest for scientists for about two hundred and fifty years. But for the last four decades this
field has become very important for both developed and developing countries. As today the power of a nation is
judged on the basis of technology. Every country is investing lot of money for the defense sector and India too is
one of them. Every country is developing new missile technology and also the safety devices to have a powerful
defense sector. The field of impact is not only confined to defence sector but it has a wide field like in
production of high speed blanking and hole flanging, in geology where scientists use improved understanding of
earth penetration processes to carry out remote seismic monitoring and surveying not only this but also the
automobile engineers are too much concerned with this field for good designing of the vehicles to have least
harm to the vehicle’s main structure and the people sitting over it.
As the penetration of fragments into targets has long been of interest in military applications, different metallic
and non-metallic armours having various thicknesses are being used to give protections to vehicles employed for
definite roles in the military operations. The phenomenon of projectile penetration can be categorized by several
schemes. For example: on the basis of effect impacts can be classified as either:
Hard Impact: when the kinetic energy of the impacting mass is transformed into plastic deformation of the
impactor.
Soft Impact: when the impactor’s kinetic energy is transformed into deformation energy in both the impactor
and the structure.
On the basis of velocity it may be classified under the following heads.
(i) Freely falling bodies (0 – 25 m/s)
(ii) Sub ordinance range (25 – 500 m/s)
(iii) Ordinance range (500 – 1300 m/s)
(iv) Ultra ordinance domain (1300 – 3000 m/s)
(v) Hyper velocity impact (above 3000 m/s)
II. Literature Review
M. Alam [1], worked on quasi – static and drop hammer loading of plain and skin reinforced concrete plates of
thickness 25 and 35mm and of regular strength 15, 25, 35 MPa, with and without edge ring. To reinforce these
plates of plain concrete, thin steel sheets (0.15 and 0.2mm thick) have been used on rear or on both faces using
Araldite glue. Experiments on these plate specimens have been performed using a cylindrical penetrator with
spherical nose positioned at the centre of the plate.
M. Kumar et al. [2], developed a relationship for computation of dynamic modulus of elasticity using non –
destructive testing. It is observed that dynamic as well as static modulii of elasticity of concrete are largely
influenced by the age and grade of concrete. However, hale variation has been observed in case of Poisson’s
ratio regardless of the age and grade of concrete.
I.K .Khan, International Journal of Engineering, Business and Enterprise Applications, 8(2), March-May., 2014, pp. 101-104
IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 102
A.K.H. Kwan et al. [3], studied that the effects of shock vibration on concrete using a newly developed test
method that applies hammer blows to prismatic specimens in the longitudinal direction and evaluates the short
and long term effects by observing crack formation, measuring the immediate change in ultrasonic pulse
velocity and measuring the reductions in 28days tensile and compressive strengths. A total of 198 prisms cast of
typical concrete mixtures with 28days cube strength ranging from 40 to 60MPa had been tested at ages of
12hours to 28days. The tests revealed that the major effect of shock vibration is the formation of transverse
cracks. Based on the test results, the shock vibration resistances of the concrete mixtures at different ages were
determined and correlated to their material properties. It was found that the single most important material
parameter governing of concrete is the dynamic tensile strain capacity finally. Several new sets of vibration
control limits, which are less conservative than most existing, ones, have been established.
N. Kishi et al. [4] – They worked on “Impact Behavior of Shear-Failure-Type RC Beams Without Shear Rebar”.
To establish a rational impact-resistant design procedure of shear-failure-type reinforced concrete (RC) beams,
falling-weight impact tests were conducted. Twenty-seven simply supported rectangular RC beams without
shear rebar were used. In these experiments, the impact force excited in the steel weight, the reaction force, and
the mid-span displacement were measured and recorded by wide-band analog data recorders. After testing,
crack patterns developed on the side surfaces of the RC beams were sketched.
III. Testing of Materials, Beam Specimens and Test Results
A. Test Set up and Testing
Materials like cement, fine and coarse aggregates, steel and concrete were tested in accordance with Bureau of
Indian Standard (B.I.S.) codes and their properties were found to be within the prescribed limits.
Impact test on concrete beams were done with the help of impact hammer testing machine, with impact hammer
of equivalent weight 25.40 kg at the level of point including weight 0.675 kg of the impact tool fixed with the
impact hammer as showing in the Figure 3 whereas it strikes the beam with a velocity of 4.14 m/s. During test
maximum deflection at the centre of beam was recorded with the help of LVDT and crack patterns were also
observed after each blow.
Total nine beams of size 150mmx150mmx500mm were cast. Each group of three beams were cast with M20, M25
and M30 grade concrete and beams in each group were designed as under , balanced and over reinforced sections
in accordance to IS 456:2000. During test beams were provided simple supports with centre to centre distance
of supports as 400mm and an overhang of 50mm on both sides to avoid overturning during testing.
The line impact test on concrete beam was done with the help of impact hammer testing machine, the impact
hammer of equivalent weight 25.4kg at the level of point, where it strikes the beam with a velocity of 4.14 m/s.
The line impact hammer was initially kept horizontal as shown in Figure 1(b) and then allowed to fall freely
under gravity to strike the beam horizontally as shown in Figure 1(c). The hammer was lifted manually and was
anchored to a wooden trigger, from where it was dropped by trigger a side. The position of trigger was properly
marked so that every time hammer is dropped, the height of fall remains constant. At the point of striking a rod
of 16 mm was fixed on the impact hammer so that the load acts as a Line load on beam.
In the impact hammer testing machine the beam to be tested was clamped with the help of steel rod and plates of
diameter 20mm and thickness of plates 12mm. The steel rod had threads at its end which were fastened by bolts.
Proper care was taken at the time of experiment to avoid loosening of bolts by wrapping the cotton thread on
rod. Wooden packing was also put to avoid any type of slippage.
Figure 1 Testing of beam under line impact load
(a)Arrangement for line impact (b) Hammer in horizontal position (c) Testing of beam
I.K .Khan, International Journal of Engineering, Business and Enterprise Applications, 8(2), March-May., 2014, pp. 101-104
IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 103
B. Observation and Test Results
For the beam cast with M30 grade concrete and designed as balanced section and designated as M30B, deflection
and physical condition of the beam after each line impact or blow is shown in the Table 1. These were also
recorded for other type of beams viz. M20B, M20O, M25U, M25B, M25O, M30U, and M30O where M20, M25 and
M30 are grades of concrete and U, B and O stands for under, balance and over reinforced sections respectively.
Test results like strain energy and theoretical deflection etc. obtained by analysis is shown in Table 2 for the
beam cast with M30B. Crack patterns observed during line impact test for beam M30B is shown in Figure 2.
Table 1 Deflection and physical condition of beam M30B
Blow no. Deflection (mm) Formation of Cracks Remark
1 8.135 Two vertical cracks First crack on left hand side
2 11.162
First and second increased and third
crack also formed
Second crack on right hand side
3 12.522 Cracks width increased
First crack distance 5cm and
second crack distance 10cm from
support
4 13.283 Cracks width increased Third crack on left hand side
5 13.872 Cracks width increased
Third crack distance 7.5 cm from
support
6 14.082 Fourth crack formed Fourth crack on right hand side
7 14.550 Cracks width increased Fourth crack distance 2cm from support
8 14.654 Maximum width of cracks Beam failed
Table 2 Strain energy and theoretical deflection values for beam M30B
Blow No. Deflection (mm) W (kN) Strain Energy ‘U’ (kJ)
Theoretical
Deflection (mm)
1 8.135 58.38 0.024 0.832
2 11.162 42.55 0.0128 0.606
3 12.522 37.93 0.0102 0.540
4 13.283 35.76 0.009 0.509
5 13.872 34.24 0.008 0.487
6 14.082 33.73 0.008 0.48
7 14.550 30.54 0.006 0.43
8 14.654 30.34 0.006 0.432
Figure 2 crack patterns for beam M30B
IV. Conclusions
On the basis of experimental testing and analysis of reinforced concrete beam under line impact load following
conclusions have been drawn:
1. Beam M20U failed at third blow, M20B failed at fifth blow and M20O failed at eight blow.
2. Beam M25U failed at fifth blow, M25B failed at seventh blow and M25O failed at ninth blow.
3. Beam M30U failed at sixth blow, M30B failed at eight blow and M30O failed at twelfth blow.
4. The maximum experimental deflection in beam M20U is 18.23mm, in beam M20B is 17.92 mm and in
beam M20O is 17.28mm.
5. The maximum experimental deflection in beam M25U is 17.94mm, in beam M25B is 16.26mm and in
beam M25O is 15.58mm.
I.K .Khan, International Journal of Engineering, Business and Enterprise Applications, 8(2), March-May., 2014, pp. 101-104
IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 104
6. The maximum experimental deflection in beam M30U is 15.70 mm, in beam M30B is 14.65mm and in
beam M30O is 12.67mm.
7. The maximum theoretical deflection in beam M20U is 3.16mm, in beam M20B is 2.90mm and in beam
M20O is 1.46mm.
8. The maximum theoretical deflection in beam M25U is 1.58 mm, in beam M25B is 1.62mm and in beam
M25O is 1.22mm.
9. The maximum theoretical deflection in beam M30U is 0.90mm, in beam M30B is 0.85mm and in beam
M30O is 0.74mm.
10. The scabbing started in beam M20U at second blow, in beam M20B at third blow and in beam M20O at
fourth blow.
11. The scabbing started in beam M25U at third blow, in beam M25 B at fourth blow and in beam M25O at
fifth blow.
12. The scabbing started in beam M30U at fourth blow, in beam M30B started at fifth blow and in beam
M30O started at sixth blow.
In view of the above results it can be concluded that with the increase in the grade of concrete and quantity of
steel more number of blows are required to cause failure in the beam, whereas maximum experimental and
theoretical deflection reduces with the increase in the grade of concrete and quantity of steel. Scabbing in the
beams started at increased number of blows as grade of concrete and steel increases in the beam.
Thus we can say that impact load carrying capacity of the beam improve by increasing in the grade of concrete
and quantity of steel.
References
1. M. Alam, “Quasi-Static & Drop Hammer Loading of Plain and Skin Reinforced Concrete Plates” PhD Thesis, Indian Institute
of Technology, Delhi, India , Dec. 1999.
2. M. Kumar, V. Kanwar. And S. Kumar, “Non – Destructive Evaluation of Dynamic Properties of Concrete”, IE (I) Journal, India,
Vol. 86, August 2005.
3. A.K.H. Kwan., W. Zhang. and I.Y.T Ng, “Effects of Shock Vibration on Concrete”, A. C. I. Material Journal, USA, Nov. –
Dec., 2005.
4. Kishi, N., H. Mikami, and T. Ando, “Impact Behaviour of Shear – Failure – Type RC Beams without Shear Rebar”. Int. J. of
Impact Engineering, Vol. 27, pp. 955 – 968, 2002.

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Ijebea14 262

  • 1. International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Journal of Engineering, Business and Enterprise Applications (IJEBEA) www.iasir.net IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 101 ISSN (Print): 2279-0020 ISSN (Online): 2279-0039 Performance of Reinforced Concrete Beam under Line Impact Loading I.K .Khan Department of Civil Engineering Aligarh Muslim University, Aligarh-2002002 (U.P.), INDIA ___________________________________________________________________________________________ Abstract: There has been a growing interest in the past few decades among the engineering community to understand the response of reinforced concrete structures subjected to extreme loads due to blast and impact. These severe transient dynamic loads are rare in occurrence but for most of the structures, their effect can result in catastrophic and sudden structural failure. Even residential buildings and other dwelling units are very commonly attacked for spreading panic by terrorists using explosive devices. Missiles and inert projectiles of spherical or cylindrical shape, hitting the structures with high kinetic energy are potent threats to the survival of structures. Thus as concrete is our main construction material it is necessary to know its behaviour under such type impact load. Nowadays, with the rising concern for improved protective civilian structures, these design methods are proving uneconomical and require development of the improved procedures and design tools for impact and blast design of conventional structures. In the present research behaviour of conventionally designed RC beam was studied under line impact using impact hammer testing machine. Keywords: Reinforced concrete, impact load, Impact hammer, Grade of concrete, Shear reinforcement, deflection Crack pattern and Strain energy. _________________________________________________________________________________________ I. Introduction Impact is a daily life phenomenon. It happens whenever two bodies collide. The study of projectile impact has been an area of interest for scientists for about two hundred and fifty years. But for the last four decades this field has become very important for both developed and developing countries. As today the power of a nation is judged on the basis of technology. Every country is investing lot of money for the defense sector and India too is one of them. Every country is developing new missile technology and also the safety devices to have a powerful defense sector. The field of impact is not only confined to defence sector but it has a wide field like in production of high speed blanking and hole flanging, in geology where scientists use improved understanding of earth penetration processes to carry out remote seismic monitoring and surveying not only this but also the automobile engineers are too much concerned with this field for good designing of the vehicles to have least harm to the vehicle’s main structure and the people sitting over it. As the penetration of fragments into targets has long been of interest in military applications, different metallic and non-metallic armours having various thicknesses are being used to give protections to vehicles employed for definite roles in the military operations. The phenomenon of projectile penetration can be categorized by several schemes. For example: on the basis of effect impacts can be classified as either: Hard Impact: when the kinetic energy of the impacting mass is transformed into plastic deformation of the impactor. Soft Impact: when the impactor’s kinetic energy is transformed into deformation energy in both the impactor and the structure. On the basis of velocity it may be classified under the following heads. (i) Freely falling bodies (0 – 25 m/s) (ii) Sub ordinance range (25 – 500 m/s) (iii) Ordinance range (500 – 1300 m/s) (iv) Ultra ordinance domain (1300 – 3000 m/s) (v) Hyper velocity impact (above 3000 m/s) II. Literature Review M. Alam [1], worked on quasi – static and drop hammer loading of plain and skin reinforced concrete plates of thickness 25 and 35mm and of regular strength 15, 25, 35 MPa, with and without edge ring. To reinforce these plates of plain concrete, thin steel sheets (0.15 and 0.2mm thick) have been used on rear or on both faces using Araldite glue. Experiments on these plate specimens have been performed using a cylindrical penetrator with spherical nose positioned at the centre of the plate. M. Kumar et al. [2], developed a relationship for computation of dynamic modulus of elasticity using non – destructive testing. It is observed that dynamic as well as static modulii of elasticity of concrete are largely influenced by the age and grade of concrete. However, hale variation has been observed in case of Poisson’s ratio regardless of the age and grade of concrete.
  • 2. I.K .Khan, International Journal of Engineering, Business and Enterprise Applications, 8(2), March-May., 2014, pp. 101-104 IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 102 A.K.H. Kwan et al. [3], studied that the effects of shock vibration on concrete using a newly developed test method that applies hammer blows to prismatic specimens in the longitudinal direction and evaluates the short and long term effects by observing crack formation, measuring the immediate change in ultrasonic pulse velocity and measuring the reductions in 28days tensile and compressive strengths. A total of 198 prisms cast of typical concrete mixtures with 28days cube strength ranging from 40 to 60MPa had been tested at ages of 12hours to 28days. The tests revealed that the major effect of shock vibration is the formation of transverse cracks. Based on the test results, the shock vibration resistances of the concrete mixtures at different ages were determined and correlated to their material properties. It was found that the single most important material parameter governing of concrete is the dynamic tensile strain capacity finally. Several new sets of vibration control limits, which are less conservative than most existing, ones, have been established. N. Kishi et al. [4] – They worked on “Impact Behavior of Shear-Failure-Type RC Beams Without Shear Rebar”. To establish a rational impact-resistant design procedure of shear-failure-type reinforced concrete (RC) beams, falling-weight impact tests were conducted. Twenty-seven simply supported rectangular RC beams without shear rebar were used. In these experiments, the impact force excited in the steel weight, the reaction force, and the mid-span displacement were measured and recorded by wide-band analog data recorders. After testing, crack patterns developed on the side surfaces of the RC beams were sketched. III. Testing of Materials, Beam Specimens and Test Results A. Test Set up and Testing Materials like cement, fine and coarse aggregates, steel and concrete were tested in accordance with Bureau of Indian Standard (B.I.S.) codes and their properties were found to be within the prescribed limits. Impact test on concrete beams were done with the help of impact hammer testing machine, with impact hammer of equivalent weight 25.40 kg at the level of point including weight 0.675 kg of the impact tool fixed with the impact hammer as showing in the Figure 3 whereas it strikes the beam with a velocity of 4.14 m/s. During test maximum deflection at the centre of beam was recorded with the help of LVDT and crack patterns were also observed after each blow. Total nine beams of size 150mmx150mmx500mm were cast. Each group of three beams were cast with M20, M25 and M30 grade concrete and beams in each group were designed as under , balanced and over reinforced sections in accordance to IS 456:2000. During test beams were provided simple supports with centre to centre distance of supports as 400mm and an overhang of 50mm on both sides to avoid overturning during testing. The line impact test on concrete beam was done with the help of impact hammer testing machine, the impact hammer of equivalent weight 25.4kg at the level of point, where it strikes the beam with a velocity of 4.14 m/s. The line impact hammer was initially kept horizontal as shown in Figure 1(b) and then allowed to fall freely under gravity to strike the beam horizontally as shown in Figure 1(c). The hammer was lifted manually and was anchored to a wooden trigger, from where it was dropped by trigger a side. The position of trigger was properly marked so that every time hammer is dropped, the height of fall remains constant. At the point of striking a rod of 16 mm was fixed on the impact hammer so that the load acts as a Line load on beam. In the impact hammer testing machine the beam to be tested was clamped with the help of steel rod and plates of diameter 20mm and thickness of plates 12mm. The steel rod had threads at its end which were fastened by bolts. Proper care was taken at the time of experiment to avoid loosening of bolts by wrapping the cotton thread on rod. Wooden packing was also put to avoid any type of slippage. Figure 1 Testing of beam under line impact load (a)Arrangement for line impact (b) Hammer in horizontal position (c) Testing of beam
  • 3. I.K .Khan, International Journal of Engineering, Business and Enterprise Applications, 8(2), March-May., 2014, pp. 101-104 IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 103 B. Observation and Test Results For the beam cast with M30 grade concrete and designed as balanced section and designated as M30B, deflection and physical condition of the beam after each line impact or blow is shown in the Table 1. These were also recorded for other type of beams viz. M20B, M20O, M25U, M25B, M25O, M30U, and M30O where M20, M25 and M30 are grades of concrete and U, B and O stands for under, balance and over reinforced sections respectively. Test results like strain energy and theoretical deflection etc. obtained by analysis is shown in Table 2 for the beam cast with M30B. Crack patterns observed during line impact test for beam M30B is shown in Figure 2. Table 1 Deflection and physical condition of beam M30B Blow no. Deflection (mm) Formation of Cracks Remark 1 8.135 Two vertical cracks First crack on left hand side 2 11.162 First and second increased and third crack also formed Second crack on right hand side 3 12.522 Cracks width increased First crack distance 5cm and second crack distance 10cm from support 4 13.283 Cracks width increased Third crack on left hand side 5 13.872 Cracks width increased Third crack distance 7.5 cm from support 6 14.082 Fourth crack formed Fourth crack on right hand side 7 14.550 Cracks width increased Fourth crack distance 2cm from support 8 14.654 Maximum width of cracks Beam failed Table 2 Strain energy and theoretical deflection values for beam M30B Blow No. Deflection (mm) W (kN) Strain Energy ‘U’ (kJ) Theoretical Deflection (mm) 1 8.135 58.38 0.024 0.832 2 11.162 42.55 0.0128 0.606 3 12.522 37.93 0.0102 0.540 4 13.283 35.76 0.009 0.509 5 13.872 34.24 0.008 0.487 6 14.082 33.73 0.008 0.48 7 14.550 30.54 0.006 0.43 8 14.654 30.34 0.006 0.432 Figure 2 crack patterns for beam M30B IV. Conclusions On the basis of experimental testing and analysis of reinforced concrete beam under line impact load following conclusions have been drawn: 1. Beam M20U failed at third blow, M20B failed at fifth blow and M20O failed at eight blow. 2. Beam M25U failed at fifth blow, M25B failed at seventh blow and M25O failed at ninth blow. 3. Beam M30U failed at sixth blow, M30B failed at eight blow and M30O failed at twelfth blow. 4. The maximum experimental deflection in beam M20U is 18.23mm, in beam M20B is 17.92 mm and in beam M20O is 17.28mm. 5. The maximum experimental deflection in beam M25U is 17.94mm, in beam M25B is 16.26mm and in beam M25O is 15.58mm.
  • 4. I.K .Khan, International Journal of Engineering, Business and Enterprise Applications, 8(2), March-May., 2014, pp. 101-104 IJEBEA 14-262; © 2014, IJEBEA All Rights Reserved Page 104 6. The maximum experimental deflection in beam M30U is 15.70 mm, in beam M30B is 14.65mm and in beam M30O is 12.67mm. 7. The maximum theoretical deflection in beam M20U is 3.16mm, in beam M20B is 2.90mm and in beam M20O is 1.46mm. 8. The maximum theoretical deflection in beam M25U is 1.58 mm, in beam M25B is 1.62mm and in beam M25O is 1.22mm. 9. The maximum theoretical deflection in beam M30U is 0.90mm, in beam M30B is 0.85mm and in beam M30O is 0.74mm. 10. The scabbing started in beam M20U at second blow, in beam M20B at third blow and in beam M20O at fourth blow. 11. The scabbing started in beam M25U at third blow, in beam M25 B at fourth blow and in beam M25O at fifth blow. 12. The scabbing started in beam M30U at fourth blow, in beam M30B started at fifth blow and in beam M30O started at sixth blow. In view of the above results it can be concluded that with the increase in the grade of concrete and quantity of steel more number of blows are required to cause failure in the beam, whereas maximum experimental and theoretical deflection reduces with the increase in the grade of concrete and quantity of steel. Scabbing in the beams started at increased number of blows as grade of concrete and steel increases in the beam. Thus we can say that impact load carrying capacity of the beam improve by increasing in the grade of concrete and quantity of steel. References 1. M. Alam, “Quasi-Static & Drop Hammer Loading of Plain and Skin Reinforced Concrete Plates” PhD Thesis, Indian Institute of Technology, Delhi, India , Dec. 1999. 2. M. Kumar, V. Kanwar. And S. Kumar, “Non – Destructive Evaluation of Dynamic Properties of Concrete”, IE (I) Journal, India, Vol. 86, August 2005. 3. A.K.H. Kwan., W. Zhang. and I.Y.T Ng, “Effects of Shock Vibration on Concrete”, A. C. I. Material Journal, USA, Nov. – Dec., 2005. 4. Kishi, N., H. Mikami, and T. Ando, “Impact Behaviour of Shear – Failure – Type RC Beams without Shear Rebar”. Int. J. of Impact Engineering, Vol. 27, pp. 955 – 968, 2002.