20320130406005

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308
INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND
(Print), ISSN 0976 – 6316(Online) Volume 4, Issue 6, November – December (2013), © IAEME

TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)
ISSN 0976 – 6316(Online)
Volume 4, Issue 6, November – December, pp. 44-54
© IAEME: www.iaeme.com/ijciet.asp
Journal Impact Factor (2013): 5.3277 (Calculated by GISI)
www.jifactor.com

IJCIET
©IAEME

FLEXURAL BEHAVIOR OF STRENGTHENED RC BEAMS USING
DIFFERENT MATERIALS AND TECHNIQUES
Yasser R. Tawfic
Asst. Prof. in Civil Engineering Dept., Minia University, Minia, Egypt

ABSTRACT
This research work is an experimental study investigates the flexural behavior of reinforced
concrete beams strengthened with various materials and techniques. The experimental program
consists of eight reinforced concrete beams having a rectangular cross-section. One beam was
subjected to flexural stresses up to failure to serve as a control beam. The remaining seven reinforced
concrete beams were preloaded until cracking and then repaired and strengthened. The strengthened
beams were reloaded under two-point loads until failure happened. Carbon fiber reinforced polymer
sheets (CFRP), glass fiber reinforced polymer sheets (GFRP), steel plates (SP), or combinations
between the previous mentioned materials were used to make the flexural repairing and
strengthening for the cracked RC beams. One of the main objectives of this research is to investigate
the flexural properties of beams strengthened with both steel plates and fiber reinforced polymers.
Generally, strengthening of RC beams resulted in higher values of yield and ultimate loads as well as
increases the stiffness of the strengthened beams. However, the ductility of the strengthened beams
was decreased.
Key words: Carbon Fiber, Glass Fiber, Repair, Steel Plates, Strengthening.
1.

INTRODUCTION

Large numbers of buildings and infrastructures around the world are facing serious
deterioration due to carbonation, chloride attack, earthquakes and due to overloading such as the
increase of the number and weight of trucks on old bridges. Repair and strengthening is essential task
to upgrade the deteriorated reinforced concrete structures so that it can withstand the applied loads
and stresses having reasonable factors of safety. Different methods and techniques of repair and
strengthening of RC structures are available, such as concrete jacketing, external pre-stressing,
sprayed concrete and repairing by attaching steel sections or fiber reinforced polymers (FRP) to the
concrete elements.
44

Many experimental and theoretical researches were conducted to investigate the flexural
behavior of the strengthened RC elements. Mohd Z. Jumaat et al. (2007) conducted experimental
study by strengthening RC beams and they concluded that the uses of steel plates or FRP laminates
are preferable to increase the flexural strength of the strengthened RC beams. They also reported
that, the FRP laminate is more effective in increasing the flexural capacity of RC beams when
compared to the steel plates. Liu et al. (2006) showed that beams retrofitted with near surface
mounted steel plates reached a strain of 0.042 at ultimate load compared to 0.014 strains for beams
retrofitted with CFRP plates. Test results showed that RC beams strengthened with steel plates have
higher values of ductility when compared with the beams strengthened with FRP laminates.
Bencardino F. et al (2002) mentioned that, the deformation of RC beams strengthened with
externally bonded fabrics is very similar to that of beams strengthened with laminates. Increasing
failure loads of the strengthened beams were accompanied by a reduction for the final deflection and
curvature. Bencardino reported that, test results showed conclusive evidence that strengthening with
externally bonded fabrics results in significant losses in the structural ductility of the strengthened
beams. Structural ductility is shown to depend not only on the type and amount of external
reinforcement but also, equally importantly, on the anchorage systems used and the concrete strength
and reinforcement details of the un-strengthened beam.
This research work is an experimental work was conducted to investigate the advantages and
disadvantages of different methods of repair and strengthening of RC beams using different materials
such as CFRP, GFRP, SP, or combinations between the previous mentioned materials. One of the
main objectives of this research is to define the strength and ductility of RC beams strengthened with
combinations of SP and CFRP or GFRP.
2. EXPERIMENTAL INVESTIGATION
An experimental program consists of eight reinforced concrete beams having a rectangular
cross section (120 x 250 mm). Two high tensile steel bars (diameter 10 mm) were used as tensile
reinforcements and two (10 mm diameter) steel bars were used as stirrups hangers. The stirrups were
5 8/m of mild steel type. These beams were tested using Universal test machine (Shimadzu-1000
KN) under flexural loading of simply supported with two point static load over a 1400 mm span, see
Fig. (1). Beam (B1) was loaded until failure occurs to serve as a reference beam. The remaining
seven beams were initially loaded until the cracking occurred. The cracked beams were rehabilitated
using carbon reinforced polymers (CFRP), glass reinforced polymers (GFRP), steel plates (SP), or
combinations between the steel plates and the fiber reinforced polymers as shown in table (1). The
strengthened beams were loaded until complete failure happened. The effect of the different methods
of rehabilitation on the deformation characteristics including the ductility, deflection and strain as
well as the failure loads were identified and discussed. The pattern of cracks and modes of failure
were also detected and illustrated.

P
2

10

30 cm

Stirrups 6

8/m

2
25 cm

2

10

2

10

25 cm

10

12 cm

140 cm
160 cm

Fig. (1): Dimensions and reinforcements details of the test specimens
45

Table (1) Test specimens
Beam
B1

FRP width
and shape
(mm)

B2
B3

Concrete Cover
thickness
(mm)

---

---

240 - U-shape

---

(20 mm)

120 - straight

Reference beam
1 Layer (carbon fiber reinforced
polymers)
2 Layer (carbon fiber reinforced
polymers)

SP dimensions
(mm)

---

Type of repair

---

(20 mm)

B4

1 Layer (glass fiber reinforced polymers)

240 - U-shape

---

(20 mm)

B5

Steel plates (SP)

120 - straight

60x1300x3.0

---

B6

1 Layer (CFRP) + (SP)

240 - U-shape

60x1300x3.0

---

B7

2 Layer (CFRP) + (SP)

120 - straight

60x1300x3.0

---

B8

1 Layer (GFRP) + (SP)

240 - U-shape

60x1300x3.0

---

2.1 Materials properties
2.1.1 Concrete
All test specimens were cast using the same type of concrete mix that has 250 kg/cm2
compressive strength after 28 days. Ordinary Portland cement produced by Beni-suef Company,
Egypt was used. The specific gravity and the surface area of the cement were 3.15 and 3500 cm2/gm,
respectively. Natural sand and gravel from local quires in Minia Governorate, Egypt were used to
prepare the concrete mixes. The specific gravity of the sand and gravel are 2.6 and 2.6, respectively.
The maximum nominal size of the gravel is 20 mm.
2.1.2 Steel
High tensile steel bars (10 mm Diameter) were used as tensile and compressive steel.
Meanwhile, mild steel reinforcement bars of diameter 8 mm were used as stirrups. Steel plates
(thickness=3.0 mm) were used to strengthen part of the test specimens. To define the mechanical
properties of the steel reinforcements, tensile tests were carried out on three elements of the
reinforcement and the average results are presented in table (2).
2.1.3 Fiber reinforced polymers
Carbon fiber reinforced polymers (CFRP) and glass fiber reinforced polymers (GFRP) which
were used for strengthening of the RC beams are unidirectional woven fiber fabric produced by Sika
Company, Egypt. The physical and mechanical properties of the FRP in dray case and as laminates
are shown in table (3).
2.1.4 Bonding agent for FRP (Sikadur-330)
Sikadur 330 is a two part, solvent free, thixotropic epoxy based impregnating resin/adhesive.
The tensile strength of the Sikadur-330 at 7-days is 300 kg/cm2 and the tensile modulus of elasticity
equal 45,000 kg/cm2. The elongation at break is 0.9%.
2.2 Strengthening process for test specimens
After preloading, test specimens were strengthened using different materials and techniques.

46

Table 2 – Mechanical properties of the steel reinforcements
Type of Reinforcement

Yield
strength
kg/cm2

Ultimate
strength
kg/cm2

% of
elongation

Bar (Diameter=8 mm)

3200

4931

19

Bar (Diameter=10 mm)

4760

6481

16

Steel plate (Thickness= 3 mm)

2900

4790

21

Table 3 – Physical and mechanical properties of the FRP

(g/m2)

Tensile
strength
(ton/cm2)

Tensile
E-Modulus

Elongation
at break

(ton/cm2)

%

1.76

230±10

43

2,380

1.8

1.00

--

--

3.5

280

--

GFRP

0.17

2.56

445±22

23

760

2.8

Laminate- GFRP

0.80

--

--

2.7

190

--

Thickness

Density

Areal weight

(mm)

(g/cm3)

Dray CFRP

0.131

Laminate-CFRP

Type of FRP

2.2.1 Strengthening using FRP
Beams were strengthened with one layer U-shape (width 240 mm) of Carbon or Glass fibers
and other beams were strengthened using two straight layers (width 120 mm) of Carbon or Glass
fibers. The preparation of the bottom surface of the test specimens was the first step for
strengthening. The casting form was originally designed to produce RC beams without bottom cover
within the strengthening area. The bottom surfaces were roughened using wire brushed to remove
any protrusions and to roughen the surfaces and then cleaned using compressed air to remove the
dust. The bonding resin (Sekadur-330) was applied to the bottom surface and the FRP layers were
fixed to the beams, see Fig. (2). The bottom surfaces were roughening by applying sand to the
surface before the hardening of the bonding resin. Finally, concrete cover was applied to protect the
FRP layers.

Fig. (2): Fixation of the CFRP sheets

47

2.2.2 Strengthening using steel plates
The bottom surface of the test specimens had no cover within the strengthening area. The
bottom surfaces were roughened using wire brushed and cleaned using compressed air. The steel
plate (60x1300x3 mm) was fixed to the bottom surface using four anchors (diameter 8 mm) and
bonding resin.
2.2.3 Strengthening using FRP and steel plates
The steps of repair began with the fixation of the FRP layers as mentioned before and then
the steel plate (60x1300x3 mm) was fixed to the bottom surface using the bonding resin and four
anchors (diameter 8 mm) as shown in Fig. (3).

Fig. (3): Fixation of the CFRP sheet and the steel plates
3 RESULTS AND DISCUSSION
3.1 Pattern of cracks and modes of failure
Beam B1 was subjected to flexural stresses up to failure. Cracks were firstly formed in the
bottom surface of the constant moment zone and in the shear span. Increasing the applied load, the
flexural cracks were extended upwards and widened. Finally, the reference specimen was failed due
to yielding of the tensile steel reinforcement. Fig. (4-a) shows the pattern of cracks for the reference
specimen.
Beam B2 (strengthened using one layer -U shape- CFRP) was failed in flexural due to debonding of the CFRP layer. The de-bonding began at the end of the CFRP sheet at the top of the two
sides of the U-shape. Before reaching the ultimate load, horizontal crack was observed between the
strengthening layer and the existing concrete. This crack was extended horizontally for all the length
of the shear zone. The flexural cracks were widened and one of the flexural cracks was extended in
an inclined direction towards the load point. Finally, the fracture of the CFRP sheet was occurred.
The pattern of cracks of beam B2 is shown in Fig. (4-b and c).
Beam B3 (strengthened with two layers of CFRP sheets) was failed mainly due to de-bonding
between the CFRP sheet and the existing concrete. Before reaching the ultimate load, horizontal
crack was observed between the strengthening layer and the existing concrete. After the extension of
the horizontal crack, slip was observed between the strengthening layer and the existing concrete.
Because of this slip, the flexural cracks were widened leading to the failure of the RC beam. It is
worth to mention that the use of U-shape CFRP sheet for strengthening B2 resulted in better bond
between the RC beam and the strengthening layer when compared to that of beam B3. The pattern of
cracks for beam B3 is presented in Fig. (4-d)
On loading beam B4, which was strengthened with one layer U-shape GFRP, the usual
flexural cracks were observed in the constant moment zone. De-bonding at the top area of the Ushape GFRP sheet was appeared in the middle of the beam leading to the failure of the specimen due
to the fracture of the GFRP and crushing of the concrete at the compression zone as shown in Fig. (4e). This failure of beam B4 was accompanied by a sudden explosive sound.

48

ine)

(a) Pattern of cracks of the reference beam B1.

(b) Pattern of cracks of beam B2.

( c) CFRP Failure.

(d) Pattern of cracks of beam B3 (de-bonding of the CFRP layers)
bonding

(e) Pattern of cracks of beam B4 (failure of the GFRP layer)

(f) Pattern of cracks of beam B5 (de-bonding of the steel plate)
(

(g) Pattern of cracks of beam B6
(g

(h) Pattern of cracks of beam B7 (de
(de-bonding of the CFRP and steel plate)
f

(i) Pattern of cracks of beam B8
)
Fig. (4): Pattern of cracks of the test specimens
49

Beam B5 was strengthened using steel plates and loaded up to failure. At first, flexural cracks
were formed at the constant moment zone. Increasing the applied load, the flexural cracks were
extended upwards and widened and new flexural cracks were formed. Finally, De-bonding of the
steel plate and pulling out the anchors, which were broken, were takes place resulting in the beam
failure; see Fig. (4-f). The fracture of beam B5 was accompanied by a loud noise.
One layer U-shape CFRP and a steel plate were used to repair beam B6. The fixation of the
strengthening layer was strong enough, so that no indication of de-bonding for the CFRP sheet and
the steel plate was appeared. Specimen B6 was failed in shear due to the extension of a flexural crack
in an inclined direction towards the load point. The pattern of cracks of this specimen is shown in
Fig. (4-g).
Beam B7 was strengthened with two straight layers of CFRP and a steel plate. The failure of
this beam was due to the pulling out of the anchors and the de-bonding of the CFRP layers. A
horizontal crack between CFRP and the existing concrete was extended inside the constant moment
zone. The flexural cracks were widened and the specimen was not capable of withstanding higher
loads. Complete separation for the strengthening layer was occurred accompanied with crushing of
the concrete in the compression zone; see Fig. (4-h).
Specimen B8 was strengthened with one layer U-shape GFRP and a steel plate. Similar to
specimen B6, beam B8 was failed in shear due to the extension of a flexural crack in an inclined
direction towards the load point. Because of the high bond strength between the U-shape GFRP and
the existing concrete, no horizontal cracks were observed until reaching the ultimate load. After
reaching the ultimate load, the load was slowly descended and small horizontal cracks began to
appear at the end of the strengthening layer, between the strengthening layer and the existing
concrete, see Fig. (4-i).
3.2 Ultimate loads of the test specimens
Fig. (5) shows the ultimate loads for all test specimens. Generally it is clear that, the repair
and strengthening of the RC beams resulted in from 35% to 50% of increase for the values of the
ultimate loads when compared with the reference beam [4, 5, 6, 7]. The values of the ultimate load of
the strengthened beams were dependent on the bond strength of the strengthening layer and the RC
beams as well as on the tensile strength of the strengthening layers. Compared with beam B3, Beam
B2 strengthened with U-shape CFRP sheet resulted in slightly higher values of ultimate loads which
is attributed to the better bond strength between the strengthening layer and the RC beam. Because of
its higher tensile strength, the use of CFRP instead of GFRP for strengthening the RC beams resulted
in about 5% of increase for the values of the ultimate loads. The use of steel plate for the repair of
beam B5 resulted in about 35% increase for the values of the ultimate loads8. However, the use of
one U-shape layer of CFRP and a steel plate for strengthening beam B6 resulted in the highest value
of ultimate load that is 50% higher than the ultimate load of the reference beam. Similar trend was
observed for beam B8 that strengthened with one U-shape layer of GFRP and a steel plate. The value
of the ultimate load of beam B6 and B8 could be higher if their shear strength were high enough to
prevent the shear type of failure.

50

Ultimate load (ton)

12
10
8
6
4
2
0
B1

B2

B3

B4

B5

B6

B7

B8

Fig. (5): Ultimate loads for the test specimens

3.3 Deflection of the test specimens
Although the strengthened beams experienced the usual elastic and inelastic deflections,
higher values of rigidity and considerably lower values of plastic deformations were recorded for the
strengthened beams when compared with the reference ones [4, 9]. This behavior may be attributed
to the high capability of the strengthening layers to restrict and minimize the number and width of
the flexural cracks. Figure (6) shows the load-deflection for the reference beam, beams B2 and beam
B3. The reference beam showed lower values of rigidity and higher values of elastic deformation
than beams B2 and B3. Same rigidity until reaching the yield stage were observed for beams B2 and
B3 which were strengthened using one U-shape CFRP sheet or two CFRP sheets, respectively.
However, beam B2 had 20% higher values of deflection at failure than beam B3 that may be
attributed to the better bond between the U-shape sheet and the bottom surface of the strengthened
beam.
Beam B5, which was strengthened with steel plate showed slightly higher values of rigidity
than specimens B2 and B4. Unexpectedly, lower values of deflection at failure was recorded for
beam B5 which may be attributed to the de-bonding of the steel plate, see Fig. (7). The use of both
steel plate and FRP sheets for strengthening the RC beams (B6, B7, and B8) resulted in slightly
higher values of rigidity and elastic deflection at failure than the beams strengthened with FRP sheets
only. The values of the elastic deformation at failure for beams B6 and B8 would be higher if these
beams could sustain higher values of shear stresses. The improvement of the elastic deformation is
thought to be related to the plastic deformation properties of the steel plates, see Fig. (8-a to c).

12

10

10

8

Load (ton)

Load (ton)

12

6
4
2

B1

B2

8
6
4
B1
B4

2

B3

0

B2
B5

0
0

5

10
15
Deflection (mm)

20

25

0

Fig. (6): Load-Mid span deflection.

5

10
15
Deflection (mm)

20

25


51


10

10
Load (ton)

12

Load (ton)

12

8
6
4

8
6
4
2

2

B1

B2

B6

0
0

10
20
Deflection (mm)
(a)

B1

B3

B7

0
0

30

10
20
Deflection (mm)
(b)

30

12
Load (ton)

10
8
6
4
2
B1

0
0

5

B4

10
15
Deflection (mm)
(c )

B8
20

25

3.4 Ductility of the test specimens
Ductility is defined as the ratio of the value of deflection at failure to the value of deflection
at yield load. Generally, lower values of ductility were recorded for the strengthened specimens
(from 1.78 to 3.33) when compared with the reference beam (4.13) as shown in Fig. (9) [10]. This
was mainly attributed to the brittle nature of the FRP sheets, the de-bonding of the strengthening
layers as well as the increase in the gross tensile reinforcement ratio, which may change the mode of
failure for the strengthened specimens from ductile flexural mode to brittle de-bonding or shear
failure.
The use of both FRP sheets and steel plates for strengthening beams B6, B7, and B8 resulted in
up to 87% increase for the values of the ductility index than those of beams B2, B3, B4, and B5
which may be attributed to the better fixation and the plastic deformations

Ductility Index

5
4
3
2
1
0
B1

B2

B3

B4

B5

B6

B7

Fig. (9): Ductility index of test specimens
52

B8

properties of the steel plates. It is worth to mention that, the use of U-shape CFRP sheet (width = 240
mm) for strengthening beam B2 resulted in 25% higher values of ductility index than the use of two
straight layers of CFRP sheet (width 120 mm) for beam B3.
3.4 Strain in FRP sheets
Fig. (10) shows the strain in the middle of the CFRP sheets for beams B2 (strengthened with
one layer U-shape CFRP sheet) and beam B3 (strengthened with two layers CFRP sheets). Higher
value of strain was recorded for the U-shape CFRP sheet (beam B2) than the value of strain in the
straight CFRP sheet which is attributed to the good fixation of the U-shape CFRP sheet that led to its
fracture. Because of the use of GFRP sheet with steel plate to strengthen beam B8 that failed due to
shear, lower values of strain was recorded in the GFRP sheet of B8 when compared with the value of
strain in the GFRP sheet that used to strengthen beam B4 which was failed due to flexural stresses,
see Fig. (11).

10

10

8

8

Load (ton)

12

Load (ton)

12

6
4
2
B2

6
4
2

B3

0

B4

B8

0
0

1000

2000

3000

4000

0

Strain in CFRP sheets x 10-6

Fig. (10): Strain in CFRP sheets.

1000
2000
3000
4000
Strain in GFRP sheets x 10-6

Fig. (11): Strain in GFRP sheets.

4. CONCLUSIONS
Based on the experimental studies, the following can be concluded:
[1]

[2]
[3]

Strengthening with FRP sheets, steel plates, or both FRP sheets and steel plates are found to
be effective techniques for upgrading the RC beams. The values of the ultimate loads of the
strengthened beams were up to 50% higher than the value of the ultimate load of the
reference beam. Because of the high fixation strength of the strengthening layer, the use of Ushape FRP sheet and a steel plate for strengthening beams B6 and B8 resulted in the best
flexural performance of the strengthened test beams.
Shear failure, fracture of the FRP sheets, and de-bonding of the strengthening layers were the
predominant modes of failure for the strengthened beams.
Although the strengthened beams experienced the usual elastic and inelastic deformations,
higher values of rigidity and considerably lower values of plastic deformations were recorded
for the strengthened test beams when compared with the reference beam which may be
attributed to the high capability of the strengthening layers to restrict and minimize the
number and width of the flexural cracks. Fixing the FRP cross-sectional area, the use of Ushape CFRP sheet (B2) or two layers of CFRP sheets (B3) showed the same rigidity until
53


[4]

reaching the yielding stage, after that beam B2 had 20% higher values of deflection at failure
than beam B3.
Considerably lower values of ductility were recorded for the strengthened RC beams when
compared with the reference beam. This was mainly attributed to the brittle nature of the FRP
sheets as well as the increase in the gross tensile reinforcement ratio, which may change the
mode of failure of the beams from ductile flexural mode to brittle de-bonding or shear failure.
To overcome and release the negative effect of strengthening on the ductility of the RC
beams, FRP sheets with steel plates are both recommended to be used for the rehabilitation of
the RC beams.

5. REFERENCES
[1]

Mohd Zamin bin Mohd Jumaat and Md Ashraful bin Alam “Strengthening of Reinforced
Concrete Structures” JURUTERA, July 2007, pp. 28-29.
[2] Liu I.S.; Oehlers D.J. and Seracino R. “Tests on the Ductility of Reinforced Concrete Beams
Retrofitted with FRP and Steel Near-Surface Mounted Plates” Journal of Composites for
Construction, ASCE, March/April 2006..
[3] Bencardino F.; Spadea G.; and Swamy R.N. “Strength and Ductility of Reinforced Concrete
Beams Externally Reinforced with Carbon Fiber Fabric” ACI Structural Journal, Vol. 99,
No.2, March-April 2002, pp. 163-171.
[4] Yasser R. Tawfic; Tsuji Y.; and Sugiyama T. “Flexural Strengthening of Reinforced
Concrete Slabs Using CFRP Grid.” Journal of Cement Science and Concrete Technology,
No. 58, 2004, pp. 460-467.
[5] Yasser R. Tawfic; Tsuji Y.; and Sugiyama T. “Flexural Performance of RC Slabs
Strengthened with Spliced CFRP Grids.” Journal of Cement Science and Concrete
Technology, No. 59, 2005, pp. 490-497.
[6] Sergio F. B.; Regan M. B.; Sharon L. W.; and Michael E. K. “Increasing Flexural Capacity of
Reinforced Concrete Beams Using Carbon Fiber-Reinforced Polymer Composites” ACI
Structural Journal, Vol. 100, No. 1, January-February 2003, pp. 36-46.
[7] Bahram M. S.; Serpil B.; and Michael B. “Flexural Strengthening of Four 76-Year-Old TBeams with Various Fiber-Reinforced Polymer Systems: Testing and Analysis.” ACI
Structural Journal, Vol. 99, No. 5, September-October 2002, pp. 681-691.
[8] Awadh E. Ajeel; Rana H. Ghedan; and Dina M. Hamza “Replacing of Internal Tension Bars
by External Bonded Plate” Journal of Engineering and Development, Vol. 15, No. 3,
Sepetember (2011), pp. 90-103.
[9] El-Mihilmy, M.T., and Tedesco, J.W. “Deflection of Reinforced Concrete Beams
Strengthened with Fiber-Reinforced Polymer (FRP) Plates.” ACI Structural Journal, Vol. 97,
No. 5, Sept.-Oct. 2000, pp. 679-688.
[10] Lamanna A.J.; Bank L.C.; and Scott D.W. “Flexural Strengthening of Reinforced Concrete
Beams Using Fasteners and Fiber-Reinforced Polymer Strips.” ACI Structural Journal, Vol.
98, No. 3, May-June 2001, pp. 368-376.
[11] Javaid Ahmad and Dr. Javed Ahmad Bhat, “Flexural Strengthening of Timber Beams using
Carbon Fiber Reinforced Polymer Plates”, International Journal of Civil Engineering &
Technology (IJCIET), Volume 4, Issue 5, 2013, pp. 61 - 77, ISSN Print: 0976 – 6308, ISSN
Online: 0976 – 6316.
[12] Mohammed S. Al-Ansari, “Flexural Safety Cost of Optimized Reinforced Concrete Beams”,
International Journal of Civil Engineering & Technology (IJCIET), Volume 4, Issue 2, 2013,
pp. 15 - 35, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.

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