Upload
ovunctezer
View
219
Download
0
Embed Size (px)
Citation preview
8/10/2019 9936 c 614512
1/6
Flexural Strengthening of RC Beams
with NSM Steel Bars
Md. Akter Hosen, Mohd Zamin Jumaat, Kh. Mahfuz Ud Darain, M. Obaydullah,
and A. B. M. Saiful Islam
AbstractIncreased service loads, imposed cyclic loading anderror in design and construction encourage the re-construction of
existing structural elements for strengthening. Externally bondedreinforcement (EBR) and near surface mounted (NSM) techniques,
are the main strengthening approaches traditionally used till date.This paper presents an experimental investigation on the flexuralstrengthening of reinforced concrete (RC) beams with NSM
technique using different ratios of steel bars. Four-point bending testswere carried out up to failure on four rectangular RC beams (125 mmwidth by 250 mm depth by 2300 mm length) strengthened withdifferent ratios of steel reinforcement (different yield and ultimate
strengths). Yield and ultimate strengths, flexural failure modes,cracking behavior and ductility are reported and discussed based onmeasured load and deflection. The test results show that flexuralstrength increased up to 53.02% and energy and deflection ductilityimproved.
KeywordsBending stiffness, Ductility, Flexural strengthening,NSM.
I.INTRODUCTION
EINFORCEDconcrete structures all over the world require
rehabilitation or strengthening at some in their life span
due to various reasons such as mechanical damage,
environmental effects, increased service loads, and errors in
design and construction. There are a number of methods forstrengthening existing reinforced concrete structures.
Externally bonded reinforcement (EBR) and the near surface
mounted (NSM) technique are among the most popular
strengthening methods [1-5]. The EBR technique involves the
external bonding of strengthening materials such as steel
plates or fiber reinforced polymer (FRP) laminates. However,
this technique suffers from the high possibility of premature
failure such as debonding of longitudinal laminates,
delamination and other types of premature failure.
Md. Akter Hosen is with the Civil Engineering Department, Faculty of
Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
(Corresponding authors Cell: +60183704547;
Mohd Zamin Jumaat is with the Civil Engineering Department, Faculty of
Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
Kh. Mahfuz Ud Darain is with the Civil Engineering Department, Faculty
of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
M. Obaydullah is with the Civil Engineering Department, Faculty of
Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
A. B. M. Saiful Islam is with the Civil Engineering Department, Faculty of
Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia.
This prevents the strengthened members from achieving
ultimate flexural capacity [6-8]. Moreover, the externally
bonded steel or FRP plates are vulnerable to thermal,
environmental and mechanical damage. Therefore, the NSM
strengthening technique offers an effective substitute to the
EBR technique. In the NSM method the surrounding concrete
protects the NSM bars or strips from thermal, environmental
and mechanical damage, as well as delaying or preventing
premature failure. The NSM technique was first used in the
1940s in Finland where steel bars were put into grooves to
strengthen a bridge deck slab [9]. The first experimentalresearch on the NSM technique using CFRP strips in grooves
cut into the concrete specimens was conducted by [10]. A
number of experimental studies have investigated the flexural
behavior of RC beams strengthened with NSM bars or strips
using FRP materials [11-16]. FRP reinforcement has various
advantages such as high strength, light weight, resistance to
corrosion and potentially high durability but is highly
expensive and not readily available. In addition, FRP
reinforcements have little ductility. On the other hand, steel
bars are readily available, less expensive, show adequate
ductility, long-term durability and bond performance [17].
NSM strengthening using steel bars has been used on masonrybuildings and arch bridges [18]. Almusallam et al. [19]
investigated the experimental and numerical behavior of RC
beams strengthened in flexure with NSM steel or GFRP bars
and found that NSM bars promoted the flexural capacity of
RC beams.
In this paper the structural behavior of RC beams
strengthened with NSM steel bars and exposed to flexural
loading is investigated. Due to its economic feasibility, steel is
used as the strengthening material. It provides a cost-effective
solution which is also structurally efficient. The test variables
are strengthening reinforcement ratio and yield strength. Load,
deflection and strain data are analyzed to understand cracking
behavior, failure modes, ductility and bending stiffness of thetested beams.
II.EXPERIMENTAL PROGRAM
A. Test Matrix
A total of four RC beam specimens were tested. The first
beam specimen was the control beam with no strengthening
and the remaining beam specimens were strengthened with
steel bars of different diameters.
R
International Conference on Food, Agriculture and Biology (FAB-2014) June 11-12, 2014 Kuala Lumpur (Malaysia)
http://dx.doi.org/10.15242/IICBE.C614512 8
8/10/2019 9936 c 614512
2/6
TABLE I
TEST MATRIX
Notation DescriptionStrengthened barstrength (MPa)
Yield Ultimate
CB Control beam
(unstrengthened)-
NSM1 Beam strengthened with
1-6 mm steel bar580 650
NSM2 Beam strengthened with
1-8 mm steel bar
379 536
NSM3 Beam strengthened with
1-10 mm steel bar520 570
B. Specimen Configuration
The specimen dimensions and reinforcement details are
shown in Fig. 1. The beams were designed as under reinforced
beams to initiate failure in flexure, in accordance with the ACI
code [20]. The cross-sectional dimensions of the beams were
125 mm x 250 mm and the length of the beams was 2300 mm
with 2000 mm as the effective span and a shear span of 650
mm. Three types of steel bars, 12 mm, 10 mm and 6 mm in
diameter, were employed in constructing the beam specimens.
The internal tension reinforcement of all beams consisted of
two deformed steel bars, 12 mm in diameter, which were bent
ninety degrees at both ends to fulfill the anchorage criteria.Two deformed steel bars, 10 mm in diameter, were used as
hanger bars in the shear span zone. The shear reinforcement
consisted of smooth steel bars, 6 mm in diameter, distributed
along the length of the beams as shown in Fig. 1.
(a)
Control beam
(b)
Strengthened beam
(c)
Cross-section of beam and groove
Fig. 1 Specimen design details
C. Material Properties
All beam specimens were cast used normal concrete.
Crushed granite was used as coarse aggregate and the
maximum size of the coarse aggregate was 20 mm. Natural
river sand was used as fine aggregate. Fresh tap water was
used to hydrate the concrete mix during the casting and curing
of the beams, cubes, prisms and cylinders. Concrete consisted
of 224 kg/m3 of water, 888 kg/m3 of fine aggregate, 892
kg/m3of coarse aggregate and 420 kg/m3of OPC and a 0.50
water/cement ratio. The 28 days average compressive strength
of the concrete was 40 MPa based on tests of three 100 mm x
100 mm x 100 mm concrete cubes. The yield and ultimate
strength of 12 mm steel bar was 550 MPa and 640 MPa
respectively. The modulus of elasticity for all bars was 200
GPa. Sikadur 30, an epoxy adhaesive, was used to bond the
strengthening materials to the concrete substrate. Sikadur 30
has two components namely component A and component B.
Component A is white in color while component B is black.
800 mm 800 mm700 mm
2000 mm
6 mm @ 50 mm
2 No.10M
2 No.12M
2000 mm
1900 mm
250 mm
125 mm
NSM Bar
Epoxy1.5 db
1.5 db
International Conference on Food, Agriculture and Biology (FAB-2014) June 11-12, 2014 Kuala Lumpur (Malaysia)
http://dx.doi.org/10.15242/IICBE.C614512 9
8/10/2019 9936 c 614512
3/6
The two components were mixed in a ratio of 3:1 until a
uniform grey color was achieved. The density was 1.65
kg/liter at 23C after mixing. The bond strength with steel is
21 MPa and with concrete is 4 MPa. The compressive, tensile
and shear strengths of this adhesive vary with curing time as
shown in Table II.
TABLE II
PROPERTIES OF SIKADUR30
Strength Curing time Amount (MPa)
Compressive strength
7days
95.00
Tensile strength 31.00Shear strength 19.00
Fig. 2 Instrumentation and loading set-up.
D. Strengthening Procedure
In the NSM technique strengthening bars are placed into
grooves cut into the concrete cover of the RC beams and
bonded using an epoxy adhesive groove filler. In this
investigation the installation of the strengthening steel bars
began with the cutting of grooves with the dimensions
specified in Table 1 into the concrete cover of the beam
specimens at the tension face in the longitudinal direction.
The grooves were made with a special concrete saw with a
diamond blade. A hammer and a hand chisel were used to
remove any remaining concrete lugs and to roughen the lower
surface of the groove. The grooves were cleaned with a wire
brush and a high pressure air jet. The details of the grooves
are shown in Fig 1. The grooves were half filled with epoxy
and then the steel rod was placed inside the groove and lightly
pressed. This forced the epoxy to flow around the inserted
steel bar. More epoxy was used to fill the groove and the
surface was leveled. To ensure the epoxy achieved full
strength, the beam was left for one week.
E. Test Set-up
The instrumentation of the beams is shown in Fig. 2. To
measure the deflection at beam mid span, one vertical linear
variable differential transducer (LVDT) was used.
To measure strains a number of gauges were used. Two 5
mm strain gauges were attached to the middle of the internal
tension bars. A 30 mm strain gauge was placed on the top
surface of the beam at mid span. Demec gauges were attached
along the depth of the beam at mid span.
All beams were tested in four-point bending using an
Instron Universal Testing Machine. Tests were carried out
using two controls. The first was load control, which was
close to the yield capacity of the beam and the second was
displacement control until failure of the beam. All data were
recorded at 10 second intervals. The rate of the actuator was
set to 5 kN/min during load control and 1.5 mm/min duringdisplacement control. A Dino-Lite digital microscope was
used to measure crack widths on the beams during testing.
III. EXPERIMENTAL RESULTS
The leading aspects considered in this study are cracking
load, crack width, yield load, ultimate load and modes of
failure. The results of the tested beams are given in Table III.
TABLE IIISUMMARY OF BEAM TEST RESULTS
A. Load-Deflection Curve
Fig. 3 shows the load versus midspan deflection for all
beam specimens. As can be seen from the figure, the curves
exhibit a tri-linear response defined by elastic, concrete
cracking to steel yielding and steel yielding to failure stages.
In the first stage, the behavior of all the beams is linear and
elastic. Before the first crack, the bond between the steel bar,
Beam
ID
Pcr
(kN)%Pcr
Py
(kN)% Py
Pu(kN)
%Pumax
(mm)
Failure
mode
CB 15.75 - 65.00 - 74.37 - 33.61 FLNSM1 17.00 7.94 75.00 15.38 80.00 7.57 41.68 FL
NSM2 20.00 26.98 90.00 38.46 101.0 35.81 40.23 FL
NSM3 22.00 39.68 100.00 53.85 113.8 53.02 39.13 FL
International Conference on Food, Agriculture and Biology (FAB-2014) June 11-12, 2014 Kuala Lumpur (Malaysia)
http://dx.doi.org/10.15242/IICBE.C614512 10
8/10/2019 9936 c 614512
4/6
adhesive and concrete is perfect. The first cracking load
increased by 7.94%, 26.98% and 39.68% for NSM1, NSM2
and NSM3 respectively, compared the control beam. In the
second stage, cracking initiates in the concrete section of the
maximum moment zone of the beam. At the beginning of this
stage, the cracks do not pass through the integrant materials
because of their higher tensile strength and low elastic
modulus. As the loading increases, the cracks become more
widespread and new flexural cracks arise. The use of NSMsteel bars increased the yield load of the strengthened beams
by 15.38%, 38.46% and 53.85% for NSM1, NSM2 and
NSM3 respectively over the control beam. In the third stage,
the internal tension steel reinforcement has yielded and the
NSM steel bar controls the cracks and the width of the cracks
up to failure of the beam. The ultimate load increased by
7.57%, 35.81% and 53.02% for NSM1, NSM2 and NSM3
respectively over the control beam.
Fig. 3 Load-midspan deflection of beams
B. Mode of Failure
The failure modes of all the beams are shown in Fig. 4. The
beam specimens exhibited two modes of failure. The firstfailure mode was by concrete crushing at the top fiber of the
RC beam cross-section and the second failure mode was by
yielding of the tension steel reinforcement. The cracking
pattern was similar for all the beams. At first, a fine flexural
crack developed at the midspan of the beam. As the external
load increased, additional cracks developed at the neutral axis
or beyond the neutral axis, with a notable increase in the
deflection of the beam. However, all strengthened beam
specimens showed narrower and finer cracks compared to the
control beam. This is due to the greater stiffness of the
strengthened beam specimens.
(a)
CB
(b)
NSM1
(c)
NSM2
(d)
NSM3
Fig. 4 Failure modes of beams
C. Crack Behavior
Fig. 5: Load-crack width
The loads versus crack widths of the beam specimens are
shown in Fig. 5. The first crack load of CB, NSM1, NSM2
and NSM3 were 15.75 kN, 17 kN, 20 kN and 22 kN
respectively. All strengthened beams showed higher first
crack loads compared to the control beam. Thus, the use of
near surface mounted steel bars increased the first crack load.
The total number of cracks of CB, NSM1, NSM2, and NSM3
were 11, 16, 17 and 19 respectively and the average crack
spacing of each beam was 240 mm, 115 mm, 125 mm and
100 mm respectively. NSM2 had wider crack spacing than
NSM1 and NSM3. This was because NSM2 was strengthened
with a low strength steel bar. However, all strengthened
beams showed smaller crack spacing than the control beam.
Thus, it can be said that beams strengthened with NSM steel
0
20
40
60
80
100
120
0 20 40 60
Load(kN)
Deflection (mm)
CB
NSM1
NSM2
NSM3
0
10
2030
40
50
60
70
80
90
0 0.2 0.4 0.6 0.8
L
oad(kN)
Crack width (mm)
CB
NSM1NSM2
NSM3
International Conference on Food, Agriculture and Biology (FAB-2014) June 11-12, 2014 Kuala Lumpur (Malaysia)
http://dx.doi.org/10.15242/IICBE.C614512 11
8/10/2019 9936 c 614512
5/6
bars exhibit more and finer cracks with closer spacing than
nonstrengthened beams.
D. Ductility
TABLE IVDUCTILITY OF TESTED BEAM
Beam
ID
Deflection ductility Energy ductility
y( mm)
u(mm)
d Ey
(kNmm)
Eu
(kNmm)E
CB 9.12 26.56 2.91 320.64 1661.25 5.18NSM1 11.74 12.74 1.08 488.25 560.00 1.15NSM2 10.68 20.18 1.88 557.57 1474.59 2.64
NSM3 12.14 23.06 1.90 679.20 1858.96 2.73
In this study two ductility indexes, deflection ductility and
energy ductility, were examined and are presented in Table 4.
The deflection ductility index is expressed as the ratio
between the deflection at ultimate load (u is the mid-span
deflection at ultimate load) and the yield load (y is the mid-
span deflection at yield load). The energy ductility index is
expressed as the ratio between the energy at ultimate state (Eu
is the area under the load-mid span deflection curve up to
ultimate displacement) and the yield state (Ey is the area
under the load-mid span deflection curve up to yield
displacement). The strength index is the ratio between the
maximum bending moment and the yield bending moment.
The deflection ductility index was reduced by 62.88%,
35.39%, and 34.71% for NSM1, NSM2 and NSM3
respectively over the control beam. The energy ductility index
was reduced by 77.79%, 49.03%, and 47.30% for NSM1,
NSM2 and NSM3 respectively over the control beam. The
strength index decreased by 6.14% and 1.75% for NSM1 and
NSM2 respectively over the control beam. However, the
strength index for NSM3 remained the same as the control
beam. The overall reduction in ductility of the strengthened
beams is most likely due to the increased tensionreinforcement ratio (tension steel bars and strengthened bars).
E. Bending Stiffness
The bending stiffness (EI)exp was computed experimentally
by applying the following equation:
( )
MEI =
expWith
aL
PM
2=
Andd
sc
+
= (1)
Where,M = bending moment (kN-m), P= applied load (kN),
La= distance between the first loading point and support, =
curvature (m-1),c
= top fiber concrete compression strain
ands
= internal tension steel strain. The bending stiffness
versus applied load are shown in Fig.6. Decrease in bending
stiffness is a result of crack formation. After the first crack
occurred, the bending stiffness of the beams decreased very
rapidly over a small increase in load. However, after the
yielding of the tension steel reinforcement, the bending
stiffness stabilizes. Thus, strengthening with NSM steel bars
not only enhances the strength of RC beams but also increases
the bending stiffness and in this way improves the mechanical
behavior of the strengthened members.
Fig. 6 Bending stiffness-load
IV.CONCLUSION
The investigation carried out in this paper on RC beams
strengthened with NSM steel reinforcement has shown that
this is a very effective strengthening technique. The following
conclusions can be derived from the experimental and
proposed theoretical model results:
-
The NSM steel reinforcement enhances the load-
deflection response of the RC beams. At any load level,
the deflections of the strengthened beams were
meaningfully less than that of the control beam except in
the case of NSM1 which was strengthened with a plain
steel rebar.
- Beams strengthened with NSM steel reinforcement have
significantly increased yield and ultimate capacities with
improvement in ductility (deflection and energy).- Increasing the amount of NSM steel reinforcement from
28.27 mm2 to 78.54 mm2 increased the ultimate load
capacity from 7.57% to 53.02%.
- The mode of failure observed in all strengthened beams
was flexural failure.
ACKNOWLEDGMENT
The authors gratefully acknowledge the financial support
from the University of Malaya High Impact Research Grant
under Account No-UM.C/HIR/MOHE/ENG/36.
REFERENCES
[1] ACI, A., 440.2 R-02: Guide for the design and construction of
externally bonded FRP systems for strengthening concrete structures.Farmingtion Hills, Michigan, American Concrete Institute, 2002.
[2] Barros, J.A., S.J. Dias, and J.L. Lima, Efficacy of CFRP-based
techniques for the flexural and shear strengthening of concrete beams.
Cement and Concrete Composites, 2007. 29(3): p. 203-217.http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001
[3] Barros, J.A. and R. Kotynia, Possibilities and challenges of NSM for
the flexural strengthening of RC structures.2008.[4] Akbarzadeh, H. and A. Maghsoudi, Experimental and analytical
investigation of reinforced high strength concrete continuous beams
strengthened with fiber reinforced polymer.Materials & Design, 2010.31(3): p. 1130-1147.
http://dx.doi.org/10.1016/j.matdes.2009.09.041
0
0.5
1
1.5
2
2.53
3.5
4
4.5
5
0 50 100 150Bendingstiffness(M
N-mm2)
Load (kN)
CB
NSM1
NSM2
NSM3
International Conference on Food, Agriculture and Biology (FAB-2014) June 11-12, 2014 Kuala Lumpur (Malaysia)
http://dx.doi.org/10.15242/IICBE.C614512 12
http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.matdes.2009.09.041http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.001http://dx.doi.org/10.1016/j.cemconcomp.2006.09.0018/10/2019 9936 c 614512
6/6
[5] Zhou, Y., et al., Reinforced Concrete Beams Strengthened with
Carbon fiber reinforced polymer by Friction Hybrid Bond Technique:
Experimental Investigation.Materials & Design, 2013.
[6] Brena, S.F., et al.,Increasing flexural capacity of reinforced concrete
beams using carbon fiber reinforced polymer composites. ACIStructural Journal, 2003. 100(1).
[7] Nguyen, D.M., T.K. Chan, and H.K. Cheong,Brittle failure and bond
development length of CFRPconcrete beams. Journal of Compositesfor Construction, 2001. 5(1): p. 12-17.
http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)
[8] Hawileh, R.A., et al., Behavior of reinforced concrete beamsstrengthened with externally bonded hybrid fiber reinforced polymer
systems.Materials & Design, 2014. 53: p. 972-982.
http://dx.doi.org/10.1016/j.matdes.2013.07.087[9] Asplund, S. Strengthening bridge slabs with grouted reinforcement. in
ACI Journal Proceedings. 1949. ACI.
[10] Blaschko, M. and K. Zilch.Rehabilitation of concrete structures withCFRP strips glued into slits. in Proceedings of the twelfth
international conference of composite materials, ICCM. 1999.
[11] Soliman, S.M., E. El-Salakawy, and B. Benmokrane, Flexuralbehaviour of concrete beams strengthened with near surface mounted
fibre reinforced polymer bars.Canadian Journal of Civil Engineering,
2010. 37(10): p. 1371-1382.http://dx.doi.org/10.1139/L10-077
[12] El-Hacha, R. and S.H. Rizkalla, Near-surface-mounted fiber-
reinforced polymer reinforcements for flexural strengthening of
concrete structures.ACI Structural Journal, 2004. 101(5).
[13] El-Hacha, R. and M. Gaafar, Flexural strengthening of reinforcedconcrete beams using prestressed, near-surface-mounted CFRP bars.
PCI journal, 2011. 56(4): p. 134-151.
[14] De Lorenzis, L., A. Nanni, and A. La Tegola. Strengthening ofreinforced concrete structures with near surface mounted FRP rods. in
International Meeting on Composite Materials, PLAST 2000,
Proceedings, Advancing with Composites. 2000.[15] Badawi, M. and K. Soudki, Flexural strengthening of RC beams with
prestressed NSM CFRP rodsExperimental and analytical
investigation. Construction and Building Materials, 2009. 23(10): p.
3292-3300.
http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005
[16] Al-Mahmoud, F., et al., Strengthening of RC members with near-surface mounted CFRP rods. Composite Structures, 2009. 91(2): p.
138-147.
http://dx.doi.org/10.1016/j.compstruct.2009.04.040
[17] Rahal, K.N. and H.A. Rumaih, Tests on reinforced concrete beams
strengthened in shear using near surface mounted CFRP and steelbars.Engineering Structures, 2011. 33(1): p. 53-62.http://dx.doi.org/10.1016/j.engstruct.2010.09.017
[18] Garrity, S. Near-surface reinforcement of masonry arch highway
bridges. in Proceedings 9 th Canadian Masonry Symposium,Fredericton. 2001.
[19] Almusallam, T.H., et al.,Experimental and numerical investigation for
the flexural strengthening of RC beams using near-surface mounted
steel or GFRP bars.Construction and Building Materials, 2013. 40: p.
145-161.
http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107[20] Committee, A., Building code requirements for structural concrete
(318-11) and commentary-(318R-11). Detroit, Michigan: American
Concrete Institute, 2011.
International Conference on Food, Agriculture and Biology (FAB-2014) June 11-12, 2014 Kuala Lumpur (Malaysia)
http://dx.doi.org/10.15242/IICBE.C614512 13
http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.conbuildmat.2012.09.107http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.engstruct.2010.09.017http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.compstruct.2009.04.040http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1016/j.conbuildmat.2009.03.005http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1139/L10-077http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1016/j.matdes.2013.07.087http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)http://dx.doi.org/10.1061/(ASCE)1090-0268(2001)5:1(12)