A Comparison between using FRP Composites and Steel Sheets

MAGNT Research Report (ISSN. 1444-8939)
Vol.2 (6): PP. 825-838
Shear Performance of Strengthened Steel Beams: A Comparison between using FRP
Composites and Steel Sheets
1
1
2
Ghadir Mehramiz and 2Kambiz Narmashiri
M.Sc. Student of Structural Engineering, Department of Civil Engineering, College of Engineering,
Zahedan Branch, Islamic Azad University, Zahedan, Iran
Assistant Professor of Structural Engineering, Department of Civil Engineering, College of Engineering,
Zahedan Branch, Islamic Azad University, Zahedan, Iran
Abstract
Over the last two decades, regarding the need of structures to meet design requirements, there
has been a great emphasize on making structures resistance throughout the world. Today,
using fiber reinforced polymer (FRP) is widely common in structural strengthening.
However, this fundamental question is yet unanswered that how much are these polymers
effective as compared to old, conventional approaches such as steel sheets. This research, by
selecting various, widely-used structural sections and through using ABAQUS limited
components software, studied the created shear capacity, stresses and maximum strains in
steel beams. Also, the two modes of applying steel reinforcement and FRP reinforcement are
compared in all cases.
1. Introduction
The new, innovative reinforcing method
with fiber reinforced polymer (FRP)
composites about steel constructs has
largely been attracted in recent years. In
spite of relatively high cost of FRP
polymeric
fibrous
materials,
their
advantages such as ratio of strength to
weight, proper durability against corrosion,
and ease of transportation and installation
caused them to be viewed as the first
option in seismic strengthening. Studying
beams and plate girders’ reinforcement in
vitro is expensive and time consuming;
moreover, there are limited patterns and
fields to be studied in experimental
researches. So, it seems necessary to apply
analytical software in order to complete
researching.
Several
studies
were
conducted. Denvid et al, in 2010, [18]
studied in vitro hybrid beams through FRP
and used FRP profiles in concrete beams
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instead of bars. Tavakolizadeh et al (2003)
[22] experimentally studied FRP effect on
the steel beams ultimate resistance. They
placed 21 different beam samples under
cyclic load, and compared cracks
development paths before and after using
FRP. Klaiber et al, in 2004, [19] explored
steel beams repair and reinforcement by
FRP sheets. The results obtained indicated
beams’ increased hardness and resistance
under corrosion. Buyukozturk et al (2004)
[17] analyzed the effect of applying FRP
on composite performance of steel and
concrete components and evaluated failure
mechanisms,
hardness
and
other
components parameters followed by FRP
using. Pierluigi et al, in 2006, [21]
experimentally and analytically studied
static behavior of the steel beams
reinforced with FRP sheets and analyzed
the strains made in FRP sheets as well as
beam failure mechanism. Zhao et al (2006)
MAGNT Research Report (ISSN. 1444-8939)
[23] experimentally studied the effect of
FRP usage on terminal shear capacity of
can beams; in addition, they also evaluated
the impact of FRP using on U- web beams
buckling. Under all conducted studies, the
two major questions are yet unanswered.
First, how does FRP usage influence on all
available and common sections in
construction industry? Second, whether
using FRP, considering its high costs, is
economic or it would be much better to use
steel sheets in beams’ shear reinforcement?
2. Theoretical study of beams under shear
When the designer is free to use the materials’
more efficiency, as the major part of bending
moment is carried by flanges and or horizontal
sections, the tendency toward using deep sections
(with high altitude) will increase. In a beam, the
beam web and or vertical part is in charge of
carrying shear force. On the other hand,
increasing web width may cause increasing beam
plate weight. In economic point of view, it is
more desired to use thin web reinforced by some
stiffeners. By making the web plates thinner, the
durability issue will be extremely critical.
Assume one part of web plate like Fig 1 in which
a shows transverse stiffeners’ distance and h is
the web height. Totally, this section of web plate
is influenced by bending stress fb with linear
height variations, shear stress along edges and
direct compression stress fc resulted by effective
loads on beam flanges [2].
Analyzing such status of combined stresses is
strongly complex not appropriate for designing.
In another method, three aforementioned stresses
are separately studied; then, the combined impact
will be determined. It is also assumed that
stresses are distributed according to materials
strength conventional relations. The stress
resulted by bending moment and shear stress are
calculated by F=Mc/I and Fv=VQ/It, respectively
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[2].
Fig 1. Beam stresses [2]
Beam web bending buckling is also influenced by
compressive stress of bending in web plate like
web sheet bending, which bending around beam
strong vector can create some stress similar to Fig
2. By solving differential equations on piece, the
critical stress of elastic buckling (Fcr), for that part
of beam web located between two traverse
stiffeners, can be obtained as follows:
)
(Equ.1)
Where E, is the elasticity coefficient; μ, the
Poisson coefficient, h is the web height and t the
web thickness. K is a coefficient dependent on
edges fixity and a/h ratio where, a, is the traverse
stiffener distance. K theoretical values are
presented by Timochenko and Winoski Gridger.
Fig 2, schematically illustrates steel beams shear
resistance against slenderness coefficient. Steel
beams are classified into three compressed, noncompressed and slenderness according to
slenderness. If
, the system is compressed;
in the case that
, the structure will be
classified in non-compressed category, and
finally, for
, the structure is in the slenderness
category; where, h is the beam height and tw is its
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thickness. The coefficients are as follows:
(Equ. 2)
(Equ. 3)
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Fig 2. Steel beam behavior under various modes
Steel beams shear potential can be calculated by
following relations obtained from AISC99
regulation (Astaneh, 2001). Shear potential, in
LRFD designing method, is attained by Vn and
Qv, where Qv=0.9 and Vn (nominal shear
strength) is computed, considering compression
conditions, as follows: [1]
a. Compressed [1]
And, E is the consuming steel elasticity module;
Kv the web piece buckling coefficient and Fyw is
the steel sheet given yield strength [2].
(Equ.4)
b. Non-compressed and slender [1]
(Equ. 5)
(Equ.6)
Cv in non-compressed mode: [1]
(Equ.7)
And in slender mode: [1]
(Equ. 8)
(Equ. 9)
Where in the aforementioned equations:
Aw: shear area; Cv: the critical shear stress ratio; dw: beam web height; tw: web thickness; and Kv: web
buckling coefficient.
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Also, the shear stress resulted from analysis must satisfy the following equation: [1]
(Equ. 10)
Vn (expected shear potential) must be computed, followed by designing, based on web sheet real area and
the expected yield strength which is used in estimating shear potential of system other elements such as
bindings.
(Equ.11)
(Equ.12)
Where
Cpr: maximum binding strength coefficient, which
is used to increase sheet yield strength shear
potential due to hardening strain.
Ry: the ratio of expected yield strength to the
minimum given yield strength. [1]
3. Modeling based on finite element method
Finite element method (FEM) is a numerical
method which can be applied in solving various
engineering problems in different stable,
transient, linear and non-linear states. This
method characterizes two features distinguishing
it from other existed methods including: a. this
method uses an integral formulation to provide an
algebraic equations system; b. smooth functions
are applied for introducing a continuous piece to
approximate unknowns.
The whole finite element method can be divided
into five main steps: a. dividing the desired area
into some subareas named elements; b. solution
initial approximation in the form of a function
with unknown constant coefficients which is
always linear or quadratic; c. extracting algebraic
equations system; d. solving the obtained
equations system; e. calculating other quantities
based on node values.
In the first step, as it was earlier stated, problem
geometry is divided into small areas called
element. Element integrations are also performed
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through using different techniques including
reduced integral to save time in integration.
Moreover, it must be mentioned that the explicit
integration method is considered as one of the
most widely used complex problem-solving
methods. This method is effective in modeling
dynamic issues in time and frequency domain
such as impact analysis and seismic effects; as
well as in non-linear problems including contact
conditions adjustment. Therefore, this study used
the reduced explicit integration method for
problem-solving. The theoretical basics of the
two stated methods are cited in many authentic
references. [11]
4. Finite element method validity
Modeling validity was determined by Zhao et al
(2009) [24] results. They, in an experimental
research, studied the effect of FRP on U-shaped
beam webs buckling and evaluated three FRP
arrangements. Now, this study, through
simulating laboratory conditions in finite
elements software ABAQUS and changing mesh
sizes, validates the results. There were four mesh
sizes. Approximate sizes are given to the software
and the software automatically determines the
mesh sizes. The meshes used here are first order
four points linear pyramid indentified as C3D4R
in ABAQUS software. The materials used for
beam piece are mild steel with the density of
7850 kg/m3, 202 GPa elasticity module, Poisson
MAGNT Research Report (ISSN. 1444-8939)
coefficient of 0.3, 429 MPa yield stress, 541 MPa
final stress and 0.25 final strain. FRP materials,
also, with 1800 kg/m3 density and 205 GPa
elasticity module and 2400 MPa tensile strength
are defined as Lamina according to laboratory
materials. Furthermore, bearing capacity chart is
obtained through removing time parameter from
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displacement time history graphs, bearing
reaction force, as well as drawing force chart
versus displacement. Following Figs (Table 1)
stated different mesh dimensions and numbers.
All dimensions were analyzed and compared with
experimental results.
Table 1. Meshing with different dimensions
Element approximate
size (mm): 5
Element numbers: 53667
Element approximate
size (mm): 10
Element numbers: 15535
The results of analysis using each meshing size
are indicated in Fig 3, extracting piece bearing
capacity chart in addition to experimentally
comparisons. According to Fig 3, using a mesh
with approximate 5 mm dimension caused that
the obtained results be nearly consistent with
experimental results; and are appropriately
consistent with each other to the 6 mm
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Element approximate
size (mm): 20
Element numbers: 4881
Element approximate
size (mm): 30
Element numbers: 2729
displacement area. So that the maximum error
equals 1.76%, at this area, which are a proper
value; and the obtained results can be cited, too.
Laboratory and numerical model are clearly
matched and corresponded regarding Figs 4 and
5. In the following, various studied models are
introduced; then, every model analysis results
are discussed after sensitivity analysis.
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Fig 3. Numerical model results validity
Fig 5. Deformation in numerical model
Since three dimensional (3D) modelling is
almost preferred and has the closest results to
experimental (Irandeghani & Narmashiri, 2012
[25]; Narmashiri et al, 2012a [26], 2012b [27];
Narmashiri & Daliri-A, 2012 [28]; Narmashiri &
Jumaat, 2011 [29]; Narmashiri et al., 2011a [30],
2011b [31], 2011c [32]; Narmashiri et al., 2010a
[33], 2010b [34]), in this research, 3D simulation
is used.
5. Models, results and discussions
To consider analysis different states, five
different widely-industrial-applied sections
including box, circular (hollow), I-shape, Ushape and Z-shape were used to access a
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Fig 4. Deformation in laboratory model
comprehensive range of beams behaviors with
steel and FRP reinforcement. Fig 6 indicates the
shear flow occurred in these section.
To analyze the sensitivity of the created models
in software, four different values were
determined for elements including 2, 1.5, 1, and
0.5 cm that were approximately entered into
software like validity section; then, the software,
automatically meshes. In addition, applied
elements are first-order linear four-point
pyramid. Structure displacement maximum
response chart was drawn (Fig 7) relative to
mesh size in order to study model sensitivity
versus mesh sizes (dimensions).
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Fig 6. Applied sections and shear flow
Fig 7. Model sensitivity analysis versus mesh size
According to the above chart, it can be observed
that all charts will be converged followed by less
than 1 cm length and the slope gets nearly to
zero; the mesh smaller than 1 cm have no effect
on response. Thus, the approximate 1 cm size
was selected for meshes. Further, BOX and Z
sections demonstrated little sensitivity to mesh
sizes. However, O, I and U sections change rates
were significant as compared to mesh sizes.
Reinforcement length by using FRP sheets and
steel sheets was twice the width of cross-section
(Zhao, 2009). And, for squared cross- section,
two different reinforcement models by steel
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sheets; and for other cross-sections, one steel
reinforcement model were performed and
compared with FRP arrangements. It is
necessary to say that steel reinforced sheet
thickness, based on Regulations Section 10th
constraints, was equal to cross-section thickness.
The other geometrical dimensions of sections are
similar to Table 2.
The maximized stress amount created in each
cross-section and maximum displacements were
compared together followed by loading and
analysis, the results are shown in Fig 8.
According to a and b in Fig 8, it is clear that
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using low reinforce in box cross-section and
upper reinforcement, make no significant
reduction in displacement and stress; whereas,
using FRP reduced displacement and stress by
45 and 22%, respectively. Interestingly, steel
reinforce performance around and throughout
the cross-section was better than FRP which
reducing displacement to almost zero. Stress, at
this state, is maximized to 47 MPa which
reduced 83% in comparison to nonreinforcement.
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Comparing two steel reinforcement and FRP
performances for I-shaped cross-section, in Fig
9, showed similar performance in reducing
maximum displacement; and, the maximum
displacement was reduced from 9 mm to almost
zero. But, using steel reinforcement caused 92%
stress reduction and the maximum stress was
reduced from 760 MPa to 60; while, using FRP,
led to 71% reduction in the cross-section
maximum stress.
Table 2. Cross-sections geometrical characteristics and applied reinforcements
Box6
I 16
O9
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U14
Z14
(b)
(a)
Fig 8. a. Maximum displacement, b. maximum stress of can-shaped cross-section in various reinforcement
states
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(b)
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(a)
Fig 9. a. Maximum displacement, b. maximum stress of I-shaped cross-section in various reinforcing
states
As the slenderness of the circular cross-section
upper wall, the two reinforcement performances
act similar in displacement getting to zero in
both states. However, steel reinforcement is
transcendent over FRP in reducing the stress
over cross-sections (Fig 10).
In U-shaped cross-section (Fig 11), no loading
reinforcement led displacement changed to 2
mm. 75% reduction in displacement is seen by
using both steel and FRP reinforcements. While,
in maximum stresses created in cross-section by
using steel reinforcement, the observed response
was better.
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Part (a) in Fig 12 Shows that the maximum
displacement in Z-shaped cross-section with no
reinforcement was about 4 mm getting to zero
followed by applying both reinforcements. But,
reinforcement caused reduction in cross-section
stresses. It is clear from (b) that all three charts
are matched at the first 0.4 S of analysis. Over
the time and load increase, the effect of
reinforcements can be seen in stress reduction.
Using steel reinforcement, in this case, also
contained better responses and smaller stresses
occurred as a result of using that.
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(b)
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(a)
Fig 10. a. Maximum displacement, b. maximum stress of O-shaped cross-section in various forms of
reinforcement
(b)
(a)
Fig 11. a. Maximum displacement, b. Maximum stress of U-shaped cross-section in different
reinforcement states
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(b)
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(a)
Fig 12. a. Maximum displacement, b. Maximum stress of Z-shaped cross-section in different
reinforcement states
6. Conclusion
After different analyses on the applied beams in
industry and comparing the two common
reinforcement method performances, it can be
stated that it is always necessary to do analyses
of any reinforcement in each particular projects
since the complexity of the composite constructs
and to make logical decisions with precisely
studying the results. However, a particular
method can be effective for reinforcing structural
elements of a project; it may be reversed in
similar projects. Reinforcement with FRP in
reducing beams’ displacement is largely similar
to steel reinforcement performance. Hence, in
those cases that maximum displacement in
drawing a construct is considered as a governed,
controlling parameter, it is only required to study
the economical aspects of the reinforcement
approaches. This study ignores implementation
costs limit. However, by comparing two
reinforcement methods for all cross-sections, it
can be totally indicated that using steel
reinforcement in reducing produced stresses is
more effective that using highly-cost FRP
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method. It must be reemphasized that any
particular
project
requires
necessary
optimizations to be adopted regarding economic
aspect in selecting the best reinforcement option.
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