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Advances in Engineering Software 176 (2023) 103373
0965-9978/© 2022 Elsevier Ltd. All rights reserved.
Innovative ANN hysteresis to predict hysteretic performance of composite
reinforced concrete beam
Gongxing Yan
a
, Jie Li
a
,
*
, Alaa Hussein Ali
b
, Tamim Alkhalifah
c
, Fahad Alturise
c
, H.
Elhosiny Ali
d
,
e
,
f
a
School of Architectural Engineering, Chongqing Creation Vocational College, Chongqing 402160, China
b
Building and Construction Techniques Engineering Department, Al-Mustaqbal University College, 51001 Hillah, Babylon, Iraq
c
Department of Computer, College of Science and Arts in Ar Rass, Qassim University, Ar Rass, Qassim, Saudi Arabia
d
Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
e
Physics Department, Faculty of Science, Zagazig University, 44519 Zagazig, Egypt
f
Research Center for Advanced Materials Science (RCAMS), King Khalid University, Abha 61413, P.O. Box 9004, Saudi Arabia
ARTICLE INFO
Keywords:
Innovative ANN hysteresis
Machine learning
Hysteretic performance
Reinforced concrete
Tension tests
Crack
Residual stiffness
Steel ber-reinforced concrete
ABSTRACT
This article assess the precise estimation of the hysteresis loop of reinforced concrete (RC) beams in distinct
failure cases to verify inelastic seismic beam function. Any test failure in RC frame columns is able to produce
hysteresis curves in low cyclic repeat load that follows the analysis of the hysteretic behavior of the frame
columns. In this case, the application of bers as a mass enhancement to improve the post-cracking of RC beams,
strength, and delay cracking has been investigated. In this research, the hysteretic response of deep and slender
SFRC beams enhanced with SF using ten beams under the reversal cyclic load was studied through innovative
ANN hysteresis. Shear and exural strength of SFRC beams were analyzed using a diverse number of bers with
content from 0.1 to 5% per volume, closed stirrups (from 0 to 0.5%), and steel reinforcing bars (0.50% and
1.50%). The innovative articial neural network hysteresis model has been utilized to dene the accuracy
prediction of the parameters and determine the hysteresis loop of RC columns failing in different modes.
Comparing the experimental ndings properly indicated the accuracy of the model to capture the main features
of the response, such as the load versus deformation cyclic envelope, SFRC tension softening effect, and the
impact of the bers on the hysteretic energy. The results revealed that SFRC beams represented developed cyclic
efciency in case of deformation, load-bearing capacity, residual stiffness, cracking and energy dissipation ability
while generating their integrity within the imposed reversal cyclic experiments.
1. Introduction
Reinforced concrete (RC) columns are essential structural elements
against wind loads and earthquakes [1–5]. Shear connectors are used to
attach a concrete slab to a steel beam to create a composite beam, which
is often used in large stadiums, buildings, bridges, and other structures
[6–10]. Age is one of the major elements determining an infrastructure’s
quality and functionality under present and future loads. Recent studies
show that enhancing outdated infrastructure lengthens their useful lives
and increases their tolerance to future loads [11]. Since the composite
beam is formed of a steel beam and a concrete slab, it is the re-
sponsibility of mechanical shear connections to bear the shear stress and
transmit it to the supporting structure. Shear connections are therefore
employed in these beams. Channel, stud, angle, and bolt are typical
shear connections [12–18]. Due to its ease of usage in structures, stud
shear connectors have been used often in recent years, and several ar-
ticles have examined this form of connection. Fanaie et al. [19] used
ABAQUS to examine channel connections and the comparison of
face-to-face and back-to-back positions in these connections. The nd-
ings demonstrated that the composite beam stiffness was equal in both
congurations, despite higher performance being shown in the
face-to-face channel position. In a composite beam, the tilted angle was
examined by Khorramian et al. in 2017 [20]. They contrasted their
ndings with those from a push-out test after utilizing nonlinear nite
element modeling to evaluate various slanted angles.
Steel reinforcement concrete (SRC) elements, particularly frame
* Corresponding author.
E-mail address: a18883946797@163.com (J. Li).
Contents lists available at ScienceDirect
Advances in Engineering Software
journal homepage: www.elsevier.com/locate/advengsoft
https://doi.org/10.1016/j.advengsoft.2022.103373
Received 31 May 2022; Received in revised form 12 November 2022; Accepted 27 November 2022
Advances in Engineering Software 176 (2023) 103373
2
columns, are often employed in high-hybrid buildings because of their
high bearing capacity and strong seismic resistance, including energy
dissipation and ductility [21–27]. Designers should use a rigorous
elastoplastic analysis of the structures to make sure that its seismic
resistance complies with the designing criteria [28]. The hysteresis
model, which can properly represent the deformation performance,
stiffness degradation and strength, and energy dissipation potential of
members and structures based on cyclic iterated load was researched as
the foundation of elastoplastic analysis, [29–31]. In general, the hys-
teresis model consists of two components: the hysteresis rule and the
skeleton curve. The structures’ extremely nonlinear nature is reected in
the latter, which is governed by all of the hysteresis feature points [32].
The smooth hysteresis (SH) and polyline hysteresis (PH) model are the
two types of hysteresis models now in use for structural seismic analysis.
The PH model is reasonably simple to explain and put into practice
[33–36] and is made up of piecewise lines derived by condensing the
hysteresis behavior of the structural parts. The SH model is used for
seismic analysis of SFRC members since it requires more processing to
provide results with more accuracy [37]. While this is going on, most of
the PH models that are now in use induce a cyclic deterioration index
that only takes energy dissipation into account to represent the stiffness
degradation and strength rules of structural parts during an earthquake
[38–40]. However, an earthquake is a random load, and the members’
capacity for seismic energy consumption is signicantly impacted by the
loading route. As a result, it is challenging to derive a standard mea-
surement of the members’ ability to dissipate energy. The hysteretic
model of structural members is produced by incorporating a damage
index (DI), which could accurately explain the stiffness degradation and
strength rules than the approaches stated before [41,42].
It has been shown that adding bers to concrete greatly improves its
toughness and encourages more ductile material behavior [43–49]. As
an additional reinforcing technology, the integration of randomly
positioned short steel bers has been devised to enhance the brittle
tensional failure fracture behavior of concrete by the pullout and bers’
debonding process [50–53]. Because of this, changed SFs with hooked
ends display anchoring action, giving improved bond properties which
signicantly enhance the post-cracking response and improve the ca-
pacity to absorb energy [54–56] (Fig. 2). Because of the poor tensile
characteristics of concrete, RC beams with a low shear span-to-depth
proportion, such as deep beams show brittle failure and are
shear-vulnerable [57]. SFs enhance the concrete’s ability to withstand
diagonal stress in beams, increasing shear resistance and perhaps pro-
moting ductility and exural failure [58–60]. Even though it proved to
be rather challenging to completely replace traditional steel stirrups
with bers, it is at least theoretically possible to partially replace closed
stirrups with SFs under certain conditions, which would result in a
desired reduction of traditional reinforcement congestion [56–59,
61–64]. Recent mathematical methods that have been suggested to es-
timate the shear capacity of SFRC beams with [65–67] or without stir-
rups [68,69] have made a major contribution in this respect. Tension
stiffening, or the ability of reinforced concrete to withstand certain
tensile loads between fractures, is the cause of the enhanced tensile
stiffness in the RC component prior to reinforcement yielding [70–73].
This effect under the service limit condition might have a signicant
impact on deections, rigidity, and crack widths. SFs may considerably
increase residual stiffness and decrease control crack splitting in con-
crete since they can withstand tensile loads along fractures [74–78]. But
the very limited use of SFRC in beams is roughly due to the challenges in
identifying rational and precise methods which depict and predict the
behavior of the material in both the service and ultimate limit states.
Tensile strength of SFRC members is often ignored at the exure ulti-
mate limit condition [79,80]. However, the member is stiffer because
SFRC could withstand tensile loads both across and between ssures. As
it has been shown that the residual stresses rise as more steel bers are
mixed with concrete mixture, this residual stiffness should be taken into
account in the estimates for the design of SFRC structural elements [81,
82]. Schematic view of reinforcing bar sizes is shown in Fig. 1.
Despite having greater compressive strength, concrete is brittle by
nature. Durability, deformability, and energy dissipation are introduced
by the connement offered by reinforced concrete structural compo-
nents. These characteristics are crucial to the seismic performance of RC
multistory structures. According to Sheikh S.M. (1978) [83], Considere
demonstrated (1903) that spiral transverse reinforcement may enhance
the axial capacity of a concrete column component. Later, researchers
have concentrated on quantifying the contribution of constriction to the
overall strength in order to properly use the strength augmentation for
high performance design. Most tests done on conned concrete in the
early 20th century concentrated on maximizing the coefcient value of
equivalent uid pressure employed in suggested representations of its
compressive strength, reported by Richart et al. (1928) [82] and Balmer
(1943) [84]. It was discovered that the volumetric rate of the longitu-
dinal and conning reinforcement, as well as their form, yield strength,
pitch, and compressive strength, also affect the compressive strength of
conned concrete. There have been several models that take these
considerations into account. The conning pressure was rst considered
to be spread evenly throughout the models. Only hoops that were tightly
spaced were suitable for the assumption. Eventually, the connement
index will include the impact of transverse reinforcement spacing on the
limited strength of concrete. Muguruma et al. (1979) [85] conducted a
series of studies on 150 mm ×300 mm cylinders that were constrained
by spiral transverse reinforcement with varying yield strengths and di-
ameters. The ndings of the regression analysis conducted on test data
and those gained via the connement index Ci suggested by Iyenger
et al. showed a signicant amount of scatter (1970) [86]. Using the ratio
between the successfully conned core and original core volume,
Watanabe et al. (1980) suggested a conning coefcient [87]. The
suggested model’s limit strain was found to be conservative [88]. In
trials on circular columns with axial loads, Mander et al. (1988) used
columns with 1500 mm heights and 500 diameters mm. The samples
had transverse reinforcement with varying yield strengths and spacings,
as well as longitudinal reinforcement ranging from 8 to 36 bars. To
predict the restricted compressive strength of concrete, a model in the
form of a fractional equation was proposed using the test ndings and
equation provided by Popovics (1973) [89]. The model accounted for
the effects of the effectively contained core volume and the arrangement
of the longitudinal and lateral enhancement through effective lateral
conning stress and conning coefcient. Comparing the ndings of test
data, it was discovered that in order to provide an efcient conning
pressure, greater strength transverse reinforcement needed higher axial
compression.
Numerous studies in earthquake engineering have been conducted as
a result of improvements in machine learning and data accessibility.
Although original research [90–94] focused on bridges, more recent
studies [93,95–97] have focused on buildings. The main focus of the
data-driven bridge research was the assessment of seismic risk or
vulnerability. In order to determine the failure mechanism of RC
beam-column joints based on 536 experimental tests, Mangalathu and
Jeon employed machine learning methods [93]. Kiani et al. [95] looked
into how the training set affected the creation of frame construction
fragility curves. A quick post-seismic building labeling process utilizing
machine learning was proposed by Mangalathu et al. [98], and the au-
thors used the 2014 Napa, California earthquake to show the use of
machine learning for building tagging. For the clustering of reinforced
masonry shear walls, Siam et al. [99] recommended using machine
learning. The authors came up with a model for machine learning based
on a set of data from 97 trials. Huang and Burton [100] examined the
effectiveness of six different machine learning algorithms for the failure
modes of RC frame structures with masonry inll panels. In each of the
aforementioned machine learning investigations, a clear relationship
between input and output parameters is found. This research showed
how ML models might be used in seismic design in the absence of
mechanics-based modeling.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
3
In terms of soft computing model [101–105], Raq et al. [106]
suggested a set of practical criteria for constructing ANN for engineering
applications. Numerous studies are now concentrating on ANN as an
effective strategy to ensure its usability in civil engineering sectors
[107–112]. A neural network model that forecasts the workability of
concrete using cement replacement materials was reported by Bai et al.
[113]. The results of their neural network model demonstrated how
neural networks can be utilized to precisely predict the workability
parameters and were equivalent to experimental ndings. Additionally,
Oreta et al. [114] investigated the use of ANN to forecast the circum-
ferential concrete columns’ limited compressive strength and associated
strain. The use of ANN to forecast the ultimate moment capacity of RC
slabs in re was studied by Erdem [115] using 294 data sets. It was
shown that ANN model accurately estimated the ultimate moment ca-
pacity (Mu) of RC slabs in re. The nal moment capacity equation’s
ndings and the moment capacities estimated by ANN were align. A
small amount of research shows how different CI approaches may be
used to forecast the remaining exural strength of reinforced concrete
beams that have corroded. The goal of the current work is to close this
research gap by recommending an improved ANN model for it. To
forecast the remaining exural strength of corroded RC beams, Imam
et al. [116] suggested four ANN models. The models demonstrated a
Fig. 1. Schematic view of reinforcing bar sizes. Large bar diameters should be avoided for beams since they produce exural cracking and need a longer length to
achieve their strength. Nevertheless, the placement cost of huge bars is lower than the installation cost of a large number of small bars (A). Supported enhanced
molded beam under to transverse point load at the center (B). Here, the strength of longitudinal reinforcing steel bar is 460 MPa and the compressive strength of
concrete is 40 MPa (B).
Fig. 2. Steel ber types used in structures members.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
4
92% decrease in error and an improvement of up to 49% in correlation
coefcient. The comparable exural strength of hybrid mesh and ber
reinforced cement-based composites was also predicted by Sakthivel
et al. [117] using an ANN. For the purpose of forecasting the exural
strength of cement-based composites, three ANN models (Models 1, 2,
and 3) were created. They came to the conclusion that these three ANN
models can be used as simple, but accurate ways to predict the exural
strength. This is because all three models were found to be in excellent
agreement with the actual results. The shear strain γ
i
and curvature ϕ
i
could be dened from Response-2000.
Δ=∑
n
i=1
[ϕidixi+γidi](1)
In this work, the shear strain and curvature (Response-2000) were
employed in two distinct processes designated as interpolation ap-
proaches and linear variation to compute displacement of Eq. (1). These
methods were compared with test ndings and Response-2000 member
responses. By integrating the contributions of the strips, the deection
corresponding to load is calculated. Eq may be used to symbolize this
Δi=ϕnixxni d+γnid+⋯+ϕji xjid+γni d+⋯+ϕ1ix1id+γni d(2)
Change the ϕ
i
and γ
i
values for the next P
i
value of the load vector and
obtain the whole load deection curve. The shear strain γ
i
is constantly
regarded at the support’s face.
1.1. Signicance of study
The ndings of the available research indicate that the primary
inuencing elements for the failure analysis of structural components
are the number of cycles and cyclic loading history. The failure index
used in the current hysteresis model, though, is unable to adequately
account for the impact of the loading cycles’ number and loading path
on the members’ nal capacity for energy dissipation and deformation.
To the best of the authors’ knowledge, this approach has only been
utilized to analyze steel structures and RC structures. There have not
been many studies on the hysterical conduct of SFRC members. The
damage process for SFRC composite members is more complicated than
that of pure steel or reinforced concrete buildings since they are made of
both steel and RC [118]. As a result, the SFRC members’ seismic per-
formance cannot be adequately reected by the existing way of devel-
oping hysteresis model based. Experiments were done with SFRC frame
columns to look at how hysteresis behaves under low-cycle repetitive
loading. By use of ANN, this study hopes to provide an accurate analysis
in Estimation of hysteretic performance of composite reinforced
concrete.
2. Proposed method
2.1. Materials
The samples serve as an example of a beam-column connection in RC
construction. All test samples had cross sections that were 150 ×300
mm (Table 4). Table 1 shows displacement ductility rates of the tested
samples. Fig. 3 displays the stress-strain correlations for concrete (at 28
days) and reinforcing bars (transverse and longitudinal). According to
Fig. 3 Left, concrete’s compressive strength (f
c
) was about 30 MPa. For a
total of 28 days, polyethylene sheets were employed to cure the con-
crete. Over the transverse reinforcement, the transparent cover was 25
mm thick. All examples were built utilizing 150 mm wide, 80 hook
stirrups spaced evenly across the beam. The samples are made up of two
pieces (a beam, a stub) (which functions as a column for applying
weights). Ten SFRC frame column specimens were developed and built
for this work (Table 6). All samples include similar cross-sectional di-
mensions and shape; but with various compression rates stirrups ratios
ρ
v
( =0.6%, 1.3%, 1.4%), n( =0.2, 0.5, 0.8), and steel rations
ρ
s
( =4.3%,
5.1%, 6.1%) as axial compression strength f
c
is 73.35 MPa, Cube average
compression strength f
cu
=81.53MPa, and elasticity modulus of con-
crete E
c
=34.36MPa. In this work, the composite beam design was
employed. The concrete slab was developed based on the AS3600,
whereas the steel beam was designed in accordance with AS4100.
AS2327.1 was the foundation for composite design, whereas AS1170.1
was utilized for loading. There were 30 connections employed as bolt
shears in the composite beam. Table 2 shows Error measurement in the
prediction of load, deformation, δ (deep beams), and P (slender beams).
Table 3 shows ultimate loads of the tested samples.
2.2. Finite element modeling
In this study, ABAQUS was used to model the composite beam as a
three-dimensional nite element. For the program, the key elements of
the composite beam, such as the steel beam, concrete slab, bolt shear
connections, and rebars, were all characterized as nonlinear. Table 5
shows the properties of steel.
2.2.1. Using Finite Elements to Analyze
For the numerical study of difcult structural and thermal issues,
nite element analysis is used. The pre-post-processor features of ANSYS
may also be used to evaluate composite materials in order to examine
their behavior under various load circumstances. Since the displace-
ments of concrete structures are negligible in comparison to their size,
geometric nonlinearity is ignored in the current research. Material
nonlinearity is taken into account [119–121] because concrete is a
non-homogeneous material and only exhibits linear behavior across a
limited portion of its strength. An effective method for identifying the
internal strain and stress distribution in concrete structures is nonlinear
nite element analysis. As a result, concrete buildings are designed to
their fullest potential [122,123].
The connections between load and deformation may be utilized to
predict how the structures will behave in real-world situations. Through
nonlinear analysis, improved information on serviceability and ultimate
strength is provided. In comparison to linear analysis, nonlinear analysis
requires much more computing time and money to solve problems. As a
result, the strategy should be as effective as feasible, and the numerical
approach used should require less calculation. For different material
nonlinearities, such as cracking, aggregate interlock at a fracture, stress-
strain behavior of concrete, the reinforcing steel’s dowel action span-
ning a crack, etc., nite element analysis is used. Concrete with com-
posite layers is a composite material in and of itself. This is still an active
topic of study for numerical modeling. A reliable technique for evalu-
ating the behavior of concrete structures during design and development
is computer simulation. Such simulation (virtual testing) may be utilized
to both locate the best and most affordable design solution as well as to
check and support the structural solutions with intricate details. Fig. 4
shows the shear and exural test.
2.3. Plasticity theory in terms of FEM
If the ndings of the plasticity theory mathematical tool’s applica-
tion to concrete for its fragmentation are to be considered in the classical
sense, then they need further clarication and shear testing. General
strength theory places a lot of emphasis on and gives practical relevance
Table 1
Displacement ductility ratios of the tested samples (mm).
test results Numerical Results
μ
Exp
μ
Num
Δ
y
Δ
u
Δ
y
Δ
u
P3 13.02 113.12 11.43 67.36 9.36 5.4
P4 11.34 110.34 10.24 92.1 11.24 8.2
P5 10.13 98.12 10.54 81.2 7.3 7.7
P6 14.12 51.15 14.2 51.37 2.65 2.6
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
5
Fig. 3. Substitution of conventional closed steel stirrups with short steel bers (left). This diagram compares the cracking and hysteretic behavior of an SF-RC beam
SH0. 37 (VSF =1.5%) with no stirrups and with a plain concrete beam SH0.37 with a stirrup ratio of w =0.33%. The empirical and analytical hysteretic behavior and
cracking patterns of SH0.37 and SH0.4 shear-critical beams without stirrups (right).
Table 2
Error measurement in the prediction of load, deformation, δ (deep beams), P (slender beams).
Name MAE at Each Cycle mean SE CV
% C 1 % C2% C3% C4% C5% MAE
Beam 1 A 1.3% 1.2% 1.6% − − 1.5% 0.5% 25%
B 26.3% 24.8% 17.2% − − 27.8% 4.2% 15%
Beam 2 A 2.2% 1.6% 2.1% − − 2.2% 0.3% 11%
B 23.4% 11.2% 12.7% − − 17.1% 4.6% 25%
Beam 3 A 1.4% 9.6% 3.9% 6.7% 6.4% 4.9% 1.7% 26%
B 3.5% 4.6% 14.6% 26.7% 17.1% 11.9% 3.7% 27%
Beam 4 A 0.1% 5.3% 1.1% 6.1% 5.2% 4.2% 1.5% 34%
B 3.1% 21.2% 24.4% 23.9% 22.2% 17.8% 2.7% 17%
Beam 5 A 5.1% 5.8% 1.5% − − 4.0% 0.9% 26%
B 5.3% 14.1% 16.5% − − 12.0% 2.2% 18%
Beam 6 A 3.5% 4.6% 2.6% − − 3.3% 1.0% 29%
B 4.7% 15.9% 16.9% − − 11.2% 2.0% 17%
Beam 7 A 0.1% 2.2% 0.0% − − 1.1% 0.7% 63%
B 1.2% 6.9% 11.6% − − 6.0% 1.5% 29%
Beam 8 A 3.3% 2.1% 5.5% − − 4.0% 1.5% 23%
B 4.8% 8.9% 13.5% − − 6.7% 1.6% 16%
C=cycle
Table 3
Ultimate loads of the tested samples.
P3 P4 P5 P6
Experimental Load P
y
kN) 65.6 84.6 121.8 183.5
P
u
(kN) 92.6 93.5 126.5 172.7
Numerical Load P
y
(kN)) 85.5 86.8 127.0 186.5
P
u
(kN) 93.2 100.8 153.0 199.8
Table 4
Mechanical test program.
Test Compression test Tension test
Sample size 150 ×300 28 ×28 ×320
Process ASTMC39/C39M-10 (2010) Shear test
Sample number 4 per mix JSCE-N82-2008 (2008)
Table 5
Material properties of steel.
Type of steel Yield
f
y
(MPa)
Elongation
(%)
Limit
f
u
(MPa)
Elasticity
modulus
E
s
(MPa)
Steel beam Q235-B 2221 23.4 343.8 2.04 ×10
5
Angle steel Q345-B
Rebar HRB400
423.8 21.3 522.2 1.87 ×10
5
Table 6
Details of the specimens.
Beam No. d′(mm)
ρ
/
ρ
b
A′
s
ρ
′(%) d(mm)
ρ
(%) f′
c(MPa)
P3 3.3 0.24 18 1.54 25.5 1.54 27.0
P4 3.4 0.34 14 1.01 25.5 1.64 28.8
P5 3.2 0.51 19 1.27 25.9 2.34 31.7
P6 3.0 0.63 18 1.68 25.2 3.24 29.7
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
6
to issues with concrete and reinforced concrete strength under shear.
The level of development and the effectiveness of the components’
number of structural solutions and connection joints are largely
dependent on the breadth of their expertise. Numerous studies have
employed the plasticity hypothesis alone to explain concrete behavior
[124–127]. The primary feature of these models is a plasticity yield
surface that contains work or strain hardening, non-associative ow
rules, pressure sensitivity, and path sensitivity. Such models, however,
did not take into account the microcracking-related deterioration of
material stiffness. Such a scientic theory should be able to explain the
physical basis of a wide range of observed phenomena, predict new
dependencies, qualities, and phenomena, and accurately dene the
quantitative relationships between the process parameters being stud-
ied. The strain tensor,
ε
, is decomposed into the plastic part,
ε
p
and
elastic part,
ε
e
according to plasticity model
ε
=
ε
e+
ε
p(3)
The elastic part is identied as the recoverable part in total strain, as:
ε
e=E−1:
σ
(4)
E, =elastic stiffness as a rank four tensor
σ
=the stress tensor [126,128]
The stress and strain relation could be as follow based on Eqs. (3), (4)
σ
=E:(
ε
−
ε
p)(5)
Here, the elastic stiffness is identied If scalar damage in stiffness
degradation is assumed:
E= (1−D)E0(6)
D =degradation variable
E
0
=initial stiffness tensor
Substituting Eq. (6) into Eq. (5) results in:
σ
= (1−D)E0:(
ε
−
ε
p)(7)
or
σ
= (1−D)
σ
(8)
σ
=effective stress
The constitutive relationship for the elastoplastic reaction is sepa-
rated from the degrading damage response, which has benets for the
numerical use based on Eq. (8). Here, the development of the yield
surface is controlled by the strength function for the effective stress,
making it easier to calibrate with test ndings. The plastic strain ratio
evaluated by a ow rule is supposed to be related to a scalar potential
function Φ. Thus, for a plastic potential in the effective-stress space, it is
˙
ε
p=˙
λ∇
σ
Φ(9)
∇
σ
Φ=
∂
Φ/
∂σ
λ =a non-negative performance referred to the plastic consistency
parameter.
The use of different method in the plasticity theory lets the gain of
theoretically reasoned, and totally simple and accurate solutions of
practical signicance [129].
2.4. Cyclic loading test procedure
Real-world circumstances seen in buildings should be replicated
through experimental test sets and loading histories. The majority of
cycle test techniques for beams do not take gravity loads into account
while loading the histories. As a consequence, the outcomes could not
Fig. 4. Flexural and shear test in laboratory.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
7
match reality. To determine the failure mechanism of beam samples
exposed to simultaneous gravity load and reversed cyclic loading, a test
campaign was run. Both samples had a combined force and displace-
ment control loading history, where force control was used to keep the
gravity load value, also displacement control was used to regulate the
cyclic displacement model. The reinforcement rate of specimens P3, P4,
P5, and P6 was diverse from sample P0 to alter the failure mode that had
previously been detected in sample P0, which was one of the goals of this
study’s assessment of the cyclic loading test technique against failure
modes. Following the traditional quasi-static tests, cyclic loading tests
are often performed to evaluate the seismic energy of beam - column
subassemblies, beam or columns. The lab was the setting for the test
campaign. The lab features a strong oor and reaction walls. Samples
were fastened vertically to the strong oor and horizontally to the re-
action wall. The rst step of the load test technique is to put on a pre-
determined gravity load. The loading history utilized for both samples
included in the imposition of the process. Each amplitude displacement
is used in 3 cycles that is started from the reference amplitude: Δ = ±1.0
⋅ d
0
,±2.0 ⋅ d
0
,±3.0 ⋅ d
0
,±4.0 ⋅ d
0
, ±5.0 ⋅ d
0
,±6.0 ⋅ d
0
,…, up to failure.
The rst yield displacement, which was measured prior the start of cy-
clic test of each beam, was used to gure out both the gravity load and
the cycle’s amplitude for each specimen (P0 and P1). First yield
displacement was computed by observing the strain in the long time
enhancement while imposing horizontal displacement to the sample. P0
displacement at yielding wasd
y
=6mm for positive bending moments
and d
y
=12mm for adverse bending moments. While the positive mo-
ments were half of the negative one, it was gained as reference
displacement amplitude (d
0 −CB0
=6mm). At rst yield for P1,
displacement was d
y
=14mm for adverse bending moments. By
selecting the samples, the reference displacement was similar as half of
it. P1 amplitude for the loading history was d
0 −CB1
=7mm.
2.4.1. Loading history & Hysteretic responses
In order to model the gravity load on the reinforced beam with an
asymmetrical cross-section shape, a quasi-static test approach was used.
The suggested method is applying a reverse cyclic displacement history
with larger amplitude (three full cycles are run for each amplitude
increment), beginning with the impacts of gravity loads. Failure happens
when either the link can no longer withstand the gravitational stress or
when the maximal specied drift is reached. Each cycle begins at the
location where the predetermined value of the idealized gravity load is
reestablished, and each cycle is made up of successive phases. The use of
this process moved to the load sequences of 1) application of a pre-
established load equal with the gravity load impacts on the beam’s
xed end (F
g
=90kN =50% of the load which is leading to the top
enhancement of the control sample to yield F
y
). It was followed by the
imposition of a reverse cyclic displacement history with amplitude’s
raising while considering the displacements of ±Δ = ±1.0d
0
,±2.0d
0
,
±3.0d
0
,±4.0d
0
,±5.0d
0
,±6.0d
0
and ±7.0d
0
; 3 cycles at each phase. The
yielding displacement was dened in the rst part of the control sample
test, as the displacement related to the yielding strain. The yielding
displacement values (d
y
)12mm for negative bending moments in the
beam connection to the column and 6mm for positive bending moments
[130].
2.5. Evaluation metrics
2.5.1. ANN development
The accuracy of a machine learning model must be evaluated as a
rst step. Networks are one way to realize a complicated system by
breaking it down into smaller components. Networks consist of a
collection of nodes and the connections that link them. The connections
control the information ow between nodes, which are known as the
computing units of networks. One kind of network that views its nodes
as articial neurons is an ANN. A computer model that takes inspiration
from natural neurons is called an "articial neuron". Articial neurons
compute their activation functions by multiplying inputs by weights.
The output of the articial neurons is estimated using a different func-
tion. Articial neural network (ANN) fusion [131]. However, one of the
most popular models of ANNs is the back-propagation method. In the
back-propagation process, neurons in the input layer feed the network
with inputs, while neurons in the output layer feed the network with
outputs. There might be numerous subsurface strata. This research es-
timates the discrepancy between actual and anticipated outcomes
(error). Until the ANN learns the training data set, the backpropagation
approach will reduce this mistake [132]. In an articial neural network
(ANN), input vectors and their associated target vectors are used to train
the network until it can roughly approximate a function and properly
correlate input vectors with certain output vectors as determined by the
user [133–136]. On the training data set for ANN, empirical risk mini-
mization (ERM) is utilized to reduce error [137–139].
In the beginning, we have an observable system made up of inde-
pendent variables, and dependent variables. Every dependent variable
must be independent of every other dependent variable, and each
dependent variable y may be thought of as a function of independent
variables. In the absence of this, the system is dened as a multiple input
- output system or an analogous ANN (Fig. 5, 6).
f(x1,x2,…,xn) = (y1,y2,…,ym)
with
net(x1,x2,…,xn) = (y1,y2,…,ym)
as the ANN equivalent to f
(10)
The Eq. (5) can be made into a set of n +m functions with n +m −1
parameter, in which each parameter of (5) is shown [140]
g1(x1,x2,…,xn,y1,y2,…,ym−1)=ym(11)
g2(x1,x2,…,xn,y1,y2,…,ym) = ym−1(12)
gm−1(x1,x2,…,xn,y1,y3,…,ym) = y2(13)
gm(x1,x2,…,xn,y2,y3,…,ym) = y1(14)
gm+1(x2,x3,…,xn,y1,y2,…,ym) = x1(15)
gm+2(x1,x3,…,xn,y1,y2,…,ym) = x2(16)
gm+n−1(x1,…,xn−2,xn,y1,y2,…,ym) = xn−1(17)
gm+n(x1,x2,…,xn−1,1y1,y2,…,ym)=xn(18)
Each equation g
j
is modeled by a multiple input - output type ANN
g
net
j
with j from 1 to n +m.
gnet1(x1,x2,…,xn,y1,y2,…,ym−1) = ym(19)
net2(x1,x2,…,xn,y1,y2,…,ym) = ym−1(20)
netm−1(x1,x2,…,xn,y1,y3,…,ym) = y2(21)
g
gnetm(x1,x2,…,xm,y2,y3,…,ym) = y1(22)
netm+1(x2,x3,…,xn,y1,y2,…,ym) = x1(23)
netm+2(x1,x3,…,xn,y1,y2,…,ym)=x2(24)
netm+n−1(x1,…,xn−2,xn,y1,y2,…,ym) = xn−1(25)
netm+n(x1,x2,…,xn−1,y1,y2,…,ym) = xn(26)
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
8
Fig. 5. ANN development.
Fig. 6. Schematic view of hidden layer of ANN.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
9
3. Comparison and discussion
3.1. Training and validation
Fig. 7 shows the load deection relationship of the specimen.
Tensional stress versus crack width (
σ
t
−w
t
) behavioral curves gained
from axial direct tension tests and estimated from the proposed model is
shown in Fig. 8: a) SFRC mixtures of the deep beams, b) SFRC mix of the
slender beams. Fig. 8 presents the diagrams of shear-critical beams with
stirrups SH0. 37 and SH0-40. Under repeated cyclic loads, each test
member has a comparable three-stage failure process: the elastic stage,
the inelastic stage with fractures, and the failure stage. At the beginning
of loading, the column’s root rst experiences a number of horizontal
fractures. The rebars are under little stress and strain, and the steel has
not yet begun to respond. The specimen is mainly in the elastic stage.
The SFRC frame columns’ current hysteresis behavior is comparable to
that of the reinforced concrete frame columns. As a result, there are
various intensities of the pinching phenomena in hysteresis loops. The
fractures continue to grow and form as the displacement amplitude and
cycle count rise. The concrete cover, however, shows extensive cracking
and partial spalling. The pinching phenomena of the hysteresis loops is
now progressively becoming better due to the impact of the core and
steel concrete. Some of the horizontal fractures turn into shear diagonal
cracks when the displacement ductility
μ
reaches 3, but the pace at which
they form is quite modest. Hysteresis loops’ pinching phenomena
essentially is disappeared. The hysteresis loop now has a hefty fusiform
structure. The steel ange, longitudinal rebars, and majority of the steel
web yield at the fracture section when the load is continuously
increased. Meanwhile, the repetitive strain causes the horizontal frac-
ture to progress slowly.
3.2. Numerical simulation
The entire procedure is fractured at the inelastic stage. Ultimately,
when the stress is increased, the specimen reaches the point of failure.
There is a signicant region of spalling in the concrete of the compres-
sion area at the base of the beam. The longitudinal rebars and stirrups
are visible, and some of them buckle. Nonetheless, since the core con-
crete is restrained by a steel ange frame, the SFRC frame column’s
capacity for compression deformation is undoubtedly improved. Due to
the transverse stirrups’ restraint on the concrete, the members’ strength
and stiffness are slowly deteriorating. The whole hysteresis cycle
procedure demonstrates the SFRC frame column’s high ductility and
capacity for energy consumption.
Steel bers have been shown by Lima Arajo et al. to signicantly
increase the shear strength of reinforced concrete beams and to narrow
cracks, which may decrease the number of stirrups in reinforced con-
crete buildings. On average, it was discovered that concrete containing
1.0 and 2.0% of steel bers had splitting tensile strengths that were
much higher than concrete without bers, on average by 70 and 99%,
respectively. This tensile strength is not only the resistance to matrix
breaking, but also the maximum strength of SF reinforced concrete. In
contrast, exural strength (f
ct,f
) was raised ~ 55%when the SF ratio was
raised from 1.0 to 2.0%. Thus, exural toughness (FT) was raised ~ 78%
when the volume of SF rate was raised from 1.0 to 2.0%. These results
showed the positive alignment of SF ratio in raising both tensile strength
and toughness of ber-reinforced concrete.
Slater et al has reported the shear strength of SF-RC beams on the
basis of the test results. 222 data set used in shear strength tests of SF-RC
beams with no stirrups was separated into 6 diverse sets depending on
their span-depth ratio (a/d⩾3 or a/d <3), shape, also concrete
compressive strength (f′
c⩾50 or f′
c<50)was utilized to improve separate
equations to predict their respective shear strength [141]. Here, few
statistical performance checks (coefcient of variation (COV), coef-
cient of determination (R
2
), performance factor (PF) = Vtest
VCalc , average
absolute error (AAE)) were used to compare the models dened from
this study with literature, dening the standard deviation (SD), mean
and coefcient of variation of the variables to dene the proximity of the
ndings. Mean of the PFs is close to 1 with small SD, it shows the ac-
curacy of test data prediction. Table 7 is the Comparative correlation
coefcient results for M-residual prediction.
Table 7 also includes a thorough representation of the training and
testing set’s data. Table 8 compares the suggested model and the ANN
model to demonstrate the coefcient of determination and R
2
value,
which provide details about the model’s goodness of t. The R
2
values of
the suggested model and the ANN model are higher (0.954 and 0.944,
respectively) than those of the model created by Azad et al. [142] has R
2
=0.862. These higher values unmistakably demonstrate that the sug-
gested ANN has a superiority over the model introduced by Azad et al.
[142]. The data correlation is established with strict acceptance stan-
dards, demonstrating that it is a more dependable procedure than the
rst suggested model. The less RMSE and higher RSQR values shows the
high accuracy of the model. If the primary goal of the model is predicted,
then the most crucial t criteria is the RMSE values, which provide a
Fig. 7. Load deection of the specimen.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
10
good indicator of how effectively the model predicts the response. The
ANN models showed more errors due to their better predictions, despite
their superior performance in terms of R
2
values.
4. Conclusion
Ten SFRC frame column samples were examined in this study under
the combination of a lateral cyclic load and axial compression. The
failure processing of the SFRC beam sample undergoes three phases
under the cycle load, including inelastic with cracks stage, elastic stage,
and the failure stage. Based on the test ndings, a hysteresis model was
constructed to mimic the hysteresis energy of the SFRC frame columns.
The SRC frame columns’ hysteresis behavior during the elastic stage is
comparable to that of the reinforced concrete frame columns. The
mutual restraint between the concrete and steel during the inelastic
stage increases the bearing capacity of both materials. The samples
function well against earthquakes, especially after the peak load. In this
work, all-encompassing method for forecasting the shear and exural
Fig. 8. Tensional stress versus crack width (
σ
t
−w
t
) behavioral curves gained from axial direct tension tests and estimated from the proposed model: (a) SFRC mix of
the slender beams (three tensional specimens from each SFRC mixture); (b) SFRC mixtures of the deep beams.
Table 7
Comparative root means square error results for residual prediction of Moment.
Model Training RMSE Testing RMSE
Proposed Model (Eq. (3)) [142] 6.93
[142] 6.81
ANN 8.665 7.565
Table 8
Comparative correlation coefcient results for M-residual prediction.
Model Training R
2
Testing R
2
Predicted Model 0.954 0.944
Azad et al. [142] 0.86 -
ANN Model (with Fixed Stratication) 0.684 0.934
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
11
load of steel reinforced RC beams has been proposed. This research also
makes a contribution to the creation of a methodology for using articial
intelligence approaches to address issues in civil engineering. For the
purpose of forecasting the remaining exure and shear strength of steel
reinforced concrete beams, an ANN model was created. For training and
testing of the ANN models, a database from an experimental investiga-
tion in literature was employed. One target variable and two input
variables were chosen for the ANN model. According to the literature,
the balanced section of P5 with a reinforcement ratio of around 50% had
the greatest performance among the study’s specimens in terms of en-
ergy dissipations. Seismostruct’s use of nite element modeling revealed
good compatibility with regard to the behavior of yielding deection
and nal condition. Additionally, raising the longitudinal reinforcement
ratio greatly boosted the specimens’ strengths in accordance with
analytical estimations.
Funding
This work was supported by Yongchuan District Natural Science
Foundation Project (2021yc-jckx20015).
CRediT authorship contribution statement
Gongxing Yan: Methodology, Validation, Supervision, Project
administration, Resources. Jie Li: Data curation, Writing – review &
editing, Conceptualization. Alaa Hussein Ali: Data curation, Writing –
review & editing, Conceptualization. Tamim Alkhalifah: Data curation,
Writing – review & editing, Conceptualization, Software. Fahad
Alturise: Data curation, Writing – review & editing, Conceptualization.
H. Elhosiny Ali: Data curation, Writing – review & editing, Conceptu-
alization, Software.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgment
The authors express their appreciation to the Deanship of Scientic
Research at King Khalid University, Saudi Arabia, for funding this work
through research groups program under grant of number R.G.P.2/231/
43. The authors extend their appreciation to the Al Mustaqbal University
college for supporting this work for grant number (MUC - E- 0122).
References
[1] Zhang W, Huang Y. Three-dimensional numerical investigation of mixed-mode
debonding of FRP-concrete interface using a cohesive zone model. Constr Build
Mater 2022;350:128818.
[2] Huang Y, Zhang W, Liu X. Assessment of Diagonal Macrocrack-Induced
Debonding Mechanisms in FRP-Strengthened RC Beams. J Compos Constr 2022;
26(5):4022056. https://doi.org/10.1061/(ASCE)CC.1943-5614.0001255.
[3] Zhang Z, Liang G, Niu Q, Wang F, Chen J, Zhao B, et al. A Wiener degradation
process with drift-based approach of determining target reliability index of
concrete structures. Qual Reliab Eng Int 2022;38(7):3710–25.
[4] Zhang Z, Li W, Yang J. Analysis of stochastic process to model safety risk in
construction industry. J Civ Eng Manag 2021;27(2):87–99.
[5] Shi T, Liu Y, Zhao X, Wang J, Zhao Z, Corr DJ, et al. Study on mechanical
properties of the interfacial transition zone in carbon nanober-reinforced
cement mortar based on the PeakForce tapping mode of atomic force microscope.
JOBE 2022;61:105248. https://doi.org/10.1016/j.jobe.2022.105248.
[6] Wei X, et al. Distribution of shear force in perforated shear connectors. Steel
Compos Struct 2018;27(3):389–99.
[7] Ismail M, et al. Strengthening of bolted shear joints in industrialized ferrocement
construction. Steel Compos Struct 2018;28(6):681–90.
[8] Shariati M, et al. Monotonic behavior of C and L shaped angle shear connectors
within steel-concrete composite beams: an experimental investigation. Steel
Compos Struct 2020;35(2):237–47.
[9] Naghipour M, et al. Effect of progressive shear punch of a foundation on a
reinforced concrete building behavior. Steel Compos Struct 2020;35(2):279–94.
[10] Shariati A, et al. Investigation of channel shear connectors for composite concrete
and steel T-beam. IJPS 2012;7(11):1828–31.
[11] Kara IF. Prediction of shear strength of FRP-reinforced concrete beams without
stirrups based on genetic programming. Adv Eng Software 2011;42(6):295–304.
[12] Oehlers DJ, Coughlan CG. The shear stiffness of stud shear connections in
composite beams. J Constr Steel Res 1986;6(4):273–84.
[13] Shariati M, et al. Comparison of behaviour between channel and angle shear
connectors under monotonic and fully reversed cyclic loading. Constr Build Mater
2013;38:582–93.
[14] Zabihi-Samani M, Ghanooni-Bagha M. Optimal Semi-active Structural Control
with a Wavelet-Based Cuckoo-Search Fuzzy Logic Controller. Iranian J Sci Tech
Trans Civ Eng 2019;43(4):619–34.
[15] Shariati A, et al. Various types of shear connectors in composite structures: A
review. Int J Phy Sci 2012;7(22):2876–90.
[16] Shariati M, et al. Comparative performance of channel and angle shear connectors
in high strength concrete composites: An experimental study. Constr Build Mater
2016;120:382–92.
[17] Shariati M, et al. Behavior of V-shaped angle shear connectors: experimental and
parametric study. Mater Struct 2015;49(9):3909–26.
[18] Nasrollahi S, et al. Investigation of pipe shear connectors using push out test.
Steel Compos Struct 2018;27(5):537–43.
[19] Fanaie N, Esfahani FG, Soroushnia S. Analytical study of composite beams with
different arrangements of channel shear connectors. Steel Compos Struct Int J
2015;19(2):485–501.
[20] Khorramian K, et al. Numerical analysis of tilted angle shear connectors in steel-
concrete composite systems. Steel Compos Struct 2017;23(1):67–85.
[21] Xiao Y, et al. Experimental and analytical performance evaluation of steel beam
to concrete-encased composite column with unsymmetrical steel section joints.
Steel Compos. Struct 2017;23(1):17–29.
[22] Yan F, et al. Experimental study on the irregular shaped steel reinforced concrete
columns of the China World Trade Center Phase III in Beijing. China Civ Eng J
2010;43(8):11–20.
[23] Zheng J, et al. Researching a Fuzzy-and Performance-Based Optimization Method
for the Life-Cycle Cost of SRHPC Frame Structures. Appl Sci 2017;7(3):269.
[24] Zeng L, et al. Seismic Damage Evaluation of Concrete-Encased Steel Frame-
Reinforced Concrete Core Tube Buildings Based on Dynamic Characteristics. Appl
Sci 2017;7(4):314.
[25] Shariati M, et al. Assessing the strength of reinforced concrete structures through
Ultrasonic Pulse Velocity and Schmidt Rebound Hammer tests. SRE 2011;6(1):
213–20.
[26] Sajedi F, Shariati M. Behavior study of NC and HSC RCCs conned by GRP casing
and CFRP wrapping. SRE 2019;30(5):417–32.
[27] Shariati M, et al. Fatigue energy dissipation and failure analysis of angle shear
connectors embedded in high strength concrete. Eng Fail Anal 2014;41:124–34.
[28] Manos G, Theofanous M, Katakalos K. Numerical simulation of the shear
behaviour of reinforced concrete rectangular beam specimens with or without
FRP-strip shear reinforcement. Adv Eng Software 2014;67:47–56.
[29] Park YJ, Reinhorn AM, Kunnath SK. IDARC: inelastic damage analysis of
reinforced concrete frame–shear-wall structures. NY: National Center for
Earthquake Engineering Research Buffalo; 1987.
[30] Ergun S, Demir A. Effect of hysteretic models on seismic behavior of existing RC
structures. J Perform Constr Facil 2015;29(6):04014160.
[31] Gu M, Cai X, Fu Q, Li H, Wang X, Mao B. Numerical analysis of passive piles under
surcharge load in extensively deep. Soft Soil Buildings 2022;12(11):1988.
[32] Zhao G, et al. The hysteresis performance and restoring force model for corroded
reinforced concrete frame columns. J Eng 2016;2016.
[33] Zeynalian M, Ronagh H, Dux P. Analytical description of pinching, degrading,
and sliding in a bilinear hysteretic system. Mechanics 2012;138(11).
[34] Wang B, et al. Hysteretic Behavior of Steel Reinforced Concrete Columns Based on
Damage Analysis. Appl Sci 2019;9(4):687.
[35] Zhou C, et al. Restoring force model for circular RC columns strengthened by pre-
stressed CFRP strips. Steel and Composite Structures 2014;17(4):371–86.
[36] Lee CS, Han SW. Computationally effective and accurate simulation of cyclic
behaviour of old reinforced concrete columns. Eng Struct 2018;173:892–907.
[37] Verduzco LF, et al. CALRECOD—A software for Computed Aided Learning of
REinforced COncrete structural Design. Adv Eng Software 2022;172:103189.
[38] Ibarra LF, Medina RA, Krawinkler H. Hysteretic models that incorporate strength
and stiffness deterioration. Earthq Eng Struct Dyn 2005;34(12):1489–511.
[39] Lei L, et al. Cyclic deterioration effect of the steel reinforced high strength
concrete frame. Eng Mech 2010;27(8):125.
[40] Rahnama, M. and H. Krawinkler, Effect of soft soils and hysteresis models on
seismic design spectra. John A. Blume Earthquake Engineering Research Centre
Report No. 108, Department of Civil Engineering. 1993, Stanford University.
[41] Takeda T, Sozen MA, Nielsen NN. Reinforced concrete response to simulated
earthquakes. J Struct Div 1970;96(12):2557–73.
[42] Kumar S, Usami T. An evolutionary-degrading hysteretic model for thin-walled
steel structures. Eng Struct 1996;18(7):504–14.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
12
[43] Conforti A, Zerbino R, Plizzari GA. Inuence of steel, glass and polymer bers on
the cracking behavior of reinforced concrete beams under exure. Structural
Concrete 2019;20(1):133–43.
[44] Smarzewski P. Effect of Curing Period on Properties of Steel and Polypropylene
Fibre Reinforced Ultra-High Performance Concrete. IOP Conference Series:
Materials Science and Engineering 2017;245:032059.
[45] Bencardino F, Nistic`
o M, Verre S. Experimental Investigation and Numerical
Analysis of Bond Behavior in SRG-Strengthened Masonry Prisms Using UHTSS
and Stainless-Steel Fibers. Fibers 2020;8(2):8.
[46] Cuenca E, Ferrara L. Self-healing capacity of ber reinforced cementitious
composites. State of the art and perspectives. KSCE J Civ Eng 2017;21(7):
2777–89.
[47] Guerini V, et al. Inuence of Steel and Macro-Synthetic Fibers on Concrete
Properties. Fibers 2018;6(3):47.
[48] Martinelli E, et al. Post-cracking response of hybrid recycled/industrial steel
ber-reinforced concrete. Special Publication 2018;326:64.1–64.10.
[49] Toghroli A, et al. Evaluating the use of recycled concrete aggregate and
pozzolanic additives in ber-reinforced pervious concrete with industrial and
recycled bers. Constr Build Mater 2020;252:118997.
[50] Belletti B, et al. Design aspects on steel ber-reinforced concrete pavements.
J Mater Civ Eng 2008;20(9):599–607.
[51] Bencardino F. Mechanical parameters and post-cracking behaviour of HPFRC
according to three-point and four-point bending test. Adv Civ Eng 2013;2013.
[52] Caggiano A, et al. Experimental characterization of the post-cracking response in
Hybrid Steel/Polypropylene Fiber-Reinforced Concrete. Constr Build Mater 2016;
125:1035–43.
[53] Afshar A, et al. Corrosion resistance evaluation of rebars with various primers and
coatings in concrete modied with different additives. Constr Build Mater 2020;
262:120034.
[54] Tsonos A. Steel ber high-strength reinforced concrete: A new solution for
earthquake strengthening of old R/C structures. WIT Trans Built Environ 2009;
104:153–64.
[55] Vougioukas E, Papadatou M. A Model for the Prediction of the Tensile Strength of
Fiber-Reinforced Concrete Members, Before and After Cracking. Fibers 2017;5(3):
27.
[56] Abambres M, Lantsoght EOL. ANN-Based Shear Capacity of Steel Fiber-
Reinforced Concrete Beams without Stirrups. Fibers 2019;7(10):88.
[57] Campione G, Minaf`
o G. Behaviour of concrete deep beams with openings and low
shear span-to-depth ratio. Eng Struct 2012;41:294–306.
[58] Tsonos A. Ultra-high-performance ber reinforced concrete: An innovative
solution for strengthening old R/C structures and for improving the FRP
strengthening method. WIT Trans Eng Sci 2009;64:273–84.
[59] Leone M, et al. Fiber-reinforced concrete with low content of recycled steel ber:
Shear behaviour. Constr Build Mater 2018;161:141–55.
[60] Shariati M, et al. Shear resistance of channel shear connectors in plain, reinforced
and lightweight concrete. SRE 2011;6(4):977–83.
[61] Ma K, et al. Shear Behavior of Hybrid Fiber Reinforced Concrete Deep Beams.
Materials 2018;11(10):2023.
[62] Smarzewski P. Analysis of Failure Mechanics in Hybrid Fibre-Reinforced High-
Performance Concrete Deep Beams with and without Openings. Materials 2019;
12(1):101.
[63] Cuenca E, Echegaray-Oviedo J, Serna P. Inuence of concrete matrix and type of
ber on the shear behavior of self-compacting ber reinforced concrete beams.
Composites Part B: Engineering 2015;75:135–47.
[64] Cucchiara C, Mendola LLa, Papia M. Effectiveness of stirrups and steel bres as
shear reinforcement. Cem Concr Compos 2004;26(7):777–86.
[65] Spinella N, Colajanni P, Recupero A. Simple plastic model for shear critical SFRC
beams. J Struct Eng 2010;136(4):390–400.
[66] Colajanni P, Recupero A, Spinella N. Generalization of shear truss model to the
case of SFRC beams with stirrups. Computers and Concrete 2012;9(3):227–44.
[67] Paknahad M, et al. Shear capacity equation for channel shear connectors in steel-
concrete composite beams. Steel Compos Struct 2018;28(4):483–94.
[68] Lantsoght EO. Database of shear experiments on steel ber reinforced concrete
beams without stirrups. Materials 2019;12(6):917.
[69] Marì Bernat A, et al. Mechanical model for the shear strength of steel ber
reinforced concrete (SFRC) beams without stirrups. Mater Struct 2020;53(2):28.
[70] Jia J, et al. Numerical performance evaluation of debonding strength in ber
reinforced polymer composites using three hybrid intelligent models. Adv Eng
Software 2022;173:103193.
[71] Bischoff PH. Tension stiffening and cracking of steel ber-reinforced concrete.
J Mater Civ Eng 2003;15(2):174–82.
[72] Mohammadhassani M, et al. Ductility and strength assessment of HSC beams with
varying of tensile reinforcement ratios. Struct Eng Mech 2013;48(6):833–48.
[73] Mohammadhassani M, et al. An experimental study on the failure modes of high
strength concrete beams with particular references to variation of the tensile
reinforcement ratio. Eng Fail Anal 2014;41:73–80.
[74] Meskenas A, et al. Determination of the Stress–Crack Opening Relationship of
SFRC by an Inverse Analysis. Mech Compos Mater 2014;49(6):685–90.
[75] Morelli F, et al. Inuence of Tension Stiffening on the Flexural Stiffness of
Reinforced Concrete Circular Sections. Materials 2017;10(6):669.
[76] Gribniak V, et al. Steel bres: Effective way to prevent failure of the concrete
bonded with FRP sheets. Adv Mater Sci Eng 2016;2016.
[77] Gribniak V, et al. Mechanical Behavior of Steel Fiber-Reinforced Concrete Beams
Bonded with External Carbon Fiber Sheets. Materials 2017;10(6):666.
[78] Gribniak V, et al. Strengthening of Fibre Reinforced Concrete Elements: Synergy
of the Fibres and External Sheet. Sustainability 2019;11(16):4456.
[79] Meda A, Minelli F, Plizzari GA. Flexural behaviour of RC beams in bre reinforced
concrete. Composites Part B: Engineering 2012;43(8):2930–7.
[80] Smarzewski P. Flexural toughness of high-performance concrete with basalt and
polypropylene short bres. Advances in Civil Engineering 2018;2018.
[81] Gribniak V, et al. Deriving stress–strain relationships for steel bre concrete in
tension from tests of beams with ordinary reinforcement. Eng Struct 2012;42:
387–95.
[82] Gribniak V, et al. Comparative analysis of deformations and tension-stiffening in
concrete beams reinforced with GFRP or steel bars and bers. Composites Part B:
Engineering 2013;50:158–70.
[83] Sheikh, S.A., Effectiveness of rectangular ties as connement steel in reinforced
concrete columns. 1980.
[84] Balmer, G.G., Shearing strength of concrete under high triaxial stress-
computation of Mohr’s envelope as a curve. Structural Research Laboratory
Report, United States Department of the Interior, Bureau of Reclamation, 1949: p.
No. SP-23.
[85] Muguruma H, et al. Effect of connement by high yield strength hoop
reinforcement upon the compressive ductility of concrete. In: Proceedings of the
Twenty-Second Japan Congress on Material Research. The Society of Material
Science; 1979.
[86] Rizwan M, et al. Computer based estimation of backbone curves for hysteretic
Response of reinforced concrete columns under static cyclic lateral loads.
Computers and Concrete 2014;14(2):193–209.
[87] Watanabe F, et al. Improving the exural ductility of prestressed concrete beam
by using the high yield strength lateral hoop reinforcement. In: FIP, Symposia on
Partial Prestressing and Practical Construction in Prestressed and Reinforced
Concrete, Proceedings: Part; 1980.
[88] Mander J, Priestley M, Park R. Observed stress-strain behavior of conned
concrete. J Struct Eng 1988;114(8):1827–49.
[89] Popovics S. A numerical approach to the complete stress-strain curve of concrete.
Cem Concr Res 1973;3(5):583–99.
[90] Seo J, et al. Metamodel-based regional vulnerability estimate of irregular steel
moment-frame structures subjected to earthquake events. Eng Struct 2012;45:
585–97.
[91] Seo J, Linzell DG. Use of response surface metamodels to generate system level
fragilities for existing curved steel bridges. Eng Struct 2013;52:642–53.
[92] Mangalathu S, Heo G, Jeon J-S. Articial neural network based multi-dimensional
fragility development of skewed concrete bridge classes. Eng Struct 2018;162:
166–76.
[93] Mangalathu S, Jeon J-S. Classication of failure mode and prediction of shear
strength for reinforced concrete beam-column joints using machine learning
techniques. Eng Struct 2018;160:85–94.
[94] Mangalathu S, Jeon JS. Stripe-based fragility analysis of multispan concrete
bridge classes using machine learning techniques. Earthq Eng Struct Dyn 2019;48
(11):1238–55.
[95] Kiani J, Camp C, Pezeshk S. On the application of machine learning techniques to
derive seismic fragility curves. Comput Struct 2019;218:108–22.
[96] Sahu D, et al. Stochastic response of reinforced concrete buildings using high
dimensional model representation. Eng Struct 2019;179:412–22.
[97] Chen J, Tong H, Yuan J, Fang Y, Gu R. Permeability Prediction Model Modied
on Kozeny-Carman for Building Foundation of Clay Soil. Buildings 2022;12(11):
1798.
[98] Mangalathu S, et al. Classifying earthquake damage to buildings using machine
learning. Earthquake Spectra 2020;36(1):183–208.
[99] Siam A, Ezzeldin M, El-Dakhakhni W. Machine learning algorithms for structural
performance classications and predictions: Application to reinforced masonry
shear walls. Structures 2019;22:252–65.
[100] Huang H, Burton HV. Classication of in-plane failure modes for reinforced
concrete frames with inlls using machine learning. J Build Eng 2019;25:100767.
[101] Safa M, et al. Potential of adaptive neuro fuzzy inference system for evaluating
the factors affecting steel-concrete composite beam’s shear strength. Steel
Compos Struct 2016;21(3):679–88.
[102] Toghroli A, et al. Prediction of shear capacity of channel shear connectors using
the ANFIS model. Steel Compos Struct 2014;17(5):623–39.
[103] Sedghi Y, et al. Application of ANFIS technique on performance of C and L shaped
angle shear connectors. Smart Struct Syst 2018;22(3):335–40.
[104] Katebi J, et al. Developed comparative analysis of metaheuristic optimization
algorithms for optimal active control of structures. Eng Comput 2019:1–20.
[105] Shariati M, et al. Identication of the most inuencing parameters on the
properties of corroded concrete beams using an Adaptive Neuro-Fuzzy Inference
System (ANFIS). Steel Compos Struct 2020;34(1):155–70.
[106] Raq MY, Bugmann G, Easterbrook DJ. Neural network design for engineering
applications. Comput Struct 2001;79(17):1541–52.
[107] Mohammadhassani M, et al. Identication of a suitable ANN architecture in
predicting strain in tie section of concrete deep beams. Struct Eng Mech 2013;46
(6):853–68.
[108] Shariati M, et al. A novel approach to predict shear strength of tilted angle
connectors using articial intelligence techniques. Eng Comput 2020:1–21.
[109] Toghroli A, et al. Potential of soft computing approach for evaluating the factors
affecting the capacity of steel–concrete composite beam. J Intell Manuf 2016;29
(8):1793–801.
[110] Sadeghipour Chahnasir E, et al. Application of support vector machine with rey
algorithm for investigation of the factors affecting the shear strength of angle
shear connectors. Smart Struct Syst 2018;22(4):413–24.
G. Yan et al.
Advances in Engineering Software 176 (2023) 103373
13
[111] Safa M, et al. Development of neuro-fuzzy and neuro-bee predictive models for
prediction of the safety factor of eco-protection slopes. Phys A: Stat Mech Appl
2020;550:124046.
[112] Shariati M, et al. Application of a hybrid articial neural network-particle swarm
optimization (ANN-PSO) model in behavior prediction of channel shear
connectors embedded in normal and high-strength concrete. Appl Sci 2019;9(24):
5534.
[113] Bai J, et al. Using neural networks to predict workability of concrete
incorporating metakaolin and y ash. Adv Eng Software 2003;34(11):663–9.
[114] Oreta AW, Kawashima K. Neural network modeling of conned compressive
strength and strain of circular concrete columns. J Struct Eng 2003;129(4):
554–61.
[115] Erdem H. Prediction of the moment capacity of reinforced concrete slabs in re
using articial neural networks. Adv Eng Software 2010;41(2):270–6.
[116] Imam A, Anifowose F, Azad AK. Residual strength of corroded reinforced concrete
beams using an adaptive model based on ANN. Int J Concret Struct Mater 2015;9
(2):159–72.
[117] Sakthivel P, Ravichandran A, Alagumurthi N. Modeling and prediction of exural
strength of hybrid mesh and ber reinforced cement-based composites using
articial neural network (ANN). Geomate J 2016;10(19):1623–35.
[118] Minh H-L, et al. Structural damage identication in thin-shell structures using a
new technique combining nite element model updating and improved Cuckoo
search algorithm. Adv Eng Software 2022;173:103206.
[119] Nanni A. Flexural behavior and design of RC members using FRP reinforcement.
J Struct Eng 1993;119(11):3344–59.
[120] Saadatmanesh H, Ehsani MR, Jin L. Repair of earthquake-damaged RC columns
with FRP wraps. ACI Struct J 1997;94:206–15.
[121] Sharif A, et al. Strengthening of initially loaded reinforced concrete beams using
FRP plates. Struct J 1994;91(2):160–8.
[122] Chajes MJ, et al. Shear strengthening of reinforced concrete beams using
externally applied composite fabrics. Struct J 1995;92(3):295–303.
[123] Reddy JN. Mechanics of laminated composite plates- Theory and analysis(Book),
1997. Boca Raton, FL: CRC Press; 1997.
[124] Willam KJ. Constitutive model for the triaxial behaviour of concrete. Proc Intl
Assoc Bridge Structl Engrs 1975;19:1–30.
[125] Menetrey P, Willam K. Triaxial failure criterion for concrete and its
generalization. Struct J 1995;92(3):311–8.
[126] Sadrnezhad, S. and A.S. Ghoreyshian, A simple unconventional plasticity model
within the multilaminate framework. 2010.
[127] Toghroli A, et al. A review on pavement porous concrete using recycled waste
materials. Smart Struct Syst 2018;22(4):433–40.
[128] Grassl P, Lundgren K, Gylltoft K. Concrete in compression: a plasticity theory with
a novel hardening law. Int J Solids Struct 2002;39(20):5205–23.
[129] Omidi O, Lot V. Finite Element Analysis of Concrete Structures Using
PlasticDamage Model in 3-D Implementation. Int J Civ Eng 2010;8(3):187–203.
[130] Gi˜
ao A, Lúcio V, Chastre C. Seismic strengthening of RC beam-column
connections. In: 15th World Conference of Earthquake Engineering; 2012.
[131] Gershenson C. Articial neural networks for beginners, formal computational
skills teaching package. Brighton, UK: COGS, University of Sussex; 2001.
[132] Rumelhart DE, McClelland JL, Group PR. Parallel distributed processing, 1. New
York: IEEE; 1988.
[133] Shariati M, et al. Prediction of concrete strength in presence of furnace slag and
y ash using Hybrid ANN-GA (Articial Neural Network-Genetic Algorithm).
Smart Struct Syst 2020;25(2):183–95.
[134] Shariati M, et al. A novel hybrid extreme learning machine-grey wolf optimizer
(ELM-GWO) model to predict compressive strength of concrete with partial
replacements for cement. Eng Comput 2020:1–23.
[135] Shariati M, et al. Hybridization of metaheuristic algorithms with adaptive neuro-
fuzzy inference system to predict load-slip behavior of angle shear connectors at
elevated temperatures. Composite Structures 2021;278:114524.
[136] Mohammadhassani M, et al. An evolutionary fuzzy modelling approach and
comparison of different methods for shear strength prediction of high-strength
concrete beams without stirrups. Smart Struct Syst 2014;14(5):785–809.
[137] Wu J-D, Chan J-J. Faulted gear identication of a rotating machinery based on
wavelet transform and articial neural network. Expert Syst Appl 2009;36(5):
8862–75.
[138] Patterson DW. Articial neural networks: theory and applications. Prentice Hall
PTR; 1998.
[139] Haykin S. Neural Networks: A Comprehensive Foundation. 2nd. NJ, USA Prentice
Hall: Englewood Cliffs; 1999.
[140] Rinke WC. An Algorithm to Transform an Articial Neural Network into its Open
Equation Form and its Potential Applications. Int J Neur Netw Adv Appl 2015. p.
2313-0563.
[141] Slater E, Moni M, Alam MS. Predicting the shear strength of steel ber reinforced
concrete beams. Constr Build Mater 2012;26(1):423–36.
[142] Azad A, Ahmad S, Al-Gohi B. Flexural strength of corroded reinforced concrete
beams. Mag Concr Res 2010;62(6):405–14.
G. Yan et al.
