European International Journal of Multidisciplinary Research
and Management Studies
8
https://eipublication.com/index.php/eijmrms
TYPE
Original Research
PAGE NO.
8-12
DOI
OPEN ACCESS
SUBMITED
11 April 2025
ACCEPTED
07 May 2025
PUBLISHED
09 June 2025
VOLUME
Vol.05 Issue06 2025
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Calculation of
Deformations of Flexural
Three-Layer Reinforced
Concrete Elements with A
Middle Layer of Arbolite
Akramov Khusnitdin
DSc, professor, Tashkent University of Architecture and Civil Engineering,
Uzbekistan
Tokhirov Jaloliddin
PhD, Tashkent University of Architecture and Civil Engineering,
Uzbekistan
Abstract:
This study presents a deformation-based
calculation approach for three-layer reinforced
concrete (RC) elements with an arbolite insulating core.
Given the insufficient theoretical foundation in current
design standards and the scarcity of experimental data,
a comprehensive experimental investigation was
undertaken. Two series of full-scale specimens were
tested to evaluate flexural behavior, particularly
focusing on the influence of vertical and inclined shear
reinforcement. Results demonstrate that deflections
prior to cracking correlate well with theoretical
predictions when both bending and shear deformations
are considered. This paper proposes refined equations
and section models for accurate deflection prediction
in such composite systems.
Keywords:
Three-layer reinforced concrete, Arbolite
core, Flexural behavior, Shear deformation, Deflection
analysis, Inclined shear reinforcement, Low-strength
concrete insulation, Composite concrete panels,
Modulus of elasticity, Layered concrete systems,
Experimental mechanics, Shear stiffness, Deflection
modeling.
Introduction:
Improving the thermal performance of
building envelopes is critical for reducing operational
European International Journal of Multidisciplinary Research
and Management Studies
9
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
energy costs and fuel resource consumption. A
promising solution is the use of three-layer RC panels,
comprising low-strength insulating concrete (such as
arbolite) in the core and dense concrete on the outer
layers. Despite their practical benefits, design
methodologies
for
such
systems
remain
underdeveloped due to limited theoretical grounding
and experimental validation. Existing codes, such as
KMK 2.03.01-96, offer limited provisions for layered RC
elements, especially when composite action and shear
deformations are significant. This research addresses
this gap by analyzing the deformation characteristics of
three-layer RC bending elements with an arbolite core
made from local cotton stalks.
One of the effective ways to increase the thermal
resistance of enclosing structures in order to reduce the
operating costs of buildings and the costs of fuel and
energy resources is the use of three-layer reinforced
concrete panels with insulation made of low-strength
concrete with a low thermal conductivity coefficient
and outer layers made of dense lightweight or heavy
concrete [1].
Based on the fact that all proposals for calculating
three-layer reinforced concrete elements with
monolithically bonded layers are not sufficiently
substantiated for inclusion in regulatory documents,
and experimental data are limited, targeted studies
were conducted on the deformations of bending three-
layer reinforced concrete elements with an insulating
layer of arbolite on local raw materials (cotton stems).
For this purpose, two series of test specimens 330 cm
long with a design span of 300 cm, a height of 25 cm
and a width of 16 cm were manufactured and tested.
The thickness of the outer layers is 4 cm, which makes
it possible to place longitudinal reinforcement in them
and ensure its protection in accordance with the
requirements of KMK 2.03.01-96 [2-5].
METHODS
Series I, consisting of eight test specimens, was
designed to study the effect of transverse
reinforcement in the form of vertical bars on the
operation of near-support sections. All specimens are
reinforced with the same longitudinal working
reinforcement of two bars with a diameter of 12 mm
made of grade A-III steel and different transverse. In six
test specimens, transverse vertical reinforcement is
installed with a pitch of 21 cm with a diameter of 4;
5.66; 6.93; 8; 8.94; 9.8 mm made of grade A-1 steel, two
test specimens do not have transverse reinforcement.
The following designation of the test specimens is
adopted: BA-I-1...BA-I-8.
Series II of
four test specimens was designed to study the
possibility of strengthening the support zones with
transverse reinforcement in the form of inclined rods.
The test specimens, as in Series I, are reinforced with
longitudinal reinforcement of two rods with a diameter
of 12 mm made of grade A-III steel. The inclined rods
are made in the form of a triangular lattice, located at
an angle of 45° and spot welded to the longitudinal
rods. One specimen, the control, is made without
transverse reinforcement, in the other three the
inclined transverse reinforcement is made of 4 and 5
mm diameters of Br-500 steel and 6 mm of A-240 steel,
respectively. The shear span in the test specimens is
2.7ho. The test specimens of the second series are
designated BA-II-1...BA-II-4, respectively.
The concrete of the outer layers is heavy with
the strength of 25 MPa, and the concrete of the middle
layer is made of arbolite - 1 MPa.
The analysis of the experimental results shows that at
the stages before crack formation, the deflections of
the samples increased proportionally to the load. The
deflections of the samples of the 1st series BA-1-1 BA-
1-8 did not differ significantly from each other. The
deflection values of the samples with transverse
reinforcement BA-1-7 and BA-1-8 were 22 and 25%
greater than the deflections of the samples without
transverse reinforcement (BA-1-1 and BA-1-2). This is
most likely due to the fact that due to the constrained
shrinkage of the concrete of the middle layer, in the
presence of transverse rods, tightening stresses arise in
it.
With an increase in the diameter of the
inclined reinforcement in the samples of the 2nd series,
the deflection values were less than in the sample
without transverse reinforcement (BA-P-1). For
samples BA-11-2 - BA-11-4 with reinforcement
diameters of 4, 5 and 6 mm, the differences were 17,
24.7 and 35%, respectively, and this is most likely due
to an increase in shear rigidity of the middle layer in the
presence of inclined bars.
For bending structures in the current KMK 2.03.01-96,
general theoretical deflections are recommended for
determining the sum of deflections from bending and
shear deformations. If the ratio of the design span to
the height of the structure section is more than 10, it is
permissible to ignore the shear deflection due to its
smallness. The specified ratio for the studied test
samples is 12. For three-layer structures with a middle
layer made of low-strength concrete, due to a
significant effect of shear deformations on the
deflections of test samples, it is recommended to take
into account the shear deflection. Based on this, the
calculation of the deflection of test samples was carried
out taking into account the bending and shear
deformations.
The theoretical values of deflections from the bending
moment to the appearance of cracks were obtained in
European International Journal of Multidisciplinary Research
and Management Studies
10
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
accordance with the recommendations of KMK
2.03.01-96 using the following formula:
f
m
=
𝑀
𝜑
𝑏𝑙
𝐸
𝑏
𝐼
𝑟𝑒𝑑
𝜌
𝑚
𝑙
2
(1)
where M is the bending moment,
𝐸
𝑏
is the initial
modulus of elasticity of concrete;
𝐼
𝑟𝑒𝑑
is the moment of
inertia of the reduced section;
𝜑
𝑏𝑙
is the coefficient
taking into account the effect of short-term creep of
concrete, taken as 0.85;
𝜌
𝑚
is the coefficient depending
on the loading scheme and the point of determining the
deflections.
RESULTS
To calculate three-layer elements for crack formation,
the three-layer section was replaced by a
homogeneous I-beam, the deformations during
bending up to based on the ratio of the initial moduli of
elasticity of concrete in the layers. The theoretical
values of deflections were compared with the
experimental ones, obtained at the middle of the span
of the samples minus the deflections under loads, i.e.,
in the section of constant moments (Table 1). As can be
seen from Table 1, the calculated values of deflections
from the bending moment differed insignificantly from
the experimental ones: in the samples of the 1st series
within 1.7-20.8%; in the samples of the 2nd series 3.2-
27.3%. The differences may be due to some
measurement error. Based on this, we can state that
the calculation of deflections of three-layer structures
from the bending moment is made according to
formula (1).
Comparison of experimental and theoretical values of
deflections from bending moment to crack formation
Table 1
Sample code
M,
kNm
Sag due to bending in the middle of the span
relative to the loads,
𝐟
𝐦
10 3 cm/%
Experience
Calculation
BA-I-1
1 ,76
29/100
28.5/98.3
BA-I-2
1 ,76
36/100
28.5/79.2
BA-I-3
1 ,76
27.8/100
28.5/102.5
BA-I-4
1 ,76
26.7/100
28.5/106.7
BA-I-5
1 ,76
31.1/100
28.5/91.6
BA-I-6
1 ,76
28/100
28.5/101.8
BA-I-7
1 ,76
31/100
28.5/91.9
BA-II-8
1 ,76
28/100
28.5/101.8
BA-II-1
1 ,76
36/100
28.9/80.3
BA-II-2
1 ,76
31.6/100
28.9/91.4
BA-II-3
1 ,76
28/100
28.9/103.2
BA-II-4
1 ,76
22.7/100
28.9/127.3
We recommend determining deflections from
transverse forces before the appearance of cracks
caused by shear deformations using the formula given
in the course "Strength of Materials" by N.M. Belyaev,
which more strictly takes into account the shape of the
section
𝑓
𝑞
= ∫
𝐾𝑄(𝑥)
𝐺𝐴
𝑏
1
0
𝑑𝑥
(2)
where
𝑄(𝑥)
is the transverse force in the section due to
the action of an external load; G is the shear modulus
of concrete, equal to 0.4E b ; A b is the cross-sectional
area of the structure; K is the coefficient taking into
account the shape of the cross-section and is
determined by the formula
𝐾 =
𝐴
𝑏
𝐼
2
∫
𝑆
2
(𝑧)
𝑏
𝑑𝑧
where I, S are the moment of inertia and the static
moment of the cross section; b is the width of the
sample.
Then, based on the ratio of the initial elastic moduli of
concrete, the three-layer section of the test samples
was replaced by a homogeneous I-beam, and the value
of the coefficient "K" is determined by the following
formula:
𝐾 = 2
𝐴
𝑏
𝐼
𝑟𝑒𝑑
2
[∫
𝑆
2
(𝑧)
𝑏
𝑓
−(
ℎ−2ℎ𝑓
2
)
−
ℎ
2
𝑑𝑧 + ∫
(𝑆
′
)
2
(𝑧)
𝑏
′
𝑑𝑧
0
−(
ℎ−2ℎ𝑓
2
)
]
(3)
where S' and S are the static moment of inertia of the
wall and flange of the reduced I-section
𝑆
′
=
𝑏
𝑓
ℎ
2
8
(1 −
4𝑧
2
ℎ
2
) −
(𝑏
𝑓
−𝑏
′
)(ℎ−2ℎ
𝑓
)
2
8
(1 −
4𝑧
2
(ℎ−2ℎ
𝑓
)
2
)
𝑆 =
𝑏
𝑓
ℎ
2
8
(1 −
4𝑧
2
ℎ
2
)
For samples of series II, the effect of inclined rods on
reducing deflections from transverse forces was taken
European International Journal of Multidisciplinary Research
and Management Studies
11
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
into account when determining the geometry of the
reduced section using the formula
b
𝑟𝑒𝑑
=
2𝐴
𝑠,𝑖𝑛𝑐
𝑎
𝐸
𝑠
𝐸
𝑏
+ 𝑏
Here is
𝐴
𝑠,𝑖𝑛𝑐
the cross-sectional area of the inclined
bar;
𝐸
𝑠
is the modulus of elasticity of the transverse
inclined reinforcement;
𝐸
𝑏
is the initial modulus of
elasticity of concrete;
𝑎
is the distance between the
transverse inclined bars normal to them.
The magnitude of the deflections from transverse
forces, determined by formula (2) at the values of the
coefficient "K" according to formula (3), differs
insignificantly from the experimental ones (Table 2). In
the samples of series I without transverse
reinforcement (BA-I-I and BA-1-2), the differences
between the calculated and experimental values of
deflections amounted to 9.3% on average, and in the
samples
reinforced
with
transverse
vertical
reinforcement BA-1-3-BA-1-8 19.2%. Here, most likely,
the decrease in shear deformations of concrete in the
middle layer had an effect due to large initial
deformations associated with shrinkage.
A sufficiently good convergence of the theoretical and
experimentally obtained values of deflections from
transverse forces occurs in the samples of series 11.
Thus, for a sample without transverse reinforcement
(BA-II-1), the difference does not exceed 2.1%. In three
other samples of this series with inclined reinforcement
in the support zone (BA-P-2 - BA-P-4), the differences
were 11.8; 119 and 14.9%, respectively.
Comparison of experimental and theoretical values of
deflections from transverse forces before crack
formation
Table 2
Sample code
Diameter of
transverse
reinforcement, mm
Q,
kN
Sag in the middle of the span due to
transverse forces.
𝐟
𝐦
10 3 cm/%
Experience
Calculation
BA-I-1
-
2.4
16.4/100
15.6/95.1
BA-I-2
-
2.4
18.1/100
15.6/86.2
BA-I-3
4.0
2.4
16.9/100
21.3/126
BA-I-4
5.66
2.4
19/100
21.3/112.1
BA-I-5
6.93
2.4
15/100
21.3/142
BA-I-6
8.0
2.4
23.8/100
21.3/89.5
BA-I-7
8.94
2.4
24.6/100
21.3/86.6
BA-II-8
9.8
2.4
24/100
21.3/88.7
BA-II-1
-
2.4
19.5/100
19.1/97.9
BA-II-2
4.0
2.4
17/100
15/88.2
BA-II-3
5.0
2.4
14.2/100
15.9/111.9
BA-II-4
6.0
2.4
13.4/100
15.4/114.9
Based on the above, it is recommended to calculate the
deflections of three-layer samples from transverse
forces to the formation of cracks using formula (2),
taking into account the shape factor of the reduced
section using formula (3).
CONCLUSIONS
•
Shear deformations significantly influence the total
deflection of three-layer RC elements with arbolite
cores.
•
The combined bending-shear model yields results
consistent with experimental data.
•
Inclined shear reinforcement substantially reduces
deflections, outperforming vertical stirrups in
layered RC elements.
•
The modified design approach should be
incorporated into future versions of structural
codes for composite concrete panels.
REFERENCES
Al Fakher, U., et al. (2021). Shear behaviour of hollow
precast concrete composite structures. Mater Struct,
54, 84.
[Zhou et al.] (2024). Investigation into the flexural
performance of novel precast sandwich wall panels.
Mater Struct.
Xie,
J. H., et al. (2022). Flexural behaviour of full scale
precast recycled concrete sandwich panels with BFRP
connectors. Materials, 17(11), 2591.
Chinenkov Yu.V., Akramov Kh.A., Nigmanov Z.M. Three-
layer wall panels with polystyrene concrete insulation
for the construction of buildings in the agro-industrial
complex // Architecture and Construction of
Uzbekistan. 1999.-
№1
-2.-P.16-17.
European International Journal of Multidisciplinary Research
and Management Studies
12
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
KMK [5]. 03.01-96. Concrete and reinforced concrete
structures. Tashkent. IVC "AKATM", 1996.
