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PUBLISHED DATE: - 27-08-2024
https://doi.org/10.37547/tajet/Volume06Issue08-10
PAGE NO.: - 84-92
CALCULATION OF FLEXIBLE CONCRETE BEAMS WITH
BASALT REINFORCEMENT
Mirzaaxmedova Ugiloy Abduxalimjonovna
Basic doctoral student at FarPI, Uzbekistan
Razzakov Sobirjon Juraevich
Professor at NamIEC, Uzbekistan
INTRODUCTION
In construction practice, using mirror composite
reinforcements, conducting research in the
directions of increasing the fire resistance and
elasticity module of concrete, and improving the
stress-deformation state, strength, and crack
resistance properties of bending elements has
become one of the urgent tasks. According to the
study and analysis of scientific research works, the
operation of flexural concrete structures equipped
with basalt reinforcements under the influence of
forces in the conditions of our republic has not yet
been sufficiently studied.
Basalt reinforcements produced in the Republic of
Uzbekistan are the most optimal option for
conducting research on normal heavy concretes,
which are used in the construction practice in the
largest volume and in all types of construction
objects.
The main part. The coolness of flexural concrete
beams with basalt reinforcement depends on the
reinforcement of the beam, the strength of the
concrete, the distance between the element
supports and the amount of the load.
At small values of the loads in the loading stages,
Q=0.2-0.3Qult, the deflections of the sample beams
did not become large (f≤0.4mm ) and they
increased almost linearly. With the increase of the
load on the steps, the graph showed a curved
character, and in cases where the load values are
Q≥0.4Qult, a sharp increase in coolness is observed.
At values of Q>0.6Kult, the thicknesses increased
sharply and their amount increased to 2.4-3.0mm.
In this case, it is possible to observe the high
deformability of baalt reinforcements.
It was observed that before the occurrence of
boundary conditions in the beams, the deflections
RESEARCH ARTICLE
Open Access
Abstract
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in them reach f=3.4-4.0mm.
Before limit states occur in flexural concrete
elements with basalt reinforcement, together with
their strength, uniformity is required. In addition to
the calculation of stability conditions, they must
also be calculated for coolness.
Determining the calculated stiffness in the sample
beams was carried out in the following order (1).
Calculation of elements of constructions according
to coolness is carried out based on the following
condition:
𝑓 ≤ 𝑓
𝑢𝑙𝑡
(1)
where: f is the cooling of the element due to
external load; f_ult is the limiting coolness allowed
in the element.
The stiffness of constructions is determined
according to the general rules of construction
mechanics, depending on the bending, sliding and
axial deformation characteristics (curvature,
angles, displacement, etc.) of its sections along the
length of the element.
For flexural elements with a constant cross-section
along the length of the element without cracks, the
deflections are determined based on the general
rules of construction mechanics using the unity of
the cross-sections.
The full curvature of bending elements is
determined by the following formulas:
- for sections without cracks in the extension zone:
1
𝑟
= (
1
𝑟
)
1
+ (
1
𝑟
)
2
(2)
- for sections with cracks in the extension zone
1
𝑟
= (
1
𝑟
)
1
− (
1
𝑟
)
2
+ (
1
𝑟
)
3
(3)
Here:
(
1
𝑟
)
1
, (
1
𝑟
)
2
- curvatures resulting from the
continuous action of short-term loads and
temporary long-term loads, respectively.
(
1
𝑟
)
1
−
curvature resulting from the non-
continuous effect of all loads, which are calculated
according to deformations;
(
1
𝑟
)
2
−
curvature resulting from the non-
permanent effects of permanent and temporary
long-term loads;
(
1
𝑟
)
3
−
curvature resulting from the continued
effect of permanent and temporary long-term
loads.
The curvature 1/r caused by the corresponding
loads is determined by the following formula:
1
𝑟
=
𝑀
𝐷
, (4)
where: M is the bending moment caused by the
external load (taking into account the moment
created by the longitudinal force N), this moment is
created with respect to the axis normal to the plane
of action, and the given cross section of the element
passes through the center of gravity;
D is the bending stiffness of the given cross-section
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of the element, its value is determined according to
the following formula:
𝐷 = 𝐸
𝑏1
∙ 𝐼
𝑟𝑒𝑑
, (5)
where: E_b1 is the deformation modulus of
compressed concrete, this modulus is determined
depending on the duration of the impact of loads
and the presence or absence of cracks; I_red is the
moment of inertia of the given cross-section
relative to the center of gravity of this section, this
moment is determined taking into account the
presence or absence of cracks.
The values of the deformation modulus of concrete
E_b1 and the moment of inertia of the given section
I_red for the elements without cracks in the
stretching zone and with cracks are determined in
accordance with the applicable normative
documents, respectively.
The stiffness of the bending element D in the
section without cracks is determined by formula
(5).
The moment of inertia of the given cross-section of
the element relative to the center of gravity of this
section Ired is determined according to the general
rules of resistance of elastic elements for a solid
div, taking into account the entire surface of the
concrete cross-section and the coefficient of
bringing the reinforcement to concrete and the
surface of the cross-section of the reinforcement
(2,3):
𝐼
𝑟𝑒𝑑
= 𝐼 + 𝐼
𝑓
∙ 𝛼
𝑓
,
(6)
where: I is the moment of inertia of the cross-
section of the concrete section with respect to the
center of gravity of the element; I_f-the moment of
inertia of the surface of the cross-section of the
cross-section of the stretched armature relative to
the center of gravity of the element;
𝛼
𝑓
is the coefficient of bringing reinforcement to
concrete,
𝛼
𝑓1
=
𝐸
𝑓
𝐸
𝑏1
(7)
The value of I is determined according to the
general
rules
for
calculating
geometric
classifications of elastic elements.
It is allowed to determine the moment of inertia
I_red without
taking into account the
reinforcement.
The values of concrete deformation in formulas (5)
and (7) are taken to be equal to:
- under non-continuous (non-continuous) impact
of loads:
𝐸
𝑏1
= 0,85 ∙ 𝐸
𝑏
, (8)
- under the continuous (continued) influence of
loads
𝐸
𝑏1
= 𝐸
𝑏𝜏
=
𝐸
𝑏
1+𝜑
𝑏,𝑐𝑟
, (9)
where: φ_(b,cr) is the creep coefficient
(characteristic) of concrete.
In compression classes of concrete, the value of
φ_(б,cr) is taken as equal to: V15
-4.8, V20-4.0, V25-
3.6, V30-3.2, V35-3.0, V40-2 ,8, V50-2.4, V55-2.2,
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V60-2.0.
In the section with cracks in the stretching zone,
the integrity of the structural element is
determined as follows.
The integrity of structural elements in sections
with cracks in the stretched zone is determined
taking into account the following conditions (4):
after deformation, the cross-section remains flat;
the tension of concrete in the compression zone is
determined as determined for an elastic div;
- the work of prestressed concrete in the section
with a normal crack is not taken into account;
- the work of prestressed concrete in the section
located between side cracks in the normal
direction is determined by means of ps_f.
The uniformity of element D in sections with cracks
is determined by formula (5) and its value is not
greater than the uniformity of the element without
cracks.
The values of the compressed concrete
deformation modulus E_(b1 ) are taken as equal to
the values of the deformation modulus E_(b,red ),
which is determined according to the following
formula (5):
𝐸
𝑏,𝑟𝑒𝑑
=
𝐸
𝑏,𝑠𝑒𝑟
𝜀
𝑏1,𝑟𝑒𝑑
, (10)
where:
𝜀
𝑏1,𝑟𝑒𝑑
-
relative deformations of concrete,
taken as follows:
- 0.0015 for heavy concrete under discontinuous
impact of loads;
- 0.0034 for heavy concrete with continuous load.
The value of
𝐼
𝑓
is determined according to the
general rules of resistance of materials, where the
distance from the most compressed fiber of
concrete (with the lifting coefficient
𝛼
𝑓1
)) to the
center of gravity of the cross section is taken
without taking into account the concrete in the
stretched zone. For bending elements:
𝑦
𝑐𝑚
= 𝑥
𝑚
(11)
where
х
т
is the average height of the concrete
compression zone, which takes into account the
effect of the stretched concrete work between the
cracks (Fig. 1).
The values of
𝐼
𝑏
and
𝑦
𝑐𝑚
are determined according
to the general rules for calculating geometric
classifications of sections of elastic elements.
The position of the neutral axis (the height of the
concrete compression zone) for bending elements
is determined from the following equation:
𝑆
𝑏0
= 𝛼
𝑓
∙ 𝑆
𝑓0
, (12)
where:
𝑆
𝑏0
and
𝑆
𝑓0
are the static moments of the
concrete compression zone and the tensile
reinforcement relative to the neutral axis,
respectively.
For elements with a rectangular cross-section, the
height of the compressed zone is determined
according to the following formula (6,7):
𝑥
𝑚
= ℎ
0
(√(𝜇
𝑓
𝛼
𝑓1
)
2
+ 2𝜇
𝑓
𝛼
𝑓1
− 𝜇
𝑓
∙ 𝛼
𝑓1
)
, (13)
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Here:
𝜇
𝑓
=
𝐴
𝑓
𝑏∙ℎ
0
Figure 1. A scheme for calculating the deformations of an element with the
given cross-section and cracks under the action of a bending moment in the
stressed-strained state.
For eccentrically compressed and eccentrically
stretched elements, the position of the neutral axis
(the height of the compressed zone) is determined
from the following equation:
𝑦
𝑁
=
𝐼
𝑏0
+𝛼
𝑓1
∙𝐼
𝑓0
𝑆
𝑏𝑜+
𝛼
𝑓1
∙𝑆
𝑓0
(14)
where:
𝑦
𝑁
is the distance from the neutral axis to
the point of application of the longitudinal force N,
which lags behind the center of gravity of the full
section (without taking into account cracks)
𝑒
0
=
𝑀
𝑁
;
𝐼
𝑏0
, 𝐼
𝑓0
, 𝑆
𝑏𝑜
, 𝑆
𝑓0
are the moments of inertia and
static moments of the concrete compression zone
and the stretched reinforcement relative to the
neutral axis, respectively.
The values of the geometric characteristics of the
element section are determined by the general
rules for calculating the sections of elastic
elements.
It is allowed to determine the uniformity of
bending concrete elements by the following
formula (8):
𝐷 = 𝐸
𝑏,𝑟𝑒𝑑
∙ 𝐴
𝑓
∙ 𝑧 ∙ (ℎ
0
− 𝑥
𝑚
)
, (15)
where z is the distance from the center of gravity of
the stretched reinforcement section to the point of
application of equally acting forces in the
compression zone.
For elements with a rectangular cross-section, the
value of "z" is determined by the following formula:
𝑧 = ℎ
0
−
1
3
𝑥
𝑚
, (16)
For elements with a rectangular cross-section, it is
allowed to take values of z equal to 0.8ho.
The values of the coefficients of bringing the
stretched reinforcement to the concrete are taken
to be equal to:
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𝛼
𝑓,1
=
𝐸
𝑓,𝑟𝑒𝑑
𝐸
𝑏,𝑟𝑒𝑑
, (17)
where
𝐸
𝑏,𝑟𝑒𝑑
is the specified modulus of
compression of concrete.
𝐸
𝑓,𝑟𝑒𝑑
-is the specified
modulus of deformation of the stretched
reinforcement, this modulus is determined by the
following formula, taking into account the effect of
the behavior of the stretched reinforcement
between the cracks:
𝐸
𝑓,𝑟𝑒𝑑
=
𝐸
𝑓
𝜓
𝑓
, (18)
It is allowed to take the value of coefficient ps_f
equal to ps_f=1.
The stiffness of elements (1/r) can be determined
according to the general rules of construction
mechanics by using direct bending singularity
characteristics D instead of curvature, by replacing
the elastic bending characteristics EI with the
specified classifications of D in the calculation
relationships, the classifications of D are calculated
according to the following formulas (9, 10).
RESULTS AND DISCUSSION
The full stiffness of the elements without cracks
and with cracks in the extended zone when
subjected to static loads is determined by adding
the stiffness resulting from the corresponding
loads in a similar way to the addition of curvatures,
where the uniformity classifications D are required
to be accepted depending on the duration of
exposure of the considered loads specified in this
point.
It is allowed to take the coefficient ps_f at the value
ps_f=1 when determining the single classification D
of elements with cracks in the stretching zone. In
this case, the total damping with cracks in the
elements due to the combined action of short-term
and long-term loads is determined by adding the
dampings resulting from the discontinuous effect
of the short-term load and the continuous effect of
the long-term load, in which the singleness
classifications take into account the corresponding
values of D as assumed for elements without
cracks. required to obtain.
The coolness of the sample beams found by
theoretical calculations was found to be in
satisfactory agreement with the experimental
results (Fig. 2).
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Figure 2. The development of cracks in sample beams
The values of operating loads corresponding to 0.5-0.65 Mult were the following values:
For I-series beams:
𝑓
ўр
= 2,8мм,
𝑓
ўр
𝑙
=
𝑙
730
< 𝑓
𝑢𝑙𝑡
=
𝑙
200
For II-series beams:
𝑓
ўр
= 2,6мм,
𝑓
ўр
𝑙
=
𝑙
855
< 𝑓
𝑢𝑙𝑡
=
𝑙
200
For III-series beams:
𝑓
ўр
= 3,2мм,
𝑓
ўр
𝑙
=
𝑙
720
< 𝑓
𝑢𝑙𝑡
=
𝑙
200
For IV series beams:
𝑓
ўр
= 3,4мм,
𝑓
ўр
𝑙
=
𝑙
674
< 𝑓
𝑢𝑙𝑡
=
𝑙
200
According to the test results, the stiffness of the
sample beams does not exceed the limit values
allowed in the standards.
CONCLUSIONS
1. The nature of the stress-deformation state of
flexural concrete beams reinforced with basalt
reinforcements under loads, the development of
deformations in the longitudinal stretching and
compression area, the increase of stiffness in the
elements under the influence of force, the
occurrence of limit states, and the form and nature
of structural failure with flexural reinforced
concrete elements with steel reinforcement. was
found to be the same.
2. Under forces, it was observed that the stiffness in
the sample beams increased in accordance with the
force value: at low loads, the stiffness increased
almost linearly, while at high loads, their sharp
increase was observed. It was observed that the
amount of coolness determined in the experiment
satisfactorily agrees with the theoretically
calculated values.
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ШНҚ
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полимер
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Fiber Reinforced Concrete & Basalt Rod
Reinforced
Concrete,
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Transportation Research Board, 1998/66.
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