Volume 02 Issue 06-2022
13
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
ABSTRACT
Using real records of seismic impacts with the maximum amplitude of acceleration and the spectra of these impacts,
the reactions of a steel frame idealized as a system with one degree of freedom were calculated on an analog machine.
In this case, the reactions were determined in the elastic and elastoplastic stages.
Forces were applied to the prototype, corresponding to the calculated values of deformations of the extreme fibers
of the frame columns.
The results of testing all samples at a constant amplitude of deformations are plotted on the graph.
KEYWORDS
Strength, deformation, dynamic load, elastic, amplitude, low-cyclic, compression, tension, elastic-plastic, testing,
destruction.
INTRODUCTION
Further development of the theory of seismic
resistance is characterized by the use of methods for
analyzing seismic loads and calculating structures, the
wider use of probabilistic methods, the assessment of
Research Article
STRENGTH AND DEFORMATION OF MATERIALS AND INDIVIDUAL
STRUCTURES UNDER REPEATED DYNAMIC LOADING
Submission Date:
May 26, 2022,
Accepted Date:
June 06, 2022,
Published Date:
June 17, 2022
Crossref doi:
https://doi.org/10.37547/ajast/Volume02Issue06-03
N.B. Shaumarov
Prof. Tashkent State Transport University, Uzbekistan
S.Kh. Khoshimov
Master student,
Tashkent State Transport University, Uzbekistan
Journal
Website:
https://theusajournals.
com/index.php/ajast
Copyright:
Original
content from this work
may be used under the
terms of the creative
commons
attributes
4.0 licence.
Volume 02 Issue 06-2022
14
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
the parameters of buildings and structures beyond the
limits of elasticity, the spatial nature of deformation
and etc.
METHODS OF RESEARCH
Much attention is paid to the study of the strength and
deformation characteristics of traditional and new
effective building materials under dynamic influences,
new design solutions for buildings and their elements
and interfaces.
The low-cycle fatigue of steel cylinders subjected to
repeated compression-tension was studied by Y.
Jaoten and K. Mitsuhata [12]. analog reaction machine
of a steel frame, idealized as a system with one degree
of freedom. In this case, the reactions were
determined in the elastoplastic stages [1].
Forces were applied to the prototype, corresponding
to the calculated values of deformations of the
extreme fibers of the frame columns. The program
included testing at a constant amplitude (series I), at
various random levels of deformations corresponding
to the calculation of the reaction of frames in the
elastic (series II) and elastic-plastic (series III) stages.
The results of testing 13 samples with a constant
amplitude of deformations are plotted on the graph in
Fig. 1. in logarithmic coordinates - ∆ε –N (∆ε residual
deformation; N is the number of cycles to failure). The
equation of the drawn correlation straight line has the
form.
∆ε ·N
0,346
=0,0624 (1)
at N=1; ∆ε
=0,0624. Note that the residual elongation
under static tension ∆ε
ост
=0,18.
The order of loading of the samples at random variable
strains corresponded to the nature of the force
spectrum determined from real accelerograms. For
each tested sample was calculated
∑
𝑛𝑖
𝑁
(where ni-
number of cycles at the corresponding level of
deformations).
Its average value was 1,51.
Fig.1. Test results of specimens under repeated loading
Volume 02 Issue 06-2022
15
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
Fig.2. Testing a reinforced concrete beam with a repeated alternating load (dimensions in cm)
In accordance with the theory of fatigue failures by
Miner and Sachs, the number of cycles to failure was
determined analytically. The nature of the destruction
of the samples tested by repeated loading in
appearance corresponds to the destruction of the
statically tested samples, although some features are
noted. Static tensile specimens failed, most often
anywhere in the middle and very rarely at the end.
Samples of series I failed, as a rule, at the end of their
working length, for samples of series II and III, the
formation of two cracks is characteristic - in the middle
and at the end of the working length [11].
The influence of the loading rate on the behavior of
reinforced concrete beams, as well as the efficiency of
repairing damaged elements, was considered by V.
Bertero, D. Ria and et al. [5]. For reinforcement, steel
grade A-V was used with yield and strength limits of 323
and 576 MPa and a relative elongation of 21%. The
strength of concrete is 28 MPa. Initially, the influence
of the loading rate on steel and concrete was studied
separately. With an increase in the strain rate, an
increase in the yield strength of steel was observed
from 16 to 28% and the tensile strength of concrete
from 12 to 20% compared with static loading.
Beams (4 pieces) during testing were placed on two
supports (Fig. 2), one of them was fixedly connected to
the beam. The test was carried out at two loading
speeds: 0.254 and 25.4 cm/s. The first corresponds to
the condition of static loading, the second is typical for
seismic effects.
Tests of two beams at different speeds showed an
increase in the lower and upper yield strengths by 11
and 22% compared to the results of static loading (Fig.
3a).
The influence of the loading rate decreases with
increasing deformation, the loading rate does not
affect the nature of the destruction of the beams. A
significant effect of the loading rate on the yield
strength was noted, which increased by 22% compared
to static loading (Fig. 3b). Beams No. 3 and 4 were not
brought to destruction. The cracks that appeared
during testing in the middle third of the span were
eliminated by injection of epoxy compositions under
pressure. The repaired beams (3R and 4R) were again
tested to failure. The yield strength of the 3R beam
increased by 12% compared to the 4R beam during the
first loading at different rates [7].
The hysteresis curves of the beams 3R are unstable
compared to the similar curves of the beams 1-4. This,
Volume 02 Issue 06-2022
16
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
apparently, is explained by the fact that it was not
possible to restore the initial rigidity of the beams and
the completely broken adhesion of the reinforcement
to concrete. Beams 3R and 4R had cracks similar to
those of beams 3 and 4, but not in the places where
they were sealed with glue. With an increase in the
amplitude of the deflection, the nature of the
destruction changed in comparison with the nature of
the beams No. 1 and 2. Significant diagonal cracks
appeared outside the middle third of the span, and the
destruction occurred during shear. The loading rate
contributed to an increase in the dynamic modulus of
elasticity by more than 10% compared to the static one.
Fig. 3. Results of testing the beams for alternating repeated loading
а -
hysteresis curves for beams No. 1 and 2 during the first loading cycle: 1 - loading speed 25.4 cm/s; 2 - the same,
0.0254 cm/s;
b
- hysteresis curves for beams No. 3 (dotted line) and No. 4 (solid line);
c
- the same for the 3R series
beam. The numbers indicate which load number the hysteresis curve corresponds to.
The crack resistance of dynamically tested beams was
obtained by 25%, higher than that of statically loaded
elements. Under dynamic loading, the absorption and
dissipation of energy increased by 5 and 20%,
respectively, compared with the conditions of static
loading. The bearing capacity of the repaired beams
did not decrease.
American specialists [13] investigated the bearing
capacity and the nature of the destruction of steel I-
beams made of mild steel under repeated alternating
loading. The magnitude of the repeated load
(amplitude) corresponded to stresses exceeding the
elastic properties of the sample material. The
deformations were estimated by the ratio of the
maximum deflection in each direction to the deflection
corresponding to the yield moment. During tests, this
ratio significantly exceeded the value expected during
seismic action.
Samples of series I (short) withstood 72% of the load
corresponding to the yield strength of the sample
material. In comparison with them, long specimens (II
series) with increasing number of loadings more
intensively reduced the bearing capacity and rigidity.
Samples of series III (with a horizontal connection)
differed from the previous ones only in that in the
center of the span the lower shelf was fixed
motionless. Although the horizontal deformations
were constrained by the bond, the hysteresis loops
proved to be unstable. With an increase in the number
of loadings, they became asymmetric, having a larger
load peak at the moment of flange compression from
the connection side.
Columns with a length of 105.9 cm (IV series) were
tested by repeated loading with additional exposure to
a static load applied along the sample axis.
Volume 02 Issue 06-2022
17
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
The axial compression was 30% of the load
corresponding to the axial compression yield strength.
The deflection amplitude was 3.71 cm. When loading
from one to three cycles, some increase in the bearing
capacity was observed. Under subsequent loading, the
decrease in the bearing capacity was more intense
compared to similar samples tested without axial
loading. The reason for the destruction of the samples
is the loss of stability of the shelves, and the walls of
the I-beam from buckling.
In some cases, the loss of stability was caused mainly
by torsion, axial loading contributed to an increase in
deformation and fracture rate. In the vast majority of
cases, buckling of the wall and cross-sectional flanges
was observed at the sample embedment boundary [4].
The buckling of a number of samples was observed at
one of the shelves at some distance from the
embedment (local buckling). The greatest damage was
noted in the case of a combination of buckling in
buckling and torsion. Additional axial loading
contributed to the rapid destruction.
B. Kato, H. Akiyama et al. [14] tested the simplest
model on a vibrating table to determine the restoring
force in the inelastic stage of its operation. The
calculation scheme of the model is represented by a
single-mass system (Fig. 4). The constant mass 3 is
located on the crossbar 2 and creates an axial force in
the column 5 equal to 0.33 Ru (Ru is the yield strength
in the column under compression). The crossbar rests
on two supports, one of them is plate 4, and the other
is a prototype of an I-section 3x3 cm and 25 cm high.
Fig. 4. Scheme of testing a prototype
a - scheme of the pilot plant; 1-vibration stand; 2-crossbar; 3- mass located on the crossbar; 4-support in the
form of a plate; 5-experimental sample of I-section; 6 accelerometer; b-section of the prototype
Samples A0, A1, A2 and A3 were tested. Mechanical
characteristics of steel: modulus of elasticity 0.211 106
MPa, yield and strength limits 258 and 304 MPa.
Sample A0 was tested statically. In (Fig. 5, a), the
dotted line in the coordinates horizontal force –
displacement shows the behavior of the model under
static loading [8,9].
A1, A2 and A3 were tested on a vibrating table with the
reproduction of the recording of the El Tsontro
earthquake, 1940. The maximum accelerations were
respectively 210, 250 and 360 cm/s. Torsional and
horizontal transverse oscillations of the model were
eliminated by auxiliary pinching. The period of natural
oscillations and the attenuation of the model were 0.17
and 0.2% (critical). The samples were destroyed from
bending along the longitudinal axis with local
destruction in the section of the sample. The restoring
force in the elastic stage is in complete agreement with
the calculation results. When calculating it for the
inelastic stage, the following equation was used:
Volume 02 Issue 06-2022
18
American Journal Of Applied Science And Technology
(ISSN
–
2771-2745)
VOLUME
02
I
SSUE
06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
mx'' +cx' +f (xx' )= - mx0'' (2)
The curvilinear dependence was introduced into the
calculation by three linear functions (Fig. 5, a). The
effect of the Р -∆ system was estimated as:
Q
р-∆
= -m
g
· x/h
It can be seen from the graph in (Fig. 5, b) that with the
appearance of local destruction in the section of the A3
sample, the restoring force significantly decreased. An
increase in the yield strength caused by the influence
of the loading rate is noted. A good agreement
between the analytical and experimental curves is
observed (Fig. 5c).
Fig. 5. Test results
a - static loading (A0), ------ experimental curve; _______ calculated curve% 1 - occurrence of local destruction; b, c
– experimental and calculated curves of restoring force change (A3), __ __ __ ___ - static loading
The work [15] is devoted to the study of the bearing
capacity of reinforced concrete columns, reinforced
with a spiral, under repeated dynamic impact of the
seismic type [6]. The prototypes were 1/2 scale models
of the column (Fig. 6). Its prototype was the column of
the main building of the medical center in California.
A transverse reload Pn was applied at the ends of the
column in opposite directions. In the termination
(increased section), moments of the opposite sign
simultaneously appeared. In addition to repeated
loading (12 cycles), the columns were loaded [10] with
a constant axial compressive load equal to 457 or 914
kN. 6 samples were tested, differing among
themselves in the percentage of longitudinal
reinforcement. Spiral diameter 9.5 mm. The maximum
deflection during loading was 6 times higher than the
allowable value.
Volume 02 Issue 06-2022
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American Journal Of Applied Science And Technology
(ISSN
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2771-2745)
VOLUME
02
I
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06
Pages:
13-20
SJIF
I
MPACT
FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
Fig. 6. Dimensions (in cm) of the prototype and reinforcement options
Calculations are made for the limit state, taking into
account the bearing capacity of the compressed zone
of concrete in the limit state. The deformations of the
longitudinal reinforcement of the column reached a
significant value, which ensured the determination of
the
boundary
conditions
for
the
analytical
dependence. Sufficient results showed that the load of
the first cycle was significantly less than the calculated
one.
Reinforcement with spirals is very effective both in
combination with longitudinal reinforcement and
without it. The maximum deformations in the spirals
did not exceed the values corresponding to the
deformations upon reaching the elastic limit of the
material. Longitudinal reinforcement with rods outside
the helix at the corners of the section (samples 4.6, see
Fig. 6) is effective only during the 1st cycle.
For samples without longitudinal rods outside the helix
(samples 1-3.5), the hysteresis curve turned out to be
stable even after the appearance of cracks in the
concrete.
The deformation of the longitudinal rods (close to
failure) at a relatively high level of axial load increased
with an increase in the number of load repetitions.
Inspection of the tested columns led to the conclusion
that the concrete within the spiral is completely
painted.
CONCLUSION
1.
The behavior of bending elements is determined
mainly by the mechanical properties of the
reinforcement. For a complete representation of
the behavior of bending elements under an
alternating load, it is necessary to know at least
two dependencies: moment - curvature, shear
force - shear deformation. The use of large-
diameter rods prevents the reinforcement from
buckling, but increases the risk of it pulling out
under alternating loading. Pulling out the
reinforcement significantly reduces the rigidity.
2.
The decrease in the rigidity of the bending
elements after the first loading and in subsequent
Volume 02 Issue 06-2022
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American Journal Of Applied Science And Technology
(ISSN
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2771-2745)
VOLUME
02
I
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06
Pages:
13-20
SJIF
I
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FACTOR
(2021:
5.
705
)
(2022:
5.
705
)
OCLC
–
1121105677
METADATA
IF
–
5.582
Publisher:
Oscar Publishing Services
Servi
cycles at the same amplitude is explained by the
accumulation of shear strains.
3.
The increase in the strength of the crossbars when
the floor slabs are put into operation should be
taken into account in the calculation.
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Bertero V.V., Rea D., Mahin S., Atalay M.B. Rate
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Ifrim M., Dobrescu A. Siplified Analysis of Shear
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Борджера Дж., Равера А. Проектирование
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сейсмических районов (перевод с анг.) М.:
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Завриев К.С. (и др.) Основы теории
сейсмостойкости зданий и сооружений. М.:
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Николаенко Н.А., Назаров Ю.П. Динамика и
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Gyoten
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Mizuhata
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Experimental Studi of how Cycle Fatiygue of a
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Vanm W.P., Thompsonh E., Whalley L.E. Ozier
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Kato B., Ariyama H., Suzuki H. Dinamic Collapse
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Karlson B., Aoyama H., Sozen M. Spirally
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