Development of Spring Hinge Models to Simulate Structural Elements

of Spherical Graphite Reinforced Concrete

LARYSA SHCHERBYNA1, ANATOLII BOBRAKOV2, DMYTRO SAVELIEV3,

SERHII BRAICHENKO4, OLEKSANDR NIKOLAIEVSKYI5

1,2Department of Civil Engineering and Project Management, Zaporizhzhia Polytechnic National

University, 64 Zhukovsky St. Zaporizhzhia, 69063, UKRAINE

3Department of Engineering and Rescue Machinery, National University of Civil Defence of Ukraine,

94, Chernyshevska St., Kharkiv, 61023, UKRAINE

4Department of Construction Industry, Lviv Polytechnic National University, S. Bandery St., 12, Lviv,

79013, UKRAINE

5Department of Mathematical Disciplines and Innovative Design, Private Higher Educational

Institution "European University", Vernadskogo boulv. 16-v, Kyiv, 03115, UKRAINE

Abstract: The goals of the study were the formation of a model of concentrated plasticity based on spherical

graphite fibers. The goal was to present indicators of the cyclic behavior of structural elements due to the lack

of consideration in modern scientific research of the issue of increasing the technical level and reliability of

structures due to the addition of innovative materials during the development of structural elements. Taking

into account the fundamental shortcomings in construction in the conditions of installing an excess amount of

reinforcement, as one of the main mechanisms for achieving strength and reliability. The aim of the study was

to develop a method of improving the quality of structural elements using innovative materials through building

spring hinge models. The study involved the mathematical simulation, comparison, and system analysis. The

result of the work is a developed spring hinge model for simulating reinforced concrete structural elements. The

work emphasizes that the obtained experimental model converges to reference data and does not reflect a

significant error with the increased number of cycles. It is emphasized that the model degrades with significant

calibration, while the numerical strength and hysteresis behaviour matches the experimental data at higher

deformation levels. The model of concentrated plasticity based on spherical graphite fibers was developed for

the range of indicators of the cyclic behaviour of structural elements. The main characteristics of the reinforced

concrete structural elements under consideration in the framework of the study are provided in a table in order

to visually separate the groups of structures according to the main parameters. A non-linear model of a spring

hinge is graphically shown, which shows the moment of movement of the spring when a monotonous load is

applied. An urgent need to build a system of indicators of the structural elements’ cyclic behaviour was

emphasized. A concentrated plasticity model based on spherical graphite fibers was built for this purpose. A

beam-column was chosen as a reinforced concrete structure, which is based on a zero-length spring pivot hinge

at the end of each individual element. This spring pivot hinge is a uniaxial material model with a moment-

rotation dependency. Such a dependency is the fundamental basis of the spring hinge model used to simulate

reinforced concrete structural elements. The comparison chart of reference and cyclic strength of a spherical

graphite reinforced concrete beam is presented graphically. Prospects for further research involve the

development of an empirical system of equations depending on the section geometry and the properties of the

structure material based on prognostic variables from the list of potential variable characteristics.

Key-Words: Spherical graphite, strength, rotation, model, plasticity, beam-column, hinge, spring, stiffness,

reinforced concrete.

Received: November 25, 2021. Revised: November 16, 2022. Accepted: December 14, 2022. Published: January 30, 2023.

1 Introduction

A stable development and the implementation of the

principles of stable improvement of any sustainable

production depends on the knowledge of the Lead

Engineer and the mechanisms of implementation of

scientific opinion within the framework of a certain

field. An important direction of the technological

process is the creation and wide application of new

structural elements using innovative materials in

order to increase the technical level and reliability of

structures, taking into account the thresholds of

WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS

DOI: 10.37394/232011.2023.18.1

Larysa Shcherbyna, Anatolii Bobrakov,

Dmytro Saveliev, Serhii Braichenko,

Oleksandr Nikolaievskyi

E-ISSN: 2224-3429

Volume 18, 2023

strength, reliability, and direct economic

performance of the manufacturer, [1].

Reinforced concrete structural elements have

seismic characteristics that fully depend on the

ability of each structural element of the general

frame for non-elastic deformation, [2]. In turn,

concrete, as a material, consists of a filler, a binder,

and water. Its fragility affects the deformation

resistance of all structural elements, leading to

damage or destruction during seismic impacts, [3].

Considering this fact, reinforcement is a promising

direction for increasing the strength of concrete, but

excessive reinforcement leads to global problems in

construction.

The formulation of complex technology for

increasing the strength and quality of structural

elements is undoubtedly promising given the

modern development of the field of construction

technologies, the technological progress in the

world, the introduction of nanotechnologies and

nanomaterials.

This research aims to formulate a method of

improving the quality of structural elements using

innovative materials through the creation of spring

hinge models.

The aim involved the following research

objectives:

 Examine the reinforced concrete structural

elements for their properties and

specifications;

 Build a concentrated plasticity model based

on spherical graphite fibers according to the

range of indicators of the cyclic behaviour

of structural elements;

 Develop a mathematical model of a spring

hinge to simulate reinforced concrete

structural elements.

2 Literature Review

The studies on the implementation of innovative

mechanisms for the simulation of reinforced

concrete structural elements are becoming more

relevant in the context of current development. In

[1] the author revealed the functionality of fracture

mechanics in relation to reinforced concrete

structures, including composite and plane-stressed

ones. The author carried out simulations of parallel

deformation schemes of reinforced concrete based

on the fracture mechanics principles, and quantified

the effects of components on the overall strength of

the structure.

In [2] the researcher dealt with the mechanism of

testing the shear strength of high-strength concrete

elements. The researcher experimentally studied the

deformed state of concrete and reinforcement near

the shear area of individual high-strength concrete

elements. Her research helped the author to improve

the calculation of the strength of high-strength

concrete and reinforced concrete elements destroyed

by shearing.

A number of authors, [3], proposed an approach

for determining the technical condition of reinforced

concrete structures under force and high-

temperature impacts. Based on the analysis of field

survey results, the authors obtained important data

on characteristic defects and structural damage, as

well as their impact on further work; data on

changes in physical and mechanical properties of

materials during their use; a mathematical model

was developed which allowed evaluating and

forecasting the technical condition of structures.

The study, [4], deals with solving the scientific

problem of establishing the actual stress-strain state

of reinforced concrete flexural, as well as

compressive & flexural structures strengthened

under the load, and the creation of calculation

methods for designing and evaluating the reliability

and residual life of those structures. The study

experimentally determined the coefficients of the

operating conditions of additional reinforcement and

concrete of reinforced concrete structures

strengthened under the load, which differ

significantly from the values recommended by the

design standards.

In [5] the authors proposed a scheme for time

integration of the system of equations with a

Lagrange grid. It became the basis for conducting

numerical experiments. As a result, they came to the

conclusion about the quality and appropriateness of

using reinforced concrete structures in the

fortification construction for operation under high-

speed impact. The fundamental basis of the research

is conducting numerical studies to explore the

processes of deformation and destruction of

reinforced concrete elements with various types of

reinforcement under high-speed impact, as well as

the development of recommendations for their

design and implementation into construction

practice.

The works of the following foreign authors are

worth noting. The authors presented and analysed

two practical solutions for the structure restoration

by establishing the level of bearing capacity of short

reinforced concrete cantilevers of the structure’s

supports, [6], which have undergone certain

degradation during their work. In [7] the researchers

proposed a new finite element model to simulate

reinforced concrete beams shear-strengthened

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DOI: 10.37394/232011.2023.18.1

Larysa Shcherbyna, Anatolii Bobrakov,

Dmytro Saveliev, Serhii Braichenko,

Oleksandr Nikolaievskyi

E-ISSN: 2224-3429

Volume 18, 2023

carbon fiber reinforced polymer plate under cyclic

loading. The authors developed a spring element for

simulating a fracture zone based on a virtual crack

in the sub-concrete material. Was evaluated by

reinforced concrete structural members, [8]. Was

developed a new type of environmentally efficient

steel fiber reinforced concrete with waste graphite,

[9]. The authors proved that steel fibers are a type of

material for strengthening concrete, and waste

graphite is used to partially replace sand aggregate.

In [10] the researchers studied the degradation of

concrete with compression cracks, the effect of

tensile reinforcement, and bond-slip to improve the

prediction of the reactions observed in reinforced

concrete elements under various loads. The authors

created a model that predicts the characteristic

features of the multiaxial behaviour observed in

experiments on simple and reinforced concrete

elements subjected to various loads.

The structural facade panel and lighting support

were simulated, [11], to study their behaviour under

wind pressure. The developed numerical simulations

were calibrated against available data from the

literature. This simulation revealed information

potentially useful for planning further experimental

tests. In [12] the researchers developed a structure

that attaches to a reinforcing bar for a reinforced

concrete structural element containing an anchor

end designed to be fixed in the anchor chamber of

the former reinforced concrete structural element.

The developed design allowed for increasing the

overall strength.

Moreover, we are presented with analytical

results which showed that high ductility frames

showed slightly better lateral load performance

compared to low ductility frames, [13]. Besides,

analytical studies revealed that the structural steel in

the column, regardless of the cross-section shape, is

the most important parameter for increasing the

bearing capacity of the frame in the transverse

direction. In [14] the researchers studied the

principles of using CNTs as reinforcement in

reinforced concrete structural elements. The authors

carried out mathematical modelling of mechanical

oscillations of the main structural element of

reinforced concrete support, and identified its

weaknesses, [15]. In [16] the researcher focuses on

the applicability of truss models and the brace and

bond method for the analysis and design of

reinforced concrete beams and structural walls with

an opening that had a complex flow of internal

stresses, as well as the development of a design

procedure for these beams and walls based on the

model.

In work [17] authors analysed the studies carried

out on retrofitted RC beams using a traditional

method such as stitching (hook method), and also

studied the relative effect of these methods on the

load-bearing capacity of beams with bending

deficiency by retrofitting. Using the closed-form

solution of the equilibrium equation and the Jacobi

auxiliary equation was determined the equilibrium

forms of the beam and their stability, [18]. The

author provided a solution for a cantilever beam

with a spring hinge that is subjected to a tensile

force. In [19] the researchers calculated the spring

hinge model through the Lagrange equation, which

describes alveolar structures and their morphometric

characteristics. The scientists considered the spring

hinge as a torsional harmonic oscillator and derived

the equations of motion and its natural frequency.

The damping effect and external torque were also

taken into account.

Authors studied and experimentally confirmed

the moment-rotation response of a tape spring hinge

in quasi-static folding and deployment processes,

[20]. Fluidity theory, derived from a combination of

the Theory of Thin Shells and the Tresca criterion,

is introduced to control loop fluidity during the

folding and deployment processes. In [21] the

researchers proposed a calculation model of the

static stability of multi-spring hinged columns

(linear analysis).

So, with all the mentioned scientific

achievements, the issue of developing spring hinge

models for modelling structural elements of

spherical graphite reinforced concrete remains open

and requires detailed study, which is the subject of

this research.

3 Research Method

The research was preceded by a survey of several

scientific achievements such as their analysis,

structuring (Table 1), monitoring of basic and

variable structural elements, their composition, and

characteristics.

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DOI: 10.37394/232011.2023.18.1

Larysa Shcherbyna, Anatolii Bobrakov,

Dmytro Saveliev, Serhii Braichenko,

Oleksandr Nikolaievskyi

E-ISSN: 2224-3429

Volume 18, 2023

Table 1. The main characteristics of the reinforced concrete structural elements under consideration in this

study, [8]

No.

Type

Ls,

Ls/d

pl, %

Ec,

МPа

fc,

МPа

ft, %

fy, %

fu, %

Δc/Ls,

500

100

6.10

1.73

18000

410

620

500

100

5.88

1.67

18000

410

620

610

406

254

3.00

1.23

16000

4.4

669

807

610

406

254

3.00

1.23

16000

4.4

669

807

685

100

250

2.98

1.11

16000

46.4

3.5

440

730

685

100

250

2.98

1.74

16000

50.3

3.5

445

710

760

127

178

5.04

0.74

16000

445

690

8.5

760

127

178

5.04

0.74

16000

445

690

813

165

203

5.04

1.45

16000

455

675

16.6

S10

813

165

203

5.04

1.45

16000

455

675

11.9

The purpose of analysing the generated data and

their interpretation became the fundamental basis of

mathematical modelling was to create the main

spring hinge model to simulate structural elements

of spherical graphite reinforced concrete. The

system analysis was used to establish structural

relationships between variables or elements of the

general structure, their influence on each other, and

the general strength metrics. The comparison

method was applied to form the cyclic response of

reinforced concrete structural elements to force and

drift with and without the use of spherical graphite.

The principles of changing the properties of

structural elements, their material, geometric

characteristics, and cross-sectional properties with a

comparable one were confirmed in accordance with

the research base.

The fundamental metric for the selection of

research results is based on a clear understanding of

the types and characteristics of failures, that is, the

structuring of the main failures of structural

elements from reinforced concrete and the need to

improve / strengthen their qualities.

4 Results

Mathematical modelling is the basis of the modern

system of experimental research to a greater extent.

Its essence is the mechanism of changing the initial

object of research into a mathematical model.

In view of the rapid pace of innovative

developments in the field of construction and

modern technological features of the formation of

material complexes to obtain highly effective

structural elements of reinforced concrete, it is

proposed to reinforce it with spherical graphite

fiber, which will increase the ductility during

tension and form improved impact toughness during

compression (Fig. 1).

Fig. 1: Continuum spring hinge model, plane stress

state of elements (author’s development based on,

[19])

The model of uniform distribution of spherical

graphite fiber in the ductile matrix (Fig. 2) is able to

prevent the reduction of structural strength, cycle

degradation, and clamping. However, it is worth

emphasizing that the model is not capable of clearly

predicting failure modes and initial rigidity.

Fig. 2: A model of uniform distribution of spherical

graphite fibers in a plastic matrix

The concentrated plasticity model based on

spherical graphite fibers (Fig. 3) allows for

obtaining the indicators of the cyclic behaviour of

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DOI: 10.37394/232011.2023.18.1

Larysa Shcherbyna, Anatolii Bobrakov,

Dmytro Saveliev, Serhii Braichenko,

Oleksandr Nikolaievskyi

E-ISSN: 2224-3429

Volume 18, 2023

structural elements. The length of the plate hinge

() enabled predicting the possibility of

displacement at the very beginning of the

reinforcement destruction. The given model takes

into account the cyclical degradation of strength and

rigidity of the structure due to changes in the

hysteresis parameters of the steel material model.

Fig. 3: The concentrated plasticity model based on

spherical graphite fibers

The building of spring hinge models is focused on

concentrated plasticity, their use is aimed at the

study of inelastic behaviour in some areas of the

hinge due to their computational efficiency and

extreme interpretation simplicity, [20].

The use of calculation models with numerical

stability is effective in the advanced nonlinear

analysis of reinforced concrete structural elements

and seismic design of structures. Spring hinge

models are based on direct structural variables that

include rotations and moments, with due regard to

the method of capturing the cyclic response of the

structural components of the overall structure.

A beam-column was chosen as a reinforced

concrete structure, which is based on a zero-length

pivot spring hinge at the end of each individual

element. The given pivot spring hinge is a uniaxial

material model with the moment  - rotation 

dependence, where the moment  is the force

applied to the rod, and the rotation  represents the

deformation, which is calculated as the

displacement of the top, ∆, divided by the length of

the shear span .

The spring performs bending movements (Fig. 4

shows the trajectory of movements with a blue line)

under the influence of a monotonous load, forming a

cyclic curve in which the elements lose strength,

rigidity, and deformation capacity within the non-

elastic area; the threshold values of moments and

rotation are shown by a red dashed line.

Fig. 4: Spring hinge nonlinear model

Fig. 5 illustrates the mathematical model of a spring

hinge for simulating reinforced concrete structural

elements.

Fig. 5: The mathematical model of a spring hinge

for simulating reinforced concrete structural

elements

Torque:



󰇛󰆒󰇜

 



󰇡 

󰆒󰇢

where , – internal compressive forces;

 – neutral axis;

,  – tensile forces along the depth of the

cross-section

The value of the threshold moment at which the

reinforcement has maximum hardness:

󰇡

󰇢󰇛󰆒󰇜

 



󰇡󰆒

󰇢

Threshold angle of rotation



 

 – rotation curvature;

 – span length.

.

, 

, *

, **

, 



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Larysa Shcherbyna, Anatolii Bobrakov,

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Rotation curvature 



The stiffness reduction coefficient:





where  – experimental stiffness,

The damage index is found as a function of the

deformation and energy damage indices:

 

󰇧

󰇨

󰇧

 󰇨

where  – maximum deformation within the

ith load cycle;

 – final deformation;

 – total energy absorbing capacity at the ith

load cycle

 – to the threshold of the residual

level, the power of energy dissipation on the

monotonic main curve;

 – coefficient of the energy level when

loading with cycles;

 – degradation rate.

Strength reduction Level:

󰇛󰇜

where  – reference strength.

Fig. 6 shows the moment of beam rotation and the

curve built on the basis of the analysis. Most of the

data were obtained from literature as a

representation of outlined data about power drift,

[7], [16], [19], [21], the minority was the results of

manual digitization of charts presented in modern

scientific literature.

Fig. 6: Comparison chart of reference and cyclic

strength of a reinforced concrete beam with

spherical graphite

The obtained calculation model converges to

reference data and does not reflect a significant error

with the increased number of cycles. However, the

model with a calibrated value of 

degrades, while the numerical strength and

hysteresis behaviour match the experimental data at

higher deformation levels, which indicates the

increased deformation resistance of fittings with

spherical graphite before the occurrence of complete

destruction under conditions of seismic impact.

5 Conclusions

The work describes the reinforced concrete

structural elements in terms of their properties and

specifications. The model of concentrated plasticity

based on spherical graphite fibers was built for the

range of indicators of the cyclic behaviour of

structural elements. The mathematical model of a

spring hinge to simulate reinforced concrete

structural elements were developed. So, the research

results showcase that the structural elements of

spherical graphite reinforced concrete have the

maximum increased seismic performance in terms

of transverse strength, plasticity, the ability to

dissipate energy, and cracking response. In

comparison with reinforced concrete structures

without spherical graphite, structural elements built

in line with the latest technology show increased

deformation resistance of spherical graphite

-50





Torque (kN*m)

Rotation (rad)

calculated value

experimental value

-5

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DOI: 10.37394/232011.2023.18.1

Larysa Shcherbyna, Anatolii Bobrakov,

Dmytro Saveliev, Serhii Braichenko,

Oleksandr Nikolaievskyi

E-ISSN: 2224-3429

Volume 18, 2023

reinforcement to complete destruction under seismic

impacts.

Prospects for further research include the

development of an empirical system of equations

depending on the section geometry and the

properties of the construction material based on

prognostic variables from the list of potential

variable characteristic data.

References:

[1] I. Iakovenko, “The deformation models of

reinforced concrete constructions on the basis

of fracture mechanics,” PhD abstract thesis,

Qualification scientific work as a manuscript,

National Aviation University, Kyiv, pp. 1-46,

2018.

[2] O. Maliovana “Strength of high-strength

concrete elements under the shear action,”

PhD abstract thesis, Qualifying scientific

work as a manuscript, Yuriy Kondratyuk

Poltava Polytechnic National University,

Poltava, pp. 1-160, 2020.

[3] Y. Otrosh, A. Ruban, A. Haponova, & D.

Morozova “A approach to the determination

of the technical state of reinforced concrete

structures at force and high-temperature

influences,” Problems of fire safety.

Collection of scientific works, vol. 46, pp.

126-131, 2019.

[4] R. E. Khmyl “Stress-deformed state and

residual life of reinforced concrete structures

reinforced under load,” Doctoral thesis, Lviv

Polytechnic National University, Lviv, p. 466,

2021.

[5] L. V. Afanasieva & D. V. Didenko,

“Application of reinforced concrete

constructions in the fortification works,”

Building Structures: Theory and Practice, vol.

1, pp. 112-117, 2017.

[6] I. Tuns & M. Măntulescu, Comparative

solutions for the rehabilitation of damaged

structural elements of reinforced concrete. In:

Proceedings Of The 2nd WSEAS International

Conference On Engineering Mechanics,

Structures And Engineering GEOLOGY,

2009.

[7] S. Shahbazpanahi, & H. F. Hama Ali,

“Numerical simulation of shear-strengthening

of reinforced concrete beams by CFRP under

cyclic loading.” Revista De La Construcción.

Journal of Construction, vol. 18, no. 2, p.

271–281, 2019.

[8] T. C. Pan, K. W. Phang, & S. T. Wong,

“Assessment of reinforced concrete structural

elements,” CEE Research Reports, Nanyang

Technological University, Singapore, 1993.

[9] H. Liu, H. Duan, H. Gao, Z. Wang, & J.

Zhang, “Graphite Tailings’ Effects on

mechanical and physical properties of eco-

efficient steel fiber-reinforced concrete,”

Buildings, vol. 12, no. 5, p. 509, 2022.

[10] A. Waghmare, & A. Ramaswamy, “Nonlinear

analysis of reinforced concrete structural

elements,” in: IABSE Symposium Prague

2022: Challenges for Existing and Oncoming

Structures, Prague, The Czech Republic, 25-

27 May 2022, pp. 1419-1426.

[11] D. Libotean, A. Chira, & F. Gobesz, “Textile-

Reinforced Concrete Structural Elements,”

Műszaki Tudományos Közlemények, vol. 8,

no. 1, p. 61-66, 2018.

[12] O. Al-Mansouri, R. Mege, N. Pinoteau, & T.

Guillet, “Reinforcing rod for a reinforced

concrete structural element, assembly of

structural elements, and method for

manufacturing an assembly of structural

elements,” European Patent Office

EP3800304A1

[13] G. Tunc, M. M. Othman, & H. C. Mertol,

“Finite element analysis of frames with

reinforced concrete encased steel composite

columns,” Buildings, vol. 12, no. 3, p. 375,

2022.

[14] C. Ramesh Babu, “Technical note on using

CNTs as reinforcements in reinforced

concrete structural elements,” AIP Conference

Proceedings, vol. 1859, no. 1, 2017.

[15] G. A. Dymov, & V. P. Belichenko, “The main

structural element of a reinforced concrete

supports: mathematical modeling of

mechanical vibrations,” Journal of Physics:

Conference Series, vol. 1843, 2021.

[16] Y. Zhao, “Strut-and-tie modeling of two-

dimensional reinforced concrete structural

elements,” Master’s thesis, Nanyang

Technological University, Singapore, 2022.

[17] P. M. Raju, “Retrofitting of reinforced

concrete structural elements - Recent

technologies and future Scope,” International

Journal of Scientific Research in Science,

Engineering and Technology, vol. 3, no. 8, p.

1-14, 2017.

[18] M. Batista, “Large deflections and stability of

spring-hinged cantilever beam,” Journal of

Mechanics of Materials and Structures, vol.

14, no. 2, p. 295-308, 2019.

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Oleksandr Nikolaievskyi

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[19] Y. Park, & D. Kim, & J.-H. Ahn, & J. Lee, &

Y. In, & Y. Kim, “Derivation of the equation

of motion for the alveolar spring-hinge

model,” In: 35th Annual Meeting of the

American Society of Biomechanics 2011,

2022.

[20] H. Ye, Y. Zhang, Q. Yang, & B. Zhang,

“Quasi-static analysis and multi-objective

optimization for tape spring hinge,” Structural

and Multidisciplinary Optimization, vol. 60,

p. 2417-2430, 2019.

[21] K. Ingerle, “Computational model for the

static stability of multi-spring-hinged columns

(linear analysis),” Non-Conservative Systems,

1st Edition, Imprint CRC Press, Boca Raton,

2018.

WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS

DOI: 10.37394/232011.2023.18.1

Larysa Shcherbyna, Anatolii Bobrakov,

Dmytro Saveliev, Serhii Braichenko,

Oleksandr Nikolaievskyi

E-ISSN: 2224-3429

Volume 18, 2023

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