Numerical analysis of axial compressed multifaceted concrete-filled tube elements

. The object of study is multifaceted steel concrete-filled poles. The subject of research is the bearing capacity and parameters of the stress-strain state of multifaceted steel concrete-filled poles. The purpose of the research is to numerically study the features of the operation of multifaceted concrete-filled structures under axial compression. Are discussed the features of creating a computational finite element model of such structures in ANSYS APDL. Analytical methods are described for determining the parameters of the nonlinearity of the materials used, as well as the physical and mechanical characteristics of concrete operating under compression conditions. On specific examples the change in the bearing capacity for the object of study under various conditions of materials adhesion (friction coefficient μ varied within 0.1...0.6 with step 0.1). Is analyzed the "unified" analytical method for determining the bearing capacity of steel multifaceted concrete-filled structures, indicating the degree of variability of ultimate compressive load depending on the variation in the number of faces and thickness of the metal wall of the multifaceted model. The considered features of creating a computational model in the ANSYS APDL finite element analysis system, using various laws of deformation of steel and concrete, made it possible to determine the qualitative and quantitative levels of variability of their bearing capacity, which in combination will allow designers of such structures to reach a qualitatively new level when creating structures based on pipe concrete elements.


Introduction
Today, aesthetics and land use are critical for tower structures located in urban areas, such as low-voltage distribution lines.(OHPL up to 110 kV), mobile and radio communication poles, lighting poles, contact racks of the urban electric transport network [1][2][3][4][5][6][7][8][9][10].The requirements are constantly increasing for these standards for the construction of buildings.In a numerical study of the bearing capacity of the modified composite solution described in this article is considered an alternative to existing structures based on metal gratings, as well as reinforced concrete, wooden analogues and hollow metal multifaceted racks,.This makes the above urban structures meet all modern urban planning requirements and at the same time increases their bearing capacity.
In this regard, the task was set to study the stress-strain state (SSS) of composite modifications of the above structures under various types of loads and impacts (central and eccentric compression, bending, torsion, various types of dynamic impact), which, of course, is relevant.It is also necessary to study effects such as shrinkage and creep of concrete compressed by metal tubes.This improves the quality of the created structures and reduces the cost and labor intensity of construction.This article discusses issues related to the study of the bearing capacity of multifaceted pipe-concrete poles filled with concrete.
Domestic and foreign experts have carried out a fairly impressive amount of research aimed at studying the behavior of concrete compressed by metal shells under various types of stress state (central and eccentric compression, bending, torsion and their combinations), including: -review studies of literary sources aimed at determining the degree of knowledge of tubeconcrete structures [1][2][3][4][5][6].
A feature of the study, the course and results of which are described in this article, which distinguishes it from previous studies, is the consideration of issues related to numerical studies of the bearing capacity of multifaceted composite structures based on multifaceted steel pipes already tested in practice.As a filling of tubes an unconventional is used self-compacting type of concrete and is taken into account the influence of contact between the materials of the composite structure.
The goal of this research is to numerically study the behavior of multifaceted tubeconcrete structures under central compression, taking into account various geometric parameters, grades and classes of materials, as well as contact conditions between steel and concrete.
To achieve this goal, the following were solved problems: -the laws of physically non-linear work of materials in composite structures are chosen in such a way as to model the behavior of pipe-concrete elements under load as accurately as possible; -to conduct the numerical study was created in ANSYS a computational finite element model of its CFT poles, taking into account variations in geometric parameters, mechanical properties of materials and conditions for their contact interaction; -was determined the variability of the bearing capacity of the CFT and analyzed which made it possible to determine the influence of the adhesion conditions of materials on the bearing capacity of the composite structure as a whole; -Is analyzed the "unified" analytical method for determining the bearing capacity of multifaceted, cylindrical (n = ∞) pipe-concrete structures, as a result of which the values of the bearing capacity of structures were obtained by varying the number of faces, pipe thickness t as well as the mechanical characteristics of materials.
The subject of research is the bearing capacity and parameters of the stress-strain state for steel-concrete multifaceted racks taking into account the characteristics of the materials' work and FE modeling.
The object of study is a multifaceted steel pole filled with concrete.

Materials and methods
The most common domestic software systems for calculating building structures by the finite element method (FEM) are Structural CAD (SCAD) and Lira, which are equally suitable for solving scientific and practical problems aimed at taking into account the physical nonlinearities of materials.However, none of the above FEM tools is able to fully simulate the contact interaction of steel and concrete when they work together as part of the composite structure under consideration (mutual work of contact surfaces).Moreover, when using domestic FEM complexes, it is difficult to manipulate concrete as a non-linear material, which definitely reduces the quality of the obtained results.
Taking into account the imperfections of domestic complexes mentioned above for the numerical researches of a multifaceted pipe-concrete element (CFT) was chosen the ANSYS finite element analysis system, which has all the necessary tools for modeling the conditions of contact interaction between materials and the nonlinear nature of their work.
In this case, the height h = 500 mm and the diameter of the circumscribed circle d = 200 mm are taken constant for all FE models.
To simulate the physical nonlinearity of the steel behavior using its isotropic hardening law are obtained bilinear and polylinear approximations of the steel deformation diagram (Ramberg-Osgood curve) shown in Fig. 1.
Concrete as a non-linear material was modeled by introducing into the initial data for the calculation of the Drucker-Prager plasticity criteria (angle of internal friction φ and cohesion c) calculated on the basis of data obtained from the Mander deformation curve (model) (Fig. 2) and for concrete compressed by a steel shell according to formulas (1) and ( 2) respectively:  The algorithm for determining the physical and mechanical characteristics necessary for constructing the Mander curve [21,31] and calculating the Drucker-Prager concrete plasticity criteria [36][37][38][39] for CFT is completed in expressions (3) - (10).
where fcprismatic (cylindrical) strength of concrete taken from EN 1992-1-1:2004 Eurocode 2 "Design of concrete structures.General rules and rules for buildings" or experimentally obtained; fi 'stress in concrete arising from lateral compression by a steel tube and determined by the formula (4): where kecoefficient of efficiency of compression of concrete by a multifaceted tube(when a round tube is used as part of a composite structure, ke is taken equal to 1); ps = As / Acratio of cross-sectional areas of steel tube to concrete; fy = design resistance of steel in terms of yield strength taken according to [21] or obtained from experimental data.
Coefficient ke is defined using the expression (5): where n -the number of faces of a steel tube (when calculating composite structures based on round tubes n = ∞).
Concrete deformation εсс, corresponding to the stage of occurrence of stresses equal to the design resistance of the compressed concrete fcc is calculated according to the expression (6): where εс0 = 0.002 -deformation of free (unconfined) concrete, corresponding to the design resistance fc.
The elasticity tangential modulus of uncompressed concrete is taken from the results of mechanical tests or is determined by the formula (7): 4700...5000 cc Ef  (7) The elasticity modulus of confined concrete must be determined according to expression (8): Based on calculations results of the physical and mechanical characteristics of concrete a Mander deformation curve was constructed for compressed concrete with a multifaceted shell with its various geometric characteristics and variation of steel grades and concrete classes.On fig. 3 shows the curve under consideration on the example of CFT with fixed geometric parameters: the number of pipe faces n = 12, thickness t = 5 mm, steel grade S235 and concrete strength class B20 (the design characteristic fc was taken from the results of mechanical tests of samples of self-compacting concrete).
On fig. 3 are introduced two characteristics that describe the ultimate compressive strength of compressed concrete [15][16][17][18][19][20]: fcu -tensile strength (tensile strength) of concrete in a steel tube; εcudeformations of concrete corresponding to its tensile strength.To create the calculation model of the CFT element in ANSYS APDL were used the following types of finite elements (FE) (Fig. 4) [22][23][24][25][26][27][28][29][30]: -for steel Solid 185 -six-sided eight-node 3D element for modeling three-dimensional structures.It has three degrees of freedom in each node (linear displacements X, Y, Z).It has the properties of plasticity, hyperelasticity, creep, large displacements and deformations; -for concrete Solid 65 -six-sided eight-node 3D element for modeling volumetric concrete or reinforced concrete bodies, which has the ability to form cracks in tension and crushing in compression.Special finite elements CONTA 173 (Fig. 5) and TARGET 170 (Fig. 6) [40] were used to simulate the contact interaction of composite structure elements according to the "surface to surface" type.In this case the contact (deformation) surface is assigned the type of FE type CONTA and the penetration surface is assigned TARGET, which refers to a more rigid material.Therefore, the inner surface of the steel tube is the deformation surface (contact surface) and the inner surface of the concrete core is the penetrating surface.The fixation of nodes located at the base of the model was introduced into the calculations as a limitation of the degree of freedom in the form of a rigid fixation.Compressive loads were modeled by introducing specified displacements along the structural vertical axis for nodes placed on the concrete surface, rather than by applying a force directly to the model surface.The above approach is implemented by combining the movements of individual nodes on the top surface of the concrete core (compression applied directly to the concrete).As a result, the support reaction of the central node of the concrete core located at the base of the model was determined.This is numerically equal to the value of the critical force and is interpreted as the force that a polyhedral pipe-concrete element is able to perceive without destruction under central compression.To reduce the calculation time, a quarter of the full-body model was used without loss of accuracy.
On Fig. 7 shows finite element models of a polyhedral pipe filled with concrete using the "ordered" type of FE mesh generation [40]:  The analysis of the obtained mosaic of deformations and principal and equivalent stresses of polyhedral and tubular concrete showed significant discrepancies not only in the very principle of distribution of the considered SSS parameters, but also in their numerical values.This is explained, first of all, by the geometric features of the section of the elements.
Based on the results obtained using ANSYS the bearing capacity (Nlim -the maximum compressive load that a pipe concrete element can withstand) and SSS parameters (principal and equivalent stresses, axial deformation) of polyhedral pipe concrete props under various conditions of interaction by friction (adhesion).Adhesion of materials (friction coefficient μ varies from 0.1 to 0.6).Changes in the bearing capacity of structures were analyzed using various steel grades (S235, S275) and concrete classes (B20…B45).The main results for the example of the octahedral CFT model are shown in Figs.10-15.In addition to finite element studies this article analyzes a "unified" analytical method for determining the bearing capacity of polyhedral (with the number of faces n = 6…12, 14, 16.18, 20 and 24) and cylindrical (n = ∞) tube-concrete structures [21,31].As a result of the analysis changes in the value of the bearing capacity of structures were determined depending on the variation in the number of faces n, tube thickness t as well as steel grades and concrete classes.Selectively, data on the calculation of 6-and 12-sided tube-concrete elements with length L = 500 mm and diameter of the circumscribed circle D = 200 mm for various tube thicknesses are given in Table 1.
In table. 2 shows the results for the analysis of the change in the bearing capacity at constant height of the structure L = 500 mm and diameter of the circumscribed circle D = 200 mm for tube thicknesses t = 3, 5 and 8 mm and different number of faces n.  -to increase the bearing capacity of CFT elements when working in compression (≈ 30%) since the coefficient of friction µ between materials decreases from 0.6 to 0.1.
-with an increase in the coefficient μ from 0.1 to 0.6 the contribution of steel tubes to the total bearing capacity increases, and that of the concrete core -decreases.
-increase in the bearing capacity of CFT elements in compression (≈ 40%) having a concrete class within B20 ... B45 the prismatic strength of which increases by 55%.-changing the steel grade from S235 to S275 with fixed tube thickness increases the bearing capacity of the CFT by about 6% depending on the number of cross-sectional faces and concrete class.
-the increased wall thickness of multifaceted tube (with all other parameters unchanged) increases the bearing capacity of the CFT by about 10%.
2) As can be seen from the table.1, for every 1 mm increase in the wall thickness of multifaceted steel tube the bearing capacity increases in the range of 15-20%.Also, with an increase in the number of faces n from 6 to 12 with the same tube thickness the above properties increase by 21...26%.
3) It can be seen from the table that with an increase in the parameter n at t = const the bearing capacity of the structure increases from 12 to 32% for the minimum allowable value n = 6.However, with each subsequent increase in n, the level of increase in the bearing capacity decreases relative to the number of previous faces according to a nonlinear law from 13 to 4%, as shown in Fig. 15.In addition, the figure graphically shows the change (according to a linear law) in the bearing capacity (in terms of yield strength) of the structure under consideration since the number of faces n and the wall thickness t varies.

Fig. 2 .
Fig. 2. Mander deformation model for concrete: fccdesign compressive strength of concrete into the tube; fcdesign compressive strength of concrete without compression by a metal sheath; ε0deformation corresponding to fc; εссdeformation corresponding to fcс.

Table 1 .
[21]bearing capacity of multifaceted concrete-filled tube for n = 6 and 12 with different tube thicknesses t (when using concrete B20 and steel S235), determined by the method[21].
* , Nu * -bearing capacity (ultimate load) in terms of yield strength and tensile strength.

Table 2 .
[21]bearing capacity of multifaceted concrete-filled tubes for t = 3, 5 и 8 mm with different number of faces n (when using concrete B20 and steel S245), determined by the method[21]