Scholarly article on topic 'FEM Model of Joint Consisting RHS and HEA Profiles'

FEM Model of Joint Consisting RHS and HEA Profiles Academic research paper on "Economics and business"

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Procedia Engineering
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{"Lattice structure" / N-joint / FEM / RHS / "HEA profile"}

Abstract of research paper on Economics and business, author of scientific article — A. Jurčíková, M. Rosmanit

Abstract The subject of this paper is modeling a joint consisting of RHS (Rectangular Hollow Section) web braces and an H - profile bottom chord. Such a type of joint is based on a practical example, and its exceptional feature is a deviation from the geometric conditions given by Eurocode. Our goal is, for the model we create, to fit the actual behavior of this type of joint, as well as a comparison of such behavior with that expected on the basis of standardized formulas.

Academic research paper on topic "FEM Model of Joint Consisting RHS and HEA Profiles"

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Steel Structures and Bridges 2012

FEM model of joint consisting RHS and HEA profiles

A. Jurcikovaa* and M. Rosmanita

a VSB-Technical University of Ostrava, Faculty of Civil Engineering, Ludvika Podeste 1875/17, 708 33 Ostrava - Poruba, Czech Republic

Abstract

The subject of this paper is modeling a joint consisting of RHS (Rectangular Hollow Section) web braces and an H -profile bottom chord. Such a type of joint is based on a practical example, and its exceptional feature is a deviation from the geometric conditions given by Eurocode. Our goal is, for the model we create, to fit the actual behavior of this type of joint, as well as a comparison of such behavior with that expected on the basis of standardized formulas.

© 2012 Published by Elsevier Ltd. Selection and review under responsibility of University of Zilina, FCE, Slovakia.

Keywords: Lattice structure; N-joint; FEM; RHS; HEA profile

1. Introduction

In practice, latticed structures consisting of hollow sections, or combinations of hollow sections and hot-rolled open sections, are often designed. Utilization of such structures has many advantages (cross section symmetric with respect to two axes, shortened effective lengths, achievement of the required load-bearing capacity while preserving lightweight structure); on the other hand, design of joints may be problematic. Design methods given by Eurocode [1], are complicated, difficult to check, and offer a limited scope of use (geometric conditions, restrictions on material characteristics, certain types of joints of given types of loads).

That is why need arises to describe behavior of joints beyond the scope of Eurocode limitations, for which standardized formulas for calculations of joints' load-bearing capacity cannot be applied exactly. For this paper we have selected a practical example - roofing with steel lattice girder containing H - profile chords and RHS web braces. This structure utilizes a joint outside of the Eurocode limitations for the use of the basic formulas in calculating the joint's load-bearing capacity. In particular, the angle of the tension brace connection to the bottom chord is smaller than 30°. Our goal here is to evaluate behavior of such a joint to see whether this

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Procedía Engineering 40 (2012) 183 - 188

Engineering

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* Tel.: +420-59-732-1391; fax: +420-59-732-1378. E-mail address: anezka.jurcikova@vsb.cz

1877-7058 © 2012 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.07.077

behavior corresponds to the expectations according to Eurocode even though the joint is not compliant with the standardized formulas.

2. Types of tubular-element joint failures according to the EN 1993-1-8

The cited Eurocode [1] considers the following failure types for CHS (Circular Hollow Section) or RHS web braces with I or H cross section chords (cf. Fig. 1), see also [2] or [3]:

• Failure of web plate by plasticization, crushing or loss of shape stability;

• Chord shear failure;

• Brace failure (cracking in the welds or in the brace members)

Fig. 1 (a) Failure of web plate; (b) Chord shear failure; (c) Brace failure.

In formulas for calculation of the load-bearing capacity, with respect to different types of failures, the Eurocode does not take into account forces or tensions occurring in individual bars. It only considers the joint's geometry, profile types and the yield stresses values. Hence, we decided to compare behavior of a joint loaded with force in the tension brace only, with that loaded with realistic forces (that is, both in the tension brace and tensile force in the bottom chord).

3. Basic data of the N-joint under consideration

The joint we decided to solve consists of H - profile bottom chord (namely HE A 160) and rectangular hollow section brace members (namely RHS 100x4). We considered two design setups for the joint investigated in our paper: first with a stiffener under the compression vertical brace, then under both the compression vertical brace and the tension diagonal brace. Geometry of the joint is shown in Fig. 2.

Fig. 2 Geometry of the N-joint consisting of an H - profile chord and RHS web braces (a) First design setup; (b) Second design setup.

If the given joint were evaluated on the basis of formulas given in the Eurocode (despite the fact that one of the geometric conditions is not met) a brace failure would be decisive within both design setups. However, the load-bearing capacity would be nearly 80% higher for the second design setup (with a stiffener under both the vertical and diagonal braces) than that valid for the setup in which the stiffener is only situated under the vertical brace.

4. Numerical model

The models of the joint were created in the FEM software ANSYS 12.0 using the finite-elements, enabling both plastic behavior of materials and influence of large deformations. For modeling the HEA profile, 3D SOLID 65 finite element was used, defined by eight nodes and isotropic material properties. For RHS bars, shell finite element SHELL 43 was used, defined by four nodes, four thickness values and orthotopic material properties [4].

The following material properties were used for the finite elements (cf., e.g. [5]): Young's module of elasticity E = 210 GPa, and Poisson's ratio v = 0.3. Both physical and geometric non-linear aspects were considered within the calculation (a plastic calculation with regard to large deformations). The elasto-plastic behavior of materials was expressed by a bilinear diagram (cf., e.g., [6]) with yield stress fy = 355 MPa and 5% hardening (value of the module of elasticity after hardening E2 = 10 GPa).

The forces acting on the joint were based on the results obtained from a simple bar model of the entire girder. On the basis of information available in the literature (e.g., [7], [8]) we originally set the boundary conditions as follows (Fig. 3(a)):

• displacements in directions of the x, y, and z axes were prevented on both ends of the bottom chord, and the web braces were prevented from displacements both within the plane and out of the plane (hence displacements along the bar axes were only allowed).

However, such boundary conditions resulted in distribution of forces that did not correspond to the assumptions implied by the bar model. That is why we were looking for boundary conditions that would better correspond to the actual behavior of the selected detail of the lattice structure. Finally, the following boundary conditions were identified (Fig. 3(b)):

• only displacements in directions of the x and z axes (i.e., movements in the chord axis and out of its plane) were prevented, or the pin on the left end was replaced with a tensile-force load. The support preventing vertical displacement (in the direction of the v axis) was placed on the vertical brace.

Fig. 3 (a) Original boundary conditions; (b) New boundary conditions; (c) Connection between the bar and 3D models

Another possible solution of the problem of identifying suitable boundary conditions in the model is given by interconnecting the structure's 3D detail with the bars and modeling the lattice structure as a whole (cf. Fig. 3 c). The boundary conditions and load would then be related to the entire structure and detail's behavior would be derived from the entire structure's behavior. Correctness of this hypothesis and implementation of such a model must, however, be subsequently verified.

5. Results of numerical modeling

Four models were studied:

• a joint with a stiffener under the compression vertical brace only, loaded with a tensile force in the diagonal brace

• a joint with a stiffener under the compression vertical brace only, loaded with a tensile force in both the diagonal brace and the bottom chord

• a joint with a stiffener under both the compression vertical brace and the tension diagonal brace, loaded with a tensile force in the diagonal brace

• a joint with a stiffener under both the compression vertical brace and the tension diagonal brace, loaded with a tensile force in both the diagonal brace and the bottom chord

Apart from the evolution of stresses, we also investigated dependency of the HEA profile flange plate central part's (point 2) vertical deformation (uy) on that of the HEA profile flange plate edge part's (point 1) deformation values (Fig. 4 and 5), namely, at two sections: under the edge of the connected diagonal brace (section A) and near the center of this brace (i.e., near the connection point of the second stiffener - section B) -cf. Fig. 6. - 8.

Fig. 4 Load-deformation curves for single-stiffener models and the comparison with the Resistance according to EC3.

Fig. 5 Load-deformation curves for double-stiffener models and the comparison with the Resistance according to EC3.

Fig. 6 Comparing the flange plate deformation values and plastic stress evolution of unstiffened (a)+(b) and stiffened (c)+(d) HEA profile when loaded with a force of 300 kN in the diagonal brace (the deformation values are 20x magnified).

It u II

Fig. 7 Comparing the flange plate deformation values and plastic stress evolution of unstiffened (a)+(b) and stiffened (c)+(d) HEA profile when loaded with a force of 444 kN in the diagonal brace (the deformation values are 20x magnified).

(a) (b) (c) (d)

Fig. 8 Comparing the flange plate deformation values and plastic stress evolution of unstiffened (a)+(b) and stiffened (c)+(d) HEA profile when loaded with a force of 508 kN in the diagonal brace (the deformation values are 20x magnified).

6. Conclusions

Seeing the load-deformation curves presented at Fig. 4 and 5 it can be concluded that the capacity of the joint with one stiffener will be around 300 kN, for the double stiffened joint the force can reach more than 508 kN. The expected failure mode can be classified as a brace failure. In one case of model (two stiffeners, two forces) the brace failure has not been reached, the failure can be classified as a chord shear failure - more advance modeling should be done.

A numerical model was created which fits the expected behavior of the joint. The load-bearing capacity of the joint is not significantly influenced by loading the tension brace only, or both the tension brace and the bottom chord. The only significant difference is given by total deformation values. This confirms the principle of calculating load-bearing capacity of such a joint according to EC3. Finally, we can conclude that even if the joint geometry goes beyond the Eurocode limitations, its behavior and load-bearing capacity are very close to the expectations implied by the Eurocode.

Acknowledgments

This research was financially supported by Project MSMT - SP2012/135.

References

[1] CSN EN 1993-1-8, Eurokod 3: Navrhovâni ocelovych konstrukci - Cast 1-8: Navrhovâni stycnikù. Cesky normalizacni institut, 2006. 126s.

[2] WALD, F., SOKOL, Z. Navrhovâni stycnikù. Praha: Vydavatelstvi CVUT, 1999. 144 pp. ISBN 80-01-02073-8

[3] WARDENIER, J. Hollow Sections in Structural Applications. CIDECT, 2001. ISBN 0-471-49912-9

[4] Release 11.0 Documentation for ANSYS [online]. [cit. 2012-4-25]. Dostupné z http://www.kxcad.net/ansys/ANSYS/ansyshelp

[5] JURCIKOVA, A., ROSMANIT, M.: Numerické modelovâni svarovaného T-stycniku. Sbornik vëdeckychpraci Vysoké skoly bâhské -Technické univerzity Ostrava, rada stavebni, Ostrava. Cislo 2, 2011. Rocnik XI. ISSN 1213-1962, 6p.

[6] de LIMA, L. R. O., VELLASCO, P. C. G. da S., da SILVA, J. G. S., NEVES, L. F. da C., BITTENCOURT, M. C. A numerical analysis of tubular joints under static loading. In Proceedings of APCOM'07 in conjunction with EPMESC XI, Kyoto, Japan. December 3-6, 2007.

[7] VEGTE, G. J. van der, MAKINO, Y., WARDENIER, J. The influence of boundary conditions on the chord load effect for CHS gap K-joints. In Connections in Steel Structures. Amsterdam. June 3-4, 2004.

[8] CHOO, Y. S., QIAN, X. D., WARDENIER, J. Effects of boundary conditions and chord stresses on static strength of thick-walled CHS joints. In Journal of Constructional Steel Research., Volume 62, Issue 4, April 2006, Pages 316-328