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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Chen, Zhewu, Zhanda Huang, Yong Guo, and Guibing Li. "Prediction of Mechanical Properties of Thin-Walled Bar with Open Cross-Section under Restrained Torsion." Coatings 12, no. 5 (April 21, 2022): 562. http://dx.doi.org/10.3390/coatings12050562.

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Анотація:

Thin-walled bars with an open cross-section are widely used in mechanical structures where weight and size control are particularly required. Thus, this paper attempts to propose a theoretical model for predicting the mechanical properties of a thin-walled bar with an open cross-section under restrained torsion. Firstly, a theoretical model with predictions of shear stress, buckling normal stress, and secondary shear stress of the thin-walled bar with open cross-section under the condition of restrained torsion was developed based on torsion theory. Then, physical test and finite element modeling data were employed to validate the theoretical predictions. The results indicate that the theoretical predictions show good agreements with data of finite element modeling and experiments. Therefore, the proposed theoretical model could be used for the prediction of the mechanical response of a thin-walled bar with an open annular section under restrained torsion.

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2

Šimić Penava, Diana, and Maja Baniček. "Critical Force Analysis of Thin-Walled Symmetrical Open-Section Beams." Applied Mechanics and Materials 827 (February 2016): 283–86. http://dx.doi.org/10.4028/www.scientific.net/amm.827.283.

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This paper analyzes critical forces and stability of steel thin-walled C-cross-section beams without lateral restraints. Mechanical properties of the rods material are determined by testing standard specimens in a laboratory. Based on the obtained data, the stability analysis of rods is carried out and critical forces are determined: analytically by using the theory of thin-walled rods, numerically by using the finite element method (FEM), and experimentally by testing the C-cross-section beams. The analysis of critical forces and stability shows that the calculation according to the theory of thin-walled rods does not take the effect of local buckling into account, and that the resulting critical global forces do not correspond to the actual behaviour of the rod. The FEM analysis and experimental test show that the simplifications, which have been introduced into the theory of thin-walled rods with open cross-sections, significantly affect final results of the level of the critical force.

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3

HEMATIYAN, M. R., and E. ESTAKHRIAN. "TORSION OF FUNCTIONALLY GRADED OPEN-SECTION MEMBERS." International Journal of Applied Mechanics 04, no. 02 (June 2012): 1250020. http://dx.doi.org/10.1142/s1758825112500202.

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Анотація:

There exist some approximate analytical methods for torsion analysis of homogeneous open cross-section members; however, no analytical formulation has been presented for solving a torsion problem of inhomogeneous open cross-section members yet. In this paper, an approximate analytical method for the torsion analysis of thin- to moderately thick-walled functionally graded open-section members with uniform thickness is presented. The shear modulus of rigidity is assumed to have a variation across the thickness. The cross-section is decomposed into some straight, curved and end segments. The torsion problem is then solved in each segment considering some appropriate approximations. By presenting three examples, accuracy of the presented method with respect to thickness, corner radius, and material parameters are investigated. The results show that the proposed method is useful for torsion analysis of thin- to moderately thick-walled functionally graded open-section members.

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4

Ecsedi, István, Ákos József Lengyel, Attila Baksa, and Dávid Gönczi. "Saint-Venant’s torsion of thin-walled nonhomogeneous open elliptical cross section." Multidiszciplináris tudományok 11, no. 5 (2021): 151–58. http://dx.doi.org/10.35925/j.multi.2021.5.15.

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Анотація:

This paper deals with the Saint-Venant’s torsion of thin-walled isotropic nonhomogeneous open elliptical cross section whose shear modulus depends on the one of the curvilinear coordinates which define the cross-sectional area of the beam. The approximate solution of torsion problem is obtained by variational method. The usual simplification assumptions are used to solve the uniform torsion problem of bars with thin-walled elliptical cross-sections. An example illustrates the application of the derived formulae of shearing stress and torsional rigidity.

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5

Gupta, R. K., and K. P. Rao. "Instability of laminated composite thin-walled open-section beams." Composite Structures 4, no. 4 (January 1985): 299–313. http://dx.doi.org/10.1016/0263-8223(85)90030-3.

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6

Sun, De Fa. "Overall Stability of Open Cold-Formed Thin-Walled Steel Members with Hat Sections and Batten Plates under Axial Loads." Advanced Materials Research 368-373 (October 2011): 89–93. http://dx.doi.org/10.4028/www.scientific.net/amr.368-373.89.

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Анотація:

Batten plates can play a significant role in reducing the bearing capacity of the entire component and preventing the upward warpage deformation in the opening section. The specific number of batten plates should be calculated for the open cold-formed thin-walled steel structure. By theoretical analysis, this study develops the flexural-torsional buckling formula for the open hat-section cold-formed thin-walled axially compressed members with batten plates. The calculating results show that, according to the configuration rule with 40 iy space between batten plates along the opening direction in the open thin-walled steel members, the warpage deformation will be effectively prevented in the opening direction. Besides, the bearing capacity of the entire member will be increased. The proposed calculation methods can actively complement the existing code.

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7

Sun, De Fa. "Overall Stability of Cold-Formed Steel Lipped Channel Axially Compressed Members with Batten Plates." Applied Mechanics and Materials 94-96 (September 2011): 953–57. http://dx.doi.org/10.4028/www.scientific.net/amm.94-96.953.

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Анотація:

Batten plates can play a significant role in reducing the bearing capacity of the entire component and preventing the upward warpage deformation in the opening section. The specific number of batten plates should be calculated for the open cold-formed thin-walled steel structure. By theoretical analysis, this study develops the flexural-torsional buckling formula for the open lipped-channel section cold-formed thin-walled axially compressed members with batten plates. The calculating results show that, according to the configuration rule with 80 iy space between batten plates along the opening direction in the open thin-walled steel members, the warpage deformation will be effectively prevented in the opening direction. Besides, the bearing capacity of the entire member will be increased. The proposed calculation methods can actively complement the existing code.

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8

Andjelic, Nina, and Vesna Milosevic-Mitic. "An approach to the optimization of thin-walled cantilever open section beams." Theoretical and Applied Mechanics 34, no. 4 (2007): 323–40. http://dx.doi.org/10.2298/tam0704323a.

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Анотація:

An approach to the optimization of the thin-walled cantilever open section beams subjected to the bending and to the constrained torsion is considered. The problem is reduced to the determination of minimum mass, i.e. minimum cross-sectional area of structural thin-walled I-beam and channel-section beam elements for given loads, material and geometrical characteristics. The area of the cross-section is assumed to be the objective function. The stress constraints are introduced. Applying the Lagrange multiplier method the equations, whose solutions represent the optimal values of the ratios of the parts of the chosen cross-section, are formed. The obtained results are used for numerical calculation.

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9

Kreja, Ireneusz, Tomasz Mikulski, and Czeslaw Szymczak. "ADJOINT APPROACH SENSITIVITY ANALYSIS OF THIN‐WALLED BEAMS AND FRAMES." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 11, no. 1 (March 31, 2005): 57–64. http://dx.doi.org/10.3846/13923730.2005.9636333.

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Анотація:

Sensitivity analysis of beams and frames assembled of thin‐walled members is presented within the adjoint approach. Static loads and structures composed of thin‐walled members with the bisymmetrical open cross‐section are considered. The analysed structure is represented by the one‐dimensional model consisting of thin‐walled beam elements based on the classical assumptions of the theory of thin‐walled beams of non‐deformable cross‐section together with superelements applied in place of location of structure nodes, restraints and stiffeners. The results of sensitivity analysis, obtained for the structure model described above, are compared with the results of the detailed FEM model, where the whole structure is discretised with the use of QUAD4 shell elements of the system MSC/NASTRAN.

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10

Omidvar, B., and A. Ghorbanpoor. "Nonlinear FE Solution for Thin-Walled Open-Section Composite Beams." Journal of Structural Engineering 122, no. 11 (November 1996): 1369–78. http://dx.doi.org/10.1061/(asce)0733-9445(1996)122:11(1369).

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11

Mohri, F., L. Azrar, and M. Potier-Ferry. "Lateral post-buckling analysis of thin-walled open section beams." Thin-Walled Structures 40, no. 12 (December 2002): 1013–36. http://dx.doi.org/10.1016/s0263-8231(02)00043-5.

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12

Roberts, T. M. "Natural Frequencies of Thin‐Walled Bars of Open Cross Section." Journal of Engineering Mechanics 113, no. 10 (October 1987): 1584–93. http://dx.doi.org/10.1061/(asce)0733-9399(1987)113:10(1584).

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13

Rajasekaran, Sundaramoorthy. "Equations for Tapered Thin‐Walled Beams of Generic Open Section." Journal of Engineering Mechanics 120, no. 8 (August 1994): 1607–29. http://dx.doi.org/10.1061/(asce)0733-9399(1994)120:8(1607).

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14

Vo, Thuc Phuong, and Jaehong Lee. "Geometrically nonlinear analysis of thin-walled open-section composite beams." Computers & Structures 88, no. 5-6 (March 2010): 347–56. http://dx.doi.org/10.1016/j.compstruc.2009.11.007.

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15

Nguyen, Tan-Tien, Nam-Il Kim, and Jaehong Lee. "Free vibration of thin-walled functionally graded open-section beams." Composites Part B: Engineering 95 (June 2016): 105–16. http://dx.doi.org/10.1016/j.compositesb.2016.03.057.

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16

Xiong, Xiao Li, Li Bing Jin, and Kai Xi Li. "A New Conception of Free Torsion Rigidity in Constraint Torsion Theory for Members with Open Thin-Walled Cross-Section." Advanced Materials Research 261-263 (May 2011): 888–94. http://dx.doi.org/10.4028/www.scientific.net/amr.261-263.888.

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Анотація:

In calculating the internal force and deformation of a thin-walled member, the influence of the free torsion rigidity must be considered and it makes the study complicated. Actually, from the analogy relations between the equilibrium equation in the constraint torsion theory of a thin-walled member and that in the plane bending theory of a tension-bending solid bar, the action of the free torsion rigidity can be regarded as a tension effect on a thin-walled member with torsion, i.e. the action can be described as a second-order effect like the tension action in the plane bending theory. Taking cantilever bars for example, the simple calculation method of the internal force and deformation of thin-walled members are deduced by the Taylor series in mathematics, and then verified by ANSYS.

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17

Różyło, P. "Experimental-numerical test of open section composite columns stability subjected to axial compression." Archives of Materials Science and Engineering 84, no. 2 (April 2, 2017): 58–64. http://dx.doi.org/10.5604/01.3001.0010.0979.

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Анотація:

Purpose: The aim of the work was to analyse the critical state of thin-walled composite profiles with top-hat cross section under axial compression. Design/methodology/approach: The purpose of the work was achieved by using known approximation methods in experimental and finite element methods for numerical simulations. The scope of work included an analysis of the behavior of thin-walled composite structures in critical state with respect to numerical studies verified experimentally. Findings: In the presented work were determined the values of critical loads related to the loss of stability of the structures by using well-known approximation methods and computer simulations (FEM analysis). Research limitations/implications: The research presented in the paper is about the potential possibility of determining the values of critical loads equivalent to loss of stability of thin-walled composite structures and the future possibility of analyzing limit states related to loss of load capacity. Practical implications: The practical approach in the actual application of the described specimen and methodology of study is related to the necessity of carrying out of strength analyzes, allowing for a precise assessment of the loads upon which the loss of stability (bifurcation) occurs. Originality/value: The originality of the research is closely associated with used the thinwalled composite profile with top-hat cross-section, which is commonly used in the fuselage of passenger airplane. The methodology of simultaneous confrontation of the obtained results of critical loads by using approximation methods and using the linear eigenvalue solution in numerical analysis demonstrates the originality of the research character. Presented results and the methodology are intended for researchers, who are concerned with the topic of loss of stability of thin-walled composite structures.

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18

Andjelić, Nina. "Nonlinear Approach to Thin-Walled Beams with a Symmetrical Open Section." Strojniški vestnik – Journal of Mechanical Engineering 57, no. 1 (January 15, 2011): 69–77. http://dx.doi.org/10.5545/sv-jme.2008.061.

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19

Alsheikh, Abdelraouf M. Sami, and D. W. A. Rees. "General Stiffness Matrix for a Thin-Walled, Open-Section Beam Structure." World Journal of Mechanics 11, no. 11 (2021): 205–36. http://dx.doi.org/10.4236/wjm.2021.1111015.

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20

Pavlenko, A. D., V. A. Rybakov, A. V. Pikht, and E. S. Mikhailov. "Non-uniform torsion of thin-walled open-section multi-span beams." Magazine of Civil Engineering 67, no. 07 (March 2017): 55–69. http://dx.doi.org/10.5862/mce.67.6.

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21

SHIZAWA, Kazuyuki, and Kunihiro TAKAHASHI. "Experimental discussions on distortion of thin-walled open cross section members." Doboku Gakkai Ronbunshu, no. 450 (1992): 193–96. http://dx.doi.org/10.2208/jscej.1992.450_193.

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22

Gonçalves, Rodrigo, and Dinar Camotim. "On distortion of symmetric and periodic open-section thin-walled members." Thin-Walled Structures 94 (September 2015): 314–24. http://dx.doi.org/10.1016/j.tws.2015.04.018.

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23

Nguyen, Tan-Tien, Pham Toan Thang, and Jaehong Lee. "Flexural-torsional stability of thin-walled functionally graded open-section beams." Thin-Walled Structures 110 (January 2017): 88–96. http://dx.doi.org/10.1016/j.tws.2016.09.021.

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24

Nguyen, Trong-Chuc, Van-Lam Tang, Thanh-Sang Nguyen, Quy-Thanh Nguyen, and Trong-Phuoc Huynh. "Analysis of Thin-Walled Bars Stress State with an Open Section." IOP Conference Series: Materials Science and Engineering 661 (November 20, 2019): 012011. http://dx.doi.org/10.1088/1757-899x/661/1/012011.

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25

Pasquino, M., and F. Marotti de Sciarra. "Buckling of thin-walled beams with open and generically variable section." Computers & Structures 44, no. 4 (August 1992): 843–49. http://dx.doi.org/10.1016/0045-7949(92)90470-k.

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26

Gupta, R. K., A. Venkatesh, and K. P. Rao. "Finite element analysis of laminated anisotropic thin-walled open-section beams." Composite Structures 3, no. 1 (January 1985): 19–31. http://dx.doi.org/10.1016/0263-8223(85)90026-1.

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27

Shik Park, Moon, and Byung Chai Lee. "Prediction of bending collapse behaviours of thin-walled open section beams." Thin-Walled Structures 25, no. 3 (July 1996): 185–206. http://dx.doi.org/10.1016/0263-8231(96)00001-8.

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28

Mentrasti, Lando. "Curved thin-walled open-closed cross section beams with finite width." International Journal of Engineering Science 33, no. 4 (March 1995): 497–524. http://dx.doi.org/10.1016/0020-7225(94)00076-x.

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29

Nguyen, Tan-Tien, Nam-Il Kim, and Jaehong Lee. "Analysis of thin-walled open-section beams with functionally graded materials." Composite Structures 138 (March 2016): 75–83. http://dx.doi.org/10.1016/j.compstruct.2015.11.052.

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30

Lanc, Domagoj, Goran Turkalj, Thuc P. Vo, and Josip Brnić. "Nonlinear buckling behaviours of thin-walled functionally graded open section beams." Composite Structures 152 (September 2016): 829–39. http://dx.doi.org/10.1016/j.compstruct.2016.06.023.

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31

Nguyen, Tan-Tien, Pham Toan Thang, and Jaehong Lee. "Lateral buckling analysis of thin-walled functionally graded open-section beams." Composite Structures 160 (January 2017): 952–63. http://dx.doi.org/10.1016/j.compstruct.2016.10.017.

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32

Ronagh, H. R., and M. A. Bradford. "Non-linear analysis of thin-walled members of open cross-section." International Journal for Numerical Methods in Engineering 46, no. 4 (October 10, 1999): 535–52. http://dx.doi.org/10.1002/(sici)1097-0207(19991010)46:4<535::aid-nme686>3.0.co;2-q.

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33

Conci, Aura. "Large displacement analysis of thin-walled beams with generic open section." International Journal for Numerical Methods in Engineering 33, no. 10 (July 15, 1992): 2109–27. http://dx.doi.org/10.1002/nme.1620331008.

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34

Choudhary, Prashant K., Prashanta K. Mahato, and Prasun Jana. "Cross-section optimization of thin-walled open-section composite column for maximizing its ultimate strength." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 236, no. 2 (October 12, 2021): 413–28. http://dx.doi.org/10.1177/14644207211046264.

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Анотація:

This paper focuses on the optimization of thin-walled open cross-section laminated composite column subjected to uniaxial compressive load. The cross-section of the column is parameterized in such a way that it can represent a variety of shapes including most of the regular cross-sections such as H, C, T, and I sections. The objective is to obtain the best possible shape of the cross-section, by keeping a constant total material volume, which can maximize the ultimate load carrying capacity of the column. The ultimate strength of the column is determined by considering both buckling instability and material failure. For material failure, Tsai-Wu composite failure criterion is considered. As analytical solutions for these parameterized column models are not tractable, the ultimate loads of the composite columns are computed through finite-element analysis in ANSYS. And, the optimization is carried out by coupling these finite-element results with a genetic algorithm based optimization scheme developed in MATLAB. The optimal result obtained through this study is compared with an equivalent base model of cruciform cross-section. Results are reported for various lengths and boundary conditions of the columns. The comparison shows that a substantial increase of the ultimate load, as high as 610%, can be achieved through this optimization study. Thus, the present paper highlights some important characteristics of open cross-sections that can be useful in the design of thin-walled laminated column structures.

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35

Yurchenko, Vitalina. "SEARCHING SHEAR FORCES FLOWS FOR AN ARBITRARY CROSS-SECTION OF A THIN-WALLED BAR: DEVELOPMENT OF NUMERICAL ALGORITHM BASED ON THE GRAPH THEORY." International Journal for Computational Civil and Structural Engineering 15, no. 1 (March 25, 2019): 153–70. http://dx.doi.org/10.22337/2587-9618-2019-15-1-153-170.

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Анотація:

Searching problem of shear stresses on outside longitudinal edges of an arbitrary cross-section (including open-closed multi-contour cross-sections) of a thin-walled bar subjected to the general load case has been considered in the paper. Detail numerical algorithm intended to solve the formulated problem using mathematical apparatus of the graph theory has been proposed by the paper. The algorithm is oriented on software implementation in systems of computer-aided design of thin-walled bar structures.

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36

Jonker, J. B. "Three-dimensional beam element for pre- and post-buckling analysis of thin-walled beams in multibody systems." Multibody System Dynamics 52, no. 1 (January 21, 2021): 59–93. http://dx.doi.org/10.1007/s11044-021-09777-x.

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AbstractThis paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

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37

Huang, Lihua, Bin Li, and Yuefang Wang. "Computation Analysis of Buckling Loads of Thin-Walled Members with Open Sections." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/8320469.

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Анотація:

The computational methods for solving buckling loads of thin-walled members with open sections are not unique when different concerns are emphasized. In this paper, the buckling loads of thin-walled members in linear-elastic, geometrically nonlinear-elastic, and nonlinear-inelastic behaviors are investigated from the views of mathematical formulation, experiment, and numerical solution. The differential equations and their solutions of linear-elastic and geometrically nonlinear-elastic buckling of thin-walled members with various constraints are derived. Taking structural angle as an example, numerical analysis of elastic and inelastic buckling is carried out via ANSYS. Elastic analyses for linearized buckling and nonlinear buckling are realized using finite elements of beam and shell and are compared with the theoretical results. The effect of modeling of constraints on numerical results is studied when shell element is applied. The factors that influence the inelastic buckling load in numerical solution, such as modeling of constraint, loading pattern, adding rib, scale factor of initial defect, and yield strength of material, are studied. The noteworthy problems and their solutions in numerically buckling analysis of thin-walled member with open section are pointed out.

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38

Ali, Jaffar Syed Mohammed, Meftah Hrairi, and Masturah Mohamad. "Stress Analysis of Thin-Walled Laminated Composite Beams under Shear and Torsion." International Journal of Engineering Materials and Manufacture 3, no. 1 (March 30, 2018): 9–17. http://dx.doi.org/10.26776/ijemm.03.01.2018.02.

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Анотація:

An educational software which can aid students in the stress analysis of thin wall open sections made of composite material has been developed. The software enables students to easily calculate stresses in different shapes of thin wall open section and evaluate the stresses in each ply under shear and torsion. Results obtained through this software have been validated against ANSYS. The software is intended to be an educational tool for effective teaching and learning process on thin-walled structures, aircraft structures and composite structures courses.

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39

Phi, Linh T. M., Tan-Tien Nguyen, Joowon Kang, and Jaehong Lee. "Vibration and buckling optimization of thin-walled functionally graded open-section beams." Thin-Walled Structures 170 (January 2022): 108586. http://dx.doi.org/10.1016/j.tws.2021.108586.

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40

MAGNUCKI∗, KRZYSZTOF, and TOMASZ MONCZAK. "OPTIMUM SHAPE OF THE OPEN CROSS-SECTION OF A THIN-WALLED BEAM." Engineering Optimization 32, no. 3 (January 2000): 335–51. http://dx.doi.org/10.1080/03052150008941303.

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Piotrowski, Andrzej, Łukasz Kowalewski, Radosław Szczerba, Marcin Gajewski, and Stanisław Jemioło. "Buckling resistance assessment of thin-walled open section element under pure compression." MATEC Web of Conferences 86 (2016): 01021. http://dx.doi.org/10.1051/matecconf/20168601021.

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42

Mo Hsiao, Kuo, and Wen Yi Lin. "A co-rotational formulation for thin-walled beams with monosymmetric open section." Computer Methods in Applied Mechanics and Engineering 190, no. 8-10 (November 2000): 1163–85. http://dx.doi.org/10.1016/s0045-7825(99)00471-5.

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43

Magnucki, K., and E. Magnucka-Blandzi. "Variational design of open cross-section thin-walled beam under stability constraints." Thin-Walled Structures 35, no. 3 (November 1999): 185–91. http://dx.doi.org/10.1016/s0263-8231(99)00031-2.

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44

Feo, Luciano, and Geminiano Mancusi. "Modeling shear deformability of thin-walled composite beams with open cross-section." Mechanics Research Communications 37, no. 3 (April 2010): 320–25. http://dx.doi.org/10.1016/j.mechrescom.2010.02.005.

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45

Laudiero, F., and D. Zaccaria. "Finite element analysis of stability of thin-walled beams of open section." International Journal of Mechanical Sciences 30, no. 8 (January 1988): 543–57. http://dx.doi.org/10.1016/0020-7403(88)90098-7.

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46

Soriano, H. L., and J. W. Haas. "Matrix compatibility of interface between thin-walled open-section column and beam." Computers & Structures 33, no. 2 (January 1989): 583–91. http://dx.doi.org/10.1016/0045-7949(89)90032-1.

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47

Pavazza, Radoslav, and Bože Plazibat. "Distortion of thin-walled beams of open section assembled of three plates." Engineering Structures 57 (December 2013): 189–98. http://dx.doi.org/10.1016/j.engstruct.2013.09.011.

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48

R. S. Talikoti and K. M. Bajoria. "New approach to improving distortional strength of intermediate length thin-walled open section columns." Electronic Journal of Structural Engineering 5 (January 1, 2005): 69–79. http://dx.doi.org/10.56748/ejse.551.

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Анотація:

This paper describes a method which can be adopted to improve the torsional and also distortional strength of thin-walled cold-formed steel columns used in pallet racking systems. Elastic buckling analysis on two different types of column sections of intermediate length was done first in our study, after finding the buckling strength and mode of failure, the column sections were made distortionally stronger by adding simple spacers. Spacers are simple concentric tubes which are used to connect the flanges of open thin walled column sections (Fig. 3.). More than 22 laboratory experiments were carried out with different spacer spacing to asses the strength and behavior of these two different column sections. All these columns tested were investigated using finite element analysis software ANSYS [1]. The experimental results were verified with finite element analysis results obtained by solving the sections using ANSYS [1] software. Details of the experimentation and finite element analysis are presented here.

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49

Valido, Aníbal J. J., and João Barradas Cardoso. "Design variation of thin-walled composite beam cross-section properties." Multidiscipline Modeling in Materials and Structures 12, no. 3 (October 10, 2016): 558–76. http://dx.doi.org/10.1108/mmms-12-2015-0081.

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Purpose The purpose of this paper is to present a design sensitivity analysis continuum formulation for the cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, on shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section. Design/methodology/approach In order to determine its properties, the cross-section geometry is modeled by quadratic isoparametric finite elements. For design sensitivity calculations, the cross-section is modeled throughout design elements to which the element sensitivity equations correspond. Geometrically, the design elements may coincide with the laminates that constitute the cross-section. Findings The developed formulation is based on the concept of adjoint system, which suffers a specific adjoint warping for each of the properties depending on warping. The lamina orientation and the laminate thickness are selected as design variables. Originality/value The developed formulation can be applied in a unified way to open, closed or hybrid cross-sections.

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50

Volovoi, V. V., and D. H. Hodges. "Theory of Anisotropic Thin-Walled Beams." Journal of Applied Mechanics 67, no. 3 (March 7, 2000): 453–59. http://dx.doi.org/10.1115/1.1312806.

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Asymptotically correct, linear theory is presented for thin-walled prismatic beams made of generally anisotropic materials. Consistent use of small parameters that are intrinsic to the problem permits a natural description of all thin-walled beams within a common framework, regardless of whether cross-sectional geometry is open, closed, or strip-like. Four “classical” one-dimensional variables associated with extension, twist, and bending in two orthogonal directions are employed. Analytical formulas are obtained for the resulting 4×4 cross-sectional stiffness matrix (which, in general, is fully populated and includes all elastic couplings) as well as for the strain field. Prior to this work no analytical theories for beams with closed cross sections were able to consistently include shell bending strain measures. Corrections stemming from those measures are shown to be important for certain cases. Contrary to widespread belief, it is demonstrated that for such “classical” theories, a cross section is not rigid in its own plane. Vlasov’s correction is shown to be unimportant for closed sections, while for open cross sections asymptotically correct formulas for this effect are provided. The latter result is an extension to a general contour of a result for I-beams previously published by the authors. [S0021-8936(00)03003-8]

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