[
Addessi, D. – Di Re, P. – Cimarello, G. (2021) Enriched beam finite element models with torsion and shear warping for the analysis of thin-walled structures, Thin-Walled Structures, vol. 159. DOI:10.1016/j.tws.2020.107259.
]Search in Google Scholar
[
Allplan Bridge - Software for Bridge Engineering. Retrieved Jan 28, 2024, from https://www.allplan.com/products/allplan-bridge/
]Search in Google Scholar
[
Back, S.Y. – Will, K. M. (1998) A shear-flexible element with warping for thin-walled open beams, International Journal for Numerical Methods in Engineering,vol. 43, No. 7, pp. 1173–1191. DOI:10.1002/(SICI)1097-0207(19981215)43:7<1173::AIDNME340>3.0.CO;2-4.
]Search in Google Scholar
[
Benscoter, S. U. (1954) A Theory of Torsion Bending for Multicell Beams, Journal of Applied Mechanics, vol. 21, No. 1, pp. 25–34. DOI:10.1115/1.4010814.
]Search in Google Scholar
[
Braess, D. (2007) Finite Elements. Theory, Fast Solvers, and Applications in Elasticity Theory, 3rd ed, Cambridge University Press.
]Search in Google Scholar
[
El Fatmi, R. (2007) Nonuniform warping including the effects of torsion and shear forces, Part I: A general beam theory, International Journal of Solids and Structures, vol. 44, Nos. 18–19. pp. 5912–5929. DOI:10.1016/j.ijsolstr.2007.02.006.
]Search in Google Scholar
[
El Fatmi, R. (2007) Nonuniform warping including the effects of torsion and shear forces. Part II: Analytical and numerical applications, International Journal of Solids and Structures, vol. 44, Nos. 18–19, pp. 5930–5952. DOI:10.1016/j.ijsolstr.2007.02.005.
]Search in Google Scholar
[
Erkmen, R. E. – Mohareb, M. (2006) Torsion analysis of thin-walled beams including shear deformation effects, Thin-walled structures, vol. 44, No. 10, pp. 1096–1108. DOI:10.1016/j. tws.2006.10.012.
]Search in Google Scholar
[
Ferradi, M. K. – Cespedes, X. – Arquier, M. (2013) A higher order beam finite element with warping eigenmodes, Engineering Structures, vol. 46, pp. 748–762. DOI:10.1016/j.engstruct.2012.07.038.
]Search in Google Scholar
[
Fialko, S. Y. – Lumelskyy, D.E. (2013) On numerical realization of the problem of torsion and bending of prismatic bars of arbitrary cross section. J Math Sci, vol. 192, pp. 664–681. DOI: 10.1007/s10958-013-1424-4.
]Search in Google Scholar
[
Genoese, A., Genoese, A., Bilotta, A., & Garcea, G. (2013). A mixed beam model with nonuniform warpings derived from the Saint Venànt rod, Computers & Structures, vol. 121, pp. 87-98. DOI:10.1016/j.compstruc.2013.03.017
]Search in Google Scholar
[
Gruttmann, F. – Sauer, R. – Wagner, W. (1999) Shear stresses in prismatic beams with arbitrary cross-sections, International Journal for Numerical Methods in Engineering, vol. 45, No. 7, pp. 865–889. DOI:10.1002/(SICI)1097-0207(19990710)45:7<865::AIDNME609>3.0.CO;2-3.
]Search in Google Scholar
[
IDEA StatiCa - Structural Engineering Software. Retrieved Jan 28, 2024, from https://www.ideastatica.com/
]Search in Google Scholar
[
Kim, N. I. – Kim, M.Y. (2005) Exact dynamic/static stiffness matrices of non-symmetric thin-walled beams considering coupled shear deformation effects, Thin-Walled Structures, vol. 43, No. 5, pp. 701–734. DOI:10.1016/j.tws.2005.01.004.
]Search in Google Scholar
[
Kugler, S. – Fotiu, P.A. – Murín, J. (2021). A novel GBT-formulation for thin-walled FGM-beam-structures based on a reference beam problem. Composite Structures, vol. 257. DOI: 10.1016/j. compstruct.2020.113158.
]Search in Google Scholar
[
Lewiński, T. – Czarnecki, S. (2021) On incorporating warping effects due to transverse shear and torsion into the theories of straight elastic bars, Acta Mechanica, vol. 232, pp. 247–282. DOI:10.1007/s00707-020-02849-7.
]Search in Google Scholar
[
Librescu, L. – Song, O. (2005) Thin-walled composite beams: theory and application, vol. 131, Springer Science & Business Media.
]Search in Google Scholar
[
Mokos, V. G., & Sapountzakis, E. J. (2011) Secondary torsional moment deformation effect by BEM, International Journal of Mechanical Sciences, vol. 53, No. 10, pp. 897-909. DOI: 10.1016/j. ijmecsci.2011.08.001.
]Search in Google Scholar
[
Murín, J. – Aminbaghai, M. – Kutiš, V. – Královič, V. – Sedlár, T. – Goga, V. – Mang, H. (2014) A new 3D Timoshenko finite beam element including nonuniform torsion of open and closed cross sections, Engineering Structures, vol. 59, pp. 153–160. DOI:10.1016/j.engstruct.2013.10.036.
]Search in Google Scholar
[
Murin, J. – Kugler, S. – Hrabovsky, J. – Kutis, V. – Paulech, J. – Aminbaghai, M. (2021). Influence of spatially varying material properties on the bimoment normal and shear stresses by warping torsion of FGM beams, Composite Structures, vol. 256, DOI: 10.1016/j.compstruct.2020.113043.
]Search in Google Scholar
[
Murín, J. – Kugler, S. – Hrabovsky, J. – Kutiš, V. – Paulech, J. – & Aminbaghai, M. (2022). Warping torsion of FGM beams with spatially varying material properties. Composite Structures, vol. 291. DOI: 10.1016/j.compstruct.2022.115592.
]Search in Google Scholar
[
Murín, J. – Kutiš, V. – Královič, V. – Sedlár, T. (2012) 3D beam finite element including nonuniform torsion, Procedia Engineering, vol. 48, pp. 436–444. DOI:10.1016/j.proeng.2012.09.537.
]Search in Google Scholar
[
Murín, J. – Kutiš, V. (2008) An effective finite element for torsion of constant cross-sections including warping with secondary torsion moment deformation effect, Engineering Structures,vol. 30, No. 10, pp. 2716–2723. DOI:10.1016/j.engstruct.2008.03.004.
]Search in Google Scholar
[
Oñate, E. (2013) Structural analysis with the finite element method. Linear statics: volume 2: beams, plates and shells. Springer Science & Business Media.
]Search in Google Scholar
[
Paradiso, M. – Vaiana, N. – Sessa, S. – Marmo, F. – Rosati, L. (2020) A BEM approach to the evaluation of warping functions in the Saint Venant theory, Engineering Analysis with Boundary Elements, vol. 113, pp. 359–371. DOI:10.1016/j.enganabound.2020.01.004.
]Search in Google Scholar
[
Pilkey, W. D. (2002) Analysis and design of elastic beams: Computational methods, John Wiley & Sons.
]Search in Google Scholar
[
Prokić, A. (1993) Thin-walled beams with open and closed cross-sections, Computers and Structures, vol. 47, No. 6, pp. 1065–1070. DOI:10.1016/0045-7949(93)90310-A.
]Search in Google Scholar
[
Prokić, A. (1996) New warping function for thin-walled beams. II: Finite element method and applications. Journal of Structural Engineering, vol. 122, No. 12, pp. 1443–1452. DOI: 10.1061/(ASCE)0733-9445(1996)122:12(1443).
]Search in Google Scholar
[
Saadé, K. – Espion, B. – Warzée, G. (2004) Nonuniform torsional behavior and stability of thin-walled elastic beams with arbitrary cross sections, Thin-Walled Structures, vol. 42, No. 6, pp. 857–881. DOI:10.1016/j.tws.2003.12.003.
]Search in Google Scholar
[
SAP2000 Structural analysis and design. Computers and Structures, Inc. (n.d.). Retrieved May 15, 2022, from https://www.csiamerica.com/products/sap2000.
]Search in Google Scholar
[
Sapountzakis, E. J., & Tsipiras, V. J. (2010). Shear deformable bars of doubly symmetrical cross section under nonlinear nonuniform torsional vibrations—application to torsional postbuckling configurations and primary resonance excitations, Nonlinear Dynamics, vol. 62, pp. 967-987. DOI: 10.1007/s11071-010-9778-3.
]Search in Google Scholar
[
SCAD Software - Structural Analysis and Design. Retrieved Jan 28, 2024, from https://scadsoft.com/en
]Search in Google Scholar
[
SCIA English Homepage. SCIA Structural Analysis Software and Design Tools. Retrieved 16 Jan 2022, from https://www.scia.net/en.
]Search in Google Scholar
[
Shakourzadeh, H. – Guo, Y. Q. – Batoz, J.L. (1995) A torsion bending element for thin-walled beams with open and closed cross sections, Computers and Structures, vol. 55, No. 6, pp. 1045–1054. DOI:10.1016/0045-7949(94)00509-2.
]Search in Google Scholar
[
Timoshenko, S. P. – Goodier, J. N. (1970) Theory of Elasticity, 3rd ed, McGraw-Hill Book Co.
]Search in Google Scholar
[
Timoshenko, S. P. X. (1922) On the transverse vibrations of bars of uniform cross-section, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 43, No. 253, pp. 125–131. DOI:10.1080/14786442208633855.
]Search in Google Scholar
[
Timoshenko, S. P. LXVI. (1921) On the correction for shear of the differential equation for transverse vibrations of prismatic bars, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. 41, No. 245, pp. 744–746. DOI:10.1080/14786442108636264.
]Search in Google Scholar
[
Tralli, A. (1986) A simple hybrid model for torsion and flexure of thin-walled beams, Computers and Structures, vol. 22, No. 4, pp. 649–658. DOI:10.1016/0045-7949(86)90017-9.
]Search in Google Scholar
[
Tran, D. B. – Navrátil, J. – Čermák, M. (2021) An efficiency method for assessment of shear stress in prismatic beams with arbitrary cross‐sections, Sustainability (Switzerland), vol. 13, No. 2. pp. 1–20. DOI:10.3390/su13020687.
]Search in Google Scholar
[
Tran, D. B. (2021) Torsional Shear Stress in Prismatic Beams With Arbitrary Cross-Sections Using Finite Element Method, Stavební obzor - Civil Engineering Journal, vol. 30, No. 2. DOI:10.14311/cej.2021.02.0030.
]Search in Google Scholar
[
Tsipiras, V. J. – Sapountzakis, E. J. (2014). Bars under nonuniform torsion–Application to steel bars, assessment of EC3 guidelines. Engineering structures, vol. 60, pp.133-147. DOI: 10.1016/j.engstruct.2013.12.027.
]Search in Google Scholar
[
Tsipiras, V. J. – Sapountzakis, E.J. (2012) Secondary torsional moment deformation effect in inelastic nonuniform torsion of bars of doubly symmetric cross section by BEM, International Journal of Non-Linear Mechanics, vol. 47, No. 4, pp. 68–84. DOI: 10.1016/j.ijnonlinmec.2012.03.007.
]Search in Google Scholar
[
Vlasov, V. Z. (1961) Thin walled elastic beams, Israel Program for Scientific Translations, Jerusalem, Israel.
]Search in Google Scholar
[
Wunderlich, W. – Pilkey, W.D. (2002) Mechanics of structures: variational and computational methods, 2d ed. CRC Press, 912 pp.
]Search in Google Scholar
[
Zienkiewicz, O. C. – Taylor, R. L. (2000) The finite element method: the basis, vol.1, 5th ed. Butterworth-Heineman.
]Search in Google Scholar
