References
- ADINA. 2014. ADINA system 9.0 release notes. Watertown, MA, USA: ADINA R&D, Inc.
- Back, S. Y., and K. M. Will. 1998. A shear-flexible element with warping for thin-walled open beams. International Journal for Numerical Methods in Engineering 43 (7):1173–91. doi:https://doi.org/10.1002/(SICI)1097-0207(19981215)43:7<1173::AID-NME340>3.0.CO;2-4.
- Bhat, U., and J. G. de Oliveira. 1985. A formulation for the shear coefficient of thin-walled prismatic beams. Journal of Ship Research 29:51–8.
- Carpinteri, A., G. Lacidogna, and S. Puzzi. 2010. A global approach for three-dimensional analysis of tall buildings. Structural Design of Tall and Special Buildings 19 (5):518–36.
- Carrera, E., M. Petrolo, and G. Giunta. 2013. Beam structures: Classical and advanced theories. Hoboken, N. J.:Wiley.
- Charney, F. A., H. Iyer, and P. W. Spears. 2005. Computation of major axis shear deformations in wide flange steel girder and columns. Journal of Constructional Steel Research 61 (11):1525–58. doi:https://doi.org/10.1016/j.jcsr.2005.04.002.
- Chen, S., Y. Ye, Q. Guo, S. Cheng, and B. Diao. 2016. Nonlinear model to predict the torsional response of U-shaped thin-walled RC members. Structural Engineering and Mechanics 60 (6):1039–61. doi:https://doi.org/10.12989/sem.2016.60.6.1039.
- Cowper, G. R. 1966. The shear coefficient in Timoshenko’s beam theory. Journal of Applied Mechanics 33 (2):335–40. doi:https://doi.org/10.1115/1.3625046.
- El Fatmi, R. 2007a. Non-uniform warping including the effects of torsion and shear forces. Part I: A general beam theory. International Journal of Solids and Structures 44:5912–29.
- El Fatmi, R. 2007b. Non-uniform warping including the effects of torsion and shear forces. Part II: Analytical and numerical applications. International Journal of Solids and Structures 44 (18–19):5930–52. doi:https://doi.org/10.1016/j.ijsolstr.2007.02.005.
- Filin, A. P. 1978. Prikladnaya Mehanika Tverdogo Deformiruemogo Tela (Applied mechanics of solid bodies). Moscow: Nauka.
- Jun, L., R. Guangwei, P. Jin, L. Xiaobin, and W. Weiguo. 2014. Free vibration analysis of a laminated shallow curved beam based on trigonometric shear deformation theory. Mechanics Based Design of Structures and Machines 42 (1):111–29. doi:https://doi.org/10.1080/15397734.2013.846224.
- Jonsson, J. 1999a. Distortional warping functions and shear distributions in thin-walled beams. Thin-Walled Structures 33 (4):245–68.
- Jonsson, J. 1999b. Distortional theory of thin-walled beams. Thin-Walled Structures 33 (4):269–303.
- Kim, N.-I. 2010. Shear and membrane locking-free thin-walled curved beam element based on sssumed strain fields. Mechanics Based Design of Structures and Machines 38 (3):273–99. doi:https://doi.org/10.1080/15397731003670576.
- Kim, N.-I., and C.-K. Jeon. 2013. Coupled static and dynamic analyses of shear deformable composite beams with channel-sections. Mechanics Based Design of Structures and Machines 41 (4):489–511. doi:https://doi.org/10.1080/15397734.2013.797332.
- Kim, N.-I., and M.-Y. Kim. 2005. Exact dynamic/static stiffness matrices of non-symmetric thin-walled beams considering coupled shear deformation effects. Thin-Walled Structures 43 (5):701–34. doi:https://doi.org/10.1016/j.tws.2005.01.004.
- Kim, N.-I., and J. Lee. 2015. Refined series methodology for the fully coupled thin-walled laminated beams considering foundation effects. Mechanics Based Design of Structures and Machines 43 (2):125–49. doi:https://doi.org/10.1080/15397734.2014.931811.
- Ladeveze, P., and J. Simmonds. 1998. New concepts for linear beam theory with arbitrary geometry and loading. European Journal of Mechanics—A/Solids 17 (3):377–402. doi:https://doi.org/10.1016/S0997-7538(98)80051-X.
- Laudiero, F., and M. Savoia. 1990. Shear effect in flexure and torsion of thin-walled beams with open and closed cross-sections. Thin-Walled Structures 10 (2):87–119. doi:https://doi.org/10.1016/0263-8231(90)90058-7.
- Maknun, I. J., I. Katili, O. Millet, and A. Hamdouni. 2016. Application of DKMQ24 shell element for twist of thin-walled beams: Comparison with Vlassov theory. International Journal for Computational Methods in Engineering Science and Mechanics 17 (5–6):391–400. doi:https://doi.org/10.1080/15502287.2016.1231240.
- Pavazza, R. 1993. Influence of shear on torsion of thin-walled beams of open section. Strojarstvo 35:103–9.
- Pavazza, R. 2005. Torsion of thin-walled beams of open section with influence of shear. International Journal of Mechanical Sciences 47 (7):1099–122. doi:https://doi.org/10.1016/j.ijmecsci.2005.02.007.
- Pavazza, R., and A. Matoković. 2017. Bending of thin-walled beams of open section with influence of shear—Part I: Theory. Thin-Walled Structures 116:357–68. doi:https://doi.org/10.1016/j.tws.2016.08.027.
- Pavazza, R., A. Matoković, and B. Plazibat. 2013a. Bending of thin-walled beams of symmetrical open cross-sections with influence of shear. Transaction of FAMENA 37:17–30.
- Pavazza, R., A. Matoković, and B. Plazibat. 2013b. Torsion of thin-walled beams of symmetrical open cross-sections with influence of shear. Transactions of FAMENA 37:1–14.
- Pavazza, R., A. Matoković, and M. Vukasović. 2017. Bending of thin-walled beams of open section with influence of shear—Part II: Application. Thin-Walled Structures 116:369–86. doi:https://doi.org/10.1016/j.tws.2016.08.026.
- Pavazza, R., and B. Plazibat. 2013. Distortion of thin-walled beams of open section assembled of three plates. Engineering Structures 57:189–98. doi:https://doi.org/10.1016/j.engstruct.2013.09.011.
- Pham, P. V., and M. Mohareb. 2014. A shear deformable theory for the analysis of steel beams reinforced with GFRP plates. Thin-Walled Structures 85:165–82. doi:https://doi.org/10.1016/j.tws.2014.08.009.
- Pilkey, W. D. 2002. Analysis and design of elastic beams. New York: Wiley.
- Roberts, T. M., and H. Al-Ubaidi. 2001. Influence of shear deformation on restrained torsional warping of pultruded FRP bars of open coss-section. Thin-Walled Structures 39 (5):395–414. doi:https://doi.org/10.1016/S0263-8231(01)00009-X.
- Sapountzakis, E. J., V. J. Tsipiras, and A. K. Argyridi. 2015. Torsional vibration analysis of bars including secondary torsional shear deformation effect by the boundary element method. Journal of Sound and Vibration 355:208–31. doi:https://doi.org/10.1016/j.jsv.2015.04.032.
- Schramm, U., L. Kitis, W. Kang, and W. D. Pilkey. 1994. On the shear deformation coefficient in beam theory. Finite Elements in Analysis and Design 16 (2):141–62. doi:https://doi.org/10.1016/0168-874X(94)00008-5.
- Shardt, R. 1966. Eine erweiterung der technishen biegelehre für die berechnung biegestreifer prismatisdcher falferke. Der Stalbbau 35:161–71.
- Senjanović, I., and Y. Fan. 1989. A higher-order flexural beam theory. Computers & Structures 32 (5):973–86. doi:https://doi.org/10.1016/0045-7949(89)90400-8.
- Senjanović, I., and Y. Fan. 1990. The bending and shear coefficient of thin-walled girders. Thin-Walled Structures 10 (1):31–57. doi:https://doi.org/10.1016/0263-8231(90)90004-I.
- Senjanović, I., S. Rudan, and N. Vladimir. 2009. Influence of shear on the torsion of thin-walled girders. Transactions of Famena 33:35–50.
- Senjanović, I., S. Tomašević, and N. Vladimir. 2009. An advanced theory of thin-walled girders with application to ship vibrations. Marine Structures 22 (3):387–437. doi:https://doi.org/10.1016/j.marstruc.2009.03.004.
- Takahashi, K., and M. Mizuno. 1978. Distortion of thin-walled open-cross-section members: One-degree-of-freedom and singly symmetrical cross-section. Bulletin of JSME 21 (160):1448–54. doi:https://doi.org/10.1299/jsme1958.21.1448.
- Timoshenko, S. P. 1921. On the correction for shear of the differential equation for transverse vibrations of prismatic bars. Philosophical Magazine and Journal of Science 41 (245):744–6. doi:https://doi.org/10.1080/14786442108636264.
- Timoshenko, S. P. 1945. Theory of bending, torsion and buckling of thin-walled members of open cross section. Journal of the Franklin Institute 239 (5):343–61. doi:https://doi.org/10.1016/0016-0032(45)90013-5.
- Timoshenko, S. P. 1958. Strength of materials, part I- Elementary theory and problems. 2nd ed. New York: D. Van Nostrand Company, Inc.
- Tralli, A. 1986. A simple hybrid model for torsion and flexure of thin-walled beams. Computers & Structures 22 (4):649–58. doi:https://doi.org/10.1016/0045-7949(86)90017-9.
- Tsipiras, V. J., and E. J. Sapountzakis. 2014. Bars under nonuniform torsion–Application to steel bars, assessment of EC3 guidelines. Engineering Structures 60:133–47. doi:https://doi.org/10.1016/j.engstruct.2013.12.027.
- Vlasov, V. Z. 1961. Thin-walled elastic beams (Tonkostennye uprugie sterzhni). 2nd ed. Jerusalem: Israel Program for Scientific Translations.
- Vukasović, M., R. Pavazza, and F. Vlak. 2017. Analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear. Archive of Applied Mechanics 87 (8):1371–84. doi:https://doi.org/10.1007/s00419-017-1256-7.
- Wang, Z. Q., J. C. Zhao, and J. H. Gong. 2011. A new torsion element of thin-walled beams including shear deformation. Applied Mechanics and Materials 94–96:1642–5. doi:https://doi.org/10.4028/www.scientific.net/AMM.94-96.1642.
- Wang, Z.-Q., and J.-C. Zhao. 2014. Restrained torsion of thin-walled beams. Journal of Structural Engineering 140 (11):4014089. doi:https://doi.org/10.1061/(ASCE)ST.1943-541X.0001010.
- Zhong-Heng, G. 1981. A unifed theory of thin-walled structures. Journal of Structural Mechanics 9 (2):179–97. doi:https://doi.org/10.1080/03601218108907382.
- Zhu, Z., L. Zhang, D. Zheng, and G. Cao. 2016. Free vibration of horizontally curved thin-walled beams with rectangular hollow sections considering two compatible displacement fields. Mechanics Based Design of Structures and Machines 44 (4):354–71. doi:https://doi.org/10.1080/15397734.2015.1075410.