Elastic-Plastic Analysis of Bending Moment – Axial Force Interaction in Metallic Beam of T-Section

Document Type : Research Paper

Authors

1 Department of Civil Engineering, Lorestan University, Khorram Abad, Iran

2 Department of Mechanical Engineering, Lorestan University, Khorram Abad, Iran

Abstract

This study derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering elastic-plastic idealizations. The interaction relations can predict strains, which is not possible in a rigid perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel T-section is considered for studying the characteristics of interaction curves for different models. On the basis of these interaction curves, most significant cases for the position of neutral axis which are enough for the establishment of interaction relations are suggested.

Keywords

Main Subjects

[1] S.B. Menkes, H.J. Opat., Broken beams, Exp Mech, 13 (1973) 480-486.
[2] N. Jones., Plastic failure of ductile beams loaded dynamically, Trans. ASME. J Eng Ind, 98 (1976) 131-136.
[3] J.H. Liu, N. Jones., Experimental investigation of clamped beams struck transversely by a mass, Int J Impact Eng, 6 (1987) 303-335.
[4] J.H. Liu, N. Jones, Plastic failure of a clamped beams struck transversely by a mass, University of Liverpool, Department of Mechanical Engineering Report ES/13/87, presented at A. Sawczuk Memorial Syp. Rytto Poland. To be published by pineridge Press, Swansea 1988.
[5] N. Jones, C.G. Soares, Higher Model Dynamic, Plastic Behavior of Beam Loaded Impulsively, Int Mech. Sci, 20 (1977) 135-147.
[6] W.Q. Shen, N. Jones, A failure criterion for beams under impulsive loading, Int J Impact Eng, 12 (1992) 101-121.
[7] M. Alves, N. Jones, Impact failure of beams using damage mechanics: Part I – Analytical model, Int J Impact Eng, 27 (2002) 837-861.
[8] M. Alves, N. Jones, Impact failure of beams using damage mechanics: Part II – Application, Int J Impact Eng, 27 (2002) 863-890.
[9] P.S. Symonds, F. Genna, A. Ciullini, Special cases in study of anomalous dynamic elastic-plastic response of beams by a simple model, Int J Solids Structures, 27 (1991) 299-314.
[10] Y. Qian, P.S. Symonds, Anomalous dynamic elastic-plastic response of a Galerkin beam model, Int J Mech Sci, 38 (1996) 687-708.
[11] A. Bassi, F. Genna, P.S Symonds, Anomalous elastic-plastic responses to short pulse loading of circular plates, Int J Impact Eng, 28 (2003) 65-91.
[12] N. Jones, Structural Impact, Cambridge: Cambridge University Press, 1989, Paperback edition, 1997.
[13] Q.M. Li, Continuity conditions at bending and shearing interfaces of rigid, perfectly plastic structural elements, Int. J. Solid and Struc., 37 (2000) 3651-3665.
[14] M. Ostoja-Starzewski, H. Ilies, The Cauchy and characteristic boundary value problems of random rigid-perfectly plastic media, Int. J. solids and Struc., 33 (1996) 1119-1136.
[15] C.A. Anderson, R.T. Shield, A class of complete solutions for bending of perfectly-plastic beams, Int. J. Solids and Struc., 3 (1967) 935-950.
[16] Q. Zhou, T.X. Yu, H. Zhuping, The large deflection of a rigid-perfectly plastic portal frame subjected to impulsive loading, Int. J. Solids and Struc., 26 (1990) 1225-1242.
[17] M.R. Brake, An analytical elastic-perfectly plastic contact model, Int. J. Solids and Struc., 49 (2012) 3129-3141.
[18] Y.T. Cheng, Ch.M. Cheng., Scaling relationships in conical indentation of elastic-perfectly plastic solids, Int. J. Solids and Struc., 36 (1999) 1231-1243.
[19] P.N. Zouain, L.A. Borges, M.B. Hecke. A force method for elastic-plastic analysis of frames by quadratic optimization, Int. J. solids and Struc., 24 (1988) 211-230.
[20] P.S. Symonds, C.W.G. Frye, On the relation between rigid-plastic and elastic-plastic predictions of response to pulse loading, Int. J. Impact Eng., 7 (1988) 139-149.
[21] T.X. Yu, Elastic effects in the dynamic plastic response of structures, In: N. Jones, T. Wierzbicki, editors. Structural crashworthiness and failure, Elsevier Applied Science, London and New York, 1993, 341-384.
[22] M. Hosseini, H. Abbas, Strain hardening in M–P interaction for metallic beam of I-section, Thin-Walled Structures, 62 (2013) 243–256.
[23] M. Shahabi, A. Nayebi, Springback Modeling in L-bending Process Using Continuum Damage Mechanics Concept, Journal of Applied and Computational Mechanics, 1(3) (2015) 161-167.
[24] A. Khademalrsoul, R. Naderi, Local and Global Approaches to Fracture Mechanics Using Isogeometric Analysis Method, Journal of Applied and Computational Mechanics, 1(4) (2015) 168-180.
[25] J. Zhao, H. Tang, S. Xue, Modelling of crack growth using a new fracture criteria based peridynamics, Journal of Applied and Computational Mechanics, 2018, DOI: 10.22055/JACM.2017.23515.1160.