A New Stiffness Matrix for a 2D-Beam Element with a Transverse Opening
Author(s)
Musab Aied Qissab
ABSTRACT
Transverse opening in a beam has a reducing effect of the beam stiffness which will cause a significant increase in beam deflection in the region on the opening. In this paper, a new stiffness matrix for a beam element with transverse opening including the effect of shear deformation has been derived. The strain energy principle is used in the derivation process of the stiffness matrix and the fixed-end force vector for the case of a concentrated or a uniformly distributed load is also derived. The accuracy of the obtained results based on the derived stiffness matrix is examined through comparison with that of the finite element method using Abaqus package and a previous study which show a good agreement with high accuracy.
Transverse opening in a beam has a reducing effect of the beam stiffness which will cause a significant increase in beam deflection in the region on the opening. In this paper, a new stiffness matrix for a beam element with transverse opening including the effect of shear deformation has been derived. The strain energy principle is used in the derivation process of the stiffness matrix and the fixed-end force vector for the case of a concentrated or a uniformly distributed load is also derived. The accuracy of the obtained results based on the derived stiffness matrix is examined through comparison with that of the finite element method using Abaqus package and a previous study which show a good agreement with high accuracy.
Cite this paper
Qissab, M. (2015) A New Stiffness Matrix for a 2D-Beam Element with a Transverse Opening. Open Journal of Civil Engineering, 5, 17-28. doi: 10.4236/ojce.2015.51003.
Qissab, M. (2015) A New Stiffness Matrix for a 2D-Beam Element with a Transverse Opening. Open Journal of Civil Engineering, 5, 17-28. doi: 10.4236/ojce.2015.51003.
References
[1] Benitez, M.A., Darwin, D. and Donahey, R.C. (1990) Deflection of Composite Beams with Web Openings. A Report on Research, University of Kansas, Lawrence. [2] Donghua, Z., Longqi, L., Jürgen, S., Wolfgang, K. and Peng, W. (2012) Elastic Deflection of Simply Supported Steel I-Beams with a Web Opening. International Conference on Advances in Computational Modeling and Simulation. Procedia Engineering, 31, 315-323. [3] Boresi, A.P. and Schmidt, R.J. (2003) Advanced Mechanics of Materials. 6th Edition, Wiley, New York. [4] (2009) Abaqus Theory Manual. Dassault Systèmes Simulia Corp. Providence.
[1] Benitez, M.A., Darwin, D. and Donahey, R.C. (1990) Deflection of Composite Beams with Web Openings. A Report on Research, University of Kansas, Lawrence. [2] Donghua, Z., Longqi, L., Jürgen, S., Wolfgang, K. and Peng, W. (2012) Elastic Deflection of Simply Supported Steel I-Beams with a Web Opening. International Conference on Advances in Computational Modeling and Simulation. Procedia Engineering, 31, 315-323. [3] Boresi, A.P. and Schmidt, R.J. (2003) Advanced Mechanics of Materials. 6th Edition, Wiley, New York. [4] (2009) Abaqus Theory Manual. Dassault Systèmes Simulia Corp. Providence.