Issue 29

D. Addessi et al., Frattura ed Integrità Strutturale, 29 (2014) 178-195; DOI: 10.3221/IGF-ESIS.29.16 195 introduced, partially removing the standard rigid section assumption. The warping displacement field has been independently interpolated along the beam axis and on the cross-sections by using Lagrange polynomials, thus allowing to model cross-sections with arbitrary geometries. The proposed enhanced beam formulation overcomes some limitations of the existing models, thus allowing to describe the influence of the boundary conditions on the warping distribution, as well as the shear lag phenomenon. The material nonlinear behavior was taken into account, by adopting a fiber discretization of the cross-sections and considering a 3D constitutive relationship at the fiber level. Thanks to the adoption of a scalar damage model for concrete-like materials, the global response curves of experimental concrete beams under torsional loads have been correctly reproduced, as well as the damage distributions over the cross-sections. To this end, it was very interesting to underline the relevant influence of the warping on the beams damaging behavior. The implemented algorithm adopted for the element state determination has resulted robust, computationally efficient and accurate in reproducing well known reference examples, as well as more complex nonlinear structural responses. R EFERENCES [1] Ciampi, V., Carlesimo, L., A nonlinear beam element for seismic analysis of structures. Proc. 8th European Conf. on Earthquake Engineering, Lisbon, 73–80, (1986). [2] Spacone, E., Filippou, F.C., Taucer, F.F., Fiber beam-column model for nonlinear analysis of RC frames: I: Formulation, Earthquake Eng. Struct. Dyn., 25(7) (1996), 711–725. [3] Saritas, A., Filippou, F.C., Inelastic axial-flexure shear coupling in a mixed formulation beam finite element, Int. J. Nonlinear Mech., 44 (2009), 913-922. [4] Mohr, S., Bairan, J.M., Mari, A. R., A frame element model for the analysis of reinforced concrete structures under shear and bending, Eng. Struct., 12 (2010), 3936–3954. [5] Zhou, S., Finite Beam Element Considering Shear-Lag Effect in Box Girder. J. Eng. Mech., 136 (2010), 1115–1122. [6] Dikaros, I. C., Sapountzakis, E. J., Generalized warping analysis of composite beams of an arbitrary cross section by BEM. I: Theoretical considerations and numerical implementation, J. Eng. Mech., DOI: 10.1061/(ASCE)EM.1943- 7889.0000775. [7] Le Corvec, V., Filippou, F. C., Enhanced 3D Fiber beam-column element with warping displacements. Proc. 3rd Int. Conf. on Computational Methods in Structural Dynamics and Earthquake Engineering COMPDYN, ECCOMAS, Barcelona, Spain, (2011). [8] Mazars, J., A description of micro- and macroscale damage of concrete structures, Eng. Fract. Mech., 25 (5-6) (1986), 729-737. [9] Kostic, S. M., Filippou, F. C., Section discretization of fiber beam-column elements for cyclic inelastic response, J. Struct. Eng., 138 (2012), 592-601. [10] Taylor, R. L., FEAP - A Finite Element Analysis Program, Version 8.4, Civil and Environmental Engineering, UC Berkeley, (2013). [11] Addessi, D., Ciampi, V., A regularized force-based beam element with a damage-plastic section constitutive law, Int. J. Numer. Meth. Eng., 70 (2007), 610-629. [12] Neuenhofer, A. and Filippou, F. C., Evaluation of nonlinear frame finite-element models, J. Struct. Eng., 123 (1997), 958–966. [13] Saritas, A., Soydas, O., Variational base and solution strategies for non-linear force-based beam finite elements, Int. J. Nonlinear Mech., 47 (2012), 54-64. [14] Karayannis, C. J., Chalioris, C. E., Experimental validation of smeared analysis for plain concrete in torsion, J. Struct. Eng., 126 (2000), 646-653. [15] Mazars, J., Kotronis, P., Ragueneau, F., Casaux, G., Using multifiber beams to account for shear and torsion. Applications to concrete structural element, Comput. Method. Appl. M., 195 (2006) 7264-7281. [16] Vlasov, V. Z., Thin-walled Elastic Beams, (1961). [17] Tralli, A., A simple hybrid model for torsion and fexure of thin-walled beams, Comp. Struct., 22 (1986), 649-658. [18] Capurso, M., Influenza delle componenti di scorrimento nella deformazione delle travi di parete sottile con sezione aperta, Giorn. Genio Civile, 122 (1984), 127-144. [19] Back, S. Y., Will, K. M., A shear-flexible element with warping for thin-walled open beams, Int. J. Numer. Meth. Eng. 43 (1998), 1173-1191.