Nonlinear Inelastic Analysis of Steel Beam‐Columns. I: Theory
This article has a reply.
VIEW THE REPLYPublication: Journal of Structural Engineering
Volume 120, Issue 7
Abstract
This paper presents a nonlinear inelastic analysis of the biaxial bending and torsion of thin‐walled steel beam‐columns based on the principle of virtual work. The effect of geometric nonlinearity is developed using position vector analysis. Approximations are not made in the early stage of the development, and thus some significant terms for buckling and postbuckling analysis are retained. The von Mises yield criterion, the associated flow rule, and the hardening rule are used in formulating the elastic‐plastic constitutive matrix for the material inelasticity. Inelastic uniform and nonuniform torsion are incorporated in the formulation as well as the linear and nonlinear geometric effects of the loads. A corresponding finite‐element model for the nonlinear incremental analysis of biaxial bending and torsion of thin‐walled beam‐columns is presented by using the principle of virtual work. Numerical results in a companion paper indicate that the model presented is capable of making accurate nonlinear analyses including postbuckling analyses.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Argyris, J. H. (1982). “An excursion into large rotation.” Comput. Meth. Appl. Engrg., 31, 85–155.
2.
Argyris, J. H., Dunne, P. C., Malejannakis, G., and Scharpf, D. W. (1978a). “On large displacement‐small strain analysis of structures with rotational degree of freedom.” Comp. Methods Appl. Engrg., 15, 99–135.
3.
Argyris, J. H., Dunne, P. C., and Scharpf, D. W. (1978b). “On large displacement‐small strain analysis of structures with rotational degree of freedom.” Comp. Methods Appl. Engrg., 14, 401–451.
4.
Baba, S., and Kajita, T. (1982). “Plastic analysis of torsion of a prismatic beam.” Int. J. Num. Methods Engrg., 18(6), 927–944.
5.
Banerjee, A. K., and Lemak, M. E. (1991). “Multi‐flexible body dynamics capturing motion‐induced stiffness.” J. Appl. Mech., 58(3), 766–775.
6.
Barsoum, R. S., and Gallagher, R. H. (1970). “Finite element analysis of torsional and torsional‐flexural stability problems.” Int. J. Num. Methods in Engrg., 2(3), 335–352.
7.
Bathe, K. J., and Blourchi, S. (1979). “Large displacement analysis of three‐dimensional beam structures.” Int. J. Num. Methods in Engrg., 14(7), 961–986.
8.
Bathe, K. J., and Chaudhary, A. (1982). “On the displacement formulation of torsion of shafts with rectangular cross‐sections.” Int. J. Num. Methods Engrg., 18(10), 1565–1568.
9.
Bathe, K. J., and Wiener, P. M. (1983). “On elastic‐plastic analysis of I‐beams in bending and torsion.” Comp. and Struct., 17(5–6), 711–718.
10.
Besseling, J. F. (1977). “Derivatives of deformation parameters for bar elements and their use in buckling and postbuckling analysis.” Comp. Methods Appl. Engrg., 12, 97–124.
11.
Besseling, J. F. (1982). “Non‐linear theory for elastic beams and rods and its finite element representation.” Comp. Methods Appl. Engrg., 31, 205–220.
12.
Bild, S., Chen, G., and Trahair, N. S. (1992). “Out‐of‐plane strength of steel beams.” J. Struct. Engrg., ASCE, 118(8), 1987–2003.
13.
Billinghurst, A., Williams, J., Chen, G., and Trahair, N. S. (1992). “Inelastic uniform torsion of steel members.” Comp. and Struct., 42(6), 887–894.
14.
Bowen, R. M., and Wang, C.‐C. (1976). Introduction to Vectors and Tensors. Plenum Press, New York, N.Y.
15.
Bridgeman, P. W. (1952). Studies in large plastic flow and fracture. McGraw‐Hill Book Company, New York, N.Y.
16.
Bushnell, D. (1977). “A strategy for the solution of problems involving large deflections, plasticity and creep.” Int. J. Num. Methods in Engrg., 11, 683–708.
17.
Cardona, A., and Geradin, M. (1988). “A beam finite element non‐linear theory with finite rotations.” Int. J. Num. Methods Engrg., 26(11), 2403–2438.
18.
Chen, G., and Trahair, N. S. (1992). “Inelastic nonuniform torsion of steel I‐beams.” J. Constr. Steel Res., 23(1–3), 189–207.
19.
Chen, H., and Blandford, G. (1989). “A C0 finite element formulation for thin‐walled beams.” Int. J. Num. Methods in Engrg., 28(11), 2239–2235.
20.
Chen, H., and Blandford, G. (1991). “Thin‐walled space frames. I: Large deformation analysis theory.” J. Struct. Engrg., ASCE, 117(8), 2499–2520.
21.
Conci, A., and Gattass, M. (1990). “Natural approach for thin‐walled beam‐columns with elastic‐plasticity.” Int. J. Num. Methods in Engrg., 29(8), 1653–1679.
22.
Crisfield, M. A. (1981). “A fast incremental/iterative solution procedure that handles snap‐through.” Comp. and Struct., 13(1), 55–62.
23.
Crisfield, M. A. (1990). “A consistent co‐rotational formulation for non‐linear, three‐dimensional, beam‐elements.” Comp. Methods Appl. Engrg., 81, 131–150.
24.
El‐Khenfas, M. A., and Nethercot, D. A. (1989). “Ultimate strength analysis of steel beam‐columns subject to biaxial bending and torsion.” Res. Mechanica, 28, 307–360.
25.
Epstein, M., and Murray, D. W. (1976). “Three‐dimensional large deformation analysis of thin‐walled beams.” Int. J. Solids Struct., 12, 867–876.
26.
Gattass, M., and Abel, J. F. (1987). “Equilibrium considerations of the updated Lagrangian formulation of beam‐columns with natural concepts.” Int. J. Num. Methods in Engrg., 24(11), 2119–2141.
27.
Gellin, S., Lee, G. C., and Chern, J. H. (1983). “A finite element model for thin‐walled members.” Comp. and Struct., 19(1), 59–71.
28.
Hasegawa, A., Liyanage, K. K., and Nishino, F. (1986). “Spatial instability and nonlinear finite displacement analysis of thin‐walled members and frames.” J. of Faculty Engrg., Univ. Tokyo, Tokyo, Japan, 38(4), 19–78.
29.
Kane, T. R., Ryan, R. R., and Banerjee, A. K. (1987). “Dynamics of a cantilever beam attached to a moving base.” J. Guidance, Control, and Dynamics, 10, 139–151.
30.
Kitipornchai, S., and Chan, S. L. (1990). “Stability and nonlinear finite element analysis.” Finite element applications to thin walled structures, J. W. Bull, ed., Elsevier Applied Science, London, England, 89–130.
31.
May, I. M., and Al‐shaarbaf, I. A. S. (1989). “Elasto‐plastic analysis of torsion using a three‐dimensional finite element model.” Comp. and Struct., 33(3), 667–678.
32.
Meek, J. L., and Lin, W. J. (1990). “Geometric and material nonlinear analysis of thin‐walled beam‐columns.” J. Struct. Engrg., ASCE, 116(6), 1473–1490.
33.
Mottershead, J. E. (1988). “Geometric stiffness of thin‐walled open section beams using a semiloof beam formulation.” Int. Num. Methods Engrg., 26(12), 2267–2278.
34.
Navak, G. C., and Zienkiewicz, O. C. (1972). “Elasto‐plastic stress analysis. A generalization for various constitutive relations including strain softening.” Int. J. Num. Methods Engrg., 5(1), 113–135.
35.
Nour‐Omid, B., and Rankin, C. C. (1991). “Finite rotation analysis and consistent linearization using projectors.” Comp. Methods Appl. Engrg., 93, 353–384.
36.
Nyssen, C. (1981). “An efficient and accurate iterative method, allowing large incremental steps, to solve elasto‐plastic problems.” Comp. and Struct., 13(1), 63–71.
37.
Pi, Y. L., and Trahair, N. S. (1994). “Nonlinear inelastic analysis of steel beam‐columns. II: Applications.” J. Struct. Engrg., ASCE, 120(7), 2062–2085.
38.
Pietraszkiewicz, W., and Badur, J. (1983). “Finite rotations in the description of continuum deformation.” Int. J. Engrg. Sci., 21(9), 1097–1115.
39.
Rajasekaran, S. (1977). “Finite element method for plastic beam‐columns.” Theory of beam‐columns, Vol. 2, Space behaviour and design, W. F. Chen and T. Atsuta, eds., McGraw‐Hill, Inc., New York, N.Y., 539–608.
40.
Reissner, E. (1985). “A variational analysis of small finite deformation of pretwisted elastic beams.” Int. J. Solids Struct., 21(7), 773–779.
41.
Rosen, A., and Friedmann, P. (1979). “The nonlinear behavior of elastic slender straight beams undergoing small strains and moderate rotations.” J. Appl. Mech., 46(1), 161–168.
42.
Saleep, A. F., and Chen, W. F. (1981). “Elastic‐plastic large displacement analysis of pipes.” J. Struct. Engrg., ASCE, 107(4), 605–626.
43.
Sandhu, J. S., Stevens, K. A., and Davies, G. A. O. (1990). “A 3‐D, co‐rotational, curved and twisted beam element.” Comp. Struct., 35(1), 69–79.
44.
Schreyer, H. L., Kulak, R. F., and Kramer, J. M. (1979). “Accurate numerical solutions for elastic‐plastic models.” J. Pressure Vessel Tech., 101(3), 226–234.
45.
Simo, J. C., and Taylor, R. L. (1985). “Consistent tangent operators for rate‐independent elastoplasticity.” Comp. Methods Appl. Engrg., 48, 101–118.
46.
Simo, J. C., and Taylor, R. L. (1986). “A return mapping algorithm for plane stress elastoplasticity.” Int. J. Num. Methods Engrg., 22(6), 649–670.
47.
Simo, J. C., and Vu‐Quoc, L. (1986). “A three‐dimensional finite‐strain rod model. Part II: computation aspects.” Comp. Methods Appl. Engrg., 58, 76–116.
48.
Simo, J. C., and Vu‐Quoc, L. (1987). “The role of non‐linear theories in transient dynamic analysis of flexible structures.” J. Sound Vibration, 119(3), 487–508.
49.
Simo, J. C., and Vu‐Quoc, L. (1991). “A geometrically‐exact rod model incorporating shear and torsion‐warping deformation.” Int. J. Solids Struct., 27(3), 371–393.
50.
Sugimoto, H. and Chen, W. F. (1985). “Inelastic post‐buckling behaviour of tubular members.” J. Struct. Engrg., ASCE, 111(9), 1965–1978.
51.
Teng, J. G., and Rotter, J. M. (1989). “Elastic‐plastic large deflection analysis of axisymmetric shells.” Comp. and Struct., 31(2), 211–233.
52.
Timoshenko, S., and Gere, J. M. (1961). Theory of elastic stability. McGraw‐Hill, New York, N.Y.
53.
van Erp, G. M., Menken, C. M., and Veldpaus, F. E. (1988). “The non‐linear flexural‐torsional behaviour of straight slender elastic beams with arbitrary cross sections.” Thin‐Walled Structures, 6(5), 385–404.
54.
Vlasov, V. Z. (1961). Thin‐walled elastic beams. Israel Program for Scientific Translation, Jerusalem, Israel.
55.
Wunderlich, W., Obrecht, H., and Schrödter, V., (1986). “Nonlinear analysis and elasto‐plastic load‐carrying behaviour of thin‐walled spatial beam structures with warping constraints.” Int. J. Num. Methods Engrg., 22(6), 671–695.
56.
Yang, Y.‐B., and McGuire, W. (1986). “Stiffness matrix for geometric nonlinear analysis.” J. Struct. Engrg., ASCE, 112(4), 853–877.
Information & Authors
Information
Published In
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Mar 5, 1993
Published online: Jul 1, 1994
Published in print: Jul 1994
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.