Engineering Transactions, 44, 2, pp. 229-251, 1996

Ultimate Load and Postfailure Behaviour of Box-Section Beams Under Pure Bending

M. Kotełko
Łódź University of Technology, Łódź
Poland

In this work the load-carrying capacity and plastic collapse mechanisms of thin-walled, rectangular and trapezoidal box-section beams subject to pure bending are investigated. The postbuckling elastic analysis is carried out using the effective width approach while the plastic buckling load is evaluated using the total strain theory. The failure of the beam is assumed to be initiated by buckling in a flange so that the flange mechanism of failure is expected. The analysis of plastic collapse mechanisms is carried out using basic assumptions of the rigid-plastic theory. The true (kinematically permissible) plastic mechanisms are taken into consideration. Three different theoretical solutions concerning the plastic moment capacity at a yield line are taken into account. Corresponding formulae for plastic moment at yield lines situated both in flanges and webs of the thin-walled beam are evaluated. The energy method is used in order to evaluate the bending moment capacity in terms of rotation angle of a global plastic hinge. The total energy of plastic deformation absorbed during rotation of the global plastic hinge is formulated and the bending moment is derived from this formula. For both rectangular and trapezoidal cross-section beams the idealized geometry of a global plastic hinge is based on the results of experimental tests. In the case of elastic buckling, the ultimate bending moment is determined approximately at the intersection point of two curves representing the bending moment in terms of the rotation angle: the postbuckling curve based upon approximate nonlinear analysis and the post-failure curve derived from the collapse mechanism analysis. Bending moment - rotation angle diagrams based on numerical results of the theoretical analysis, are compared with graphs recorded during experimental four-point tests.

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References

A.S. VOLMIR, Stability of deformable media [in Russian], Nauka, Moskva 1967.

Post-buckling and load carrying capacity of thin-walled girders of flat walls [in Polish], M. KRÓLAK [Ed.], PWN, Warszawa-Łódź 1990.

M. KRÓLAK and Z. KOŁAKOWSKI, Stability and post-buckling of thin-walled, box­section girders subject to bending and compression (tension) [in Polish], Arch. Bud. Maszyn, 28, 2, 1981.

W.T. KOITER and M. PIGNATARO, A general theory for the interaction between local and overall buckling of stiffened panels, Delft University, WTHD Report No 556, 1976.

Z. KOŁAKOWSKI, Interactive buckling of thin-walled, elastic structures [in Polish], Zesz. Nauk. Politech. Łódzkiej, No 653, Łódź 1992.

J. RHODES, Effective widths in plate buckling; contribution to: Developments in thin-walled structure-1, J. RHODES and A.C. WALKER [Eds.], Applied Science Publishers, London 1981.

R. GRĄDZKI and K. KOWAL-MICHALSKA, Post-buckling behaviour of orthotropic compressed columns in elastic and elasto-plastic range [in Polish], Proc. of VIIth Symposium of Stability of Structures, Bielsko-Biała 1994.

D. KECMAN, Bending collapse of rectangular and square section tubes, Int. J. Mech. Sci., 25, 9-10, 1983.

K. W. SIN, The collapse behaviour of thin-walled sections, Ph.D. Thesis, Dept. of Mech. Engng., Univ. of Strathclyde, Glasgow UK 1985.

M. KOTEŁKO and M. KRÓLAK, Collapse behaviour of triangular cross-section girders subject to pure bending, Thin-Walled Struct., 15, 2, Elsevier Appl. Sci., 1993.

N.W. MURRAY, Introduction to the theory of thin-walled structures, Clarendon Press, Oxford 1986.

M. KOTEŁKO, Comparative theoretical and experimental analysis of collapse mechanisms in box-section girders [in Polish], Proc. of VIIth Symposium of Stability of Structures, Bielsko-Biała 1994.

M. KOTEŁKO and VYNX T.H. LIM, The large deflection behaviour of thin-walled trapezoidal cross-section beams under pure bending [in Polish], Proc. of VIIth Conf. "Developments in Heavy Duty Machines Design", Zakopane 1994.

M. KOTEŁKO, J. RHODES and VYNX T.H. LIM, Post-failure behaviour of box-section beams under pure bending (an experimental study) [accepted to be published in Thin-Walled Struct., Elsevier Appl. Sci.].

X.L. ZHAO and G.J. HANCOCK, A theoretical analysis of the plastic moment capacity of an inclined yield line under axial force, Thin-Walled Struct., 15, 3, Elsevier Appl. Sci., 1993.

M. KOTEŁKO and M. KRÓLAK, An approximate method of load-carrying capacity evaluation in thin-walled beams subject to bending [in Polish], Proc. of VIth Conf. "Heavy Duty Machines - Developments in Design, Operating and Investigation", Zakopane 1993.

Z. KOŁAKOWSKI, Influence of modification of boundary conditions on load-carrying capacity in thin-walled columns in the second order approximation, Int. J. Solids and Struct., 30, 19, 1993.

M. KOTEŁKO and Z. KOŁAKOWSKI, Post-buckling and collapse behaviour of thin­walled beam-columns, Proc. of Int. Conf. on Lightweight Struct. in Civil Engng. (LSCE'95), Warszawa 1995.




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