ISSN 0021-8944, Journal of Applied Mechanics and Technical Physics, 2018, Vol. 59, No. 1, pp. 176–184.
Pleiades Publishing, Ltd., 2018.
Original Russian Text
Ch.K. Rao, L.B. Rao.
TORSIONAL POST-BUCKLING OF A SIMPLY SUPPORTED
THIN-WALLED OPEN-SECTION BEAM RESTING
ON A TWO-PARAMETER FOUNDATION
UDC 539.3; 624
Ch. K. Rao
and L. B. Rao
Abstract: The problem of the post-buckling response of a simply supported thin-walled beam
subjected to an axial compressive load and supported by the Winkler–Pasternak foundation is studied
in this paper. The strains are assumed to be small and elastic. The shear deformations and the
in-plane cross-sectional deformations are assumed to be negligible. The post-buckling paths of the
simply supported beam are determined for diﬀerent values of the Winkler and Pasternak stiﬀness
parameters. Bifurcation points are found.
Keywords: beam, open section, post-buckling, warping, Winkler–Pasternak foundation.
The study of the post-buckling behaviour of prismatic thin-walled open-section beams has wide-ranging
applications in automotive, marine, civil, and aircraft structures. Some base-frame structures of rotating machinery
also consist of thin-walled open-section beams.
Under some critical loading conditions, these beams undergo either pure torsional or coupled ﬂexural-
torsional buckling, which poses severe design problems in various industrial applications.
Linear torsional buckling problems were widely studied, and the results for many cases were presented
in [1, 2]. However, it is impossible to determine the post-buckling behavior in the linear formulation.
The nonlinear behaviour of thin-walled beams in uniform torsion was ﬁrst investigated by Young, who
considered circular cross-sections. The results of that study were described in . The related problem of torsional
stiﬀness of narrow rectangular sections under axial tension was examined by Buckley . Cullimore  studied the
behaviour of thin-walled I and Z sections. A more accurate theory of nonlinear nonuniform torsion of thin-walled
open-section beams was presented by Ghobarah and Tso [6, 7], who used the principle of the minimum potential
energy and took into account large torsional deformations under general loading and boundary conditions.
The nonlinear torsional behaviour of thin-walled beams was studied in much detail in [8–13]. Grimaldi and
Pignataro  investigated the post-buckling behavior of thin-walled open cross-section compression members by
using the general nonlinear theory of elastic stability.
However, in all those studies, the eﬀect of a continuous elastic foundation was not considered. Kameswara
Rao et al. [15, 16] studied the eﬀect of the Winkler-type elastic foundation on the linear torsional stability of
thin-walled open-section beams [17, 18], but its eﬀect on the post-buckling behaviour was not analyzed in [15, 16].
Kameswara Rao and Mirza  investigated the post-buckling response of a thin-walled beam subjected to an axial
compressive load and supported by the Winkler foundation. Simao  presented a post-buckling bifurcational
Nalla Narsimha Reddy Engineering College, Chowdariguda, 500088 India; email@example.com.
of Mechanical and Building Sciences, VIT University, Chennai, 600127 India; bhaskarbabu
lated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 204–213, January–February, 2018.
Original article submitted August 15, 2016; revision submitted December 27, 2016.
2018 by Pleiades Publishing, Ltd.