Beam element verification for 3D elastic steel frame analysis

In the past decade, there has been more widespread
use of 3D frame analysis programs in civil engineering
design offices to determine the buckling loads and the
member forces of steel framed structures. In most cases,
the use of 3D analysis has been necessitated by the
topology of the designed structure that does not permit
the use of 2D analysis, such as in the case of a sports
stadium. More recently, however, 3D frame analyses
have also been carried out on multi-storey multi-bay
rectangular frames such as high-rise storage rack frames.
The fact that this type of steel structure is generally
composed of open sections rather than tubular sections,
the latter normally used in space roof trusses and offshore
structures, has important implications for the
frame stability that are not generally well understood by
practising engineers. In design practice, either linear
buckling analysis or second-order elastic analysis is
performed to assess the frame stability.
The elastic buckling behaviour and the second-order
effects due to geometric nonlinearity of steel plane
frames are well understood and well documented in the
literature [1–4]. Commercial frame analysis programs
that can handle most or all of these two stability aspects
of planar (2D) steel structures have also been available
for many years. For the purpose of verifying a 2D beam
element or a 2D frame analysis program, there are many
well established and well defined benchmark examples
[5–7]. However, neither situation is true for 3D beam
elements or 3D frame analysis programs. Although 3D
linear elastic analysis is a fairly straightforward extension
of 2D analysis, at the member level there may be 3D
couplings between axial, flexural and torsional deformation
modes that control the buckling behaviour of
open sections. The comment of Springfield [8] that few
commercial frame analysis/design programs could deal
with out-of-plane buckling of beams or beam-columns
by other than empirical means is still largely true today,
except for the more expensive general-purpose finite
element analysis packages such as ADINA [9] and
ABAQUS [10].
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