Second order moments in torsion members

2004

Computers & Structures

The paper describes the attributes that should be possessed by a benchmark example for verifying the beam elements used to carry out 3D linear buckling analysis and 3D second-order elastic analysis of steel frames. Based on the attributes described, the paper proposes a suite of benchmark examples selected from the literature. The necessary features of a beam element required to pass the proposed benchmark problems are given, and beam elements that possess these features are cited. The paper also explains the merits of linear buckling analysis examples, and provides a commentary on two well-known examples.

Section: Geometrically Nonlinear Analysis Of An Angle Cantilever Undementioning

confidence: 89%

“…In order to account for this effect, the third order terms of the twist rate must be included in the element formulation [35,40,[43][44]. The ability to model this effect is of a higher order than the ability to predict the flexural buckling of a torsion member [42].…”

Section: Geometrically Nonlinear Analysis Of An Angle Cantilever Undementioning

confidence: 99%

Beam element verification for 3D elastic steel frame analysis

2004

Computers & Structures

“…On the other hand, Teh & Clarke (1997) and Trahair & Teh (2001) point out that, contrary to the popular belief among computational mechanics researchers, a conservative moment needs not be made up of forces fixed in direction. Teh & Clarke (1997) propose a new definition of conservative moment that, within a certain range of rotations, behaves like a follower (tangential) moment.…”

Section: Work-conjugacy Between Bending Moments and Rotation Parametersmentioning

confidence: 92%

“…If this restriction is removed, then there should be no loss of joint equilibrium as the plane of the torque T in Fig. 7 rotates fully with the cross-section (Teh & Clarke 1997, Trahair & Teh 2001.…”

Section: Other Intricate Issues Associated With Spatial Rotationsmentioning

confidence: 99%

Spatial Rotation Kinematics and Flexural–Torsional Buckling

2005

J. Eng. Mech.

Abstract:This paper aims to clarify the intricacies of spatial rotation kinematics as applied to 3D stability analysis of metal framed structures with minimal mathematical abstraction. In particular, it discusses the ability of the kinematic relationships traditionally used for a spatial Euler-Bernoulli beam element, which are expressed in terms of transverse displacement derivatives, to detect the flexural-torsional instability of a cantilever and of an L-shaped frame. The distinction between transverse displacement derivatives and vectorial rotations is illustrated graphically. The paper also discusses the symmetry and asymmetry of tangent stiffness matrices derived for 3D beam elements, and the concepts of semi-tangential moments and semi-tangential rotations. Finally, the fact that the so-called vectorial rotations are independent mathematical variables are pointed out.

“…Fortunately, the spatial cubic beam element has been shown to be versatile for detecting the torsional buckling of a column [25], the flexuraltorsional buckling of the members of a "plane" frame due transverse shear forces [63], the flexural-torsional buckling of the members of a spatial frame due to transferred bending moments [25], the flexural-torsional buckling of a mono-symmetric column [62], and the flexural buckling of a torsion member [64]. On the other hand, Hancock [17] pointed out that no stability functions had been developed for flexural-torsional instability.…”

Section: Three-dimensional Analysis and "Out-of-plane" Bucklingmentioning

confidence: 99%

Cubic beam elements in practical analysis and design of steel frames

2001

Engineering Structures

This paper discusses various issues in the use of cubic beam elements for computer structural analysis/design of steel frames. It is pointed out that the concern expressed in recent literature regarding the number of cubic elements required to model a steel member is not justified, and that the inaccuracy of one cubic element in Euler buckling analysis of a simply supported column is largely irrelevant to the second-order elastic analysis/design or advanced analysis of steel frames. The sources of inaccuracy of the cubic element are elucidated. It is also explained that the plastic-zone analysis method is not so inefficient as was previously believed. The spatial cubic element is shown to be capable of accurately accounting for the coupling between axial, flexural and torsional deformation modes. It is concluded that for the purposes of second-order elastic analysis/design and advanced analysis of 2D and 3D steel frames, the well-documented cubic element is a versatile and efficient choice.