Plastic-Zone Analysis of 3D Steel Frames Using Beam Elements

Teh, Lip H.; Clarke, Murray J.

doi:10.1061/(asce)0733-9445(1999)125:11(1328)

Cited by 83 publications

(34 citation statements)

References 40 publications

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“…In the literature, the following kinematic relationships of a spatial Euler-Bernoulli beam are commonly used (Argyris et al 1979, Teh & Clarke 1999a Pi & Bradford (2001) state that the use of the kinematic relationships (1)-(3) in formulating the energy equation leads to a beam element that is unable to predict the correct flexuraltorsional buckling load of a beam subjected to non-uniform bending moments (and therefore, subjected to transverse shear forces). Pi & Bradford (2001) also suggest that the researchers who use such kinematic relationships, and hence implicitly use the "small rotation matrix" R 1 , have apparently noted the problem and subsequently modified their finite element by adding a term which is the work done by the transverse shear forces to their energy equations.…”

Section: Kinematic Relationships In the Energy Equation For Flexuraltmentioning

confidence: 99%

Spatial Rotation Kinematics and Flexural–Torsional Buckling

Teh

2005

J. Eng. Mech.

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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.

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Section: Kinematic Relationships In the Energy Equation For Flexuraltmentioning

confidence: 99%

Spatial Rotation Kinematics and Flexural–Torsional Buckling

Teh

2005

J. Eng. Mech.

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“…Such a procedure ignores the fact that the cubic element is a displacement-based finite element which does not necessarily satisfy the static boundary conditions [1]. As recently explained by Teh & Clarke [53], the proper force recovery procedure of the plastic-zone cubic element involves integration over the volume of the element which results in satisfaction of the principle of virtual work.…”

Section: Second-order Inelastic Analysis and Advanced Analysismentioning

confidence: 99%

“…For this purpose, the cubic beam element has been demonstrated to be simple, accurate and efficient [53,[56][57]. In general, only three cubic elements are required to model a storey column, and four or five cubic elements are sufficient to model a fixed base column accurately [46,53].…”

Section: Second-order Inelastic Analysis and Advanced Analysismentioning

confidence: 99%

“…At present, advanced analysis/design of steel frames is restricted by design codes to planar frames composed of compact members that are not subjected to lateral buckling [44]. Notwithstanding this formal restriction, it appears that at least for space frames composed of compact tubular sections, advanced analysis based on the plastic-zone approach is now practically feasible [47,53,59]. …”

Section: Second-order Inelastic Analysis and Advanced Analysismentioning

confidence: 99%

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Cubic beam elements in practical analysis and design of steel frames

Teh

2001

Engineering Structures

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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.

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“…In addition, strongly non-linear constitutive behaviours can be difficult to handle using displacement based solution strategies. In extreme cases, nodal forces cannot be determined accurately by direct integration over the whole element length and cross-section [10,11] because the element deformation is too complex to model using cubic Hermitian shape functions, especially when the inelastic deformation gradient is very steep. In such cases the equilibrium equations will not be fully satisfied [12].…”

Section: Introductionmentioning

confidence: 99%