Geometric stiffness matrix for space frames

Spillers, William R.

doi:10.1016/0045-7949(90)90171-w

Cited by 30 publications

(18 citation statements)

References 9 publications

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“…The local member force-deformation relationships are based on the beam-column approach, and the change in member chord lengths caused by axial strain and flexural bowing is taken into account [6,7]. An Eulerian formulation [8,9] which takes into consideration the effects of large joint rotations with finite rotation is used. And the joint element is added to that element by the static condensation process [10,11] for the semi-rigid connection condition.…”

Section: Semi-rigid Elasto-plastic Beam-column Elementmentioning

confidence: 99%

“…For the case of the stresserection process analysis of Strarch frame or any other space frames with finite rotations, it is necessary to consider the non-commutative nature of rotations in three dimensions which makes these space frames more difficult to analyze than trusses or plane frames in nonlinear analysis. In this paper, we used the previous work of Spillers [8] and Levy and Spillers [9] for the Eulerian finite rotation to calculate the relative and rigid body rotation of beam-column. We briefly described as follows.…”

Section: Eulerian Formulation For Finite Rotationmentioning

confidence: 99%

“…Thus, a 3D rotation can be represented by a vector-like entity, but such entities cannot be added like vectors. Furthermore, it is assumed that these vector-like entities possess Taylor series expansions whose increments are the small rotation vectors of linear structural analysis [8,9]. To separate the large rigid body rotation of a member from its relative rotation, which is assumed to be small, an Eulerian or local member coordinate system was used, as shown in Fig.…”

Section: Eulerian Formulation For Finite Rotationmentioning

confidence: 99%

“…Given these circumstances, an analysis method for the stresserection process for the Strarch system is developed using a large deformational elasto-plastic beam-column element [6,7], considering Eulerian finite rotation [8,9] and various joint connection properties of rigid, semi-rigid and hinged joints [10,11] and using an explicit quasistatic dynamic relaxation method (DRM) [12][13][14][15][16][17][18][19]. Using this method, the stress-erection process for a Strarch structure constructed in Incheon, Korea, shown in Fig.…”

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confidence: 99%

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Analysis of the stress-erection process of Strarch frames considering the joint connection properties

Lee

Han

2014

Journal of Constructional Steel Research

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Section: Semi-rigid Elasto-plastic Beam-column Elementmentioning

confidence: 99%

Section: Eulerian Formulation For Finite Rotationmentioning

confidence: 99%

Section: Eulerian Formulation For Finite Rotationmentioning

confidence: 99%

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confidence: 99%

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Analysis of the stress-erection process of Strarch frames considering the joint connection properties

Lee

Han

2014

Journal of Constructional Steel Research

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“…One can mention here, e.g., the works of Livesley (1956), Livesley and Chandler (1956), Halldorsson and Wang (1968), Majid (1972), Williams (1981) and Ekhande et al (1989) in connection with linear stability analysis and those of Majid (1972), Atluri (1985, 1986), Ekhande et al (1989) and Chandra et al (1990) in connection with nonlinear stability analysis using an exact FEM based on displacement functions which are the exact solutions of the governing equations of member stability behavior. One can also mention here, e.g., the works of Gallagher and Padlog (1963) and Hartz (1965) in connection with linear stability analysis and those of Hill et al (1989) and Spillers (1990) in connection with non linear stability analysis using the approximate or conventional FEM based on polynomial type displacement functions. Beskos (1977) presented a comparison study between the exact and approximate or conventional FEM with respect to their accuracy, while Manolis and Beskos (1983) discussed the internal axial force distribution effect both on the basis of plane trusses and frames in the framework of linear elastic stability analysis of plane trusses and frames.…”

Section: Introductionmentioning

confidence: 99%

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

Bazeos¹,

Xykis²

2002

Computational Mechanics

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A finite element method is presented for the determination of the elastic buckling load of three-dimensional trusses and frames with rigid joints. The beam element stiffness matrix is constructed on the basis of the exact solution of the governing equations describing the coupled flexural-torsional buckling behaviour of a threedimensional beam with an open thin-walled section in the framework of a small deformation theory. Large deformation effects are taken into account approximately through consideration of P À D effects. The structural stiffness matrix is obtained by an appropriate superposition of the various element stiffness matrices. The axial force distribution in the members is obtained iteratively for every value of the externally applied loading and the vanishing of the determinant of the structural stiffness matrix is the criterion used to numerically determine the elastic buckling load of the structure. The effect of initial member imperfections is also included in the formulation. Comparisons of accuracy and efficiency of the present exact finite element method against the conventional approximate finite element method are made. Cases where the axial force distribution determination can be done without iterations are also identified. The effect of neglecting the warping stiffness of some mono-symmetric sections is also investigated. Numerical examples involving simple and complex three-dimensional trusses and frames are presented to illustrate the method and demonstrate its merits. IntroductionStability analysis of steel trusses and frames is a very important aspect of analysis and design of these structures. Today, all major steel design codes include the use of second-order elastic analysis through which a stability analysis can also be accomplished (Galambos 1998).Second-order analysis in the elastic region is usually done approximately by considering P À d effects at the element level and P À D effects at the structure level. Thus the effect of the axial compressive force on the member flexure and the effect of the vertical load on the laterally displaced structure, respectively, can be taken into account. An accurate second-order elastic analysis of steel trusses and frames including buckling load determination and taking into account flexural-axial coupling as well as that of large deflections can only be done by numerical methods such as the finite element method (FEM).The FEM has been successfully used for the elastic stability analysis of beam-columns and plane and space trusses and frames composed of members with doublysymmetric cross-section in the framework of either a linear analysis involving small deformations (where only P À d effects are taken into account) or a nonlinear analysis involving large deformations (where in addition P À D effects are taken into account). One can mention here, e.g., the works of Livesley (in connection with nonlinear stability analysis using an exact FEM based on displacement functions which are the exact solutions of the governing equations of member sta...

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A comparison of simulated annealing and genetic algorithm for optimum design of nonlinear steel space frames

Degertekin

2007

Struct Multidisc Optim

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Geometric stiffness matrix for space frames

Cited by 30 publications

References 9 publications

Analysis of the stress-erection process of Strarch frames considering the joint connection properties

Analysis of the stress-erection process of Strarch frames considering the joint connection properties

Elastic buckling analysis of 3-D trusses and frames with thin-walled members

A comparison of simulated annealing and genetic algorithm for optimum design of nonlinear steel space frames

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