scholarly journals Buckling length of a frame member

2018 ◽  
Vol 51 (2) ◽  
pp. 49-61
Author(s):  
Teemu Tiainen ◽  
Markku Heinisuo
Keyword(s):  
Stiffness Matrix ◽  
Strain Energy ◽  
Integrated Design ◽  
Buckling Mode ◽  
Frame Design ◽  
Basic Task ◽  
Geometric Stiffness ◽  
Definition Of ◽  
Buckling Length ◽  
Frame Member

In steel frame design, the definition of buckling lengths of members is a basic task. Computers can be used to calculate the eigenmodes and corresponding eigenvalues for the frames and using these the buckling lengths of the members can be defined using Euler's equation. However, it is not always easy to say, which eigenmode should be used for the definition of the buckling length of a specific member. Conservatively, the lowest positive eigenvalue can be used for all members. In this paper, methods to define the buckling length of a specific member is presented. For this assessment, two ideas are considered. The first one uses geometric stiffness matrix locally and the other one uses strain energy measures to identify members taking part in a buckling mode. The behaviour of the methods is shown in several numerical examples. Both methods can be implemented into automated frame design, removing one big gap in the integrated design. This is essential when optimization of frames is considered.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

A Study on the Simulation of Flexible Link Mechanics Based on FEM

1997 ◽  
Author(s):  
Koichi Honke ◽  
Yoshio Inoue ◽  
Eiko Hirooka ◽  
Naoki Sugano
Keyword(s):  
Stiffness Matrix ◽  
Large Displacement ◽  
Dynamics Analysis ◽  
Flexible Link ◽  
Finite Rotation ◽  
Fem Model ◽  
Elastic Vibrations ◽  
Link Structure ◽  
Geometric Stiffness ◽  
Inertia Matrix

Abstract The dynamics analysis of link structure, including elastic vibrations, is presented. The two nodes element including large displacement is developed. This element is based on the theory of finite rotation, and includes geometric stiffness. The stiffness matrix and the inertia matrix are obtained from the FEM model by the theory of Guyan’s reduction including large displacement motion. In this paper, we explain the theory of this element and show some examples of analysis.

Global Buckling of Frames with Laced Compression Members

2016 ◽  
Vol 837 ◽  
pp. 103-108 ◽  
Author(s):  
Michal Kovac ◽  
Zsuzsanna Vanik
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Engineering Practice ◽  
Buckling Mode ◽  
Column Method ◽  
Global Buckling ◽  
Second Order Effects ◽  
Buckling Length ◽  
Simplified Procedure

The planar frames whose members consist of a laced built-up members are often used in civil engineering practice. For chords of these structures the 1st order theory internal forces and the assessment by equivalent column method are mostly used. In the equivalent column method the buckling length according to the global buckling mode of the structures should be used. If the distance between neighboring nodes is used as the buckling length of the chord, which is the common case, the second order effects with only the bow imperfections between nodes are taken into account in the equivalent column method. For frames sensitive to buckling in a sway mode the second order effects on structures with initial sway imperfection should be taken into account. Therefore, also in frames with the laced compression columns, where the effects of additional sway deformation cause additional normal forces in the chords, the sway imperfection should be applied and the second order in frame analysis should be performed to check these additive forces. This paper deals with the simplified procedure how to evaluate additive forces due to second order effects on the structure with the global sway imperfection.

A variational definition of the strain energy for an elastic string

1991 ◽  
Vol 25 (2) ◽  
pp. 137-148 ◽  
Author(s):  
Emilio Acerbi ◽  
Giuseppe Buttazzo ◽  
Danilo Percivale
Keyword(s):  
Strain Energy ◽  
Elastic String ◽  
Definition Of
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