In this paper, two types of steel frames, steel frame without side sway permission and another with side sway permission are created in Abaqus with 10 multiple slenderness ratio of the columns by changing the length every time starting from 1 M and ending with 10 M length of the columns, Twenty models of steel frames with single story and single bay were created, the models are with the same 2D dimensions and material properties, the cross section of the steel is (0.5*0.5) M ,and the supports are fixed, two equal forces P= 1000 N are exerted on the frames in the position mentioned in fig 6, a beam section was defined for the frame integrated before analysis with Young modulus of elasticity E=1*107 N/M2 , and shear modulus G = 3.8*106 N/M2 and poisons ratio ν = 0.3.
A linear perturbation step is created for buckling and 10 eigenvalues are requested for analysis, a standard quadratic beam element type is generated with global seeding of 0.6, and 20 Jobs are created for every situation and conclusions have been obtained, the critical buckling loads of the frames fall in the ranges between the Euler loads forms which has been proved for each type of frames and this scientific approach was verified in this research, in addition to that the relation between the length of the column and the eigenvalues that represent the critical loads of buckling verified, and the simulations of the mode shapes of buckling of the steel frames were identified adopting finite element analysis which shows the amount of loads necessary to reach each mode shape of buckling for each type of steel frames mentioned before.
Table of Contents
Introduction to buckling
Stability concept
Euler Column
Critical Buckling Load
Buckling of frames
Buckling strength
Buckling modes of frames
1- Symmetric buckling
2- Side sway buckling
Conclusions and recommendations
Objectives and Topics
This research aims to analyze the buckling critical loads of single-story, single-bay steel frames using the finite element method. By comparing two types of frames—those with and without side sway permission—across ten different column length configurations, the study seeks to verify the relationship between column slenderness ratios, critical buckling loads, and mode shapes.
- Finite element modeling of steel frames using Abaqus.
- Investigation of critical buckling loads for varying slenderness ratios.
- Comparative analysis of frames with and without side sway permission.
- Identification of buckling mode shapes and their corresponding eigenvalues.
- Validation of theoretical Euler load calculations against numerical simulation results.
Excerpt from the Book
Introduction to buckling
If a beam element is under a compressive load and its length if the orders of magnitude are larger than either of its other dimensions such a beam is called a column. Due to its size its axial displacement is going to be very small compared to its lateral deflection called buckling.
Slender or thin‐walled components under compressive stress are susceptible to buckling and is called “Euler buckling” where a long slender member subject to a compressive force moves lateral to the direction of that force, as illustrated in Figure 1. The force, F, necessary to cause such a buckling motion will vary by a factor of four depending only on how the two ends are restrained. Therefore, buckling studies are much more sensitive to the component restraints that in a normal stress analysis. The theoretical Euler solution will lead to infinite forces in very short columns, and that clearly exceeds the allowed material stress. Thus in practice, Euler column buckling can only be applied in certain regions and empirical transition equations are required for intermediate length columns. For very long columns the loss of stiffness occurs at stresses far below the material failure.
Quite often the buckling of column can lead to sudden and dramatic failure. And as a result, special attention must be given to design of column so that they can safely support the loads.
Summary of Chapters
Introduction to buckling: Explains the fundamental mechanics of buckling in columns and the transition from stable structures to failure under compressive loads.
Stability concept: Discusses the theoretical background of equilibrium states for compressed bars and how external influences affect stability.
Euler Column: Details the idealized assumptions and boundary conditions required to mathematically derive the Euler buckling load.
Critical Buckling Load: Defines the mathematical relationship between eigenvalues, eigenvectors, and the point at which a structure loses its ability to carry load.
Buckling of frames: Categorizes frame behavior based on side sway constraints and introduces the structural mechanics involved in frame buckling.
Buckling strength: Analyzes the influence of individual column buckling within a story and the development of shear resistance in exterior columns.
Buckling modes of frames: Provides specific analysis and results for symmetric and side sway buckling modes using numerical simulations.
Conclusions and recommendations: Summarizes the findings regarding eigenvalue interpretation, the validation of theoretical values, and proposes future research directions.
Keywords
Euler column, stiffness matrix, critical buckling load, eigenvalues, eigenvectors, side sway, finite element analysis, slenderness ratio, buckling modes, frame stability, structural mechanics, compression.
Frequently Asked Questions
What is the primary focus of this research?
The research focuses on the finite element analysis of buckling critical loads in single-story steel frames with varying slenderness ratios.
Which specific structural components are analyzed?
The study examines single-story, single-bay steel frames under different configurations of column length to determine their buckling behavior.
What is the main objective of the study?
The goal is to determine and verify the critical buckling loads and identify mode shapes for steel frames with and without side sway permission.
Which scientific method is utilized for this analysis?
The research employs the finite element method, specifically utilizing Abaqus software to simulate buckling steps and extract eigenvalues and eigenvectors.
What does the main body of the paper cover?
The main body details the theoretical background of buckling, the specific modeling assumptions, simulation results for different frame types, and visual representations of buckling modes.
Which keywords characterize this work?
Key terms include Euler column, stiffness matrix, buckling load, finite element analysis, and slenderness ratio.
How does side sway permission affect frame buckling?
Frames with side sway permission exhibit different critical buckling loads compared to those where side sway is prevented, requiring distinct structural considerations.
What is the significance of the eigenvalues in this paper?
Eigenvalues represent the critical coefficients which, when multiplied by the applied load, indicate the threshold for structural instability in a specific mode shape.
What conclusions were drawn regarding column length?
The study concluded that increasing the slenderness ratio by shortening the column length leads to higher values of eigenvalues and higher required critical loads for buckling.
Why are negative critical coefficients (eigenvalues) considered in the analysis?
Negative coefficients indicate that the load would need to be applied in the opposite direction to achieve that specific buckling mode; therefore, they are typically neglected in practice.
- Arbeit zitieren
- Nazim Nariman (Autor:in), 2013, Finite element analysis of the buckling critical loads in un-braced steel frames with multiple slenderness ratio configurations, München, GRIN Verlag, https://www.grin.com/document/262659
