In this article, you will learn a complete overview of buckling such as its definition, types, factors affecting, column buckling and the last also know what is the difference between buckling and bending.
So, let’s know about each of the aspects related to buckling in detail.
What is Buckling?
In science, buckling is a mathematical instability that leads to a failure mode.
Buckling is characterized by the sudden sideways failure of a structural member that is subject to high compressive stress, where the compressive stress at the point of failure is less than the ultimate compressive stress that the material is able to bear.
Mathematically, buckling is instability that leads to a failure mode.
Theoretically, buckling occurs due to bifurcation in the solutions of equations of stable equilibrium.
| Buckling |
Factors Affecting Buckling
The following factors affect the buckling:
- Lack of straightness
- Eccentric loading
- Variability in cross-section
- Residual stresses
- Yielding
Types of Buckling
The following types of buckling are:
- Flexural Buckling
- Torsional Buckling
- Torsional Flexural Buckling
- Local Buckling
- Distortional Buckling
See in the figure different types of buckling which are described below in detail.
The dashed lines in the figure represent the original shape and the solid lines represent the shape after buckling.
| Types of Buckling |
Flexural Buckling
Under axial loading or simultaneous axial and moment loading, a beam can buckle in a plane without twisting is called flexural buckling.
If a member undergoes a pure axial load, it may bend laterally and take the shape of a sinus wave.
The number of waves can vary and is dependent on support position and lateral restrictions.
This type of buckling is also called the Euler buckling case.
Torsional Buckling
Members with a small torsional stiffness may buckle in the way that the cross-section is twisted when an axial load is applied.
Torsional Flexural Buckling
Torsional-flexural buckling can occur for an axially loaded beam with a monosymmetric I-section and a channel cross-section.
When it buckles the beam will twist together and subsequently deflect. When a pure moment acts on an I-beam about its major axis, one flange undergoes compression and the other undergoes tension.
If the lateral stiffness is insufficient, the compression flange will buckle before the plastic.
Local Buckling
When buckling is governed by beams with slender webs or flanges called local buckling.
This can be recognized by the web or many small buckles along the flanges. For the local buckling of the web, the length of the buckling is approximately equal to the width of the web.
Distortional Buckling
Distortional buckling generally occurs for comparatively smaller beams.
This is the result of an interaction between the two buckling modes; Lateral - torsion buckling and local buckling, the two of which are usually designed separately.
When distortional buckling occurs, the web is deformed and the flanges twist and subsequently deflect, the result being a low torsional resistance.
Global Buckling
Buckling that occurs globally and affects the beam is called global buckling.
This type of buckling can be further subdivided depending on the type of deformation that occurs and the type of load acting on the beam.
Column Buckling
Short compression members will fail once the stress exceeds the compressive yield strength of the material.
However, members with long compression will fail due to buckling before the yield strength of the member is reached.
Buckling occurs suddenly and is characterized by large deflections perpendicular to the axis of the column.
A simple way to demonstrate column buckling is to hold a ruler at either end and push your hands toward each other. The ruler will buckle in the center.
Euler's Theory of Column Buckling
Euler's theory of column buckling was invented by Leonhard Euler in 1757.
Euler's theory of column buckling is used to estimate the critical buckling load of a column as the stress in the column remains elastic.
Buckling failure occurs when the length of the column is greater than its cross-section.
Euler's theory is based on certain assumptions relating to axial load application, column material, cross-section, stress limit, and point of column failure.
The validity of Euler's principle is subject to the condition that the failure is due to buckling.
Euler's theory states that the stress in the column due to a direct load is smaller than the stress due to buckling failure.
Based on this statement, a formula is derived to calculate the critical buckling load of the column.
So, the equation is based on the bending stress and neglects the direct stress due to the direct load on the column.
Assumption
- Initially, the column is completely straight.
- The cross-section of a column is uniform throughout its length.
- The load is axial and passes through the centroid of the segment.
- The tensions in the column are within the elastic limit.
- The materials of the column are homogeneous and isotropic.
- The self-weight of the column itself is ignored.
- Column failure is only due to buckling.
- The length of the column is large in comparison to its cross-sectional dimensions.
- The ends of the columns are frictionless.
Euler's formula for buckling,
Pₑ = π²EI / le²
Where,
Pₑ = Buckling load
E = Modulus of Elasticity ( Mpa )
I = Moment of inertia ( mm⁴ )
Le = Effective length ( mm )
Slenderness Ratio
The slenderness ratio indicates the sensitivity of the column to buckling. Columns with higher slenderness ratios are more sensitive to buckling and are categorized as long columns. The long columns are analyzed by Euler's formula given above.
It is denoted by λ.
Slenderness ratio ( λ )
Slenderness Ratio =
The effective length of column / Minimum radius of gyration
λ = le / kmin
If λ is more, its load-carrying capacity will be less.
Radius of Gyration
The distance from the given axis at which all small elements of the lamina are placed, the moment of inertia of the lamina about the axis does not change.
This distance is called the radius of gyration.
It is denoted by K.
K = √( I / A )
Or,
I = AK²
Difference Between Buckling and Bending
| Buckling | Bending |
|---|---|
| When a load is applied along the axis of the member-like column & struts such that it results in displacement sideward means perpendicular to axial load is called bucking. | Bending is generally observed in beam and slab because the displacement that occurs in such members trying to bend them along the direction of load is bending. |
| Buckling is the state of instability when an axial load is acting on it, they experience deflection and deformation of structural member-like column leading to a collapse of structural members. | Bending is the state of stress developed in it when a transverse load is applied to it, they experience two types of stress compression and tension and there is a neutral axis between compression and tension zone. |
| Buckling is caused due to axial and eccentric load in a structure member-like column. | Bending is caused due to transverse load in a structure member-like beam. |
| Buckling indicates failure, irrespective of magnitude. | Bending under transverse load is natural and is not considered a failure as long as the deflection is within limits. |
| When buckling occurs, then that is a failure. | When a member is over-stressed in bending, it can form plastic hinges and absorb that extra energy in the form of rotations. |
| In buckling, moment and deflection are interdependent so moment, deflection, and stress are not proportional to load. | In bending, moments are substantially independent of the resulting deflections. |
Related Article:
Moment of Force
Column and Strut
Theories of Failure
Principal Stress
Bending Stress
So here you have to know all aspects related to the buckling. If you have any doubt then you are free to ask me by mail or on the contact us page.
Thank You.
