Buckling is a critical phenomenon in structural engineering, representing a form of instability that can lead to the sudden failure of structural members under compressive or other forms of loading. Even without material yielding or fracturing, buckling significantly reduces a member’s load-carrying capacity and overall stability. This behavior is particularly important in slender columns, beams, and other compressive members, as their design and integrity heavily depend on preventing such instabilities. The analysis of buckling requires a detailed understanding of parameters like slenderness ratio, radius of gyration, and critical buckling load, all of which are key to ensuring the safety and functionality of structures. This blog will explore the different types of buckling, column buckling, and parameters influencing its occurrence.
1. What is Buckling?
Buckling refers to a type of structural instability in which a structural member, under compressive loads or other forms of loading, experiences a sudden lateral deformation. This deformation can lead to a significant reduction in the stiffness of the member and drastically decrease its load-carrying capacity. This phenomenon does not necessarily result in material yielding or fracture, but it is considered a failure mode because, after this, the member loses its ability to support any load.
For example, buckling can occur in compressive members like columns, beams subjected to lateral loads, or even in structures exposed to bending or torsional loading.
Figure 1: A depiction of buckling
2. Types of Buckling in Structural Engineering
Buckling can manifest in various forms depending on the type of loading, structural member geometry, and boundary conditions. Understanding the different types of it is essential for accurately analyzing and preventing failures in structures. In this section, we will explore the main categories of buckling, which include:
2.1. Global buckling
This phrase refers to the instability and failure of a structural member due to lateral deformations caused by compressive loads. This condition can manifest in three different forms: flexural buckling, torsional buckling, and flexural-torsional buckling, which will be discussed in the following sections. In this category, the overall lateral stability of the structure is compromised due to compressive stresses.
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2.1.1 Flexural Buckling
This type is characterized by deformation due to bending, which typically occurs around the axis with the highest slenderness ratio—usually the weaker axis of the section or the one with the smaller radius of gyration. Members subjected to different types of loading, regardless of their shape, can experience this form of buckling.
Figure 2: Flexural Buckling
2.1.2. Torsional Buckling
Torsional buckling occurs when a structural member fails due to twisting around its longitudinal axis. This failure mode is common in members under compressive loads where the entire section rotates or twists as a whole. Typically seen under pure compression loads where a significant component of torsional stress is present. Most prone in open cross-sections, such as channels or angles, and can occur in doubly symmetric shapes like I-beams when conditions favor torsional instability.
2.1.3. Flexural-Torsional Buckling
A more complex mode combining lateral bending and twisting, flexural-torsional buckling involves both the bending of a member and its simultaneous twisting. It often resembles lateral-torsional buckling observed in unbraced beams but applies specifically to compression members. Occurs under axial compression, especially when the centroid and shear center of the cross-section do not align. It affects non-doubly symmetric cross-sections, such as channels, angles, and some types of beams. Doubly symmetric sections (e.g., wide flange sections) typically experience simpler torsional or flexural buckling rather than this combined mode.
Figure 3: Types of global buckling
2.2. Local Buckling
In local buckling, only a portion of the member subjected to buckles and loses its load-bearing capacity, often due to the slenderness of that specific part of the member. Local buckling can occur under both distributed and concentrated loads. In this type, the axis of the member does not deform, but the cross-section of the beam buckles significantly reduces the load-carrying capacity of the affected area. In this case, the overall stability of the structure may not be compromised.
Figure 4: a) global buckling b) local Buckling
2.3. Elastic Buckling
Elastic Buckling occurs when a structure deforms elastically (reversibly) under various types of loading. In this state, the structure returns to its original shape once the load is removed. This type is commonly observed in metallic structures and those exhibiting elastic behavior. Euler’s formula for determining the critical buckling load is one of the most important equations in this field.
2.4. Plastic Buckling
Plastic Buckling occurs when a structure undergoes plastic (irreversible) deformation under various types of loading. In this type of buckling, permanent deformation is induced in the structure, and once the load is removed, the structure does not return to its original state. This form of buckling is typically observed in concrete structures or those operating in the plastic region.
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Note: There is a example of buckling in our blog Abaqus Examples in the second free PDF. It teaches you step by step how to do an Abaqus buckling. Of course you can find other stuff and examples in this blog for free.
3. When Does Buckling Occur?
In this section, we will first examine the parameters influencing buckling analysis, which include factors such as member length, support conditions, and cross-sectional geometry. Then, we will discuss the concept of critical buckling load and how it is calculated using Euler’s formula, along with its effects on the structural stability.
It is important to note that the taller and slimmer the member, the more susceptible it is to buckling. Various structural members such as columns, beam-columns, tie beams, and braces are prone to buckling. Structural engineers must perform accurate calculations and proper design of members against buckling to ensure that the structure remains safe under potential loads.
3.1. Parameters Influencing Buckling Analysis
The resistance of members to buckling depends on various factors such as the length, shape, cross-sectional area of the members, stiffness, support conditions, and so on. To account for these effects, parameters are defined that allow for the calculation of the critical buckling load based on the applied compressive force. The critical buckling load is the maximum load that a member can support without buckling.
- Effective Length Factor
This parameter essentially reflects the length of the member where the risk of buckling is higher. As this length increases, the likelihood of buckling also rises. The effective length factor, commonly represented by the letter K depends on the support conditions at both ends of the member. It is worth noting that achieving ideal boundary conditions (such as perfectly rigid supports) is often impractical in reality. Therefore, for design purposes, effective length factors are sometimes set higher than the theoretical values.
Figure 5: Approximate values of effective length factor k
- Effective Length
The effective length is defined as the product of 𝐾 and the free span between supports (𝐿). This length represents the equivalent length of the member if it were constructed with pinned supports at both ends.
- Radius of Gyration
To better understand the concept of the radius of gyration and its effect on the stability of structures, we can explain it with a more tangible example.
Imagine a spinning top:
The faster it spins, the more stable it becomes and the less likely it is to tip over. One of the main reasons for this stability is how the mass of the top is distributed.
If the top has a heavy base with more mass concentrated near the bottom, it will be more stable. This is because the mass is closer to the surface it’s in contact with, making it more resistant to tipping.
If the top has a wider base, its stability also increases. This means it requires more force to tilt the top, and its center of gravity is positioned in a way that maintains its balance and rotation.
Now, let’s apply this concept to engineering structures like columns or beams. Columns are under compressive forces and might buckle due to sudden pressure (which means losing stability and rapidly deforming).
The radius of gyration can be seen as the “base” of the column:
A larger radius of gyration indicates that the cross-sectional area of the column is designed so that more material is distributed farther from the center. Just like a top with a wider base, the column becomes more resistant to lateral forces and buckling.
For example, if a column has a wider or better-distributed cross-section, it will be more stable and resist sudden deformations more effectively. Just like the top with a wider base is more stable and less likely to tip over, a column or beam with a larger radius of gyration is less prone to buckling.
In the end, the radius of gyration represents how the material in a structure is distributed to resist buckling. The larger the radius, the more efficiently the material is used, resulting in a structure that is better able to withstand destabilizing forces.
In fact, the larger the radius of gyration, the more stable the column is, just like a top with a wider base, making it less prone to tipping or sudden deformation.
When the radius of gyration is not equal about the two principal axes of a cross-section, the section tends to buckle around the weaker axis, which has the smaller radius of gyration.
The radius of gyration about the x-axis is calculated using the following formula:
The moment of inertia is a measure of an object’s resistance to rotational motion about a specific axis. It depends on the object’s mass distribution relative to the axis of rotation and is crucial in the study of dynamics, especially in the analysis of rotational systems.
- Slenderness Ratio
The slenderness ratio is defined as the ratio of the effective length of a member to the radius of gyration of its cross-section (KL/r). This parameter significantly influences the failure modes of a section. Based on the definition of the slenderness ratio, sections are categorized into three main types, which help in analyzing the behavior of sections under axial loading. These three categories are as follows:
- Short (Stocky) Sections: These sections have a low slenderness ratio, leading them to fail under compressive stress (yielding) without experiencing any buckling.
- Long (Slender) Sections: These sections generally fail due to buckling before reaching their yield strength. The behavior of such sections is influenced by their modulus of elasticity E.
- Intermediate Sections: Sections with a slenderness ratio between the short and long categories exhibit a failure mode that combines both buckling and compressive stress.
3.2. Critical Buckling Load
Imagine you have an aluminum pipe that is intended for use in constructing a radio tower. This pipe is positioned vertically, and a compressive load is applied from above, such as the weight of equipment or wind force. Initially, when a small load is applied to the pipe, it experiences linear compression and shrinks. However, as this load gradually increases, there will come a moment when the pipe suddenly deforms laterally and bends; this moment is precisely when the pipe can no longer withstand additional load. The load that leads to this instability and sudden deformation is called the critical buckling load.
As you can see, buckling can occur in various types of structures, but the most well-known and common example is the critical buckling load in columns. We will discuss this topic in detail in the next section.
4. Buckling of Columns | Column Buckling
Since columns are primary load-bearing elements of almost all types structure building and are directly subjected to compressive forces, the potential for column buckling must be thoroughly evaluated. Buckling can occur in both concrete and steel columns. In concrete columns, if longitudinal reinforcements are not properly secured, they may buckle, leading to a decrease in the column’s strength and ductility. To mitigate this risk, ties should be correctly placed at specified intervals to ensure all longitudinal reinforcements are properly braced, minimizing the chance of buckling.
The probability of buckling in concrete columns decreases with a larger cross-sectional area and improved seismic load-bearing performance. However, poor concrete quality can lead to concrete spalling around the reinforcements during seismic events, reducing its role in supporting gravity loads. In such cases, the gravity loads are primarily carried by the longitudinal reinforcements, and due to their slenderness, global buckling of the column may occur.
Figure 6: Buckling of Columns
To calculate the critical load due to buckling in columns, you can use Euler’s formula (buckling euler) as follows:
Figure 7: Euler’s Buckling
The length of the column that is placed between the supports and is less than the original length in some cases is called the effective length of the Le.
5. Conclusion
In this article, we focused on buckling, a significant type of structural instability that affects the performance of members under compressive loads. Buckling plays a crucial role in structural engineering because it can cause sudden failure without any material yielding or fracture, making it essential for engineers to understand and prevent it.
We started by explaining what buckling is, highlighting its impact on structural members’ load-carrying capacity. We explored the types of buckling, including global buckling with forms like flexural, torsional, and flexural-torsional buckling, and described how each type affects members differently. We covered local buckling, where only parts of the member deform, and distinguished between elastic buckling (reversible) and plastic buckling (permanent).
Next, we discussed when buckling occurs, outlining key parameters like member length, cross-sectional shape, and support conditions, which influence a structure’s resistance to buckling. We explained how engineers calculate the critical buckling load using Euler’s formula to predict the point of instability. In the section on buckling of columns, We emphasized the importance of designing columns with appropriate cross-sections and reinforcements to prevent buckling, especially in concrete structures.
In conclusion, we provided an in-depth look at buckling, its various types, and methods for analyzing and preventing it. This knowledge equips engineers with the tools to design safer structures that can withstand compressive loads and avoid sudden failures.
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