Buckling Analysis Solved Example | Buckling of connecting rod

Описание: Buckling of connecting rod is discussed in this video the Solved Problem as follows
A connecting rod of length l may be considered as a strut with the ends free to turn on the crank pin and the gudgeon pin. In the directions of the axes of these pins, however, it may be considered as having fixed ends perpendicular to that direction. Assuming that Euler’s formula is applicable, determine the ratio of b/h for the given cross-section so that the connecting rod is equally strong in both planes of buckling.

++++ What is buckling failure +++++
Buckling happens when a structural element, like a column or beam, fails under high compressive stress, leading to a sudden bending or collapse. Instead of compressing smoothly, the structure starts to deform sideways or out of its original plane. This issue arises when a slender structure, such as a column, is compressed to the point where it loses stability. The point at which buckling occurs is known as the buckling or critical load. Buckling can be particularly dangerous in engineering projects, like bridges and buildings, because it can lead to sudden, catastrophic failures.
Types of Buckling:

Euler Buckling: Applies to long, slender columns, with Euler's formula helping predict the load at which buckling will occur.
Local Buckling: When just a section of the structure, like a thin-walled part of a beam or column, buckles, but the rest remains stable.
Lateral-torsional Buckling: Involves both twisting and sideways movement, typically seen in beams under bending stress.
Elastic vs. Inelastic Buckling: Elastic buckling occurs before the material yields, while inelastic buckling happens when the material has already begun to deform beyond its elastic limits.

The buckling load is influenced by factors such as the length and slenderness of the structure, the material properties, and boundary conditions (e.g., whether the ends are fixed or free to move). To prevent buckling, engineers use safety factors and often tweak designs to improve a structure’s resistance to buckling.

Euler Theory

The critical load for an ideal elastic column is known as the “Euler Load” after the mathematician Leonhard Euler (1707-1783) who first investigated the phenomenon of instability.

Assumptions for Euler Theory
1. Both ends are ball jointed (often referred to as pin-jointed).
2. The material is homogenous.
3. The material is isotropic.
4. The longitudinal axis is perfectly straight.
5. The load, initially, is applied along the axis.
6. The strut is of uniform cross-section and prismatic

Factors affecting buckling

1. The strength of the material itself (eg Tensile Strength) does not appear in the formula for the critical load. Thus the buckling load is not increased by using a stronger material. However, the load can be increased by using a stiffer material (ie a material with a larger modulus of elasticity E).

2. The buckling load will be larger the higher the second moment of area ‘I’ of the cross-section. The second moment of area ‘I’ maybe increased by distributing the material away from the centre of the cross-section. Hence, tubular structures are more economical columns than solid ones having the same cross-sectional area. Reducing the wall thickness of tubular columns and increasing its lateral dimensions while keeping the cross-sectional area constant increases the buckling load because ‘I’ is increased. This process has a practical limit because eventually the wall itself becomes unstable and localized buckling occurs in the form of small corrugations or wrinkles.

3. The buckling load is inversely proportional to the square of the length of the strut. So halving the length will quadruple the buckling load and so anything that can be done to shorten the length of a strut will pay dividends in increasing the buckling load.

4. If a strut or column is free to buckle in any direction then it will bend about the axis with the smallest second moment of area.