Short Answer:

Crippling load is the maximum load a column or strut can carry before it fails by buckling. When this load is reached, the column suddenly bends or deflects sideways, leading to complete instability and failure. This failure happens not due to crushing but due to loss of balance caused by compression.

In simple terms, crippling load is also called the buckling load or critical load. It represents the point beyond which the column cannot support the load anymore and collapses. The value of crippling load depends on the material, length, cross-section, and end conditions of the column.

Detailed Explanation :

Crippling Load

The crippling load is the limiting axial compressive load at which a column or strut becomes unstable and fails by buckling. It is an important concept in strength of materials and is used in the design of columns, struts, and other compression members. When a column is subjected to an increasing axial load, it initially shortens in length due to compression. However, after reaching a certain limit, the column suddenly bends or deflects sideways, even without any increase in the applied load. The load corresponding to this condition is known as the crippling load.

This phenomenon is also known as buckling, and the failure due to this is called buckling failure. The crippling load is different from crushing load, which causes failure due to the material’s compressive strength being exceeded. Crippling failure occurs even when the actual stress is less than the crushing stress, mainly due to instability caused by slenderness and column geometry.

Factors Affecting Crippling Load

Several factors affect the value of the crippling load of a column:

1. Length of the column:
   Longer columns are more likely to buckle under smaller loads because the slenderness ratio (L/r) increases with length. Hence, the crippling load decreases as the length increases.
2. End conditions of the column:
   The way the ends of a column are supported affects its effective length. Columns with both ends fixed can carry higher crippling loads, while those with both ends free or pinned carry less.
3. Material of the column:
   The modulus of elasticity (E) and compressive strength of the material directly influence the crippling load. Stiffer materials like steel can resist higher loads before buckling compared to weaker materials like wood.
4. Moment of inertia (I) and cross-sectional shape:
   The shape and distribution of the material in the cross-section affect the column’s resistance to bending. A higher moment of inertia provides better stability and increases the crippling load.
5. Radius of gyration (r):
   The radius of gyration determines how the material is distributed about the centroidal axis. A higher radius of gyration means better resistance to buckling and higher crippling load.

Euler’s Formula for Crippling Load

For long and slender columns, the crippling load can be calculated using Euler’s Formula:

Where,

•  = Crippling load or buckling load (N)
•  = Young’s modulus of the material (N/m²)
•  = Moment of inertia of the cross-section (m⁴)
•  = Effective length of the column (m)

This formula is applicable to perfectly straight and elastic columns where failure occurs due to buckling, not crushing.

Effective Length and End Conditions

The value of effective length  varies with the end conditions of the column.

• For both ends hinged:
• For both ends fixed:
• For one end fixed and other free:
• For one end fixed and other hinged:

The smaller the effective length, the greater the crippling load, because the column becomes more stable and resists buckling.

Difference Between Crushing Load and Crippling Load

• Crushing Load: Failure occurs due to compressive stress exceeding the material’s yield or ultimate compressive strength. This happens in short and thick columns.
• Crippling Load: Failure occurs due to buckling, even when the stress is within the elastic limit. This happens in long and slender columns.

In practical design, both conditions are considered to ensure safety and reliability.

Practical Example

Suppose a mild steel column has:
,
,
and .

Then,

 

Thus, the crippling load for this column is approximately 15.8 MN. Beyond this load, the column will buckle and fail.

Importance of Crippling Load in Design

1. It helps engineers determine the safe load a column can carry.
2. It ensures that buckling failure is prevented in structures like bridges, towers, and buildings.
3. It allows designers to select the appropriate cross-section and material for columns.
4. It forms the basis for other empirical relations such as Rankine’s formula, which modifies Euler’s theory for real columns.

Conclusion

The crippling load is the maximum compressive load that causes a column to buckle and lose stability. It depends on the column’s geometry, material, and end conditions. For long and slender columns, it can be accurately predicted using Euler’s formula. In design, the crippling load plays a vital role in ensuring the safety and strength of compression members used in various mechanical and structural applications.