Short Answer:

Eccentricity is the distance between the line of action of a load and the centroidal axis of the section on which it acts. In simple words, when a load does not pass through the center of a member but acts at some offset distance, that distance is called eccentricity.

Eccentricity causes a bending moment in addition to the direct stress due to the load. As a result, the member experiences combined direct and bending stresses. This concept is important in the design of columns, foundations, and other structures where loads are often applied off-center.

Detailed Explanation:

Eccentricity

In engineering mechanics and strength of materials, eccentricity is defined as the perpendicular distance between the line of action of a load and the centroidal axis of the section on which it acts. The line of action is the imaginary straight line along which the force is applied, and the centroidal axis is the central axis that passes through the geometric center (centroid) of the section.

When the line of action of the applied load coincides with the centroidal axis, the load is said to be centrically applied, and the member experiences only direct (normal) stress.
However, when the load is applied away from the centroidal axis, it produces both direct stress and bending stress in the member. This offset distance is what we call eccentricity (e).

Mathematically,

The presence of eccentricity introduces a bending moment (M) in the section, given by:

where,

•  = Applied load,
•  = Eccentricity.

Hence, eccentric loading results in combined direct and bending stress, which must be carefully analyzed for safe design.

Effect of Eccentricity on Stress Distribution

When a load acts eccentrically, the stress across the section is non-uniform.

• On one side of the section, the stress increases because both direct stress and bending stress act in the same direction.
• On the opposite side, the stress decreases because the bending stress acts opposite to the direct stress.

The total stress at any point can be written as:

Substituting ,

where,

•  = Total stress at a point,
•  = Load applied,
•  = Cross-sectional area,
•  = Eccentricity,
•  = Distance from neutral axis,
•  = Moment of inertia of the section.

This shows that the eccentric load produces a combination of direct stress (P/A) and bending stress (P × e × y / I).

If the eccentricity is large, one side of the section may experience tensile stress, which can be dangerous for materials like concrete or masonry that are weak in tension.

Units of Eccentricity

Eccentricity is measured in units of length, such as millimeters (mm) or meters (m), depending on the dimensions of the member.

For example, if a load acts 20 mm away from the centroidal axis, the eccentricity is 20 mm.

Significance of Eccentricity in Engineering

1. Causes Bending Moment:
   The presence of eccentricity introduces bending moment, which increases the total stress in the member.
2. Non-Uniform Stress Distribution:
   Unlike concentric loading, where stress is uniform, eccentric loading causes one side to be more stressed than the other.
3. Possibility of Tension:
   If the load acts too far from the centroid, the section may develop tensile stress on one side, leading to cracks or failure in brittle materials.
4. Design Consideration:
   Engineers must consider eccentricity in the design of columns, foundations, brackets, and other components where loads are rarely perfectly centered.
5. Stability and Safety:
   Accounting for eccentricity ensures that structures remain stable, and members do not fail due to unexpected bending or buckling.

Practical Examples of Eccentricity

1. Column with Off-Centered Load:
   When a vertical column carries a load that does not pass through its centroid, the column experiences both direct compression and bending due to eccentricity.
2. Footings and Foundations:
   If the resultant of the column load acts away from the center of the foundation base, eccentricity occurs. This can lead to unequal soil pressure, causing tilting or settlement.
3. Crane Hook:
   The load on a crane hook is applied away from the central axis, resulting in eccentric loading that produces both bending and direct stress.
4. Beams with Off-Centered Loads:
   A beam carrying a load applied away from the neutral axis experiences bending due to eccentricity.
5. Machine Parts:
   Shafts, brackets, and other machine components often experience eccentric loads due to misalignment or external attachments.

Effects of Large Eccentricity

When eccentricity becomes large compared to the dimensions of the section, the stress distribution becomes extreme:

• The compressive stress on one side increases sharply.
• The other side may experience tensile stress.
• This condition can lead to bending failure or cracking in brittle materials and buckling in slender columns.

Hence, in design practice, engineers always limit the value of eccentricity to ensure that the entire section remains under compression, particularly for materials like concrete and masonry.

Methods to Reduce Eccentricity

1. Proper Alignment of Load:
   Ensuring that the line of action of the load passes through the centroid of the section reduces eccentricity.
2. Use of Reinforcement:
   Reinforcing materials such as steel can resist tension that develops due to unavoidable eccentricity.
3. Symmetrical Design:
   Making structures symmetric reduces uneven loading and helps minimize eccentric moments.
4. Use of Larger Sections:
   Increasing the section size or area helps reduce stress caused by eccentric loads.

Conclusion

Eccentricity is the perpendicular distance between the line of action of a load and the centroidal axis of the section. It plays a major role in structural design because it introduces a bending moment that changes the stress distribution from uniform to non-uniform. Large eccentricity can lead to tension or even failure in the section. Therefore, engineers must carefully analyze and minimize eccentricity to ensure the strength, safety, and stability of structures and machine components.