Short Answer:
When a load passes outside the core of a section, the stress distribution across the section changes such that part of the section comes under tension while the other part remains in compression. This is because the eccentric load creates a bending moment in addition to the direct compressive load.
As a result, materials like concrete, brick, and stone, which are strong in compression but weak in tension, may crack or fail. Hence, to ensure safety, the load should always pass within the core of the section so that the entire section remains under compression and no tensile stress is produced.
Detailed Explanation:
When Load Passes Outside the Core
The core of a section (also known as the kern) is the central area within which a load can act such that the entire section remains under compression. If the line of action of the load passes through this area, no tension is produced anywhere in the section.
However, when the load acts outside the core, the bending effect becomes so large that a part of the section experiences tensile stress. This happens because the eccentric load causes a bending moment, which combines with the direct stress due to the load and changes the stress distribution across the section.
This situation is very critical for structures made of brittle materials like concrete, masonry, and stone, which can resist compressive forces effectively but are unable to withstand tension. Once tensile stresses develop, cracks appear, and the structural member may become unsafe or even fail.
Concept of Core and Load Position
To understand the effect, let us recall that for a rectangular section:
- The core extends up to one-sixth of the depth from the center, i.e., .
- For a circular section, the core radius is .
As long as the eccentricity of the load is within these limits, the load is said to act within the core, and the entire section remains in compression.
If the eccentricity increases beyond this limit, i.e., the load acts outside the core, the bending moment becomes too large, and the compressive stress on one edge reduces to zero. Beyond this point, tensile stresses appear on the opposite edge of the section.
Mathematically,
where,
- = total stress at a point,
- = applied load,
- = cross-sectional area,
- = eccentricity,
- = distance from neutral axis,
- = moment of inertia of the section.
For the entire section to remain under compression, the minimum stress should be zero or positive, i.e.,
When , the term becomes negative, and thus tensile stress develops. This condition means the load has passed outside the core.
Stress Distribution When Load Passes Outside the Core
When the load acts outside the core, the distribution of stress across the section changes as follows:
- One Side in Compression:
The side of the section closer to the line of action of the load experiences increased compressive stress because the bending moment adds to the direct stress. - Opposite Side in Tension:
The opposite side of the section, farther from the load, experiences tension because the bending stress acts opposite to the direct stress. - Neutral Axis Shifts:
The neutral axis (the line where stress is zero) shifts from the center towards the loaded side. This makes one region of the section tensile and the other compressive. - Cracking in Brittle Materials:
Materials like concrete and brick cannot resist tension. Therefore, when tension develops, cracks appear on the tension side of the section, leading to structural weakness or failure.
Practical Example
Example 1:
Consider a rectangular column base 300 mm × 450 mm carrying a vertical load acting with an eccentricity of 100 mm from the center.
The maximum permissible eccentricity for this section is .
Since , the load acts outside the core.
As a result, one edge of the base will experience tension, and the other edge will have excessive compression, possibly causing cracks in the concrete base or uneven settlement in the foundation.
Effects of Load Acting Outside the Core
- Development of Tension:
The most direct effect is the development of tensile stresses on one side of the section. This can lead to cracks, especially in brittle materials. - Cracking and Damage:
Cracks appear on the tension side, weakening the structure and making it unsafe for further loading. - Unequal Stress Distribution:
The stress becomes non-linear and uneven across the section, leading to local overstressing on the compression side. - Loss of Stability:
The structure may tilt or bend, especially in columns or walls, causing instability or even collapse. - Reduced Load-Carrying Capacity:
Since part of the section is ineffective in resisting tension, the effective area in compression is reduced, lowering the member’s load-carrying capacity.
Precautions to Avoid Load Acting Outside the Core
- Ensure Proper Load Alignment:
The load must be applied through the centroidal axis of the section whenever possible. - Provide Adequate Base Area:
A larger base helps reduce eccentricity and prevents the load from shifting outside the core. - Use Reinforcement:
In structures made of concrete, reinforcing steel bars can carry the tension developed when loads act eccentrically. - Control Eccentricity:
Eccentricity should always be kept within permissible limits to ensure that the entire section remains in compression. - Periodic Inspection:
Regular monitoring of structural members ensures that no cracks or settlements occur due to eccentric loading.
Conclusion
When the load passes outside the core of a section, part of the section comes under tension while the rest remains in compression. This condition is unsafe for brittle materials like concrete and masonry, which cannot resist tension. It may lead to cracking, instability, or even structural failure. Therefore, in design and construction, loads should always act within the core area to ensure that the entire section remains under compression and the structure remains strong, stable, and durable.