What is core of a section?

Short Answer:

The core of a section is the central area or zone within a structural section where a load can be applied without causing any tensile stress in the section. In other words, if the load passes through the core area, the entire section remains under compression.

When the load acts outside the core, part of the section experiences tension and may lead to cracking or failure. The concept of the core of a section is very important in designing compression members such as columns, foundations, and masonry structures, where materials are weak in tension and strong in compression.

Detailed Explanation:

Core of a Section

The core of a section (also known as the kern of a section) is the area within a structural cross-section where a load must act so that the stress developed across the section remains completely compressive. If the load acts through this core, no part of the section will be subjected to tensile stress.

In simple terms, the core is the region where the line of action of a compressive load can be applied without producing any tension on the section. When the load is applied outside this region, part of the section goes into tension, which may be undesirable in materials like concrete, stone, or brickwork because these materials have very low tensile strength.

The concept of the core is therefore very important in masonry and concrete design, as it ensures that all stresses remain compressive and the section remains safe from cracking or damage.

Condition for the Core of a Section

When a load is applied at a distance (eccentricity) from the centroid of a section, it causes both direct stress and bending stress. The total stress at any point on the section is the sum of these two:

where,

  •  = Load applied,
  •  = Cross-sectional area,
  •  = Eccentricity of the load,
  •  = Moment of inertia,
  •  = Distance of the point from the neutral axis.

For the entire section to remain under compression, the minimum stress (σmin) must not become zero or negative (tensile).

From this condition, the maximum allowable eccentricity (emax) for the section can be found. The area within which the line of action of the load must fall to satisfy this condition is called the core of the section.

Core for Different Sections

  1. Rectangular Section:
    For a rectangular cross-section of width b and depth h, the core is a smaller rectangle at the center.

    • Maximum eccentricity along depth = h/6
    • Maximum eccentricity along width = b/6
      Hence, the core of a rectangular section is a central rectangle of dimensions (b/3 × h/3).
  2. Circular Section:
    For a circular cross-section of radius r, the core is also circular with a radius equal to r/4.
    So, if the load acts within this circle, the entire section remains under compression.
  3. Triangular Section:
    For a triangular section, the core is located at a distance of h/3 from the base and has a very small area compared to the total section.

Thus, the shape and size of the core depend upon the geometry of the section.

Importance of the Core of a Section

  1. Prevention of Tension:
    When a load is applied within the core, the entire section remains under compression, preventing tension and cracking in brittle materials.
  2. Structural Safety:
    Ensuring that the load acts within the core improves the safety and durability of structures, particularly for columns, retaining walls, and foundations.
  3. Accurate Design of Columns and Foundations:
    The concept helps engineers determine safe loading positions and eccentricities for designing structural members.
  4. Efficient Load Transfer:
    It ensures uniform stress distribution, leading to better load-carrying efficiency of the section.
  5. Applicable in Real Structures:
    In masonry or concrete structures where slight eccentricity is common, the design ensures that the load remains within the core to avoid failure.

Example to Understand Core of a Section

Example 1:
Consider a rectangular column of cross-section 300 mm × 450 mm.

  • Width (b) = 300 mm,
  • Depth (h) = 450 mm.

The core dimensions will be:

  • Along width = b/3 = 300/3 = 100 mm,
  • Along depth = h/3 = 450/3 = 150 mm.

Hence, the core area is a rectangle of size 100 mm × 150 mm at the center.
If the load acts anywhere within this smaller rectangle, the entire section will be in compression.

Example 2:
For a circular column of radius 200 mm,
Core radius = r/4 = 200/4 = 50 mm.
Hence, the load should act within a circular area of radius 50 mm at the center to avoid tension.

Practical Applications

  1. Columns in Buildings:
    To avoid cracks or tilting, loads on columns are kept within the core area.
  2. Foundations:
    The pressure on the soil below a foundation remains compressive when the resultant load acts within the core.
  3. Masonry and Concrete Structures:
    Ensures that tension does not develop in weak tensile materials like brick or concrete.
  4. Retaining Walls and Dams:
    The resultant of forces due to water pressure and weight should pass through the core to maintain stability and prevent overturning.
Conclusion

The core of a section is the central region within which a load must act to keep the entire section under compression. If the load acts outside this area, part of the section will experience tension, leading to cracks or structural failure. The size and shape of the core depend on the geometry of the section — rectangular, circular, or triangular. The concept of the core is very important in the design of compression members like columns, foundations, and walls to ensure stability, safety, and durability of structures.