Looking for information on the Core of a section, eccentric loading/unsymmetrical bending

  • #1
morpheus343
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Anyone know of any book on mechanics of materials that covers finding the core of a section in eccentric loading. I am not sure what the term is in english but the direct translation is core of the cross section, it is the region in which if a load is applied, there will be only tensile or only compressive stress. I have looked at Hibbeler's book and Beer's (Mechanics of Materials) and haven't found anything like it. I have encountered this question in unsymmetrical bending due to eccentric loading in an unsymmetrical cross section. Maybe it is on another subject and not mechanics of materials?
 
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  • #2
morpheus343 said:
I have encountered this question in unsymmetrical bending due to eccentric loading in an unsymmetrical cross section. Maybe it is on another subject and not mechanics of materials?
It is an advanced topic in the mechanics of materials.

The core of a section is a neutral axis, in the case when the section is subjected to asymmetric loading.

The kernel or kern of a section is the region in which a compressive point load may be applied without producing any tensile stress on the cross-section.

Google 'Core or Kernel of a section'
 
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What is the core of a section in structural engineering?

The core of a section, often referred to in the context of structural engineering, is the central area within the cross-section of a column or beam where, if an axial load passes through any point within this area, it will not cause the column to bend or buckle. This area is crucial for understanding and predicting the stability of structures under load.

How does eccentric loading affect a beam or column?

Eccentric loading occurs when a force is applied at a distance from the centroidal axis of a structural member, causing bending in addition to direct compression or tension. This type of loading can lead to increased stress and deformation, potentially leading to failure if not properly accounted for in the design of the structure.

What is unsymmetrical bending?

Unsymmetrical bending refers to the bending of a beam or a structural element where the plane of load application does not coincide with any of the principal axes of its cross-section. This results in a more complex stress distribution and deformation pattern, requiring a detailed analysis to ensure structural integrity.

How do you determine the core of a section?

The core of a section can be determined by plotting the kern points, which are points on the cross-section beyond which, if a load is applied, it would cause the section to tip over or buckle. For simple shapes like rectangles and circles, the core can be easily determined geometrically. For more complex shapes, computational methods or software might be necessary to accurately find the core.

What are the implications of loading outside the core of a section?

Loading outside the core of a section generally leads to significant bending and torsional stresses because the load is not being applied through the centroid of the section. This can compromise the structural stability and increase the risk of failure under normal service loads. It is critical in structural design to ensure that loads are ideally applied within the core, or that adequate reinforcement and design considerations are made when external loads are unavoidable.

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