The central core is an important material strength concept in the sizing of elongated parts subjected to mechanical bending and compression. Its rigidity is flexible.

Mathematically, the central core is a geometric region contained in the plane of a cross section of a mechanical prism such that if the point of application of the resulting force on said section is contained in the central core, the stresses will have the same sign throughout the section (that is, the entire section will be either in tension or in compression). In other words, if it is the point of application of the resulting force, it is the trace "Trace (geometry)") of the neutral fiber with the plane that contains a cross section and designates the central core.

That is, if a point force is applied at some point inside the central core, then the trace of the neutral fiber will not intersect with the section, in addition:.

General formulas

Considering a convex section delimited by a perimeter that is a simple closed curve that encloses and is considered a polar coordinate system with origin the center of gravity of the section. Then it can be shown that any point on the contour of the figure can be written as:.

with the origin of coordinates chosen so that:.

Where the OZ axis is taken aligned with one of the main axes of the section. In these conditions the border "Border (topology)") or contour of the central core is a curve given by:.

Where:.

Central area of ​​the horizontal section of a column through which the resulting compression forces must pass so that it is subjected only to compression stresses, since applying the load outside that area would produce tensile stresses.

In the construction of stone buildings, the concept of the central core is particularly important, since if a virtual cut of the structure is conceived, and the action and reaction force that a part of the structure exerts on the rest of the structure through said virtual cut is considered, it follows that, if the resulting force on said virtual cut is a compression force, it is contained in the central core of the section obtained by seeking the intersection of the structure with said virtual cut, the entire section will be compressed and therefore there will be no traction along of said cut. This condition is important since usually in stone constructions the mortar between the stone blocks has a tensile strength much lower than its compression strength.