Core or Kernel of section

• The load is likely to be eccentric about both the axis XX and YY as shown in figure, the condition that tensile stress will not occur is when the load is applied anywhere within the rhombus EFGH whose diagonals are and .
• The figure EFGH within which the load may be placed so as not to produce tensile stresses is called the core or kernel of the section. .

Middle third rule

• Consider a rectangular column section, for the section shown, Z=(ab^2)/6 and A=ab.

• Hence, the condition that tensile stress should not occur is , Therefore e must be less than or equal to b/6. Hence if the load is applied at any distance less than b/6 from the axis, on any side of the axis XX the stresses are wholly compressive.

• Hence the range within which the load can be applied so as not to produce any tensile stress, is within the middle third of the base.

• Similarly, if the load had been eccentric w.r.t the axis YY, the condition that tensile stress will not occur is when the eccentricity of the load w.r.t this axis YY does not exceed a/6.

• Hence the range within which the load may be applied is within the middle a/3.