Section Kern under Eccentric Compression

The section kern is the region around the centroid within which a compressive force must act so that normal stresses remain compressive or zero throughout the cross-section.

For a rectangular section of width $b$ and height $h$, the kern is a rhombus with vertices at:

$$e_x=\pm\frac{b}{6},\qquad e_y=\pm\frac{h}{6}.$$

For a solid circular section of diameter $d$, the kern is a concentric circle of radius:

$$r_k=\frac{d}{8}=\frac{R}{4}.$$

• $e_x$, $e_y$ — limiting eccentricities for a rectangular section;
• $b$, $h$ — rectangle dimensions;
• $d$ — circle diameter;
• $R$ — circle radius;
• $r_k$ — kern radius.

The kern boundary is obtained from the condition that normal stress becomes zero at one extreme point. Loading outside the kern produces tensile normal stress in part of the section according to the full-section linear model.

The calculator below evaluates the kern radius or diameter for a solid circular section.