Define shape factor

Shape factor is the ratio of the plastic moment capacity $M_p$ of a cross-section to its yield moment $M_y$ (the moment at which the extreme fibre first reaches the yield stress):

$$S = \frac{M_p}{M_y} = \frac{\sigma_y Z_p}{\sigma_y Z_e} = \frac{Z_p}{Z_e}$$

where $Z_p$ is the plastic section modulus (the sum of the first moments of the areas above and below the equal-area axis, taken about that axis) and $Z_e$ is the elastic section modulus. It depends only on the shape of the section and shows the reserve of strength after first yield.

Typical values: rectangle 1.5, solid circle 1.70, I-section about 1.10 to 1.15, thin-walled circular tube about 1.27, triangle 2.34, T-section about 1.7 to 2.0.