\[k=\frac{Z_p}{S}\]
Variables
kshape factor
Zpplastic section modulus (m³)
Selastic section modulus (m³)
Description
What is this formula?
The shape factor is the ratio between the plastic section modulus and the elastic section modulus of a structural cross-section. It measures the reserve bending strength available after first yield.
When to use it
Use this formula when comparing structural shapes for plastic design or when estimating the increase in moment capacity between first yield and full plastic collapse.
Example
A steel beam has:
Zp = 0.00360 m³
S = 0.00240 m³
Formula:
k = Zp / S
Substitution:
k = 0.00360 / 0.00240
Result:
k = 1.50
This means the fully plastic moment capacity is approximately 50% greater than the elastic yield moment.
Applications
Plastic analysis, steel design, structural optimization, collapse load evaluation, moment redistribution studies, and comparison of beam cross-sections.