\[Z_p=A_cy_c+A_ty_t\]
Variables
Zpplastic section modulus (m³)
Accompression area above the plastic neutral axis (m²)
ycdistance from plastic neutral axis to centroid of compression area (m)
Attension area below the plastic neutral axis (m²)
ytdistance from plastic neutral axis to centroid of tension area (m)
Description
What is this formula?
The plastic section modulus is a geometric property used in plastic design of structural members. It represents the maximum moment-carrying capacity of a cross-section when the entire section has yielded.
When to use it
Use this formula when evaluating the plastic moment capacity of steel beams and other ductile structural members. It is commonly applied in limit state design and plastic analysis.
Example
A symmetrical steel section has:
Ac = 0.010 m²
yc = 0.15 m
At = 0.010 m²
yt = 0.15 m
Formula:
Zp = Ac*yc + At*yt
Substitution:
Zp = (0.010*0.15)+(0.010*0.15)
Result:
Zp = 0.0030 m³
Applications
Plastic beam design, steel structures, moment capacity calculations, collapse analysis, structural optimization, and limit state engineering.