Plastic Moment Capacity (Rectangular)
Plastic Moment Capacity (Rectangular)
Plastic design uses the moment at which the whole section has yielded, giving a higher capacity than first-yield elastic design.
For a rectangle the plastic modulus is Z = bh²/4 and the plastic moment is M_p = f_y·Z. where b and h are the breadth and depth and f_y the yield strength.
Inputs
b := 150 mm=150 mm
h := 300 mm=300 mm
f_y := 275 MPa=275 MPa
The plastic section modulus assumes a fully yielded stress block.
Z := b·h^2/4=3.38e-03 m^3
The plastic moment is the yield stress times the plastic modulus.
M_p := f_y·Z=928125 Nm
Results
The ratio Z/S (here 1.5 for a rectangle) is the shape factor — the reserve strength beyond first yield. M_p is the basis of plastic and limit-state design.
Assumptions & limitations
- Elastic-perfectly-plastic material.
- Section is compact (no local buckling).
- Pure bending.