Plastic Analysis – Yield Stress from Plastic Modulus and Plastic Moment A section has plastic modulus Zp = 4.8 × 10^−4 m^3. The shape factor is 1.2. If the plastic moment capacity is Mp = 120 kN·m, what is the yield stress of the material?

Introduction / Context:
In plastic analysis, the fully plastic moment Mp is related to the yield stress σy and the plastic section modulus Zp by Mp = σy * Zp. Knowing Zp and Mp allows direct computation of σy, independent of the elastic modulus or shape factor (the latter relates Zp to the elastic modulus Ze but is not needed once Zp is given).

Given Data / Assumptions:

• Plastic modulus: Zp = 4.8 × 10^−4 m^3.
• Plastic moment capacity: Mp = 120 kN·m = 120,000 N·m.
• Small-strain plasticity assumptions; uniform yield stress σy across the plastic blocks.

Concept / Approach:

Use Mp = σy * Zp. Units must be consistent: N·m for moment and m^3 for modulus give N/m^2 (Pa) for stress. Convert the result to MPa for convenience.

Step-by-Step Solution:

Verification / Alternative check:

The provided shape factor (Zp/Ze = 1.2) is a cross-check; it is not required here since Zp and Mp are already known.

Why Other Options Are Wrong:

• 100 MPa, 240 MPa, 300 MPa: Do not satisfy Mp = σy * Zp for the given values.

Common Pitfalls:

Mixing units (kN·m with mm^3); using elastic modulus Ze instead of Zp when Mp is given; forgetting to convert to MPa.

Final Answer:

250 MPa