---
title: "Define plastic moment"
subject: "Theory of Structures II"
chapter: 5
key: "semester_5/theory_of_structures_ii:define-plastic-moment"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-plastic-moment
site: BCT Engineering
---

# Define plastic moment

Theory of Structures II · Chapter 5: Introduction to plastic analysis

- Asked in: 2072 Chaitra, 1.5 marks
- Video: [Plastic Section Modulus, Zx ,  Plastic Moment, Mp,  Elastic Section Modulus, Sx, Shape Factor](https://www.youtube.com/watch?v=hcMBSHj63uU) — Nasser Yari PhD, PE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/define-plastic-moment
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-5

## Question

Define plastic moment.

## Short answer

Plastic moment Mp is the maximum moment when entire section yields, given by Mp = yield stress times plastic section modulus.

## Answer

The **plastic moment** $M_p$ is the moment of resistance of a cross-section when the whole section has yielded, that is, when every fibre has reached the yield stress $\sigma_y$ (tension on one side of the plastic neutral axis and compression on the other). It is the maximum moment the section can carry:
$$
M_p = \sigma_y\,Z_p
$$
where $Z_p$ is the plastic section modulus. For a rectangular section $M_p = \sigma_y\dfrac{bd^2}{4}$ (and the yield moment is $M_y = \sigma_y\dfrac{bd^2}{6}$, so $M_p/M_y = 1.5$).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The plastic moment Mp of a section is the moment at which:
   A. The extreme fibre first reaches yield
   B. The whole section has yielded
   C. The section fractures
   D. The shear reaches its maximum
   Answer: B. Mp is the moment of resistance when every fibre has reached yield stress. (Key point: Meaning of plastic moment)

2. Which expression gives Mp?
   A. sigma_y / Z_p
   B. sigma_y x Z (elastic modulus)
   C. sigma_y x Z_p
   D. Z_p / sigma_y
   Answer: C. Mp = sigma_y Z_p, where Z_p is the plastic section modulus. (Key point: Formula)

3. For a rectangular section, Mp = sigma_y bd^2/4 and My = sigma_y bd^2/6. What is Mp/My?
   A. 1.5
   B. 1.0
   C. 2.0
   D. 0.67
   Answer: A. (1/4)/(1/6) = 1.5. (Key point: Shape factor)

## Related in Theory of Structures II

- [Plastic moment capacity of frame](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aplastic-moment-capacity-frame-80kn-20knm) — Theory of Structures II, chapter 5
- [Plastic moment capacity of frame, 60 kN](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aplastic-moment-capacity-frame-60kn-40kn) — Theory of Structures II, chapter 5
- [Plastic moment capacity Mp of frame](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Aplastic-moment-capacity-frame-3mp-2mp) — Theory of Structures II, chapter 5

## Related in other subjects

- [Limiting plastic moment is 1.5 times elastic moment](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aplastic-moment-rectangular-1-5) — Strength of Materials, chapter 7
- [Define plastic moment capacity of beam](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Aplastic-moment-capacity-definition) — Strength of Materials, chapter 7
- [Plastic moment and shape factor of a beam](https://www.bctengineer.com/question.md?key=semester_5%2Fmechanics_of_solids%3Ashape-factor-plastic-moment-rectangle) — Mechanics of Solids, chapter 12