---
title: "Elastic vs plastic analysis; plastic hinge"
subject: "Theory of Structures II"
chapter: 5
key: "semester_5/theory_of_structures_ii:elastic-vs-plastic-analysis-plastic-hinge"
source: https://www.bctengineer.com/q/semester_5/theory_of_structures_ii/elastic-vs-plastic-analysis-plastic-hinge
site: BCT Engineering
---

# Elastic vs plastic analysis; plastic hinge

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

- Asked in: 2065 Shrawan, 5+5 marks
- Video: [Plastic Analysis - Fundamental Concepts Part 1](https://www.youtube.com/watch?v=oj0nzJe_L4c) — Michael Clapham (davesidea)
- 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/elastic-vs-plastic-analysis-plastic-hinge
- Whole chapter: https://www.bctengineer.com/md/semester_5/theory_of_structures_ii/chapter-5

## Question

List the differences between elastic and plastic analysis. What is meant by Plastic Hinge?

## Short answer

Elastic analysis assumes linear elasticity, uses working stresses and elastic modulus, requires compatibility and no redistribution. Plastic analysis uses ultimate load, plastic modulus, equilibrium and mechanism condition, allows moment redistribution with reserve strength. A plastic hinge is a fully yielded section rotating at constant moment Mp.

## Answer

#### Difference between elastic and plastic analysis
| Point | Elastic analysis | Plastic analysis |
|---|---|---|
| Basis | Material is linearly elastic (Hooke's law); stresses stay below yield | Material is ductile and is stressed beyond yield; behaviour is taken as elastic-perfectly plastic |
| Design criterion | The stress at any point must not exceed the permissible stress (working stress method) | The structure is designed to collapse only at the ultimate (factored) loads |
| Failure considered | First yield of the extreme fibre | Formation of a mechanism after enough plastic hinges form |
| Section property used | Elastic section modulus $Z_e$; moment $M_y = \sigma_y Z_e$ | Plastic modulus $Z_p$; moment $M_p = \sigma_y Z_p$ |
| Indeterminate structures | Needs compatibility conditions (deflections, settlements, $EI$) | Needs only equilibrium and the yield (mechanism) condition; independent of $EI$ and settlement |
| Moment redistribution | Not considered; the moment distribution is fixed by the stiffnesses | Moments are redistributed after the first hinge forms, so the reserve strength is used |
| Safety | Factor of safety applied to stress | Load factor applied to the collapse load |
| Economy | Heavier sections | Lighter and more economical sections, particularly for continuous beams and frames |
| Applicability | Valid generally, including fatigue and deflection checks; simple to apply | Not valid where fatigue, buckling, brittle fracture or deflection controls |

#### Plastic hinge
A **plastic hinge** is a section of a beam at which the bending moment has reached the plastic moment $M_p$, so that the entire cross-section has yielded. The section can then rotate at a constant moment $M_p$, like a hinge that still transmits $M_p$. Its main points:
- It forms at the sections of maximum moment (fixed ends, joints, under point loads).
- A plastic hinge has a finite length (the zone where $M_y < M \le M_p$), though it is treated as a point in analysis.
- Unlike a real hinge, it resists rotation with the constant moment $M_p$ and rotates only in the direction of the moment.
- A structure with degree of indeterminacy $r$ becomes a mechanism and collapses when $r + 1$ plastic hinges form (fewer if only part of the structure fails).

## Check yourself

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

1. What failure condition does plastic analysis use compared with elastic analysis?
   A. First yield of the extreme fibre in both
   B. Elastic: first yield of extreme fibre; plastic: formation of a mechanism after hinges form
   C. Elastic: mechanism; plastic: first yield
   D. Both use buckling
   Answer: B. Elastic design limits stress at first yield; plastic design allows hinges to form until the structure becomes a mechanism. (Key point: Basis of failure)

2. What does plastic analysis of indeterminate structures need that elastic analysis does not avoid?
   A. Compatibility and EI, needed by plastic analysis
   B. Only equilibrium and the yield (mechanism) condition, independent of EI and settlement
   C. Slope-deflection equations
   D. Settlement values
   Answer: B. Plastic analysis uses equilibrium and yield conditions; elastic analysis needs compatibility, stiffness and settlements. (Key point: Indeterminate structures)

3. What is a plastic hinge and how many are needed for a mechanism in a structure of indeterminacy r?
   A. Section at Mp, fully yielded, rotating at constant Mp; r + 1 hinges
   B. Section at My with no yielding; r hinges
   C. A frictionless pin; r - 1 hinges
   D. Section with zero moment; r + 2 hinges
   Answer: A. A plastic hinge is a fully yielded section carrying Mp while rotating; r + 1 hinges convert the structure into a mechanism. (Key point: Plastic hinge definition)

## Related in Theory of Structures II

- [Plastic hinge versus elastic hinge](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adefine-plastic-hinge-compare-elastic) — Theory of Structures II, chapter 5
- [Define plastic hinge](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adefine-plastic-hinge) — Theory of Structures II, chapter 5, asked 2×
- [Plastic hinge and its length](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Adefine-plastic-hinge-length) — Theory of Structures II, chapter 5
- [Shape factor, plastic hinge properties, T-beam](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Ashape-factor-t-beam-plastic-hinge) — Theory of Structures II, chapter 5

## Related in other subjects

- [Short note: elastic and plastic behaviour](https://www.bctengineer.com/question.md?key=semester_3%2Fcivil_engineering_materials%3Aelastic-plastic-behaviour) — Civil Engineering Materials, chapter 1
- [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
- [Elastic-plastic torsion of a circular shaft](https://www.bctengineer.com/question.md?key=semester_5%2Fmechanics_of_solids%3Aplastic-torsion-circular-shaft) — Mechanics of Solids, chapter 12
- [Binomial vs negative binomial differences](https://www.bctengineer.com/question.md?key=semester_5%2Fprobability_and_statistics%3Anb-vs-binomial-diff-similarities) — Probability and Statistics, chapter 2, asked 4×