---
title: "Elastic properties and modulus of elasticity"
subject: "Concrete Technology and Masonry Structure"
chapter: 4
key: "semester_5/concrete_technology_and_masonry_structure:elastic-properties-modulus"
source: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/elastic-properties-modulus
site: BCT Engineering
---

# Elastic properties and modulus of elasticity

Concrete Technology and Masonry Structure · Chapter 4: Properties of hardened concrete

- Asked in: 2075 Chaitra, 6 marks; 2072 Chaitra, 6 marks; 2070 Chaitra, 3 marks (asked 3 times)
- Video: [Modulus of Elasticity of Concrete | Stress Strain Curve of Concrete | Static Modulus of Elasticity](https://www.youtube.com/watch?v=0wc3OU4fpGk) — CementPDM by CemNex
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/concrete_technology_and_masonry_structure/elastic-properties-modulus
- Whole chapter: https://www.bctengineer.com/md/semester_5/concrete_technology_and_masonry_structure/chapter-4

## Question

Describe the elastic properties and the modulus of elasticity (Young's modulus) of concrete.

## Short answer

Concrete is not perfectly elastic; at working stress it is linear with modulus Ec=5000√fck (e.g.,22360 N/mm² for M20). Poisson's ratio is0.15–0.20. Modulus increases with higher strength, stiffer aggregates, age, and moisture.

## Answer

#### Elastic properties
Concrete is a composite of paste, aggregate and interface, and so it is not truly elastic. On loading, the stress-strain curve is nearly straight up to about 30 to 40% of the ultimate stress, then curves as microcracks grow. For design, concrete is treated as elastic at working stress. The elastic properties are the **modulus of elasticity** $E$, **Poisson's ratio** $\mu$ (0.15 to 0.20 for concrete) and **modulus of rigidity** $G = E/[2(1+\mu)]$.

#### Modulus of elasticity (Young's modulus)
It is the ratio of stress to strain within the elastic range:

$$
E = \frac{\sigma}{\varepsilon}
$$

- **Initial tangent, tangent, secant and chord moduli** are used (secant at about 33% of $f_c$ is the static modulus).
- **Dynamic modulus** from UPV or resonant frequency is higher than static modulus.
- **IS 456 (Cl. 6.2.3.1):** $E_c = 5000\sqrt{f_{ck}}$ N/mm$^2$. For M20: $E_c = 5000\times4.472 = 22360$ N/mm$^2$.

#### Factors affecting $E$
- Higher strength (lower W/C) gives a higher $E$.
- Stiffer aggregates (granite) and a higher aggregate content give a higher $E$; light-weight aggregate gives a lower $E$.
- Moist concrete has a higher $E$ than dry concrete; porosity reduces $E$.
- $E$ increases with age. A slower rate of loading gives a lower apparent value because of creep.

$E$ is used to calculate deflection, to find the modular ratio $m = 280/(3\sigma_{cbc})$ (IS 456, Annex B) and to find the stress distribution in composite sections.

## Check yourself

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

1. Concrete is not truly elastic because:
   A. it is a pure single-phase material
   B. it is a composite of paste, aggregate and interface, with microcracks growing as load rises
   C. it always fails at low strain
   D. it has a very high Poisson's ratio
   Answer: B. The stress-strain curve is linear only to about 30-40% of ultimate stress. (Key point: Why not truly elastic)

2. For M20 concrete the IS 456 modulus E_c is about:
   A. 22360 N/mm^2
   B. 20000 N/mm^2
   C. 100000 N/mm^2
   D. 5000 N/mm^2
   Answer: A. 5000 x sqrt(20) = 5000 x 4.472 = 22360 N/mm^2. (Key point: IS 456 modulus)

3. Which makes the modulus of elasticity higher?
   A. Lightweight aggregate
   B. Greater porosity
   C. Stiffer aggregate and lower W/C (higher strength)
   D. Higher W/C ratio
   Answer: C. Stiff aggregate and high strength raise E; porosity and lightweight aggregate lower it. (Key point: Factors affecting E)

4. Modulus of rigidity of concrete in terms of E and Poisson's ratio is:
   A. G = E / (1 - 2 mu)
   B. G = 2E(1 + mu)
   C. G = E x mu
   D. G = E / [2(1 + mu)]
   Answer: D. This is the standard elastic relationship; mu is 0.15 to 0.20 for concrete. (Key point: Modulus of rigidity)

## Related in Concrete Technology and Masonry Structure

- [Hardened concrete properties; elastic behaviour](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Ahardened-properties-elastic-behaviour) — Concrete Technology and Masonry Structure, chapter 4
- [Types of modulus of elasticity](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Amodulus-of-elasticity-types) — Concrete Technology and Masonry Structure, chapter 4, asked 4×
- [Properties of hardened concrete](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Ahardened-concrete-properties) — Concrete Technology and Masonry Structure, chapter 4, asked 3×
- [Physical properties of OPC and concrete behaviour](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Acement-physical-properties) — Concrete Technology and Masonry Structure, chapter 1
- [Aggregate properties and their influence on concrete](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Aaggregate-properties-influence) — Concrete Technology and Masonry Structure, chapter 1
- [Modulus of rupture and flexural test](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Amodulus-of-rupture-determination) — Concrete Technology and Masonry Structure, chapter 5, asked 4×

## Related in other subjects

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- [Relation between elastic moduli and Poisson's ratio](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Amodulus-e-g-k-relation) — Strength of Materials, chapter 3, asked 3×
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