Know how to calculate modulus of elasticity

The use of concrete in construction is becoming more common worldwide. Concrete is a mixture of sand, cement, and aggregate in a specific proportion. This mixture undergoes hydration when water is added, resulting in the hard mass referred to as concrete. It is important to assess the quality of concrete used in construction due to the extensive use of concrete structures. One such test is determining the modulus of elasticity of concrete.

The ratio of the applied stress on the concrete to the strain-induced is generally referred to as the modulus of elasticity of concrete.

Compression testing is the procedure used to determine the concrete’s elastic modulus on a cylindrical concrete sample.

A compressometer is set up for the test, and cycles of compressive stress up to 40% of the determined compressive stress are applied.

Below in the article, we’ll talk about the modulus of elasticity of concrete, its types, calculations, formulas to determine its importance, and factors affecting it. So, continue reading to get a complete overview of the modulus of elasticity of concrete that’ll make your construction work much easier!

 

Modulus of elasticity of concrete: An overview 

The modulus of elasticity of concrete, or how much it will deflect under load, is a measurement of the concrete’s stiffness. The behaviour of the concrete under load, including deflections, is analysed using this method. Note that this is also frequently referred to as the “Young’s modulus of concrete” after Thomas Young, a scientist who featured the idea that solid materials exhibit a linear elastic relation between tension and strain when subjected to low stresses.

The importance of modulus of elasticity in engineering

Engineers classify the behaviour of elastic material by the Modulus of Elasticity. Using this one can identify how materials behave, what material have to be chosen for device design and how one can calculate the stress present in a material.

It should be noted that a higher concrete elasticity modulus is usually not desirable in a concrete member since materials with higher stiffness will attract more stress and fail sooner than materials with higher elasticity. That is unless the stiffer materials’ strength is enhanced according to their elasticity modulus. This is commonly the case with concrete because its strength and elastic modulus typically correlate quite well. However, this is not always the case. It is not suggested that the designer focuses on stiffness only, but rather that stiffness is prioritised exclusively as a result of greater strength.

 

Expression for modulus of elasticity of concrete

According to IS 456:2000, the following expression for concrete’s elasticity modulus is recommended:

Ec = 5000 √fck

where fck is the concrete’s characteristic strength.

 

Is concrete an elastic material?

By elasticity, the original shape of the material is regained when the load is withdrawn.

Yes. To a certain extent, concrete is an elastic material, i.e. at low stresses.

The elastic characteristics and morphology of concrete’s component materials impact the material’s behaviour since concrete is a heterogeneous, multi-phase substance. As a result, Hooke’s law is not precisely followed by the stress-strain curve.

When the cement paste and aggregate concrete components are individually loaded, they exhibit a linear stress-strain relationship.

 

 

Understanding the Modulus of Elasticity formula

Due to the difficulty of measuring elasticity, a formula for Modulus of Elasticity of Concrete is used for design, which links the concrete’s modulus of elasticity to the compressive strength. Since the correlations are primarily reliable and the procedure often doesn’t significantly impact Young’s modulus of concrete as long as it stays within normal parameters, this is commonly accepted. However, it should be kept in mind that strength and elasticity are not inversely proportional. Therefore, these correlations are always, at best, approximations. The density, not the strength, is what correlates.

 

Procedure for determining the modulus of elasticity

The procedure for determining the modulus of elasticity has the following series of steps:

• Setting up of compressometer

Setting up the compressometer is the first step.

The tool used to measure the deformation and strain behaviour of cylindrical concrete specimens is known as a compressometer.

Following are the steps involved in setup:

• The spacers adjust the compressometer top and bottom frames.
• The pivot rod is locked firmly in place by being kept on the screws.
• Following that, the compressometer is carefully placed at the specimen’s centre.
• While the compressometer is kept in place, screws are tightened.
• Lastly, the spacers are unscrewed and removed after the positioning is complete.

 

• Testing of the specimen

The following steps are primarily involved in testing the specimen:

• The load is applied at 140 kg per cm2 per minute once the specimen has been appropriately positioned.
• The load applied is gradually increased until the stress value of (c+5)kg/cm2 is reached. C stands for one-third of the average compressive stress.
• After the value mentioned above is reached, the load is maintained for about a minute. The stress is subsequently decreased to 1.5 kg/cm2.
• The loading rate has been increased to (c+1.5) kg/cm2, and the reading is noted.
• The load is similarly increased at 1T intervals, and the data is recorded.
• The obtained values are then used to plot the graph.

 

Types of modulus of elasticity of  concrete

The modulus of elasticity of concrete can be classified into two groups:

• Static Elastic Modulus
• Dynamic Modulus

Static elastic modulus

We can define static elastic modulus using the modulus of elasticity defined under compression or uniaxial tension. The following curve is obtained as we experiment with the sample in compression or uniaxial tension:

The concrete forms a curving line in the stress-strain relationship since it is an imperfectly elastic material. The elasticity modulus can be determined in three different ways:

• Initial tangent modulus
• Tangent modulus
• Secant Modulus

When the stress-strain curve is at its initial phase, or when it is straight, a digression meets the source. The initial deviation modulus refers to this tangent’s slope. Engineers won’t employ this modulus along with their designs, though, because it has no use in real life. It only applies to low-stress values, which do not accurately depict concrete’s actual behaviour.

The tangent modulus can be obtained on the stress-strain angle at any given point. The term “tangent modulus” refers to that modulus. It is complicated and inaccurate to get the tangent modulus.

The secant modulus, also known as the chord modulus, is the other type. It is considered one of the vastly popular types of elasticity modulus used for concrete. To calculate, a specific point on the curve is chosen, and a chord is drawn using the initial linear portion. The secant modulus refers to this curve’s slope. When calculating the secant modulus of concrete, the stress must be considered because the value of this modulus will vary depending on the stress level.

Dynamic modulus

Concrete is under pure tensile or compressive stress during its service life. Instead, it combines these stressors and creeps. As a result, the dynamic modulus of elasticity is the modulus of elasticity formed during the actual loading of concrete. The specimen is subjected to longitudinal vibration at its natural frequency to determine its dynamic modulus, which is why it is so named.

 

Factors affecting modulus of elasticity of concrete

It is considered one of the most important characteristics of concrete that can be influenced by the concrete aggregate, mix proportion, factors of the growth zone, strength, cement paste, and moduli of elasticity of the ingredients. The substantial elasticity is controlled and governed by the below factors

1. Strength of concrete

Concrete’s modulus elasticity increases roughly in proportion to the square root of its resilience.

2. Cement paste

The hydrated cement’s elastic modulus influences concrete’s elastic modulus. The elastic modulus of concrete increases when porosity decreases due to an increase in the elastic modulus of cement paste. Cement paste’s porosity is regulated by air scope, degree of cement hydration, cement-to-water ratio, and admixture dosage.

3. Aggregates

The porosity substantially impacts the elastic modulus of aggregate; aggregate with low porosity has a high elastic modulus. The proportion of coarse aggregate leads to a high value of elastic modulus.

4. Concrete wetness condition

It is shown that the wet specimen’s modulus of elasticity is 15% higher than the dry specimen’s modulus of elasticity. The attribute demonstrates that drying builds more microcracks, generating more microcracks in the transition zone under dry conditions.

5. Transition zone

As the transition phase weakens due to the C-H crystal cracks and empty spaces already existing, the modulus of elasticity decreases. The interface between solidified cement paste and coarse aggregate particles is the transition zone.

6. Mix proportion

The modulus of elasticity increases with the increase in the quantity of cement. 

7. Concrete age

As the concrete becomes old, the elasticity modulus increases. 

8. Curing regime

The steam-cured concrete’s modulus of elasticity is somewhat less than water-cured concrete for the same strength.

 

Calculating modulus of elasticity: A step by step guide

For the computation of elastic modulus of concrete, applicable standard codes worldwide, such as European Code, Canadian standard association, ACI Code, British Standards, and Indian standard, have provided a formula.

The following equations from different codes are used to calculate the concrete’s modulus of elasticity:

 

1. Modulus of elasticity based on ACI 318-14

The modulus of elasticity of concrete is determined by ACI 318-14 section 19.2.2 as follows:

For concrete, the unit weight(WC) per cubic metre ranges from 1440 to 2560 Kg.

Ec = wc1.50.043√f’c (in MPa)

Ec = 57000√f’c (in psi)

 

For standard weight concrete :

Ec = 4700√f’c (in MPa)

Ec = wc1.533√f’c (in psi)

 

2. Modulus of elasticity based on CSA

Based on Canadian Standard Association (CSA A23.3), the modulus of elasticity for normal-weight concrete is as follows:

Ec = 4500√f’c (in MPa)

For high-strength concrete:

Ec = (3300√f’c +6900) (W/2300)1.5 (in MPa)

 

3. Modulus of elasticity based on EC

The following expression can be used to calculate the concrete’s modulus of elasticity based on the Eurocode:

Ecm = 22[(fcm)/10]0.3 

Where,

Ecm: mean modulus of elasticity

fcm: according to BS EN 1992-1-1: 2004, it means compressive strength of concrete at 28 days

 

4. Modulus of elasticity based on British standard

BS 8110: Part II 1985 provides the elastic modulus value at 28 days of concrete age.

Ec.28 = k0 + 0.2√fcu,28 

Where:

k0: for regular weight concrete, it is 20 KN per square millimetre

fcu,28: concrete compressive strength at 28 days.

 

5. Modulus of elasticity based on IS 456

The following formula can be used to calculate the concrete modulus of elasticity based on Indian standards:

Ec = 5000√f’c 

Also read: Concrete slab: An essential element for construction

 

Importance in design of concrete structure

The concrete’s elasticity modulus must be determined to design concrete structures properly. In the case of pre-stressed concrete that exhibits uncracked sections until the failure, for example, linear analysis of elements, based on the theory of elasticity, is utilised to satisfy requirements of both serviceability limit states and ultimate.

Compute deflections must also be kept to a minimum as part of the serviceability requirements for all structures. Finally, understanding the high-strength concrete’s modulus of elasticity is critical for preventing excessive deformation, ensuring adequate serviceability, and avoiding the most economical designs.

 

FAQs

What is the E value of concrete?

Tensile strength - σ: 2 - 5 MPa (300 - 700 psi) Modulus of elasticity - E: 14 - 41 GPa (2 - 6 x 106 psi)

What are the 4 main properties of concrete?

The 4 main properties of concrete are: Compressive strength Tensile strength Shear strength Flexural strength

What is the modulus of elasticity of M50 grade concrete?

Elasticity's modulus and strength are obtained for 1.5% for concrete of M50 grade.

What is the unit weight of concrete?

In the range of 140 to 150 lbs./cu. ft., concrete is considered to be normal weight. A change of 1.5 kg./cu. ft. in unit weight for concrete of average weight.

What is the modulus of elasticity of M25 concrete?

15000 MPa was found to be the long-term elastic modulus of M25 Concrete.

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