The modulus of elasticity of concrete (Ec) represents the relationship between applied stress and resulting strain. It serves as an indicator of both the concrete’s ability to withstand deformation under stress and its stiffness. Essentially, it measures how much the concrete can deflect elastically. The modulus of elasticity is influenced by factors such as the type of aggregate used and the proportions of the concrete mixture.
When designing concrete structures, the modulus of elasticity plays a significant role and needs to be determined. It is particularly important in the linear analysis of elements based on elastic theory. This approach is utilized in certain cases to meet the requirements of both ultimate and serviceability limit states, such as in the design of pre-stressed concrete structures.
Various widely recognized codes worldwide, including the ACI Code, European Code, British Standards, Canadian Standard Association, and Indian Standard, provide formulas for calculating the elastic modulus of concrete.
Calculation of Elastic Modulus of Concrete
The modulus of elasticity of concrete can be calculated using equations from different codes. Here are the presented equations for this computation.
1. Modulus of Elasticity Based on ACI 318-14
The modulus of elasticity of concrete, as stated in ACI 318-14 section 19.2.2, is determined using specific criteria. The unit weight (wc) of concrete typically falls within the range of 1440 to 2560 Kg per cubic meter.
For normal weight concrete :
2. Modulus of Elasticity Based on CSA
The modulus of elasticity for normal weight concrete, according to the Canadian Standard Association (CSA A23.3), refers to the measure of a material’s stiffness or its ability to deform elastically under applied stress. It is an important property in structural engineering as it affects the behavior of concrete elements subjected to various loads. The CSA A23.3 standard provides guidelines and specifications for determining the modulus of elasticity of normal weight concrete, ensuring that it meets the required performance and safety standards in construction projects.
For high strength concrete:
3. Modulus of Elasticity Based on EC
The modulus of elasticity of concrete can be determined using the formula provided in the Euro code.
Where,
In the context of concrete properties, two important parameters are the mean modulus of elasticity (Ecm) and the mean compressive strength of concrete at 28 days (fcm), as defined in Table 3.1 of the BS EN 1992-1-1:2004 standard. Ecm represents the average measure of a material’s elasticity, indicating how much it deforms under stress. On the other hand, fcm denotes the average compressive strength that concrete can withstand after 28 days of curing. These values are crucial in designing and assessing the structural integrity of concrete elements according to the specified standard.
4. Modulus of Elasticity Based on British Standard
In the British Standard 8110: Part II 1985, the value of the Elastic modulus at the age of 28 days for concrete is provided. This standard serves as a reference for the design and construction of concrete structures. The Elastic modulus is an important parameter that represents the stiffness and ability of concrete to withstand external loads without significant deformation.
By specifying the value of the Elastic modulus at 28 days, the standard acknowledges the fact that concrete gains strength and develops its properties over time. The 28-day mark is commonly used as a benchmark to assess the performance and durability of concrete structures, as it represents a significant period in which the concrete has undergone substantial curing and hydration processes.
The Elastic modulus, often referred to as Young’s modulus, indicates how much a material can deform under stress. In the context of concrete, it reflects the material’s ability to resist compression and tension forces. By providing a specific value for the Elastic modulus at 28 days, the BS 8110: Part II 1985 enables engineers and designers to make accurate calculations and predictions regarding the behavior of concrete structures during their service life.
The inclusion of this information in the standard emphasizes the importance of considering the time-dependent properties of concrete. It recognizes that the mechanical properties of concrete change with age, and engineers must account for this in their designs. The value of the Elastic modulus at 28 days serves as a reference point that facilitates the design process and ensures the structural integrity of concrete elements in accordance with the established standards and regulations.
Where:
The compressive strength of concrete is often measured to determine its load-bearing capacity and overall structural integrity. One common measure used is the concrete’s compressive strength at 28 days, denoted as fcu,28. This value represents the maximum amount of compressive stress that the concrete can withstand after 28 days of curing.
However, it seems that there is some confusion regarding the provided information. The unit “20 KN per square millimeter” does not typically represent the compressive strength of normal weight concrete. Compressive strength values are typically expressed in units of megapascals (MPa) or pounds per square inch (psi), rather than kilonewtons per square millimeter (KN/mm²). It’s possible that there may be a mistake or a different context that needs clarification.
To summarize, the compressive strength of concrete is often measured using the fcu,28 value, which represents the maximum compressive stress the concrete can withstand after 28 days of curing. However, the given unit of “20 KN per square millimeter” does not align with typical units used to express concrete compressive strength. Further clarification or correction is necessary to provide accurate information.
5. Modulus of Elasticity Based on IS 456
The calculation of the modulus of elasticity for concrete, as per the Indian standard, involves utilizing the following expression.
Importance in Design of Concrete Structure
The definition of the modulus of elasticity of concrete plays a highly crucial role in the design of concrete structures. It serves as a fundamental parameter in the linear analysis of elements, which is based on the theory of elasticity. This analysis is essential for meeting the requirements of both the ultimate limit state, ensuring structural integrity up to failure, and the serviceability limit state, which ensures that the structure performs adequately under normal conditions.
One specific application where the modulus of elasticity is vital is in the design of pre-stressed concrete structures. These structures are designed to maintain an uncracked section even under significant loads until failure occurs. The modulus of elasticity is utilized in the linear analysis to accurately predict and control the deflections of the structure. By limiting the deflections within acceptable ranges, the serviceability requirements of the structure are satisfied.
Moreover, a thorough understanding of the modulus of elasticity is particularly important when dealing with high-strength concrete. High-strength concrete offers superior structural performance but also tends to exhibit lower deformability compared to conventional concrete. By accurately determining the modulus of elasticity of high-strength concrete, excessive deformations can be avoided, ensuring satisfactory serviceability of the structure. Additionally, this knowledge aids in achieving cost-effective designs by optimizing the structural elements based on the specific modulus of elasticity of the high-strength concrete being used.