Modulus of Elasticity of Concrete Calculator

Elastic Modulus Formula:

\[ E_{cmd} = 5000 \times \sqrt{f_{ck}} \]

Elastic Modulus (MPa):

Allowable Range (MPa):

1. What is Modulus of Elasticity of Concrete?

Definition: The modulus of elasticity of concrete is a measure of its stiffness, defined as the ratio of stress to strain in the elastic range.

Purpose: It helps structural engineers design concrete elements that will behave predictably under load.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E_{cmd} = 5000 \times \sqrt{f_{ck}} \]

Where:

\( E_{cmd} \) — Modulus of elasticity (MPa)
\( f_{ck} \) — Characteristic compressive strength (MPa)

Explanation: The modulus is calculated as 5000 times the square root of the characteristic compressive strength.

3. Importance of Elastic Modulus Calculation

Details: Accurate modulus values are crucial for deflection calculations, crack control, and serviceability design of concrete structures.

4. Using the Calculator

Tips: Enter the characteristic compressive strength in MPa and allowable variation percentage (default ±5%). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for concrete's modulus of elasticity?
A: For normal weight concrete, it typically ranges from 14,000 to 41,000 MPa.

Q2: Why do we include an allowable variation?
A: Concrete properties can vary due to material differences, so we account for this with a ±5% tolerance by default.

Q3: How does strength affect modulus of elasticity?
A: Higher strength concrete generally has a higher modulus of elasticity, following the square root relationship.

Q4: Is this formula applicable to all concrete types?
A: This formula is for normal weight concrete. Lightweight concrete requires different coefficients.

Q5: Where is this modulus used in design?
A: It's used in deflection calculations, seismic design, and when analyzing structural behavior under load.