Empirical Formula for Secant Modulus Proposed by Jensen Calculator

Secant Modulus Formula:

\[ E_c = \frac{6 \times 10^6}{1 + \frac{2000}{f'_c}} \]

Secant Modulus (E_c):

1. What is Secant Modulus?

Definition: Secant Modulus is one of several methods used to calculate modulus of elasticity, which is a measurement of a material's elasticity.

Purpose: It represents the slope of the secant line drawn from the origin to any specified point on the stress-strain curve of concrete.

2. Jensen's Empirical Formula

The calculator uses Jensen's empirical formula:

\[ E_c = \frac{6 \times 10^6}{1 + \frac{2000}{f'_c}} \]

Where:

\( E_c \) — Secant modulus of elasticity (MPa)
\( f'_c \) — Cylinder compressive strength of concrete (MPa)

Explanation: This formula provides an estimate of the secant modulus based on the compressive strength of concrete.

3. Importance of Secant Modulus

Details: The secant modulus is crucial for structural analysis and design, as it represents the stiffness of concrete at a particular stress level.

4. Using the Calculator

Tips: Enter the cylinder compressive strength in MPa and the desired tolerance percentage (default ±5%). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for secant modulus?
A: For normal strength concrete (20-40 MPa), the secant modulus typically ranges between 20,000 to 30,000 MPa.

Q2: Why include a tolerance percentage?
A: The tolerance accounts for variations in material properties and provides a practical range for engineering applications.

Q3: How does cylinder strength affect the modulus?
A: Higher strength concrete generally has a higher modulus of elasticity, though the relationship is non-linear.

Q4: When would I use secant modulus vs tangent modulus?
A: Secant modulus is used for overall stiffness calculations, while tangent modulus (slope at a point) is used for incremental stress-strain analysis.

Q5: Are there limitations to this empirical formula?
A: Yes, it's most accurate for normal weight concrete with strengths between 20-40 MPa. For high-strength or lightweight concrete, other formulas may be more appropriate.