Tensile Strength of Concrete in Combined Stress Design Calculator

Tensile Strength Formula:

\[ f_r = 7.5 \times \sqrt{f'_c} \]

Tensile Strength (f_r):

Tolerance Range (±5%):

1. What is Tensile Strength of Concrete?

Definition: Tensile strength is the maximum stress that concrete can withstand while being stretched or pulled before breaking. Concrete is weak in tension but strong in compression.

Purpose: This calculator helps engineers determine the tensile strength of concrete based on its compressive strength, which is important for combined stress design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ f_r = 7.5 \times \sqrt{f'_c} \]

Where:

\( f_r \) — Tensile strength of concrete (MPa)
\( f'_c \) — Specified 28-day compressive strength of concrete (MPa)

Explanation: The formula calculates the modulus of rupture (tensile strength) from the square root of the compressive strength multiplied by 7.5.

3. Importance of Tensile Strength Calculation

Details: While concrete is primarily designed for compressive strength, knowing its tensile strength is crucial for:

Crack control calculations
Shear strength determination
Design of reinforced concrete members
Serviceability limit state checks

4. Using the Calculator

Tips:

Enter the specified 28-day compressive strength in MPa
Enter tolerance percentage (default is ±5%)
Compressive strength must be > 0 MPa
Tolerance must be between 0-100%

5. Frequently Asked Questions (FAQ)

Q1: Why is the tensile strength lower than compressive strength?
A: Concrete contains microcracks that propagate easily under tension but are compressed under compressive loads.

Q2: What's the typical ratio of tensile to compressive strength?
A: Typically 8-15% of compressive strength, which is why reinforcement is needed for tensile loads.

Q3: When would I need to adjust the tolerance?
A: Adjust based on material variability, testing accuracy, or specific project requirements.

Q4: How do I find the 28-day compressive strength?
A: Through standard cylinder compression tests after 28 days of curing.

Q5: Does this formula apply to all concrete types?
A: It's most accurate for normal-weight concrete. Lightweight or high-strength concrete may require adjustments.