Understanding Concrete Flexural Tensile Strength

Concrete is strong in compression but relatively weak in tension. Flexural tensile strength, also known as the Modulus of Rupture, is a measure of concrete's ability to resist bending forces that cause tensile stress. This property is crucial in the design of concrete structures like beams and pavements, where bending occurs.

Calculating Flexural Tensile Strength

Various empirical formulas are used to estimate the flexural tensile strength of concrete based on its compressive strength. One widely accepted formula, often found in design codes like IS 456:2000, relates the flexural tensile strength to the characteristic compressive strength of concrete.

The characteristic compressive strength, denoted as \( f_{ck} \), is the strength below which not more than 5% of the test results are expected to fall. It is usually measured from standard cylinder or cube tests.

The formula commonly used to calculate the flexural tensile strength (Modulus of Rupture), \( f_{cr} \), from the characteristic compressive strength \( f_{ck} \) is:

\( f_{cr} = 0.7\sqrt{f_{ck}} \)

Here, \( f_{ck} \) is in MPa (or N/mm²), and the resulting \( f_{cr} \) is also in MPa.

Analyzing the Given Options

Let's look at the provided options and compare them to the standard formula for flexural tensile strength:

1. \(\frac{280}{3 \times \sigma_{abc}}\): This formula involves \( \sigma_{abc} \), which typically represents the permissible bending compressive stress in concrete. This formula is not directly used for calculating the flexural tensile strength.
2. \(5700\sqrt{f_{ck}}\): This formula is an empirical expression commonly used to estimate the modulus of elasticity of concrete, \( E_c \), in MPa, based on the characteristic compressive strength \( f_{ck} \). It is not the formula for flexural tensile strength.
3. \(0.7\sqrt{f_{ck}}\): This formula directly matches the standard empirical expression used to calculate the flexural tensile strength (Modulus of Rupture) of concrete based on its characteristic compressive strength \( f_{ck} \).
4. \(5000\sqrt{f_{ck}}\): This is another empirical formula, sometimes used to estimate the short-term static modulus of elasticity of concrete, \( E_c \), based on \( f_{ck} \). It is also not the formula for flexural tensile strength.

Conclusion

Based on standard concrete design principles and code provisions, the formula used to calculate the flexural tensile strength (Modulus of Rupture) of concrete is \(0.7\sqrt{f_{ck}}\).