**Flexural strength of Concrete**, also known as **Modulus of rupture,** is an indirect measure of the tensile strength of unreinforced concrete. Modulus of rupture can also be defined as the measure of the extreme fibre stresses when a member is subjected to bending. Apart from external loading, tensile stresses can also be caused by warping, corrosion of steel, drying shrinkage and temperature gradient.

Concrete is strong in compression but weak in tension because of which the flexural strength accounts for only 10% to 20% of the compressive strength.

**Determination of Flexural Strength of the Concrete**

## Experimental Estimation of Flexural Strength using One-point loading test and the Two-point loading test

Unlike compression, tensile strength of a member can not be found directly as no apparatus or specimen model has been developed to evenly distribute the tensile force to the member. However, the indirect measurement of the flexural strength like the **One-point loading test and the Two-point loading test **fetch satisfying results.

### Principle / Mechanism

Modulus of rupture is the measure of extreme fibre stresses in a member under flexure where the beam can be loaded using One-point loading or the symmetrical Two-point loading. When a simply supported beam is subjected to bending, tensile stresses are developed at the bottom of the beam and once the tensile stresses exceed the flexural strength of the beam, cracks start to occur at the point of maximum bending moment. The load causing the crack and the pattern of the crack can be used to calculate the flexural strength of the given concrete member.

### Procedure for Calculating Flexure Strength of Concrete

- Unreinforced concrete specimens of size 400 mm x 100 mm x 100 mm are casted using the desired concrete grade and cured properly for 28 days.
- The test specimens are allowed to rest in water for 2 days at a temperature of 24˚C to 30˚C before testing.
- The testing is done immediately after removal of the specimen from the water and while the specimens are
**in wet condition.** - Reference lines are drawn using chalks at 5 cm from the edges of the specimen on either side to indicate the position of the roller supports
- The prismatic specimens are supported on rollers of the testing machine. These rollers provide a simply supported condition for the test.
- The load is gradually applied through two symmetrical rollers on the axis of the beam.
- Further, load is applied without shock and increased continuously at a rate such that the stress in the extreme fibre increases at approximately
**7kg/cm**^{2}/minute. - Finally, the load is applied until the specimen fails and the maximum load is noted.

### Calculation of Flexural Strength from Lab Test

The Flexural Strength or Modulus of Rupture (f_{b}) is given by

**f _{b }= Pl/bd^{2}** (when a > 13.3 cm)

**f _{b }= 3Pa/bd^{2}** (when a < 13.3 cm)

Where,

**a** = the distance between the line of fracture and the nearest support, measured on the center line of the tensile side of the specimen (cm)

**b** = width of specimen (cm)

**d** = failure point depth (cm)

**l** = supported length (cm)

**P** = Maximum Load taken by the specimen (kg)

## Empirical Formula for Estimating Flexural Strength of Concrete

As per IS 456 2000, the flexural strength of the concrete can be computed by the characteristic compressive strength of the concrete

**Flexural strength of concrete = 0.7 **sqrt(*fck*)

Where**, ***fck* is the characteristic compressive strength of concrete in MPa.

Characteristic compressive strength (MPa) | Flexural Strength (MPa) |

20 | 3.13 |

25 | 3.50 |

30 | 3.83 |

35 | 4.14 |

40 | 4.43 |

45 | 4.70 |

50 | 4.95 |

## Significance of Flexural Strength

Though the modern construction practice uses reinforcement steel to increase the tensile strength of the concrete, the computation of the flexural strength is significant as the steel reinforcement can only take care of the extreme fibre stresses in the member.

The tensile stress caused by **warping, corrosion of steel, drying shrinkage and ****temperature gradient** can also cause failure. The determination of flexural strength is an important factor in **the design of pavements** especially when there is inadequate subgrade support.

## How to Increase the Flexural Strength of Concrete?

The use of **crushed ****aggregates** in the place of rounded aggregates increases the bond strength between the aggregates and the cement matrix and therefore increases the flexural strength. When reactive aggregates like the **Calcareous aggregates **are used, it reacts with the excess calcium hydroxide among the products of hydration to yield by-products which increases the flexural strength of the member.

Another way of increasing the flexural strength is by replacing a part of cement with **pozzolanic additives** like fly ash or Ground Granulated Blast Furnace Slag (GGBS). The pozzolanic additives play a major role in reducing the size and concentration of the Calcium Hydroxide crystals and invoking the formation of the most vital **Calcium Silicate Hydrate Gel** (CSH gel).

The other ways of increasing the flexural strength includes the overall strengthening of the member by reducing the total **porosity** and by reducing the **water cement ratio **of the concrete mix.

## FAQ

### What is characteristic compressive strength?

Characteristic compressive strength of concrete is the strength below which not more than 5% of the test results should fall. It is denoted by *fck***.**

For example, the characteristic compressive strength of M20 grade of concrete is 20 MPa.