Modulus is the measure of the concrete slabs' or beams' tensile strength. Flexural strength is the measure of how much stress and force an unreinforced concrete slab or beam can withstand without bending. Modulus of fracture is also known by flexural strength (bend strength), fracture strength and flexural strength.

## Standard Test Methods for determining the Modulus Of Rupture of a Beam

To test the flexural strength a concrete beam, the span length must be at least three times its depth. The modulus of rupture (MR), expressed in psi (MPa) is the measure of flexural strength. Two standard methods can be used to determine concrete beam's flexural strength.

### 1. ASTM C 293. Center point loading test

This test applies the entire load at the beam's center. This test method uses a higher flexural strength (or modulus de rupture) than the third point loading. Only the center of the beam is where the maximum stress occurs.

### 2. Third point loading test according to ASTM C78

This test involves applying half of the load to each third the beam's length. This test uses a lower flexural strength (or modulus of fracture) than the center point loading testing. The center-one-third of the beam is the area where the maximum stress is found.

The compressive strength of concrete beams can vary from 10% to 20% depending on the type, volume and size of coarse aggregate. Laboratory tests are the best way to determine the correlation between specific materials and the mix design.

Third point loading results in a lower concrete modulus of rupture than center point loading. Sometimes, it can even be as high as 15%.

Also Read: Concrete Tensile Strenght

## Standard Test Procedures to Assess Modulus of Rutture of Concrete Beam

Concrete beams must span at least three times their depths to be tested for flexural strength.

The flexural strength can be expressed as the MR (MPa) in psi.

Two common tests can be used to determine the flexural strength of concrete beams:

### 1. Centre Point Loading Test (as per ASTM C 293):

This measurement technique uses the entire beam's length to measure the load.

The three-point bending load test exceeds the flexural strength.

The beam's center is where the most stress is.

### 2. Third Point Loading (as per ASTMC 78)

The load is applied at each third of the beam's length.

This is because the flexural strength of the steel is lower than that of the rupture modulus, which was determined in the center-point loading test.

This test places the greatest stress in the centre third of the beam.

The flexural modulus can vary between 10 to 20% depending on the type, size and quantity of coarse aggregate used for a concrete beam.

The best correlation is achieved by laboratory tests of the specific materials and the mix design.

It is determined using the third point loading, up to 15% lower than MR.

Also Read: Parapet

## Calculation of Modulus of Rupture

The rupture formula can be different for different types of loading systems.

A rectangular sample is subjected to a three-point bend configuration.

Equation 1= (3FL/(2bd2)

F is the force (load), at the fracture point (N).

L is the length of the support span.

D is the thickness and b the width.

2. To load a rectangular survey, a four-point bending configuration can be used. The loading span is one third of the support span.

Equation 2: Modulus Of Rupture = (FL/bd2)

F is the force (load) at the fracture point in a four-point loading.

L is the length of the support (outer) and span is its thickness.

3. The 4-point bend configuration is used if the loading span exceeds the support span.

Equation 3: Modulus Of Rupture = (3FL/(4bd2)

4. If the load span of the four-point bend configuration is not 1/3 or 1/2 the support span.

Equation 4= (3F[L-Li])/(2bd2)

Li refers to the size of the inner load span.

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