# Understanding Stresses and Modular ratio | RCC Structures

#### Stresses in Steel and Concrete | Building Construction

In one of our previous articles, we discussed “Basic definitions and formulas”.

Now we will move on with our discussion on “Permissible stresses in concrete and steel” and “Understanding Modular ratio”.

#### Permissible Stresses in Concrete

Reinforced concrete designs make use of M15 grade concrete. The permissible stresses for different grades of concrete is different. They are given below:

 Sr. No. Concrete Grade M15 M20 M25 M30 1. Stress in compression Bending 5 7 8.5 10 Direct 4 5 6 8 2. Stress in bond (average) for plain bars 0.6 0.8 0.9 1.0 3. Characteristics compressive strength 15 20 25 30

Also refer for other values in IS:456-1978

#### Permissible Stresses in Steel

The permissible stresses for different grades of steel are given in the table above.

The different grades steel available in the market with their market names are as follows:

Mild Steel

Grade I steel is known as mild steel. The abbreviation used for Mild steel is (m.s.)

High Tensile deformed steel has two types. They are as follows:

1. Grade Fe415 (Tor-40 or Tistrong I)
2. Grade Fe500 (Tor-50 or Tistrong II)

The names of the high tensile deformed steel have been derived from their manufacturers.

#### For example:

• Tor-Isteg Steel Corporation in Calcutta manufactures Tor-40 and Tor-50. Hence, the name.
• Tata Iron and Steel Co. Ltd, Calcutta manufactures Tistrong I and Tistrong II.

(Being aware of the names of the manufacturers is important for students especially those studying Civil and Structural Engineering.)

#### Understanding Modular Ratios

It is defined as the ratio of moduli of steel to the moduli of concrete. It is denoted by the letter “m”.

m=Es/Ec

The modular ratio is not constant for all grades of concrete. It varies with the grade of concrete. Es/Ec is generally not used to calculate modular ratio for reinforced concrete designs.

As per IS: 456-1978;

m is calculated by the following formula:

m = 280/3σcbc

where,

σcbc = permissible compressive stress in concrete in bending.

#### Calculation of Modular ratio values for different grades of concrete

 Grade of concrete Modular ratio M15 m = 280/3×5 = 18.66 M20 m = 280/3×7 = 13.33 M25 m = 280/3×8.5 = 10.98 M30 m = 280/3×10 = 9.33

It should be remembered that rounding off the modular ratio values is not permitted by Indian Standard.

### 5 thoughts on “Understanding Stresses and Modular ratio | RCC Structures”

1. What is the modular ratio m ? how much FSI permissible for Construction of Residetial Building ?

2. Any one can clarify my doubt. The modular ratio is m = 280/3σcbc.How to get the numerical value of 280.Why the Characteristics compressive strength of concrete is 3 times higher than bending Stress in compression of concrete.