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

5  7  8.5  10 

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:4561978
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:
 Grade Fe415 (Tor40 or Tistrong I)
 Grade Fe500 (Tor50 or Tistrong II)
The names of the high tensile deformed steel have been derived from their manufacturers.
For example:
 TorIsteg Steel Corporation in Calcutta manufactures Tor40 and Tor50. 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: 4561978;
m is calculated by the following formula:
m = 280/3σ_{c}_{bc}
where,
σ_{c}_{bc }= 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.
We shall discuss the following in our succeeding articles:
 Assumptions for singly reinforced sections
 Design procedure for Singly reinforced section – I
 Solved Numericals for Singly reinforced beam  Method I
 Design of Singly reinforced sections  Design Method 2
 Solved Numericals for Singly reinforced beam  Method 2
 Moment of Resistance for Singly reinforced sections
 Solved numerical example  Moment of resistance
 Solved numerical example 2  Guide to singly reinforced sections
What is the modular ratio m ? how much FSI permissible for Construction of Residetial Building ?
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.
very good and understanding material available.
May I also add to the concept of modular ratio. Please correct me if I am wrong. Suppose I ask u to add 1 apple + 1 guava, u cannot add them because they are two different item. Now while comparing the moment of area of steel and concrete in a beam (say), the area of concrete is several times larger than steel, hence their moment of area cannot be compared because these 2 materials have different properties. Hence the area of steel has to be converted in terms of concrete area and modular ratio is used as the conversion factor. As for example σst = m x σcbc, means the equivalent area of steel in terms of concrete.
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