What is modular ratio of concrete grade M30 when effect of creep is NOT considered?

Concept:

Modular ratio:

In the elastic theory for the reinforced concrete structure, concrete and reinforcing steel are converted into one material. This is done by using the modular ratio ‘m’.

It is the ratio of modulus of elasticity of steel and concrete.

\(\rm m = \frac{{{E_s}}}{{{E_c}}}\)

However, concrete has varying moduli, as it is not a perfectly elastic material.

Short term modulus of elasticity:

The short-term modulus of elasticity is given by

 \(\left( {{E_c} = 5000\sqrt {{f_{ck}}} } \right)\) 

Long term modulus of elasticity:

The long-term modulus of elasticity is considered to take into account the effect of creep and shrinkage.

The modular ratio is taken as

\(m = \frac{{280}}{{3 \times {\sigma _{cbc}}}}\)

where σcbc is permissible compressive stress in concrete in bending.

Calculation:

Grade of concrete = M30

Modular ratio ‘m’ (without considering creep effect)

 \(m = \frac{{{E_s}}}{{{E_c}}} = \frac{{2 \times {{10}^5}}}{{5000\sqrt {{f_{ck}}} }} =\frac{{2 \times {{10}^5}}}{{5000\sqrt {{30}} }}\) = 7.30