As per IS 456:2000, which grade of concrete has a tensile stress of 3.2 N/mm² under limit state method?

Concept:

Characteristic strength of concrete (fck):

The compressive strength of concrete is given in terms of the characteristic compressive strength of  150 mm size cubes tested after 28 days

The characteristics strength is defined as the strength of concrete below which not more than 5% of the test results are expected to fall

Flexural strength of concrete:

The theoretical maximum flexural tensile stress occurring in the extreme fibres of RC beam, which causes cracking is referred to as the modulus of rupture (fCr)

The clause 6.2.2 of IS 456 gives the modulus of rupture of flexural tensile strength as

\({{\rm{f}}_{{\rm{cr}}}} = 0.7\sqrt {{{\rm{f}}_{{\rm{ck}}}}} \)

Calculation:

Given,

fcr = 3.2 N/mm2

\(3.2 = 0.7\sqrt {{\rm{f_{ck}}}}\)

f_ck = (3.2/0.7)² = 20.897 ≈ 21 N/mm²

Hence, the most appropriate answer is option 3.