A rectangular concrete cantilever beam is made of M25 grade concrete and Fe415 grade steel is used. What is the modular ratio of the section assuming the modulus of elasticity of steel as 2 × 10⁵ MPa?
- A1/8
- B1/4
- C4
- D8Correct
Solution
Concept
Modular ratio m = Es/Ec, where Ec = 5000√fck as per IS 456.
Formula
Ec = 5000√fck ; m = Es/Ec
Step-by-step solution
1. Ec = 5000 × √25 = 25000 MPa 2. Es = 2 × 105 MPa 3. m = Es/Ec = 200000 / 25000 4. m = 8
Explanation
Modular ratio is the ratio of the modulus of steel to the modulus of concrete. For M25, Ec = 5000√25 = 25000 MPa. So m = 200000/25000 = 8.
Why the other options are wrong
A (1/8) is Ec/Es, which is the inverse. B (1/4) and C (4) do not come from correct values.
Shortcut
For M25, Ec = 25 GPa, so m = 200/25 = 8.
Common mistake
Taking Ec/Es instead of Es/Ec gives 1/8.
Correct answer: D) 8