If the modulus of sub-grade reaction using 30 cm diameter plate is 16 kg/cm², then the value of the same using the standard plate of 75 cm diameter is
- A6.4 kg/cm²Correct
- B7.4 kg/cm²
- C8.0 kg/cm²
- D9.3 kg/cm²
Solution
Concept
Plate size correction of k
Formula
k₇₅ = 0.4 k₃₀ (IRC)
Step-by-step solution
1. The modulus of subgrade reaction (k) is found from a plate load test. 2. The value for a 30 cm plate is converted to that for the standard 75 cm plate by k₇₅ = 0.4 × k₃₀. 3. k₇₅ = 0.4 × 16 = 6.4 kg/cm³.
Explanation
The modulus of subgrade reaction decreases as the plate diameter increases. IRC uses the standard plate of 75 cm and gives the relation k₇₅ = 0.4 k₃₀ for conversion. (The question writes the unit as kg/cm², but k is actually kg/cm³.)
Shortcut
Bigger plate → smaller k: k₇₅ = 0.4 k₃₀.
Common mistake
Multiplying by 2.5.
Correct answer: A) 6.4 kg/cm²