Q.63 An RCC beam of width 250 mm and effective depth 450 mm is subjected to a nominal shear stress of 1.25 N/mm². What is the value of shear force due to design load coming on the section?
- A1.40625 kN
- B140.625 kNCorrect
- C14.0625 kN
- D1406.25 kN
Solution
Concept
Nominal shear stress is the design shear force divided by width times effective depth.
Formula
τv = Vu / (b × d), so Vu = τv × b × d
Step-by-step solution
1. Given: b = 250 mm, d = 450 mm, τv = 1.25 N/mm². 2. Use Vu = τv × b × d. 3. Vu = 1.25 × 250 × 450 = 140625 N. 4. Convert to kN: 140625 / 1000 = 140.625 kN.
Explanation
Nominal shear stress is shear force divided by the area b × d. Multiply the stress by width and effective depth to get the shear force. The result is 140625 N, which is 140.625 kN.
Why the other options are wrong
A: 1000 times too small, a unit error. C: 10 times too small, a decimal error. D: 10 times too large, a decimal error.
Shortcut
1.25 × 250 × 450 / 1000 = 1.25 × 112.5 = 140.625 kN
Common mistake
Wrong conversion from N to kN, which shifts the decimal place.
Correct answer: B) 140.625 kN