For an RCC beam of width 230 mm and effective depth 300 mm subjected to a shear force of 69 kN due to design loads, what will be the nominal shear stress in the beam?
- A10 N/mm²
- B1 N/mm²Correct
- C0.01 N/mm²
- D0.1 N/mm²
Solution
Concept
Nominal shear stress in an RCC beam is the factored shear force divided by width × effective depth.
Formula
τv = Vu / (b × d)
Step-by-step solution
1. Given Vu = 69 kN = 69000 N, b = 230 mm, d = 300 mm. 2. b × d = 230 × 300 = 69000 mm². 3. τv = 69000 / 69000 = 1 N/mm².
Explanation
Nominal shear stress is found by dividing the design shear force by the area b × d. Here the shear force in N and the area in mm² have the same value, so the stress is 1 N/mm².
Why the other options are wrong
A (10), C (0.01) and D (0.1) come from wrong unit conversion of kN to N.
Shortcut
69000 N / 69000 mm² = 1 N/mm² directly.
Common mistake
Forgetting to convert kN to N, or using the overall depth instead of the effective depth.
Correct answer: B) 1 N/mm²