A rectangular RCC beam section having a width of 200 mm and depth of 300 mm is subjected to a factored shear force of 60 kN. Determine the nominal shear stress acting in the section if the effective cover is 50 mm and grade of concrete is M 20 and the grade of steel is Fe 415.
- A1.2 N/mm²Correct
- B1.4 N/mm²
- C1 N/mm²
- D0.86 N/mm²
Solution
Concept
Nominal shear stress is the factored shear force divided by the width times the effective depth.
Formula
τv = Vu / (b × d)
Step-by-step solution
1. Effective depth d = 300 - 50 = 250 mm 2. b = 200 mm, Vu = 60 kN = 60000 N 3. τv = Vu / (b × d) = 60000 / (200 × 250) 4. τv = 60000 / 50000 = 1.2 N/mm²
Explanation
Nominal shear stress uses the effective depth, not the overall depth. Effective depth is 300 - 50 = 250 mm. So τv = 60000 / (200 × 250) = 1.2 N/mm².
Why the other options are wrong
B: 1.4 N/mm² does not come from Vu/(b d). C: 1.0 N/mm² comes from using the overall depth of 300 mm, which is wrong. D: 0.86 N/mm² is not from the correct formula.
Shortcut
kN × 1000 / (b × d in mm) gives N/mm² directly: 60000/50000 = 1.2.
Common mistake
Using the overall depth D = 300 mm instead of the effective depth d = 250 mm.
Correct answer: A) 1.2 N/mm²