A rectangular section beam (b = 200 mm and d = 400 mm) is reinforced in tension by Fe-415 grade steel bars, for which, according to IS 456: 2000 x u,max = 0.48d. If the neutral axis of the section lies at 200 mm from the top fiber, then the section type and the strain in steel at ultimate loads will be __________, respectively
- Abalanced and 0.0035
- Bunder-reinforced and 0.0035
- Cover-reinforced and 0.0035Correct
- Dbalanced and 0.0038
Solution
Concept
Comparison of actual neutral axis depth with the limiting neutral axis depth determines whether an RC section is under-reinforced, balanced, or over-reinforced.
Formula
xu,max = 0.48d
Step-by-step solution
Step 1: Identify the given parameters: b = 200 mm, d = 400 mm, grade of steel = Fe-415. Step 2: Calculate the limiting neutral axis depth (xu,max) using IS 456:2000 provisions for Fe-415 steel: xu,max = 0.48 × d = 0.48 × 400 = 192 mm. Step 3: Compare the actual neutral axis depth (x = 200 mm) with xu,max (192 mm). Step 4: Since x (200 mm) > xu,max (192 mm), the section is over-reinforced. Step 5: For an over-reinforced section at ultimate limit state, the extreme fiber concrete strain reaches 0.0035, while the strain in steel is less than the yield strain, but the maximum concrete compressive strain is established as 0.0035.
Explanation
According to IS 456:2000, the limiting depth of neutral axis (xu,max) for Fe-415 grade steel is 0.48d. Given effective depth d = 400 mm, xu,max = 0.48 × 400 = 192 mm. Since the actual neutral axis depth (x = 200 mm) is greater than xu,max (200 mm > 192 mm), the section is over-reinforced. In an over-reinforced section at ultimate load, the concrete reaches its maximum strain of 0.0035 before the steel yields.
Why the other options are wrong
A: Section is over-reinforced, not balanced. B: Section has x > xu,max, so it cannot be under-reinforced. D: Balanced section condition (x = x
Correct answer: C) over-reinforced and 0.0035