Assuming the stress block diagram of the rectangular concrete beam section as per IS 456-2000, the depth of the centre of compressive force measured from the neutral axis is given by: (Assuming Xu as the depth of neutral axis from top compression fiber)
- A0.58 XuCorrect
- B0.36 Xu
- C0.67 Xu
- D0.42 Xu
Solution
Concept
In the IS 456 stress block, the compressive force acts at 0.42 Xu from the top fibre, so it is 0.58 Xu from the neutral axis.
Formula
C = 0.36 fck b Xu; distance from top = 0.42 Xu; distance from NA = Xu - 0.42 Xu = 0.58 Xu
Step-by-step solution
1. IS 456 stress block: parabola for the lower 4/7 of Xu, rectangle for the upper 3/7 of Xu 2. The centroid of the total compressive force lies at 0.42 Xu from the top compression fibre 3. Distance from the neutral axis = Xu - 0.42 Xu 4. = 0.58 Xu
Explanation
As per IS 456, the resultant compressive force acts at 0.42 Xu below the top fibre. The question asks for the distance from the neutral axis. So the answer is Xu - 0.42 Xu = 0.58 Xu.
Why the other options are wrong
B: 0.36 is the coefficient in the force C = 0.36 f
Correct answer: A) 0.58 X_u
