Consider the following statements regarding the strength of flanged sections in flexure where the moment of resisting capacity of flanged sections depends upon the depth of neutral axis xu : 1. If xu ≤ Df, compressive force is in the flange only. 2. If (3/7) xu > Df, compressive stress in the flange is uniform. 3. If xu > Df and (3/7) xu > Df, compressive stress in flange is non uniform. Which of the above statements is/are correct ?
- A1 and 3
- B2 and 3
- C1 and 2Correct
- D1 only
Solution
Concept
Neutral axis position in flanged beams (IS 456 G-2.2)
Formula
Rectangular stress zone extends to 3/7 xu from the top
Step-by-step solution
1. If xu ≤ Df the whole compression zone lies inside the flange (statement 1 true). 2. The stress is uniform (0.446 fck) over the top 3/7 xu. If 3/7 xu > Df, the whole flange is within the rectangular part (statement 2 true). 3. If xu > Df and 3/7 xu > Df, the flange stress is also uniform, so "non-uniform" is false. Non-uniform stress occurs when 3/7 xu < Df.
Explanation
Only when the flange extends below the rectangular part (Df > 3/7 xu) does the flange carry the parabolic part of the stress block.
Why the other options are wrong
Statement 3 says non-uniform, which would be true only for Df > 3/7 xu.
Shortcut
Df ≤ 3/7 xu → uniform; Df > 3/7 xu → non-uniform.
Common mistake
Confusing the direction of the inequality.
Correct answer: C) 1 and 2