Question

The effective length of unsupported length of column L when effectively held in position at both ends and restrained against rotation at one end is

• A. 1.0 L
• B. 0.85 L
• C. 0.80 L
• D. 0.65 L

Hint:

For exams, it's crucial to know the recommended design values from IS 456, which can differ from pure theoretical values.
- Fixed-Fixed: 0.65 L
- Fixed-Pinned: 0.80 L
- Pinned-Pinned: 1.0 L
- Fixed-Free: 2.0 L

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the effective length of a column with specific end support conditions, as per IS 456.

Step 2: Detailed Explanation:
The end conditions described are:
- "Effectively held in position at both ends": This means translation (sideways movement) is prevented at both ends.
- "Restrained against rotation at one end": This means one end is fixed.
- Since it is not restrained against rotation at the other end, that end must be pinned (hinged).
Therefore, the condition is

Fixed-Pinned.
According to IS 456:2000 (Annex E), which provides effective lengths for columns, the code gives two values for each condition: a theoretical value and a recommended design value.
For a column that is effectively held in position at both ends and restrained against rotation at one end (Fixed-Pinned):
- The theoretical effective length factor is $K = 1/\sqrt{2} \approx 0.7$.
- The recommended design value given in the code is a more conservative value. Let's check the options. The available options are 1.0, 0.85, 0.80, and 0.65.
The value recommended by IS 456 for a column fixed at one end and pinned at the other is actually 0.80 L. The theoretical value is 0.707 L, and the code recommends a slightly higher value for practical design.
Wait, let's recheck IS 456 Table 28. - Effectively held in position and restrained against rotation at both ends (Fixed-Fixed): Recommended value is 0.65 L. - Effectively held in position at both ends, restrained against rotation at one end (Fixed-Pinned): Recommended value is 0.80 L. - Effectively held in position at both ends, but not restrained against rotation (Pinned-Pinned): Recommended value is 1.00 L. The described condition perfectly matches the Fixed-Pinned case.

Step 3: Final Answer:
The effective length for a column held in position at both ends and restrained against rotation at one end is 0.80 L.