According to IS 800 - 2007, the effective length of prismatic compression member of unsupported length L is restrained against rotation and translation at both ends will be ______.
0.65 L
Understanding the effective length of a compression member is crucial for designing steel structures to prevent buckling failures. The effective length is the length of an equivalent pin-ended column having the same buckling strength as the actual compression member.
Effective Length as per IS 800 - 2007
According to IS 800 - 2007, the design code for steel structures in India, the effective length of a compression member depends significantly on its end conditions. The unsupported length of the member is denoted by L. The effective length ($\text{L}_{\text{eff}}$) is calculated using the formula:
$$\text{L}_{\text{eff}} = \text{k} \times \text{L}$$
Where 'k' is the effective length factor, which accounts for the restraint conditions at the ends of the member.
End Conditions and Effective Length Factor
IS 800 - 2007 specifies various end conditions and provides recommended values for the effective length factor 'k'. The question describes a specific end condition:
- Restrained against rotation at both ends.
- Restrained against translation at both ends.
This condition represents a fixed-fixed or both ends fixed scenario in structural analysis terms.
Referring to Table 11 (Effective Length of Prismatic Compression Members) in IS 800 - 2007, for a compression member with the ends restrained against translation and rotation, the recommended effective length factor (k) is 0.65.
| End Condition Description | Theoretically Clean Condition | Recommended Value (IS 800 - 2007) |
| Effectively held in position and restrained against rotation at both ends | 0.5 L | 0.65 L |
| Effectively held in position at both ends, and restrained against rotation at one end only | 0.7 L | 0.8 L |
| Effectively held in position at both ends, but not restrained against rotation | 1.0 L | 1.0 L |
| Effectively held in position and restrained against rotation at one end, and effectively restrained against translation but not against rotation at the other end | 1.0 L | 1.2 L |
| Effectively held in position at one end and restrained against rotation, and partially restrained against translation but not against rotation at the other end | - | 1.5 L |
| Effectively held in position and restrained against rotation at one end, and not held in position or restrained against rotation at the other end | 2.0 L | 2.0 L |
Calculating the Effective Length
Given the unsupported length L and the recommended effective length factor k = 0.65 for the specified end condition, the effective length is calculated as:
$$\text{L}_{\text{eff}} = \text{k} \times \text{L} = 0.65 \times \text{L} = 0.65 \text{L}$$
Therefore, the effective length of the prismatic compression member with both ends restrained against rotation and translation, according to IS 800 - 2007, is 0.65 L.
Comparing this result with the given options, the value 0.65 L matches one of the choices.
Important Questions from Compression Member
The maximum slenderness ratio of a compression member which carry loads resulting from dead loads and superimposed loads
A strut is a structural member subjected to
Effective length of steel column effectively held at both ends in position but not restrained in directions is ‘x’ times its length between two ends, where ‘x’ is equal to
What is the Imperfection factor for buckling class "A & B"
To calculate the compressive strength of compression member, Imperfection factor considered for Buckling 'class d' is ______.
