Question
Download Solution PDFAs per Euler's theory, for which of the following end conditions is the longest effective length of a column obtained?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- Effective length is defined as the distance between two adjacent points of zero bending moment or contra flexure.
The value of the effective length varies according to the support condition.
|
End condition |
Both ends hinged |
One end fixed other free |
Both ends fixed |
One end fixed and other hinged |
|
Effective length |
L |
2L |
L/2 |
L/√2 |
According to Euler's column theory, the crippling load for a column of length L,
\({P_{cr}}= \;\frac{{{\pi ^2}EI}}{{{{\left( {L_e} \right)}^2}}}\)
Where Leq is the effective length of the column.
Explanation:
- The equivalent length of a column as per Euler's theory, whose effective length is the longest is When one end of the column is fixed and the other end is free.
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