Question

Euler buckling load for one end fixed and other hinged is given by: 
1. π2El / l2
2. 2π2El / l2
3. 4π2El / l2
4. π2El / 4l2

Answer 1

Correct Answer - Option 2 : 2π2El / l2

Explanation:

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.

Support Condition	Effective Length
Both ends hinged	\({L_e} = L\)
Both ends fixed	\({L_e} = \frac{L}{2}\)
One end fixed other end free	\({L_e} = 2L\)
One end fixed other end hinged	\({L_e} = \frac{L}{\sqrt{2}}\)

Now,

From the above table 

According to Euler's column theory, the crippling load of a column of length (l), with one end is fixed and the other end is hinged is \({P_{cr}}= \;\frac{{{2\pi ^2}EI}}{{{{\left( {L} \right)}}}}\)