GATE 2003 Civil Engineering PYQ

Question

A long structural column (length $$-L$$) with both ends hinged is acted upon by an axial compressive load $$P.$$ The differential equation governing the bending of column is given by: $$$EI{{{d^2}y} \over {d{x^2}}} = - Py$$$

Where $$y$$ is the structural lateral deflection and $$EI$$ is the flexural rigidity. The first critical load on column responsible for its buckling is given by

GATE 2003 organizing institute · Accepted Answer

$${{{\pi ^2}EI} \over {{L^2}}}$$

GATE 2003 organizing institute · Answer

$${{\sqrt {2{\pi ^2}EI} } \over {{L^2}}}$$

GATE 2003 organizing institute · Answer

$${{2{\pi ^2}EI} \over {{L^2}}}$$

GATE 2003 organizing institute · Answer

$${{4{\pi ^2}EI} \over {{L^2}}}$$