1
GATE CE 2013
+1
-0.3
Two steel columns $$P$$ (Length $$L$$ and yield strength $${f_y} = 250\,\,MPa)$$ and $$Q$$ (length $$2L$$ and yield strength $${f_y} = 500\,\,MPa$$) have the same cross-sections and end-conditions. The ratio of buckling load of column $$P$$ to that of column $$Q$$ is
A
$$0.5$$
B
$$1.0$$
C
$$2.0$$
D
$$4.0$$
2
GATE CE 2012
+1
-0.3
The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to
A
$$0.5$$
B
$$1.0$$
C
$$2.0$$
D
$$4.0$$
3
GATE CE 2010
+1
-0.3
The effective length of a column of length $$L$$ fixed against rotation and translation at one end is
A
$$0.5$$ $$L$$
B
$$0.7$$ $$L$$
C
$$1.414$$ $$L$$
D
$$2$$ $$L$$
4
GATE CE 2003
+1
-0.3
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

A
$${{{\pi ^2}EI} \over {{L^2}}}$$
B
$${{\sqrt {2{\pi ^2}EI} } \over {{L^2}}}$$
C
$${{2{\pi ^2}EI} \over {{L^2}}}$$
D
$${{4{\pi ^2}EI} \over {{L^2}}}$$
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