Consider a steel (Young’s modulus $$E = 200$$ $$GP$$a) column hinged on both sides. Its height is $$1.0$$ $$m$$ and cross-section is $$10 mm$$ $$ \times $$ $$20 mm$$. The lowest Euler critical buckling load (in $$N$$) is __________ .

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is

A pin-ended column of length $$L,$$ modulus of elasticity $$E$$ and second moment of the cross-sectional area $$I$$ is loaded centrally by a compressive load $$P.$$ The critical buckling load $$\left( {{P_{cr}}} \right)$$ is given by

For the case of a slender column of length $$l,$$ and flexural rigidity $$EI$$ built-in at its base and free at the top, the Euler’s critical buckling load is