A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight W as shown. If the maximum value of W to avoid buckling of the beam AB is obtained as βπ²EI, where π is the ratio of circumference to diameter of a circle, then the value of β is

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