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

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

If the length of a column is doubled, the critical load becomes:

An initially stress-free massless elastic beam of length $$L$$ and circular cross-section with diameter $$d (d < < L)$$ is held fixed between two walls as shown. The beam material has Young's modulus $$E$$ and coefficient of thermal expansion $$\alpha .$$

If the beam is slowly and uniformly heated, the temperature rise required to cause the beam to buckle is proportional to

A column has a rectangular cross-section of 10 mm $$ \times $$ 20 mm and a length of 1 m. The slenderness ratio of the column is close to

The rod $$PQ$$ of length $$L$$ and with flexural rigidity $$EI$$ is hinged at both ends. For what minimum force $$F$$ is expected to buckle?