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?

A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspended along with its upper rim. The density of water is $$1000$$kg/m³ and acceleration due to gravity is $$10$$ m/s². The self weight of the cylinder is negligible. The formula for hoop stress in a thin walled cylinder can be used at all points along the height of the cylindrical container.

The axial and circumferential stress $$\left( {{\sigma _{a,}}\,{\sigma _c}} \right)$$ experienced by the cylinder wall a mid-depth ($$1$$ m as shown) are

A cylindrical container of radius $$R=1$$m, wall thickness $$1$$mm is filled with water upto a depth of $$2$$m and suspended along with its upper rim. The density of water is $$1000$$kg/m³ and acceleration due to gravity is $$10$$ m/s². The self weight of the cylinder is negligible. The formula for hoop stress in a thin walled cylinder can be used at all points along the height of the cylindrical container.

If the Young's modulus and Poisson's ratio of the container material are $$100$$GPa and $$0.3$$, respectively. The axial strain in the cylinder wall at mid height is

The strain energy stored in the beam with flexural rigidity $$EI$$ and loaded as shown in the figure is