A cylindrical tank of radius $$'r'$$ and wall thickness $$'t'$$ has flat end closures. The tank is subjected to an internal pressure $$P.$$ The longitudinal $$\left( {{\sigma _x}} \right)$$ and the circumferential $$\left( {{\sigma _\theta }} \right)$$ stresses respectively are given by:

A rigid rod $$AB$$ of length $$L$$ is hinged at $$A$$ and is maintained in its vertical position by two springs with spring constants $$K$$ attached at end $$B.$$ The system is under stable equilibrium under the action of load $$P$$ when $$P < \,{P_{Cr}}$$. The system will be in unstable equilibrium when $$P$$ attains a value greater than

The static Indeterminacy of the structure shown below is

The fixed beam $$AB$$ has a span of $$3000$$ $$mm$$ and is of uniform cross-section. The plastic moment capacity $$({M_P})$$ of the beam's cross-section is $$1.5 \times {10^8}\,\,N$$-$$mm.$$

The beam will have like a simply supported beam when the magnitude of distributed load $$P$$ attains a value equal to: