A bolt of major diameter $$12$$ $$mm$$ is required to clamp two steel plates. Cross sectional area of the threaded portion of the bolt is $$84.3$$ $$m{m^2}$$ . The length of the threaded portion in grip is $$30$$ $$mm,$$ while the length of the unthreaded portion in grip is $$8$$ $$mm.$$ Young's modulus of material is $$200$$ $$GPa.$$ The effective stiffness (in $$MN/m$$) of the bolt in the clamped zone is _______.

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $$100$$ $$MPa.$$ The yield and ultimate strengths of the shaft material in tension are $$300$$ $$MPa$$ and $$450$$ $$MPa,$$ respectively. The factor of safety using maximum distortion energy (Von - Mises) theory is __________.

Ball bearings are rated by a manufacturer for a life of $${10^6}$$ revolutions. The catalogue rating of a particular bearing is $$16$$ $$kN.$$ If the design load is $$2$$ $$kN,$$ the life of the bearing will be $$P \times {10^6}$$ revolutions, where $$P$$ is equal to ___________.

In a rolling process, the maximum possible draft, defined as the difference between the initial and the final thickness of the metal sheet, mainly depends on which pair of the following parameters?
$$P:$$ Strain
$$Q:$$ Strength of the work material
$$R:$$ Roll diameter
$$S:$$ Roll velocity
$$T:$$ Coefficient of friction between roll and work.