Consider the schematic of a riveted lap joint subjected to tensile load $$F,$$ as shown below. Let $$d$$ be the diameter of the rivets, and $${S_f}$$ be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of the plates? Assume the plates to be identical.

A machine element has an ultimate strength $$\left( {{\sigma _u}} \right)$$ of $$600\,\,N/m{m^2},$$ and endurance limit $$250$$ $$\,N/m{m^2}.$$ The fatigue curve for the element on log-log plot is shown below. If the element is to be designed for a finite of $$10000$$ cycles, the maximum amplitude of a completely reversed operating stress is _________ $$\,N/m{m^2}.$$

A sprue in a sand mould has a top diameter of $$20mm$$ and height of $$200mm.$$ The velocity of the molten metal at the entry of the sprue is $$0.5m/s.$$ Assume acceleration due to gravity as $$9.8\,\,m/{s^2}$$ and neglect all losses. If the mould is well ventilated, the velocity (upto $$3$$ decimal points accuracy) of the molten metal at the bottom of the sprue is ______________________ $$m/s.$$

In a metal forming operation when the material has just started yielding, the principal stresses are $${\sigma _1} = \,\, + 180\,\,MPa,\,\,\,$$ $${\sigma _2} = \,\, - 100\,\,MPa,\,\,\,$$ $${\sigma _3} = 0.$$ Following Von Mises' criterion, the yield stress is _____________ $$MPa.$$