A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is subjected to an internal pressure varying from $$4$$ to $$8MPa.$$ Assume that the yield, ultimate and endurance strength of material are $$600,800,400MPa$$respectively. The factor of safety as per Goodman's relation is

A cylindrical shafts is subjected to an alternating stress of $$100MPa.$$ Fatigue strength to sustain $$1000$$ cycles is $$490MPa.$$ If the corrected endurance strength is $$70MPa,$$ estimated shaft life will be

A ductile material having an endurance limit of $$196$$ $$N/m{m^2}$$ and the yield point at $$294$$ $$N/m{m^2}$$ is stressed under variable load. The maximum and minimum stresses are $$147$$$$N/m{m^2}$$ and $$49$$$$N/m{m^2}$$. The fatigue stress concentration factor is $$1.32.$$ The available factor of safety for this loading is