In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $$50$$ $$MPa$$ and $$150$$ $$MPa,$$ respectively. The endurance, yield, and the ultimate strengths of the material are $$200$$ $$MPa,$$ $$300$$ $$MPa$$ and $$400$$ $$MPa,$$ respectively. The factor of safety using modified Goodman criterion is

A bar is subjected to fluctuating tensile load from $$20$$ $$kN$$ to $$100$$ $$kN.$$ The material has yield strength of $$240$$ $$MPa$$ and endurance limit in reversed bending is $$160$$ $$MPa.$$ According to the Soderberg principle, the area of cross-section in $$m{m^2}$$ of the bar for a factor of safety of $$2$$ is

A forged steel link with uniform diameter of $$30mm$$ at the centre is subjected to an axial force that varies from $$40kN$$ in compression to $$160kN$$ in tension. The tensile $$\left( {{S_U}} \right),$$ yield $$\left( {{S_y}} \right)$$ and corrected endurance $$\left( {{S_e}} \right)$$ strengths of the steel material are $$600MPa, 420MPa$$ and $$240MPa$$ respectively. The factor of safety against fatigue endurance as per Soderberg’s criterion is

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