The principal stresses at a point in a critical section of a machine component are $${\sigma _1} = 60\,\,MPa,\,\,{\sigma _2} = 5\,\,MPa$$ and $${\sigma _3} = - 40\,\,MPa.$$ For the material of the component, the tensile yield strength is $${\sigma _y} = 200\,\,MPa.$$ According to the maximum shear stress theory, the factor of safety is

The principal stresses at a point inside a solid object are $${\sigma _1} = 100\,\,MPa,\,\,{\sigma _2} = 100\,\,MPa$$ and $${\sigma _3} = 0\,\,MPa.$$ The yield strength of the material is $$200$$ $$MPa.$$ The factor of safety calculated using Tresca (maximum shear stress) theory is $${n_T}$$ and the factor of safety calculated using Von Mises (maximum distortional energy) theory is $${n_V}$$. Which one of the following relations is TRUE?

A machine element is subjected to the following bi-axial state of stress: $$\,\,{\sigma _x} = 80MPa;\,\,{\sigma _y} = 20MPa;\,\,{\tau _{xy}} = 40MPa.$$ If the shear strength of the material is $$100 MPa,$$ the factor of safety as per Tresca’s maximum shear stress theory is

The state of stress at a point is given by $$\,\,{\sigma _x} = - 6\,MPa,\,\,{\sigma _y} = 4\,\,MPa,$$ and $${\tau _{xy}} = - 8\,\,MPa.$$ The maximum tensile stress (in MPa) at the point is ____________.