Project ForgeAt a critical point in a component, the state of stress is σxx=100 MPa, σyy=220 MPa, σxy=σyx=80 MPa, and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is ___ (round off to one decimal place).
Explanation
In-plane principal stresses: σavg=(100+220)/2=160; R=√[((100−220)/2)²+80²]=√(3600+6400)=100. So σ1=260, σ2=60. The third (out-of-plane) principal stress is σ3=0, which is actually the true minimum (0<60). Maximum shear stress theory uses the largest and smallest of ALL THREE principal stresses: FOS = Sy/(σ1−σ3) = 468/(260−0) = 1.8.
Source: GATE ME 2019 Session 1 (Set 1) (2019)
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