Ahot-rolled steel has a yield strength of syr-sye-170 kpsi and a true strain at fracture of 0.55. estimate the factor of safety for the following stress state, by using a) the maximum shear stress theory b) the distortion energy theory. (30 points) s1. ox-30 kpsi, o,' =-15 kpsi, τ kpsi.

a) Factor of safety ≤ 1.689

b) Factor of safety ≤ 1.944

Explanation:

Given data:

Yield strength,

True strain factor = 0.55

Now, principle stress is given as:

on substituting the values we get

or

and

a) By maximum shear stress theory

we have

on substituting the values, we get

or

Factor of safety ≤ 1.689

b) By the distortion energy theory

since no force is acting in the z- direction, thus

on substituting the values, we get

or

Factor of safety ≤ 1.944

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explanation: