A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-energy and maximum-shear-stress theories, determine the factors of safety for the following plane stress states. a. σx = 94 MPa, and τxy = -75 MPa
b. σx = 110 MPa, σy = 100 MPa
c. σx = 90 MPa, σy = 20 MPa, τxy =−20 MPa

Explanation:

From  the given question:

Using the distortion energy theory to determine the  factors of safety  FOS can be expressed  by the relation:

where; syt = strength in tension and compression = 350 MPa

The maximum shear stress theory  can be expressed as:

where;

a. Using distortion - energy theory formula:

FOS = 2.183

USing the maximum-shear stress theory;

FOS = 1.977

b. σx = 110 MPa, σy = 100 MPa

Using distortion - energy theory formula:

FOS =3.322

USing the maximum-shear stress theory;

FOS = 350/2×25

FOS = 350/50

FOS = 70

c. σx = 90 MPa, σy = 20 MPa, τxy =−20 MPa

Using distortion- energy theory formula:

FOS = 350/88.88

FOS = 3.939

USing the maximum-shear stress theory;

FOS = 4.341

it was a fall down when it happens

explanation: