A point has σₓ = 10 MPa and σᵧ = 100 MPa, plus some shear stress. On an element rotated by 20° the normal stress in the rotated x′ direction is 39.8 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point on the surface of a shaft in torsion is in pure shear with τₓᵧ = −40 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 15° counter-clockwise from the x-axis.
A point in a loaded part has σₓ = 130 MPa, σᵧ = −20 MPa and τₓᵧ = 60 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.
A point in a loaded part has σₓ = 80 MPa, σᵧ = 10 MPa and τₓᵧ = 20 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.
A point in a loaded part has σₓ = −80 MPa, σᵧ = −10 MPa and τₓᵧ = 50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.
A point in a thin plate is in plane stress: σₓ = −60 MPa, σᵧ = −50 MPa and τₓᵧ = −60 MPa (σz = 0). The material has a yield strength of 250 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.
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