A point has σₓ = 70 MPa and σᵧ = 50 MPa, plus some shear stress. On an element rotated by 25° the normal stress in the rotated x′ direction is 112.4 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 = 60 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.
A point in a loaded part has σₓ = 110 MPa, σᵧ = 30 MPa and τₓᵧ = 20 MPa (tension positive). Find the maximum in-plane shear stress τmax.
A point in a loaded part has σₓ = 150 MPa, σᵧ = 20 MPa and τₓᵧ = 50 MPa (tension positive). Find the maximum in-plane shear stress τmax.
A point in a loaded part has σₓ = −10 MPa, σᵧ = −60 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis.
A point in a thin plate is in plane stress: σₓ = −80 MPa, σᵧ = −70 MPa and τₓᵧ = −30 MPa (σz = 0). The material has a yield strength of 420 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.
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