A point has σₓ = 60 MPa and σᵧ = 40 MPa, plus some shear stress. On an element rotated by 60° the normal stress in the rotated x′ direction is 62.3 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point in a loaded part has σₓ = 140 MPa, σᵧ = 0 MPa and τₓᵧ = 40 MPa (tension positive). Find the smallest principal stress σ2.
A point in a thin plate is in plane stress: σₓ = 140 MPa, σᵧ = 40 MPa and τₓᵧ = −30 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).
A point has σₓ = 10 MPa, σᵧ = −50 MPa and τₓᵧ = 10 MPa (tension positive). The element is rotated 25° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.
A point in a thin plate is in plane stress: σₓ = 80 MPa, σᵧ = 90 MPa and τₓᵧ = 30 MPa (σz = 0). The material has a yield strength of 300 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.
A solid shaft of diameter 30 mm carries a bending moment of 300 N·m together with a torque of 200 N·m. At the top surface, where the bending stress is tensile and largest, find the largest principal stress σ1.
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