A point has σₓ = 130 MPa and σᵧ = 120 MPa, plus some shear stress. On an element rotated by 20° the normal stress in the rotated x′ direction is 167.4 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point in a loaded part has σₓ = 30 MPa, σᵧ = 30 MPa and τₓᵧ = 20 MPa (tension positive). Find the smallest principal stress σ2.
A point in a loaded part has σₓ = −60 MPa, σᵧ = −50 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 thin plate is in plane stress: σₓ = −30 MPa, σᵧ = −50 MPa and τₓᵧ = −20 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).
A point in a thin plate is in plane stress: σₓ = 0 MPa, σᵧ = 70 MPa and τₓᵧ = 20 MPa (σz = 0). The material has a yield strength of 275 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.
A point in a loaded part has σₓ = −70 MPa, σᵧ = −10 MPa and τₓᵧ = 20 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.
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