A point has σₓ = 160 MPa and σᵧ = −20 MPa, plus some shear stress. On an element rotated by 40° the normal stress in the rotated x′ direction is 26.5 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point in a loaded part has σₓ = 10 MPa, σᵧ = 60 MPa and τₓᵧ = 10 MPa (tension positive). Find the smallest principal stress σ2.
A point in a loaded part has σₓ = 150 MPa, σᵧ = −30 MPa and τₓᵧ = 50 MPa (tension positive). Find the maximum in-plane shear stress τmax.
A point in a thin plate is in plane stress: σₓ = 70 MPa, σᵧ = −40 MPa and τₓᵧ = 40 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).
A point in a loaded part has σₓ = 0 MPa, σᵧ = 30 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.
A solid shaft of diameter 40 mm carries an axial tensile force of 110 kN together with a torque of 2000 N·m. At the surface of the shaft, find the maximum in-plane shear stress τmax.
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