A point has σₓ = 10 MPa and σᵧ = 90 MPa, plus some shear stress. On an element rotated by 35° the normal stress in the rotated x′ direction is 73.9 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 = −100 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 25° counter-clockwise from the x-axis.
A point has σₓ = −20 MPa and σᵧ = 20 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 65 MPa?
A point has σₓ = −50 MPa, σᵧ = 50 MPa and τₓᵧ = 20 MPa (tension positive). The element is rotated 20° 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 loaded part has σₓ = 10 MPa, σᵧ = −10 MPa and τₓᵧ = −50 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 20° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).
A point in a loaded part has σₓ = 110 MPa, σᵧ = −80 MPa and τₓᵧ = 40 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 15° counter-clockwise from the x-axis.
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