A point has σₓ = 160 MPa and σᵧ = 40 MPa, plus some shear stress. On an element rotated by 15° the normal stress in the rotated x′ direction is 142 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point in a loaded part has σₓ = 60 MPa, σᵧ = 80 MPa and τₓᵧ = 30 MPa (tension positive). Find the smallest principal stress σ2.
A point in a loaded part has σₓ = −60 MPa, σᵧ = 40 MPa and τₓᵧ = −60 MPa (tension positive). Find the maximum in-plane shear stress τmax.
A point in a loaded part has σₓ = −10 MPa, σᵧ = 90 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 loaded part has σₓ = 10 MPa, σᵧ = 90 MPa and τₓᵧ = −40 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 loaded part has σₓ = 90 MPa, σᵧ = 100 MPa and τₓᵧ = −50 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 40° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).
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