A point has σₓ = 70 MPa and σᵧ = 90 MPa, plus some shear stress. On an element rotated by 50° the normal stress in the rotated x′ direction is 121.1 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point in a loaded part has σₓ = 160 MPa, σᵧ = 70 MPa and τₓᵧ = 30 MPa (tension positive). Find the largest principal stress σ1.
A point in a loaded part has σₓ = −70 MPa, σᵧ = 60 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 = 130 MPa, σᵧ = 90 MPa and τₓᵧ = 10 MPa (tension positive). Find the maximum in-plane shear stress τmax.
A point in a loaded part has σₓ = 140 MPa, σᵧ = −50 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis.
A solid shaft of diameter 25 mm carries an axial compressive force of 200 kN together with a torque of 750 N·m. At the surface of the shaft, find the largest principal stress σ1.
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