A point has σₓ = 10 MPa and σᵧ = 100 MPa, plus some shear stress. On an element rotated by 35° the normal stress in the rotated x′ direction is −16.8 MPa. Find the normal stress σy′ in the rotated y′ direction.
A bar with cross-sectional area 1000 mm² carries an axial tensile force of 60 kN. Find the normal stress σθ on a section whose normal makes an angle of 30° with the bar axis (tension positive).
A point has σₓ = −10 MPa and σᵧ = 60 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 80 MPa?
A point has σₓ = −10 MPa, σᵧ = −20 MPa and τₓᵧ = −50 MPa (tension positive). The element is rotated 20° clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.
A solid shaft of diameter 60 mm carries a bending moment of 500 N·m together with a torque of 1000 N·m. At the top surface, where the bending stress is tensile and largest, find the maximum in-plane shear stress τmax.
A point in a loaded part has σₓ = 140 MPa, σᵧ = −10 MPa and τₓᵧ = 60 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 15° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).
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