A point has σₓ = 120 MPa and σᵧ = −50 MPa, plus some shear stress. On an element rotated by 35° the normal stress in the rotated x′ direction is 101.7 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point has σₓ = −70 MPa and σᵧ = 80 MPa, plus some shear stress. On an element rotated by 60° the normal stress in the rotated x′ direction is 59.8 MPa. Find the normal stress σy′ in the rotated y′ direction.
A point in a thin plate is in plane stress: σₓ = 30 MPa, σᵧ = −20 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 = 150 MPa, σᵧ = 90 MPa and τₓᵧ = −60 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.
A thin-walled cylindrical tank of inner diameter 800 mm and wall thickness 12 mm holds gas at a gauge pressure of 3 MPa. It is made from plate welded along a helical seam at 30° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.
A solid shaft of diameter 50 mm carries a bending moment of 200 N·m together with a torque of 500 N·m. At the top surface, where the bending stress is tensile and largest, find the largest principal stress σ1.
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