A point has σₓ = 160 MPa and σᵧ = 30 MPa, plus some shear stress. On an element rotated by 60° the normal stress in the rotated x′ direction is 79.8 MPa. Find the normal stress σy′ in the rotated y′ direction.
At a point in a loaded part the in-plane principal stresses are σ₁ = −40 MPa and σ₂ = −120 MPa (tension positive). Find the maximum in-plane shear stress τmax.
A point in a thin plate is in plane stress: σₓ = 90 MPa, σᵧ = 30 MPa and τₓᵧ = −20 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).
A point has σₓ = 150 MPa, σᵧ = 70 MPa and τₓᵧ = 40 MPa (tension positive). Find the angle θs, between −90° and 90°, from the x-axis to the normal of the plane on which the shear stress has its maximum positive value +R (shear positive in the same sense as τₓᵧ).
A thin-walled cylindrical tank of inner diameter 600 mm and wall thickness 15 mm holds gas at a gauge pressure of 1.5 MPa. It is made from plate welded along a helical seam at 35° to the axis of the cylinder. Find the magnitude of the shear stress |τn| acting along the weld seam.
A point in a loaded part has σₓ = 90 MPa, σᵧ = −70 MPa and τₓᵧ = −30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° counter-clockwise from the x-axis.
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