A point has σₓ = 140 MPa and σᵧ = 100 MPa, plus some shear stress. On an element rotated by 25° the normal stress in the rotated x′ direction is 140.5 MPa. Find the normal stress σy′ in the rotated y′ direction.
A bar with cross-sectional area 500 mm² carries an axial tensile force of 190 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 25° with the bar axis.
A point in a loaded part has σₓ = 10 MPa, σᵧ = 100 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 point has σₓ = 80 MPa, σᵧ = 90 MPa and τₓᵧ = 50 MPa (tension positive). The element is rotated 35° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.
A point in a thin plate is in plane stress: σₓ = 20 MPa, σᵧ = −30 MPa and τₓᵧ = −20 MPa (σz = 0). Find the von Mises equivalent stress σvM.
A point in a thin plate is in plane stress: σₓ = −30 MPa, σᵧ = −70 MPa and τₓᵧ = 50 MPa (σz = 0). The material has a yield strength of 355 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.
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