Mohr’s circle & stress transformation worksheet with answers

At a point in a loaded part the in-plane principal stresses are σ₁ = 130 MPa and σ₂ = 60 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

A bar with cross-sectional area 800 mm² carries an axial compressive force of 180 kN. Find the magnitude of the shear stress |τ_θ| on a section whose normal makes an angle of 25° with the bar axis.

A point in a loaded part has σₓ = 100 MPa, σᵧ = 110 MPa and τₓᵧ = 40 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

A point in a loaded part has σₓ = 80 MPa, σᵧ = 40 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θ_p from the x-axis to the direction of the largest principal stress, between −90° and 90°.

A thin-walled cylindrical tank of inner diameter 1200 mm and wall thickness 6 mm holds gas at a gauge pressure of 1.5 MPa. It is made from plate welded along a helical seam at 55° to the axis of the cylinder. Find the normal stress σ_n acting across the weld seam.

A solid shaft of diameter 50 mm carries an axial tensile force of 80 kN together with a torque of 400 N·m. At the surface of the shaft, find the largest principal stress σ₁.