Question:
A horizontal cantilever is 2m long and rigidly fixed to a wall. The cantilever is 50mm diameter and carries a vertical end load of 1kN together with an axial tensile force of 20kN and a torque of 3kNm. Calculate the magnitude and location of the principle and maximum shear stresses.
Answer:
Firstly a diagram to help visualize the problem:
Calculate the area of the cantilever beam:
Calculate the Area Moment of Inertia of the cantilever beam:
Calculate the Polar Moment of Inertia of the cantilever beam:
Calculate the Direct Stress:
Calculate the Bending Stress:
Max Stress will occur at the outer fibres where y = 25mm = 0.025m
Calculate the Torsional Shear Stress. Max shear stress occurs at the outer radius; r = 25mm.
Worst condition at 'o' where direct and bending stress are both tensile.
No shear stress on principle planes.
Theta 1 has to lie between 0° and 90°, when shear stress is positive.
Max Shear Stress acts at 45° from principle planes (72.34°, 162.34°)
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