Hi Kam, great question. Check out the stress element at 1:25, which comes from the top of Section B-B. Subject to pure torsion, the shear stress (yellow vector) at the top of the square is opposed by an equal and opposite vector at the bottom of the square by Newton's 3rd law, and that counter-clockwise couple is opposed by a clockwise couple at the left and right sides. But we want the direction of normal stress... Normal stress is defined as being perpendicular to a cross section. Along the body's axes of symmetry, we see only shear stress. If we want maximum normal stress (green vector at 1:31,) we need to sum vectors and determine what plane they are perpendicular to. The angle created by summing two equal vectors happens to be 45°, because the opposite leg divided by the adjacent leg is 1, and arctan(1)=45°.
Great video
Thanks Jonathan
How do we know that max normal stress will be 45 degrees off the plane?
Hi Kam, great question. Check out the stress element at 1:25, which comes from the top of Section B-B.
Subject to pure torsion, the shear stress (yellow vector) at the top of the square is opposed by an equal and opposite vector at the bottom of the square by Newton's 3rd law, and that counter-clockwise couple is opposed by a clockwise couple at the left and right sides. But we want the direction of normal stress...
Normal stress is defined as being perpendicular to a cross section. Along the body's axes of symmetry, we see only shear stress. If we want maximum normal stress (green vector at 1:31,) we need to sum vectors and determine what plane they are perpendicular to. The angle created by summing two equal vectors happens to be 45°, because the opposite leg divided by the adjacent leg is 1, and arctan(1)=45°.