ES222 Strength of Materials
Section 03
Spring 2010
Dr. Whelan
In-Class Demonstration: Inclined Plane Stresses under Pure Shear/Torsion
In this demonstration, we note how a state of pure shear stress on the planes parallel and
normal to the shear force/stress will produce normal stresses on the inclined plane at 45°.
We draw 2 squares on the side of the textbook: one normal to the plane, one at a 45°
angle.
When we impact a shear force, we see that there is angular distortion of the normal
square (ie. a shear strain), but the sides of the 45° square remain perpendicular to each
other (ie. no shear strain. However, there is a clear distortion of this square causing it to
look like a rectangle. This is a result of a normal tensile stress and a normal compressive
stress on the faces of this square that arise due to stress transformation on the 45° plane.
If we apply the shear force in the opposite direction, we see the same phenomenon, but
the directions are reversed. Note that, due to sign convention, this is what we see in the
case of positive torsion.