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-4—

h h-* t

Figure 2.11 Beam undergoing torsional deformation.

Figure 2.11 Beam undergoing torsional deformation.

dx dx

Figure 2.12 Cross-sectional slice of beam undergoing torsional deformation.

where

Here A is the cross section of the beam, v and z are cross-sectional Cartesian coordinates, and p is the mass density of the beam. When p is constant over the cross section, then Ip is the area polar moment of inertia per unit length. When p varies over the cross section, one may interpret pip as the mass polar moment of inertia for the cross section.

The twisting moment can be written in terms of the twist rate and the Saint-Venant torsional rigidity as

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