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The elastic center that point of a beam in the plane of the section lying midway between the flexural/shear center and the center of twist in that section.

The flexural center and the shear center are the same thing. It is that point through which the loads must act if there is to be no twisting, or torsion. The shear center is always located on the axis of symmetry; therefore, if a member has two axes of symmetry, the shear centre will be the intersection of the two axes. Channels have a shear center that is not located on the member.

The center of twist is the point about which the section rotates when subjected to torsion.

If the object is homogeneous and symmetrical in both directions of the cross-section then they are all equivalent and are located at the beam centroid.

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