Beam Shear Center and Cross Section Twisting

The shear center of a beam's cross section is a crucial point. It is defined as the point through which the resultant shear force must pass to avoid twisting of the cross section. When a shear force is applied at any point other than the shear center, it creates a torque (twisting moment) about the shear center, which causes the beam cross section to twist.

In sections that have one axis of symmetry, the shear center lies on this axis of symmetry. If the cross section has two axes of symmetry, the shear center is located at the intersection of these axes, which usually coincides with the centroid.

The question states that the axis of symmetry in the vertical plane does not coincide with the shear center. This scenario occurs for certain cross sections, such as channel sections, angle sections, or thin-walled open sections with only one axis of symmetry.

If a vertical shear force is applied to such a beam along the vertical axis of symmetry, but this axis does not pass through the shear center, the force is effectively applied at a distance (eccentricity) from the shear center. This eccentric force creates a moment about the shear center.

Let the shear force be \(V\) and the distance between the axis of symmetry (where \(V\) is applied) and the shear center be \(e\). The moment created about the shear center is \(M_t = V \times e\). This moment is a twisting moment, also known as torque.

Therefore, when the axis of symmetry in the vertical plane does not coincide with the shear center, applying a load along this axis results in a twisting moment being applied to the cross section.

Let's consider the given options:

• Axial pull: This is caused by a tensile force acting along the longitudinal axis of the beam. This is not directly related to the position of the shear center relative to the symmetry axis under a shear load.
• Bending: Bending is caused by moments or transverse loads that create moments. While a shear force does cause bending, the question specifically asks about the effect when the shear force location relative to the shear center and symmetry axis is considered. The non-coincidence primarily adds a rotational effect (twisting) in addition to bending.
• Twisting: This is caused by a torque or twisting moment. As explained above, when the shear force is applied eccentrically with respect to the shear center, a twisting moment is induced. The scenario described in the question directly leads to such an eccentric application relative to the shear center if the load is applied along the axis of symmetry.
• Compression: This is caused by a compressive force acting along the longitudinal axis of the beam. This is also not directly related to the position of the shear center relative to the symmetry axis under a shear load.

Thus, the primary effect experienced by the cross section due to the eccentricity of the applied shear force (if applied along the axis of symmetry) relative to the shear center is twisting.