Read the following statements related to shear centre and choose the correct option.

1. The shear centre is also known as the centre of twist.

2. For a cross-sectional area having one axis of symmetry, the shear centre is always located on the axis of symmetry.

3. Shear centre coincides with the centroid for unsymmetrical cross-sections in both axes.

Explanation:

Understanding Shear Centre

The shear centre is a point on the cross-section of a beam where the application of transverse shear loads does not cause any twisting. It is crucial in the design and analysis of structural elements to ensure stability and prevent undesired deformation.

• Shear Centre and Twist: The shear centre is also known as the centre of twist because it is the point through which shear forces can be applied without causing the section to twist.

• Axis of Symmetry: For sections with one axis of symmetry, the shear centre lies on that axis. This simplifies the location of the shear centre for common symmetrical shapes.

• Shear Centre and Centroid: For sections that are not symmetrical about both axes, the shear centre does not necessarily coincide with the centroid. This distinction is important for non-standard cross-sections.

Analyzing the Given Statements

1. "The shear centre is also known as the centre of twist." (Correct)

   • This statement is true because the shear centre is indeed the point where transverse shear loads cause no twisting.

2. "For a cross-sectional area having one axis of symmetry, the shear centre is always located on the axis of symmetry." (Correct)

   • This statement is true as the shear centre for such sections lies on the axis of symmetry due to the uniform distribution of shear flow.

3. "Shear centre coincides with the centroid for unsymmetrical cross-sections in both axes." (Incorrect)

   • This statement is false because, for unsymmetrical sections, the shear centre does not generally coincide with the centroid.

   • The centroid is the geometric centre, while the shear centre is determined by the distribution of shear forces.

Conclusion: Based on the analysis, statements 1 and 2 are correct, and statement 3 is incorrect.