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Consider the cross-section of a beam made up of thin uniform elements having thickness t (t << a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure. The coordinates of the shear center of this cross-section are:

Consider the cross-section of a beam made up of thin uniform elements having thickness t (t << a) shown in the figure. The (x, y) coordinates of the points along the center-line of the cross-section are given in the figure. The coordinates of the shear center of this cross-section are: Correct Answer x = 0, y = 3a

Concepts:

Shear center:

  • Shear center is a point on the cross-section where the application of loads does not cause its twisting.
  • The shear center position is dependent on the cross-section of the beam.

The following points should be remembered for finding the location of shear center.

1. For symmetrical sections, the shear center and center of gravity are the same and coincides   with each other.

2. For unsymmetrical section, the shear center lies on the axis where it has axis of symmetry.

3. For sections made by joining the thin rectangular sections, then shear center lies on the points of intersection of individual symmetrical axis of this rectangular section. 

In this problem point No. 3 is used to find out the location of shear center.

The horizontal thin rectangular section has axis of symmetry along X-axis as shown in the dotted line and the vertical thin rectangular section has an axis of symmetry Y-axis itself (also shown as dotted line) and their point of intersection lies at (0, 3a).

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