Question

Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

• A.

  

• B.

  

• C.

  

• D.

  

Hint:

The shear centre of an angle section lies where the centre lines of its two legs intersect, at the corner.

Answer 1

The Correct Option is D

Step 1: Recall what the shear centre is and why an angle section needs one.
The shear centre of a cross-section is the point through which a transverse shear force must act for the beam to bend without twisting. Sections with an axis of symmetry have their shear centre on that axis. An angle (L-shaped) section made of two thin legs is an open thin-walled section with no such symmetry in general, so its shear centre does not coincide with its centroid and must be located separately.

Step 2: Use the thin-walled open-section rule for angle sections.
For an open section built from thin, straight flat plate segments meeting at a common point, as in an angle section made of two rectangular legs joined at a corner, each leg individually resists shear force along its own mid-plane, because a thin flat plate can only develop shear flow along its own length; it cannot resist twisting shear across its own thickness. Since both legs are thin flat plates whose shear resistance lines pass through their own mid-thickness lines, the resultant shear centre of the whole section must lie where these two mid-thickness lines cross:
\[ \text{Shear centre = intersection of the centre lines of the two legs} \]

Step 3: Locate this intersection point on the figure.
Each leg's centre line runs along the middle of its thickness, parallel to that leg. For a typical angle with a horizontal leg and a vertical leg, the horizontal leg's centre line is a horizontal line through the mid-thickness of that leg, and the vertical leg's centre line is a vertical line through the mid-thickness of that leg. These two centre lines cross essentially at the inside corner of the angle, at the junction where the two legs meet, not out in open space away from the section and not on the outer face of either leg.

Step 4: Eliminate the other options.
Any option that places the dot well away from the corner, floating inside the open area enclosed by the two legs, does not correspond to the true intersection of the two leg centre lines, so those options are incorrect. The correct option places the dot right at the meeting point of the two leg centre lines, at the corner of the angle.

Final Answer:
The shear centre of an angle section lies at the intersection of the centre lines of its two legs, at the corner, matching option (D). \[ \boxed{\text{Option (D)}} \]