GATE CE 2024 Set 2 — Question 18
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Structural Engineering → Stress, Strain & Beams → Shear Centre
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Question
For a thin-walled section shown in the figure, points P, Q , and R are located on the major bending axis of the section. Point Q is located on the web whereas point S is located at the intersection of the web and the top flange of the section.
(Figure NOT to scale)Qualitatively, the shear center of the section lies at
Correct answer
(C) R
Solution
The shear center is the point through which the resultant of the internal shear forces passes. For a section with one axis of symmetry, the shear center must lie on that axis. In this case, the horizontal axis is the axis of symmetry, so the shear center lies on it.Consider a vertical shear force acting downwards on the section. This force induces shear flow in the flanges, given by .
1.Top Flange (): The shear flow is directed from the tips towards the web. Since the left segment () is longer than the right segment (), the net horizontal force in the top flange is directed to the left.
2.Bottom Flange (): The shear flow is directed from the web towards the tips. Consequently, the net horizontal force in the bottom flange is directed to the right.
3.Internal Couple: These two equal and opposite horizontal forces in the flanges form a counter-clockwise couple.
4.Equilibrium: To maintain equilibrium, the external downward force must be applied at a position that creates an equal and opposite (clockwise) moment about the web. A downward force applied to the right of the web will produce a clockwise moment.
Therefore, the shear center lies to the right of the web, which corresponds to point R.Continue learning with Success Tracker
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